Department of Physics University of Jyväskylä

DEPARTMENT OF PHYSICS UNIVERSITY OF JYVASKYL¨ A¨ RESEARCH REPORT No. 3/2007

PRECISION MASS MEASUREMENTS OF NEUTRON-RICH NUCLIDES AROUND A = 100

BY ULRIKE HAGER

Academic Dissertation for the Degree of Doctor of Philosophy

To be presented, by permission of the Faculty of Mathematics and Natural Sciences of the University of Jyväskylä, for public examination in Auditorium FYS-1 of the University of Jyväskyläon July 9, 2007 at 12 o’clock noon

Jyv¨askyl¨a, Finland July 2007

Preface The work reported in this thesis was carried out during the years 2004-2007 at the Department of Physics of the University of Jyväskylä, and at the ISOLDE facility at CERN, Geneva. I would like to thank the whole staff of the Department of Physics for the friendly working atmosphere.

I wish to thank my supervisor professor Juha Ayst¨ofor¨ giving me the opportunity to carry out this work, and for his guidance and support. I would also like to thank the members of the IGISOL group, past and present, especially Dr. Stefan Kopecky, Dr. Ari Jokinen, Tommi Eronen, Jani Hakala, Viki Elomaa, Dr. Iain Moore and Thomas Kessler.

Part of this work was carried out at CERN, and I would like to thank the whole ISOLTRAP group for their warm welcome. Martin Breitenfeldt, Romain Savreux, M´elanie Marie-Jeanne, Michael Dworschak, Dr. Chabouh Yazidjian and Dr. Alexander Herlert have made my time at CERN not only educational but also fun. In addition, I would like to express my warmest thanks to Dr. habil. Klaus Blaum for his support and the interest he showed in my work.

The ﬁnancial support from the Graduate School of Particle and Nuclear Physics is gratefully ac- knowledged.

Finally, I would like to thank my family, especially my brothers, for their support and encouragement.

i Abstract The masses of 73 neutron-rich fission products were measured with high precision using the JYFLTRAP Penning trap setup at the IGISOL facility in Jyväskylä. These new data enable mapping of the mass surface in this region of the nuclear chart. The data are compared to nuclear model calculations, and various systematic trends are analysed. Since these measurements are part of one of the first precision mass measurement campaigns conducted at JYFLTRAP, the systematic uncertainties of the setup were explored and quantified as far as possible. In addition, analysis programs had to be written to handle the raw data efficiently. At the mass spectrometer ISOLTRAP, CERN, a new project was initiated to install a tape station at the end of the setup. Exploiting the high resolving power of this setup, this will provide the possibility for decay spectroscopy with pure samples. A first design for the new apparatus is presented in this work.

ii Contents

1 Introduction 1

2 Nuclear masses 3 2.1 Globalmassmodels ...... 3 2.2 Pairinganddeformation ...... 5 2.3 The astrophysical r-process ...... 7

3 Mass measurement techniques 11 3.1 Indirect techniques ...... 11 3.2 Direct techniques ...... 11 3.2.1 Time-of-ﬂight measurements ...... 11 3.2.2 Storagerings ...... 12 3.2.3 Radio frequency transmission spectrometers ...... 12 3.2.4 Penningtraps...... 12 3.2.5 Comparison...... 13

4 Experimental methods 15 4.1 Radioactive ion beam production ...... 15 4.1.1 Overview ...... 15 4.1.2 The ISOL technique ...... 15 4.1.3 IGISOL ...... 15 4.1.4 ISOLDE...... 16 4.2 Radio frequency-coolers/bunchers ...... 18 4.3 Penning traps ...... 19 4.3.1 Principles...... 19 4.3.2 Precision mass measurement ...... 22 4.3.3 Cooling and isobaric puriﬁcation ...... 22 4.3.4 Decay spectroscopy with pure samples ...... 25 4.3.5 JYFLTRAP...... 26 4.3.6 ISOLTRAP...... 28

5 Precision mass measurements at JYFLTRAP 31 5.1 Evaluation of the statistical uncertainties ...... 31 5.2 Systematic uncertainties ...... 32 5.2.1 Countrate ...... 32 5.2.2 Fluctuations ...... 33 5.2.3 Mass-dependent uncertainties ...... 33 5.3 Results...... 35 5.4 Discussion...... 39 5.4.1 Comparison to previous data ...... 39 5.4.2 Comparison to global models ...... 44

iii iv CONTENTS

5.4.3 Study of systematic trends ...... 49

6 Spectroscopy at ISOLTRAP 63 6.1 Currentsituation...... 63 6.2 Designing the new extraction beamline in SIMION ...... 63 6.3 Construction of the new detection setup ...... 65 6.3.1 Diﬀerential pumping section ...... 66 6.4 Status ...... 66

7 Summary and outlook 73

A Analysis programs 75 A.1 Frequency calibration and contaminations ...... 75 A.2 Dataﬁtting ...... 75 List of Figures

2.1 Nuclear binding energy per nucleon ...... 4 2.2 Schematic view of a deformed nucleus ...... 7 2.3 Nilsson diagram for neutrons and protons with Z or N ≤ 50 ...... 8 2.4 Nilsson diagram for neutrons 50 ≤ N ≤ 80...... 9 2.5 r-process path ...... 10

3.1 Uncertainties of diﬀerent mass measurement techniques ...... 13

4.1 ISOLmethods ...... 16 4.2 IGISOL working principle ...... 17 4.3 Fissionionguide ...... 17 4.4 Schematic layout of the ISOLDE hall ...... 18 4.5 Two possible Penning trap electrode structures ...... 19 4.6 MotionofanioninaPenningtrap ...... 21 4.7 Time-of-flight resonance spectrum ...... 23 4.8 Motion of ions in the trap without and with buffer gas ...... 24 4.9 Ion motion in the trap with buffer gas and ωc-excitation ...... 24 4.10 Cooling resonances for A =101...... 25 4.11TheJYFLTRAPsetup...... 26 4.12 Sketch of the IGISOL RFQ cooler/buncher ...... 27 4.13 Electrode configuration of the JYFLTRAP purification trap ...... 27 4.14 Sketch of the ISOLTRAP triple trap setup ...... 29

5.1 Countrateclassanalysis...... 34 5.2 Field fluctuations ...... 35 5.3 Previous measurements of strontium ...... 40 5.4 Previous measurements of zirconium ...... 41 5.5 Previous measurements of molybdenum ...... 43 5.6 Comparison to the HFB2 model predictions...... 44 5.7 Comparison to the HFB9 model predictions...... 45 5.8 Comparison to the HFBCS-1 model predictions...... 45 5.9 Comparison to the FRDM model predictions...... 46 5.10 Comparison to the ETFSI-1 model predictions...... 46 5.11 Comparison to the ETFSI-2 model predictions...... 47 5.12 Comparison to the 10 parameter Duflo-Zuker model predictions...... 47 5.13 Comparison to the 28 parameter Duflo-Zuker model predictions...... 48 5.14 Comparison to the KTUY model predictions...... 48 5.15 S2n as a function of N ...... 49 5.16 S2n as a function of Z ...... 51 5.17 S2n and the E2 transition energy ...... 52 2 N−50,N 5.18 S2n and < δ > ...... 53

v vi LIST OF FIGURES

5.19 Sn ...... 54 ee 5.20 δVpn ...... 55 eo 5.21 δVpn ...... 56 oe 5.22 δVpn ...... 56 ee 5.23 δVpn against N and Z ...... 57 + + 5.24 E(41 )/E(21 )...... 57 ee 5.25 δVpn , HFB-9 for even-even nuclei...... 59 ee 5.26 δVpn , FRDM for even-even nuclei...... 59 ee 5.27 δVpn , Duﬂo-Zuker (28 parameters) for even-even nuclei...... 60 ee 5.28 δVpn , ETFSI-2 for even-even nuclei...... 60 ee 5.29 δVpn , KTUY for even-even nuclei...... 61 5.30 Extrapolated binding energies using theoretical δVpn values ...... 61 5.31 Neutron odd-even staggering three-point indicator ∆ν ...... 62

6.1 Yields at ISOLDE for mercury, thallium and francium ...... 64 6.2 PictureofISOLTRAP ...... 64 6.3 Current SIMION IOB of the precision trap and extraction ...... 65 6.4 SIMION, new ISOLTRAP extraction geometry ...... 65 6.5 SIMION IOB of the new extraction geometry with Channeltron ...... 66 6.6 Design of both new crosses and the two valves after the ISOLTRAP precision trap . 67 6.7 The trap and the detector/tape station table with three detectors ...... 68 6.8 Differential pumping/slit system to guide the tape into vacuum ...... 69 6.9 Differential pumping/slit system: inner part ...... 70 6.10 Differential pumping/slit system: outer part ...... 71 6.11 Lower cross and extension piece ...... 71 6.12 New beamline parts with flanges and electronic feedthroughs ...... 72

7.1 ν+ Ramsey scan in the precision trap ...... 74 7.2 Time-of-ﬂight resonance spectra of 115Sn and 115In using Ramsey cleaning ...... 74

A.1 Frequency calculator GUI ...... 76 A.2 FittingprogramGUI...... 77 List of Tables

5.1 Nuclides studied in June 2005 ...... 36 5.2 Results...... 37 5.3 Previous measurements of strontium...... 39 5.4 Previous measurements of zirconium...... 42 5.5 Previous measurements of molybdenum...... 42 5.6 Comparison of δVpn and R4/2 ...... 58

vii 1 Introduction

An important parameter in studies of nuclear structure and in nucleosynthesis is the mass of the nucleus, which is connected to the mass of its constituents and the binding energy:

M(N,Z) = N · mn + Z · mp − B(N,Z) (1.1) with mn the mass of the neutron, mp the mass of the proton and B(N,Z) the binding energy of a nucleus with N neutrons and Z protons. Therefore, from the exact knowledge of the nuclear masses follow the binding energies, which in turn are needed for models of nuclear interactions.

For several decades the neutron-rich region between A ≈ 80 and A ≈ 130 has been subject to intense study via decay spectroscopy. The reason for this is the suggested shape transition in the rhodium, palladium region from an SU(5) vibrational state to a O(6) γ-unstable state, as noted by Stachel et al. [1], though no sharp onset of deformation was expected. Indication of this transition was also found by Aryaeinejad et al. [2] for neutron-rich palladium, suggesting that the occupation of the νh11/2 orbital may cause the very slow change in excitation energies from N = 64 to N = 70 and lead to oblate deformation. Lhersonneau et al. [3] noted that nuclei with N ≥ 60 have strong ground state quadrupole deformations, while the intermediate N = 59 isotones of strontium, yttrium and zirconium still have spherical ground states. This rapid change is explained by unusually large deformations on the one hand and a strong subshell closure on the other hand. Houry et al. [4] agree on the importance of the νh11/2 orbital, but claim prolate rather than oblate deformation. Additionally, the deformation parameter is calculated to decrease with increasing mass, leading smoothly to a quasi- spherical shape for 121Pd without the need for shape transitions. More recently, it has been suggested that the N = 82 shell closure might weaken or be quenched far from stability. This quenching has been predicted by models and experimental indication has been found [5]. Shell closures manifest, for example, in sudden jumps in the evolution of the two-neutron separation energy S2n along an isotopic chain. One example of the appearance of a neutron subshell was found at N = 60 around the zirconium region, as described in [3], and could recently be conﬁrmed by measurements conducted with JYFLTRAP [6]. That work has since been continued towards the neutron shell closure at N = 82 by measuring neutron-rich isotopic chains of technetium, ruthenium, rhodium and palladium, and also towards lighter nuclei, i.e. isotopes of rubidium and bromine.

Another reason for interest in this region of the nuclear chart is its importance for stellar nucleosynthesis, as the rapid neutron capture process (r-process), is assumed to proceed here, producing more than half the nuclei heavier than iron existing in the universe today [7].

A variety of methods have been developed to measure nuclear and atomic masses (for an overview over different methods, see [8]). One of these is the Penning trap, which employs a strong magnetic field combined with an electric quadrupole field to trap ions. These ions can then be excited at their cyclotron frequency, a process which is mass selective. This method was first employed for radioactive species at ISOLTRAP at the ISOLDE facility at CERN. At the IGISOL facility at the University of Jyväskyläa double Penning trap system, JYFLTRAP, has been installed. It consists of a trap for isobaric beam purification and one for precision mass measurements. This latter trap

1 2 Introduction

was commissioned in 2003. Some of the ﬁrst data taken with it is presented in this work.

Another application of the Penning trap is to provide a pure sample for decay spectroscopy, reducing the background considerably. Such trap-assisted spectroscopy has already been conducted at JYFLTRAP [9]. A similar setup is planned for ISOLTRAP.

The experimental work presented in this thesis was carried out at the JYFLTRAP experiment at the accelerator laboratory of the University of Jyväskyläand at the ISOLTRAP experiment at ISOLDE, CERN. The author of this thesis was involved in commissioning the JYFLTRAP precision trap and in preparing and performing the subsequent precision mass measurements. She has written a data analysis program and analysed all the data presented in this work. At the ISOLTRAP experiment, the author has begun the design of a tape station setup for trap-assisted decay-spectroscopy, including ion-optical simulations and various technical drawings. The thesis is based on the following enclosed publications: First Precision Mass Measurements of Refractory Fission Fragments U. Hager, T. Eronen, J. Hakala, A. Jokinen, V. S. Kolhinen, S. Kopecky, I. Moore, A. Niemi- nen, M. Oinonen, S. Rinta-Antila, J. Szerypo, and J. Aystö¨ Phys. Rev. Lett. 96 (2006) 042504

Precision mass measurements of neutron-rich Tc, Ru, Rh and Pd isotopes U. Hager, V.-V. Elomaa, T. Eronen, J. Hakala, A. Jokinen, A. Kankainen, S. Rahaman, S. Rinta-Antila, A. Saastamoinen, T. Sonoda, J. Ayst¨o¨ Phys. Rev. C 75 (2007) 064302

Precise atomic masses of neutron-rich Br and Rb nuclei close to the r-process path S. Rahaman, U. Hager, V.-V. Elomaa, T. Eronen, J. Hakala, A. Jokinen, A. Kankainen, P. Karvonen, I. D. Moore, H. Penttil¨a, S. Rinta-Antila, J. Rissanen, A. Saastamoinen, T. Sonoda and J. Ayst¨o¨ Eur. Phys. J. A, 32 (2007) 87

Precision mass measurements of neutron-rich yttrium and niobium isotopes U. Hager, A. Jokinen, V.-V. Elomaa, T. Eronen, J. Hakala, A. Kankainen, S. Rahaman, J. Rissanen, I. D. Moore, S. Rinta-Antila, A. Saastamoinen, T. Sonoda, J. Aystö¨ accepted for publication in Nucl. Phys. A This thesis consists of the following chapters: Chapter 2 gives a short introduction to global nuclear models and pairing, and then explains the principles of the astrophysical r-process. Chapter 3 compares different techniques used to measure the mass of the nucleus. Chapter 4 describes the experimental methods used in this work at both IGISOL in Jyväskylä, and ISOLDE at CERN, starting with the production of radioactive ion beams (RIBs) and going on to give an overview of the Penning traps installed at the two facilities. Chapter 5 presents the data taken at JYFLTRAP and its analysis. Systematic trends in the mass surface are examined. Chapter 6 deals with the ongoing effort of placing a tape station at the end of the ISOLTRAP beam line for trap-assisted spectroscopy. 2 Nuclear masses

2.1 Global mass models

Figure 2.1 shows the nuclear binding energy per nucleon as a function of the mass number A. The binding energy per nucleon is roughly 8 – 8.5 MeV, with a maximum around iron. The ﬁrst attempt at theoretically describing the binding energy of the nucleus was the semi-empirical mass formula by von Weisz¨acker [11]. This liquid drop model is based on the assumption that the nucleus behaves like a drop of nuclear matter. The density distribution is assumed to be constant inside a sharp boundary and zero outside. A good approximation for the radius of a nucleus is then

1/3 R = r0 · A ; r0 ≈ 1.3 fm (2.1)

The total binding energy depends on the volume (∝ A), the surface area of the nucleus (∝ A2/3), the 2 2 ∝ Z ∝ (N−Z) Coulomb repulsion between the protons ( A1/3 ) and the proton-neutron asymmetry ( A ). From this follows the semi-empirical Weizs¨acker formula for the binding energy:

Z2 (N − Z)2 B = a · A − a · A2/3 − a · − a · + δ(A) . (2.2) vol sur coul A1/3 asymm A The additional δ(A) term comes from pair binding, which increases the binding energy for nuclei of even proton or neutron number. The factors avol, asur, acoul, aasymm and δ are obtained by ﬁtting to the experimental data. The pairing can be approximated by δ ≈ 12A−1/2 MeV [12].

The liquid drop model describes the approximate development of the binding energy for increasing mass number quite well, with the largest binding energies being found around iron. As can be seen from Fig. 2.1, though, the binding energy is not a completely smooth function of the mass number. Increasingly precise mass measurements have revealed structures not described in the liquid drop model. Certain nuclei with so-called magic proton or neutron numbers are found to be especially stable. This observation led to the introduction of the shell model, also known as the independent particle model. The formation of a shell structure requires a common ﬁeld in which the particles move largely independently of each other, leading to the conclusion that the nucleonic interactions must smooth themselves out into a mean ﬁeld.

Different approaches are used to combine the liquid-drop and shell model aspects of the nucleus into one model. The most fundamental of these is the Hartree-Fock (HF) model [10], which is based on solving the Schrödinger equation with a model wave function using effective interactions. For heavier nuclei this method becomes computationally demanding due to the large dimensionality of the matrix of the exact Hamiltonian to be diagonalised in a basis of shell-model states. As a simplification, one can assume that all nucleons move in a single-particle field, that is, an independent-particle model. The trial wave function takes the form of a Slater determinant (the wave function of a many-fermion system satisfying the Pauli principle) and variational methods are employed to find the solution. Dif- ferent effective forces are used in these calculations, a popular one being the Skyrme force [8], which is of zero range and includes a three-body term. It’s 5 parameters are adjusted to the experimental

3 4 Nuclear masses

Figure 2.1: Nuclear binding energy per nucleon as a function of mass number A. The circles mark experimental values, the line was calculated using Eq. 2.2. The picture was taken from [10].

binding energies and radii.

Not all experimentally observed features can be explained in this mean-field picture but rather have to be expressed as a configuration mixing of Slater determinants. One of these features is the pairing of like nucleons; if a nucleus has an even number of both protons and neutrons, the nucleons will couple to yield the angular momentum 0. This also shows in the binding energies in that nuclides with even proton or neutron numbers are bound more strongly than their neighbours of odd particle number. In analogy to the theory of superconductivity, pairing correlations can be included in the HF approach by applying the BCS (Bardeen-Cooper-Schrieffer) method. In the resulting HF-BCS model [13], the pairing is treated as constant and not variational like the single-particle functions. The Hartree-Fock-Bogoliubov (HFB) model [14], on the other hand, is fully variational, and the pairing correlations are treated similarly to the single-particle part. Another problem of the mean-field calculations is that they systematically underbind N = Z nuclei. An additional, so-called Wigner term has been proposed to correct for this effect, though a more direct description in terms of proton-neutron pairing seems more suitable. An important change that was made in the second version of the HFB model, HFB-2, compared to HFB-1 is the treatment of the pairing cutoff [15], i.e. the single-particle states included in the pairing calculation. In the HFB-1 calculations the cutoff energy was ¯hω = 41A−1/3 MeV, whereas for the HFB-2 the spectrum was confined to an interval around the Fermi energy of EF ± 15 MeV. While the former approach leads to a narrowing of the available spectrum for neutrons as one moves towards the neutron dripline, the latter one actually widens the single-particle spectrum included in the neutron-pairing calculations. This will result in the weakening of the neutron-shell far from stability, i.e. shell quenching, which indeed seems to be confirmed by experiment. 2.2 Pairing and deformation 5

A different way of combining the liquid-drop and the shell model is to graft microscopic corrections onto the liquid-drop model, also called the microscopic-macroscopic (’mic-mac’) approach. Various models have evolved from this idea. One of these is the finite-range droplet model (FRDM) [16]. As opposed to the drop model, the droplet model takes into account the finite thickness of the nuclear surface and the finite compressibility of nuclear matter. The densities are thus only approximately constant in a system with a diffuse surface region. The finite range of the nucleonic interaction is accounted for by the Yukawa force. Shell corrections are included using the Strutinsky averaging method; also included are BCS pairing corrections and a Wigner term. The adopted pairing parametrisation leads to a steady weakening of the pairing gap when moving towards the neutron dripline. Therefore, no shell quenching is predicted.

A mic-mac model closer to the HF method is the ETFSI (extended Thomas-Fermi plus Strutinski integral) algorithm [17]. It is based on the Skyrme force, and the energy of the nuclide is calculated using the Thomas-Fermi approximation (i.e. the energy of the system is calculated using a functional of the particle density). Since the Thomas-Fermi approximation, originating from atomic physics, is not well suited for many-body systems with very short-range two body forces, an extended Thomas- Fermi (ETF) method is used. From this the macroscopic part is derived. The microscopic part is calculated based on the same Skyrme force as the macroscopic part, hence both parts are more closely related than is the case for the FRDM. The model yields a close approximation to the HF calculations, with the advantage of being faster. With increasing computational power, however, it becomes less important.

More fundamental than the mic-mac models is the mass formula by Duflo and Zuker [18]. Similar to the HF calculations, it assumes effective interactions, pseudopotentials, but then separates the Hamiltonian into monopole and multipole terms. The former gives the single-particle properties, while the latter describes the residual interactions with a very general configuration mixing. In this manner, the model includes pairing and Wigner correlations, and the magic numbers arise naturally. Though the model disagrees with experimental results around N0 = 50, it does reproduce experimental trends around both N0 = 82 and N0 = 126 and predicts strong quenching of these shells. Two versions of the model exist, one with 28 free parameters, and another with 10 parameters. Yet another, less fundamental way of obtaining a mass formula is the KUTY/KTUY model [19]. It again consists of two parts, one describing global trends, the other one fluctuations about these trends. The model fits 34 parameters to the data, more than the other models. When moving towards the neutron dripline, this model binds more strongly than the FRDM. The models discussed above have been compared to some of the data presented in this work in [20, 21].

2.2 Pairing and deformation

As stated in the introduction, deformation plays an important role in the region around neutron-rich zirconium. A uniﬁed shell-model [22] picture can be employed in order to explain – to some extent – these properties. In this model, a shell structure that persists even for strong collective behaviour is assumed. A central potential representing the average interaction of the nucleons leads to the existence of a shell structure, where single-particle levels group into shells with small energy gaps separated by larger energy gaps. These levels all have the same parity (normal levels), except for one of opposite parity (intruder level). Since the energy gap between shells is large, once a shell is ﬁlled, the nucleons will form an inert core and the nuclear properties arise from the behaviour of the valence nucleons above that shell.

The interaction of two nucleons with each other depends on whether they are identical or not. Identical nucleons interact strongly in the case that they both occupy the same orbit (nlj) and 6 Nuclear masses

couple to J π = 0+. This is called pairing. Otherwise the short range of the nuclear force together with the Pauli principle, which keeps like nucleons apart, will hinder interaction. However, once such a pair of nucleons is formed, the pair as a whole can be scattered into a diﬀerent valence orbit, leading to a smearing out of the Fermi surface. The pairing is stronger the larger the angular momentum and the larger the spatial overlap. Since the outer nucleons in heavier nuclei are further apart, the pairing strength decreases with increasing mass number. On the other hand, a proton and a neutron can interact in any pair of orbits (nπlπjπ) and (nν lν jν ). The strength of the interaction is determined by the respective orbits [22] and is particularly large for

lν − lπ nπ = nν and small . (2.3) lν + lπ

In other orbits, the neutron-proton matrix elements will be weaker than those for the pairing of like nucleons.

One consequence of the pairing interaction of like nucleons is that the ground state spin and parity of odd-mass nuclei is determined by the spin of the last unpaired nucleon. Another consequence is that the interaction between like nucleons, due to the very weak quadrupole force, will produce only spherical shapes. The neutron-proton interaction, on the other hand, has a strong quadrupole component, which can produce deformation. Therefore, deformation will occur when the neutron- proton correlations dominate over those of like nucleons. In a system of Nn valence neutrons and Np valence protons, the energy due to pairing is proportional to the number of valence nucleons, since each nucleon can only couple with one like nucleon,

Epair ∝ Mpair(Nn + Np) , (2.4)

where Mpair is an average of the relevant pairing matrix elements. The neutron-proton interaction, by contrast, is proportional to the product of valence protons and neutrons, since any neutron and proton can interact,

En−p ∝ Mn−pNnNp , (2.5)

with Mn−p being an average of the neutron-proton quadrupole matrix elements. In most cases, Mn−p is smaller than Mpair. Still, for suﬃciently large numbers of valence nucleons, En−p will dominate over Epair. If, however, the active shell is small, En−p will dominate only if the conditions given in Eq. 2.3 are met, leading to larger matrix elements Mn−p.

In addition to the quadrupole part of the neutron-proton interaction, the monopole component plays an important role in shifting the spherical single-particle energies. This component, too, is strongest between protons and neutrons in orbits fulfilling Eq. (2.3). Once the protons and neutrons are filling pairs of such orbits, the spectrum of single-particle levels can change rapidly. To study the behaviour of a single-particle level in a deformed potential, Nilsson [23] used a modified harmonic oscillator potential, though a more realistic calculation can be performed using a Woods-Saxon potential. The (2j + 1)/2-fold degeneracy of the spherical orbits is broken in such a potential, and j is no longer a π good quantum number. Commonly, the asymptotic quantum numbers Ω [NnzΛ] are used to describe the state, where Ω is the projection of the single-particle angular momentum onto the symmetry axis, see Fig. 2.2, N is the principle quantum number, nz is the number of oscillator quanta along the symmetry axis, i.e. the number of nodes in the wave function along the symmetry axis, and Λ the projection of the orbital angular momentum li on the symmetry axis. The parity π is given by (−1)N . The resulting level schemes relevant to the region covered in this work as a function of the deformation are shown in Figs. 2.3 and 2.4. 2.3 The astrophysical r-process 7

Figure 2.2: Schematic view of a deformed nucleus, taken from [24]. M is the projection of total angular momentum J on the laboratory axis, R the angular momentum from the collective motion of the nucleus, Ω the projection of total angular momentum j (orbital l plus spin s ) of the odd nucleon on the symmetry axis, and Λ the projection of angular momentum along the symmetry axis. Ω = Λ + Σ where Σ is the projection of intrinsic spin along the symmetry axis.

2.3 The astrophysical r-process

As mentioned above, about half of the elements heavier than iron existing in the universe today are assumed to have been produced in the r-process [7, 25]. This process takes place in an environment 24 3 with a high neutron density nn ≈ 10 /cm and a temperature of T ≈ 1-2 GK. Under these conditions neutron-capture will be faster than β-decay. The neutron-capture reactions will proceed until an equilibrium is reached between neutron-capture (n,γ) and photodisintegration (γ,n). The respective reaction rates are connected by 3/2 T − Sn ( k T ) λγn ∝ e B λnγ Nn When this waiting point is reached, the reaction stops and waits for β-decay.

(Z, A + i) → (Z + 1, A + i) + β− + ν

From the resulting nuclide (Z+1,A+i) a new reaction chain starts, absorbing neutrons until the next waiting point is reached. Thus, the r-process path lies about 10–20 neutrons to the neutron-rich side from stability. The neutron separation energy at the waiting point at a given temperature T and neutron density Nn is the same for all proton numbers and is about Sn ≈ 3 MeV. When the neutron ﬂow stops freeze-out occurs and the neutron-rich nuclei β-decay to stable isobars. The longer than average β-decay half-lives at the magic number waiting points result in larger abundances for these nuclides. Thus, the r-process abundance peaks at A ≈ 80,130,195 due to the closed neutron shells at N = 50,82,126. Possible astrophysical sites for the r-process to occur are Type II Supernovae and Neutron Star Mergers. A part of the r-process path, relevant to this work, is shown in Fig. 2.5. 8 Nuclear masses

Figure 2.3: Nilsson diagram for neutrons and protons with Z or N ≤ 50, taken from [24]. 2.3 The astrophysical r-process 9

Figure 2.4: Nilsson diagram for neutrons 50 ≤ N ≤ 80, taken from [24]. 10 Nuclear masses

Figure 2.5: Schematic outline of the stellar r-process relevant to this work. The thick squares mark the assumed path of the r-process [26], the black ﬁlled boxes mark stable nuclei, the ﬁlled grey boxes denote masses studied at JYFLTRAP [6, 20, 21, 27]. The crosses mark the heaviest isotope of each element with known half-lives [28, 29]. 3 Mass measurement techniques

Mass measurement techniques are often divided into indirect, i.e. reaction and decay, and direct measurements, e.g time-of-ﬂight measurements, as the former yield mass diﬀerences rather than masses. Since, however, the direct techniques rely on reference masses, these, too, do not yield absolute masses, unless the reference mass is 12C, on which the atomic mass unit is based.

3.1 Indirect techniques

A nuclear reaction A(a, b)B can be used to determine the mass of the unknown product B if the incoming and outgoing particles and the target mass are known. In addition, the kinematics of the unknown mass or the reaction Q-value must be determined. These requirements limit the applicability of reaction studies somewhat. However, since B does not need to be bound, it is possible to study nuclei that would otherwise not be accessible.

The mass of a radioactive nuclide can also be derived from its decay Q-value. This, however, will only yield a mass difference between parent and daughter nucleus; obtaining the mass of the parent requires linking this mass difference to a known mass, which can be quite far away, thus leading to cumulative errors along a decay chain. Additional uncertainties arise from an insufficient knowledge of the decay scheme, where high-lying decay branches might not be detected. β decay is especially complicated in that it is a three-body process, with a neutrino being emitted along with the β-particle carrying away part of the decay energy:

− − A(Z, N) → A(Z + 1, N − 1) + e + νe ; β

It is therefore necessary to determine the maximum energy of the β particle, the endpoint of the β spectrum.

3.2 Direct techniques

3.2.1 Time-of-flight measurements An example of using a time-of-flight measurement to determine the mass of a nucleus is the spectrometer SPEG located at GANIL [30]. The nuclides produced in fragmentation reactions are pre- separated in a α-shaped spectrometer. They then enter the SPEG, where their magnetic rigidity Bρ and their velocity are measured. The flight path is 82 m, leading to a typical time of flight of 1 µs. The detector response limits the time resolution to about 2 · 10−4. The determination of the magnetic rigidity by a position sensitive detector achieves a relative momentum resolution of about 10−4. The advantages of SPEG are its single-ion sensitivity and the short measurement time enabling a rough mapping of the mass surface very far from stability. In order to improve the resolution of a time-of-flight measurement, a longer flight path is needed. This can be achieved by using a cyclotron, where the ion path increases to over 1 km, as is done at the CSS2 at GANIL [31]. A mass resolution of 3 · 10−5 can be reached for nuclides with half-lives down to a few tens of µs.

11 12 Mass measurement techniques

3.2.2 Storage rings The revolution frequency of an ion in a storage ring depends on the circumference, which in turn depends on the ion optical settings. For an ensemble of ions, the difference in revolution frequencies is determined by the different mass to charge ratios ∆(m/q)/(m/q) and the different velocities ∆v/v ∆f 1 ∆(m/q) ∆v γ2 = − + 1 − . (3.1) f γ2 m/q v γ2 t t γt is the so-called transition energy at which the revolution frequency is independent of the energy for an ion species with fixed m/q-ratio and depends on the ion optical settings of the storage ring and can thus be varied. For relation 3.1 to be velocity independent and thus enable mass measurements, the second term on the right hand side must be zero. This can be achieved either by reducing the velocity spread ∆v, or by operating the ring in isochronous mode with γ = γt. Reducing the velocity spread is a prerequisite of Schottky mass spectrometry [32] and requires an ion-cooling mechanism. One possible method is stochastic cooling using an active electronic feedback system. This is most effective for hot beams and therefore suited for pre-cooling. A second technique is electron cooling, where the hot ions are cooled in collisions with cold, collinear electrons, resulting in beams of small size and momentum spread. The cooling time is proportional to the cube of the velocity spread. Electron cooling works better the lower the initial temperature of the ions.

Once the highly-charged ions are cooled, the revolution frequency of the ions can be measured by sampling the induced signal – the Schottky noise – in a pair of electrodes. From this, an ion’s mass can be derived if a reference mass is present in the ring at the same time for calibration. With this method many different ion species can be studied simultaneously with single-ion sensitivity. However, the relatively long cooling times set a limit on the half-life of the nuclide of about a second. With this method mass resolving powers of better than 106 have been reached [33]. Isochronous mass spectrometry does not suffer this limitation, as no cooling is required. The ions are injected at the transition energy, rendering the revolution time for a certain species independent of the velocity. A thin-foil detector placed in the ions’ path registers each passage of each stored ion. Thus a time- of-flight spectrum is obtained from which the masses can be derived if a suitable reference mass is present. The number of simultaneously stored ions is limited to about 50, but the single ion sensitivity remains. A resolving power of about 105 has been reached [34].

3.2.3 Radio frequency transmission spectrometers The MISTRAL experiment [35, 36] at ISOLDE, CERN combines a magnetic mass spectrometer with a time-of-flight spectrometer. It determines the cyclotron frequency νc of an ion in a homogeneous magnetic field from transmission peaks. The ions enter the field and follow a helicoidal trajectory for two turns. After one half turn their kinetic energy is modulated using a radio frequency signal. The change in kinetic energy leads to a changed cyclotron radius. One turn later, this modulation is repeated. If the modulation frequency νRF is

νRF = (n + 1/2)νc (3.2) the net eﬀect of the two modulations is zero. Only ions for which this is the case are transmitted through a narrow slit and are detected. Since no cooling or other beam preparation is required, this method is very fast, and hence very short-lived (T1/2 ≈ 10 ms) nuclides are accessible. The mass resolving power is limited by the emittance of the ISOLDE beam and the width of the exit slit. A resolving power of better than 105 can be reached.

3.2.4 Penning traps Penning traps employ a superposition of a strong homogeneous magnetic ﬁeld with a weak electric qB quadrupole ﬁeld to trap ions. The determination of the ion’s cyclotron frequency νc = 2πm relative 3.2 Direct techniques 13

Figure 3.1: Uncertainties of diﬀerent mass measurement techniques, taken from [8]. The numbers in brackets give the number of points for each experiment. to a well-known reference nuclide yields the ion’s mass. Penning traps have been used to measure the masses of nuclides with half-lives down to about 60 ms, and relative precisions of ≤ 10−8 can be reached [37]. The working principle of the Penning trap will be explained in more detail in Chapter 4.

3.2.5 Comparison The precisions that can be reached by diﬀerent direct mass measurement techniques are compared in Fig. 3.1. As can be seen, the farther one goes from stability, the lower the reached precision. The highest precisions are currently reached in Penning trap measurements, whereas the SPEG spectrometer can access nuclides the farthest from stability. A more detailed comparison is given by Lunney et al. [8]. 14 Mass measurement techniques 4 Experimental methods

The experiments described in this work were conducted using the JYFLTRAP setup at the IGISOL facility in Jyväskylä, Finland. Additional work was conducted at the ISOLTRAP setup at ISOLDE, CERN, Switzerland. Both experiments use the ISOL-method to produce radioactive beams which are first prepared in an RFQ-cooler/buncher and then transferred to a double Penning trap setup.

4.1 Radioactive ion beam production 4.1.1 Overview Different methods exist to produce beams of radioactive ions for different applications. The two most common techniques are the in-flight separation and the on-line isotope separation (ISOL). The former produces high-energy beams by fragmentation, preserving the forward momentum of the fragments, while for the latter the nuclear reaction products are stopped and reaccelerated. In the following, the ISOL technique will be described in more detail.

4.1.2 The ISOL technique To produce radioactive nuclei, a target is bombarded with high-energetic particles from an accelerator, inducing spallation, ﬁssion and fragmentation reactions. The reaction products are stopped either in the thick target, or, if a thin target is used, stopped in a separate catcher. This is schematically shown in Fig. 4.1. In the case of a thick target, the nuclides are evaporated out by heating the target and then transferred to an ion source, where they are ionised using e.g. surface, plasma or laser ionisation. In either case the ions are reaccelerated and mass separated using a bending magnet.

4.1.3 IGISOL The working principle of the IGISOL technique [38] is shown in Fig. 4.2. The beam coming from the accelerator, the JYFL K130 cyclotron, hits the target and induces nuclear reactions. The products of these reactions recoil out of the target and are stopped in helium gas at a pressure of about 100–300 mbar. Because of charge exchange processes with the gas the ions will be singly charged, or even be neutralised in the presence of a plasma. The ions are then transported with the helium ﬂow out of the chamber. A skimmer or a sextupole ion beam guide is placed outside the exit hole to reduce the helium ﬂow to the beamline. The neutralised reaction products are pumped away with the helium. The singly-charged positive ions, however, are accelerated towards the extraction electrode.

Diﬀerent ion guides are available, depending on the nuclear reaction needed to produce the desired reactions products:

• The Light-Ion Ion Guide will give a beam of neutron-deﬁcient ions produced in proton-, deuteron- or 3He-induced fusion evaporation reactions (e.g. (p,xn)) on a target. Since the

15 16 Experimental methods

PRIMARY PRIMARY BEAM BEAM

THIN THICK TRAGET TARGET + CATCHER CATCHER GAS SOLID

He-JET IONSOURCE

IONGUIDE MASS SEPARATION

Figure 4.1: ISOL methods, using thick or thin targets with solid or gaseous catcher.

reaction products have a small recoil energy, the target is placed inside the gas chamber

• The HIGISOL Heavy-Ion Ion Guide is used for reactions induced by a primary beam of heavier nuclei creating a compound nucleus which subsequently decays. Since the reaction products have a large forward momentum distributed in a cone shape, the target is placed outside the gas cell, and the primary beam is prevented from entering the cell by a beam stopper located in front of the cell’s entrance window. Because of the ions’ large kinetic energy, the gas cell is operated at higher buﬀer gas pressures of over 200 mbar.

• The Fission Ion Guide, Fig. 4.3, is used to produce neutron-rich isotopes by proton- or neutron- induced fission of uranium or thorium. The resulting ions cover a large mass range due to the asymmetric fission of uranium. The target is placed outside the stopping volume at an angle of 7◦ with respect to the beam, leading to an effective thickness of 120 mg/cm2. Separating the target from the stopping volume avoids the problem of beam-induced plasma forming in the buffer gas. The buffer gas pressure in the gas cell is between 100 and 400 mbar.

The IGISOL technique is chemically non-selective and very fast (sub-ms).

4.1.4 ISOLDE The ISOLDE facility [39] at CERN, Switzerland, can provide beams of about 800 isotopes of over 60 different elements with half-lives down to a few milliseconds for volatile elements. It uses the classical ISOL technique, with 1.4 GeV protons from the Proton Synchrotron booster impinging on a thick target and inducing fission, spallation and fragmentation reactions in the target. The protons are pulsed, which on the one hand side means great stress for the target during the impact of the high- intensity bunch, but on the other hand also enhances the release of short-lived species from the target. The reaction products diffuse out of the target, a process enhanced by the heating of the target to about 2000◦C. The atoms can be ionised in different ways, for example, an ECRIS and the laser ion 4.1 Radioactive ion beam production 17

Figure 4.2: IGISOL working principle, the empty red circles indicate ions, the ﬁlled ones have been neutralised in charge exchange reactions with the buﬀer gas.

Figure 4.3: The ﬁssion ion guide. The numbered parts are 1) the exit nozzle, 2) the stopping volume, 3) the separating foil, 4) the uranium target, 5) the helium inlet, 6) beam window, 7) graphite collimator, and 8) the accelerator beam. 18 Experimental methods

RADIOACTIVE LABORATORY

1-1.4 GeV PROTONS ROBOT

GPS

HRS CONTROL ROOM REX-ISOLDE

EXPERIMENTAL HALL

Figure 4.4: Schematic layout of the ISOLDE hall source setup RILIS are available. The ions are accelerated to typically 60 keV and mass separated, for which two magnetic mass separator systems have been implemented, namely the General Purpose Separator (GPS) and the High Resolution Separator (HRS). The GPS consists of a 60◦ bending magnet with a resolving power of about 1000, followed by a switchyard, where the primary beam can be split into three beams within a mass range of ±15% from the central mass, which can be sent to three different experiments simultaneously. The HRS consists of two bending magnets, the first one of 90◦, and the second one of 60◦ in the opposite direction. A resolving power of 15000 can be reached, while during normal operation a resolving power of 5000 is typically achieved. The resulting radioactive ion beam typically has a transverse emittance of the order of ǫ95% ≈ 10 − 20π-mm-mrad, and an energy spread of normally less than a few eV. Its intensity is proportional to the target thickness, the primary beam intensity, the production cross section, and the release and ionisation efficiency, which in turn depend on the element and isotope to be produced, on the target and on the ion source. This technique is chemically selective, as volatile elements will easily leave the target, whereas refractory elements cannot be extracted at all. This can be an advantage, as it reduces the background, but at the same time it limits the range of available beams. To enhance the extraction of a certain element, chemically reactive elements or molecules can be added, which form molecules of higher vapour pressure with the elements to be extracted. Additional chemical selectivity is provided by the choice of the ion source, with laser ion sources producing almost clean beams of one element.

4.2 Radio frequency-coolers/bunchers

Since the ion beams produced by the ISOL method are DC beams and usually have too large an emittance and energy spread for direct injection into a magnetic field, linear Paul traps are used to prepare the beams for injection into a Penning trap. When the ions enter the cooler, they are first decelerated by an electrostatic lens system. They then enter the radio frequency quadrupole (RFQ), a structure of four parallel rods with an oscillating radio frequency field of opposing phases applied to adjacent rods. This focuses the ions towards the center of the structure, trapping them in the transverse direction. The rods are each divided into segments, so that different potentials can be 4.3 Penning traps 19

z0 B U r 0 0 U r 0 r0

Figure 4.5: Two possible Penning trap electrode structures: using a hyperboloid ring electrode (left), and a cylindrical electrode (right). Correction electrodes are not shown. applied along them to form a potential well into which the ions are guided along the cooler axis and where they are stored and bunched. In order to cool the ions, the RFQ is ﬁlled with helium buﬀer gas. The thermalised ions are then extracted out of the cooler and re-accelerated.

4.3 Penning traps 4.3.1 Principles A Penning trap employs an electric quadrupole field in combination with a strong homogeneous magnetic field to trap ions. There are two methods commonly used to create the quadrupole field: (1) a hyperboloid ring electrode with two endcap electrodes, with the surfaces of the electrodes following the equipotential surfaces of the field, or (2) a set of cylindrical ring electrodes which together form the field around the axis of the central electrode. Both possibilities are shown schematically in Fig. 4.5. Method (1) has the advantage of a very precise field geometry, whereas method (2) is a more open construction and simplifies the injection of ions or buffer gas into the trap. Otherwise, the methods are equivalent, and the motion of ions in the traps can be described in the same way.

An ion of charge q and mass mion in a magnetic field B with a velocity component v perpendicular to the magnetic field will perform a circular motion with the angular frequency q ωc = · B (4.1) mion and radius ρ = v/ωc. The frequency νc = ωc/2π is the ion’s cyclotron frequency. The ion is thus bound in the radial direction. The electric quadrupole field in the trap provides confinement in the axial direction, and gives rise to a potential of the form

U 0 · 2 − 2 U(ρ, z) = 2 2 (2z ρ ) (4.2) 2z0 + r0 where 2z0 is the spacing between the endcap electrodes, and r0 is the inner radius of the ring 20 Experimental methods

electrode. For the motion in the axial direction, this leads to the equation of motion qU mz¨ + 0 z = 0 (4.3) d2 where d is the characteristic trap dimension 2 2 2 4d = r0 + 2z0 . This equation describes a harmonic oscillation; the angular frequency is

qU0 ωz = 2 . (4.4) rmd To describe the motion in the radial direction, both the electric and the magnetic ﬁeld have to be included in the equation of motion v2 U − m = −q · v · B + q 0 ρ . (4.5) ρ 2d2

Using the above relations for ωc and ωz, and ω = v/ρ this leads to 1 ω2 = ω · ω − ω2 . (4.6) c 2 z This quadratic equation has the two solutions

2 2 ωc ωc ωz ω± = ± − . (4.7) 2 r 4 2 There are thus two types of radial motion, ω+ is called the reduced cyclotron frequency and ω− is the magnetron frequency. Following this, the position of an ion in the trap is given by

x = ρ+ cos(ω+t + φ+) + ρ− cos(ω−t + φ−) (4.8)

y = ρ+ sin(ω+t + φ+) + ρ− sin(ω−t + φ−) (4.9)

z = ρz cos(ωzt + φz) , (4.10) where ρ+,−,z and φ+,−,z are the amplitudes and phases of the three types of motion, respectively. The three superposed motions of an ion in the trap are depicted in Fig. 4.6.

From Eq. 4.7 it is obvious that the sum of both radial frequencies equals the true cyclotron frequency.

ωc = ω+ + ω− . (4.11) Since this sum frequency only depends on the magnetic field B and the charge-over-mass ratio of the ions, measuring it allows for mass determination if the charge is known and the magnetic field can be determined by measuring a reference ion of well-known mass. From Eq. 4.7 it can also be seen that ω+ > ω−, and with normal settings ω+ >> ω−. It also follows that to first order the magnetron motion is mass independent U0 ω− ≈ . (4.12) 2Bd2 The potential energies of the radial motions are given by

U0 2 2 2 m 2 − q ρ± = −mρ±ω = ρ±(ω ω−) , (4.13) d2 z 2 + and the total energy of the ion in the trap is the sum of the energies of all three types of motion

m 2 2 m 2 2 m 2 2 E = ρ (ω ) + ρ (ω − ω ω−) + ρ−(ω− − ω ω−) . (4.14) 2 z z 2 + + + 2 + 2 The total energy of the radial eigenmotions is proportional to (ω± − ω+ω−). Considering again that ω+ > ω−, it can be seen that the total energy of the magnetron motion is in fact negative while that of the cyclotron motion is positive. Thus, energy loss will lead to an increase of the magnetron motion’s amplitude whereas the amplitudes of the cyclotron and axial motion will decrease. 4.3 Penning traps 21

ω z

ω − ω Total +

Figure 4.6: Motion of an ion in the trap. ω− is the magnetron motion, ω+ the reduced cyclotron motion, ωz the axial motion.

Dipole excitation Each of the eigenmotions can be excited independently by a dipole rf field of the corresponding frequency. For the axial motion, the exciting field has to be in the axial direction, i.e. between the endcaps, while for the two radial motions a radial field is needed. To create this field the ring electrode has to be split into segments and the rf voltage applied between opposite segments. The applied field will cause the motion’s amplitude to increase. However, depending on the initial phase of the external rf field and the position of the ion, it might initially decrease [40]. Radial dipole excitation can thus be used to place the ions in a certain orbit. Since the magnetron frequency is almost mass independent, an excitation at this frequency will affect all ions, while an excitation at the reduced cyclotron frequency only increases the radius for ions of a specific mass.

Quadrupole excitation The ion motion can be excited at sums and differences of the three eigen frequencies. The two motions can thus be coupled and the one converted into the other and back, this is called beating. The most important quadrupole excitation is that at ω+ + ω− = ωc. The azimuthal quadrupole needed to create the rf field requires the ring electrode to be split into four segments. The rf voltage is then applied between adjacent segments. The conversion time from one pure motion to the other pure motion depends on the magnetic field B and the amplitude of the rf field Vrf 2 B Tconv = 4πa . (4.15) Vrf a is the radius at which Vrf is the potential and can be approximated by the inner radius of the ring electrode. If the frequency of the excitation field does not match the ion’s cyclotron frequency, the conversion will be incomplete. The energy gain of the ion motion can be given as a function of the detuning ∆ω = ωrf − ωc q2V sin2(ΩT ) E (∆ω) = rf rf (4.16) r 32ma2 Ω2 where Ω is the beating frequency. During a full conversion of magnetron motion into cyclotron motion, the ion gains kinetic energy

m 2 2 2 2 ∆E = (ω − ω−)(ρ− − ρ ) (4.17) r 2 + ,0 +,0 where ρ−,0 and ρ+,0 are the magnetron and cyclotron amplitudes before quadrupole excitation. 22 Experimental methods

4.3.2 Precision mass measurement Since the cyclotron frequency of an ion is dependent on its mass, determining this frequency enables the measurement of the mass. One way to determine this frequency is the time-of-flight technique [41]. In a first step, a dipole excitation at the magnetron frequency is employed to move all ions in the trap to a well-defined radius. A quadrupole excitation then converts the magnetron motion into cyclotron motion with the same radius if ωRF = ωc for the ions stored in the trap. When the ions are extracted from the trap, their magnetic moments interact with the magnetic field gradient and they experience an axial force F = −µ·∇B converting radial kinetic energy into axial kinetic energy. Since the ions whose cyclotron frequency ωc is in resonance with the excitation frequency ωRF gain radial energy during excitation, they will be accelerated relative to those off resonance. This can be detected by measuring the time of flight to a detector, which is given by

zdet m T (ω ) = dz , (4.18) RF 2(E − qU(z) − µ(ω )B(z) Z0 r 0 RF where the integration is along the flight path of the ions from the trap center (z = 0) to the detector (z = zdet). By scanning through different quadrupole excitation frequencies ωRF , a time-of-flight spectrum for the ion species in question can be obtained. For an example of a resonance spectrum obtained with the JYFLTRAP precision trap, see Fig. 4.7. The sideband minima are due to the Fourier transformation of the square pulse envelope of the quadrupole excitation. Having thus determined the cyclotron frequency, it can be translated into the ion’s mass by measuring the time-of-flight resonance spectrum for a reference ion of known mass:

ωref c − mmeas = meas (mref me) + me . (4.19) ωc

ref meas ωc , ωc are the cyclotron frequencies of the reference ion and the measured ion, respectively, mref , me and mmeas the masses of the reference ion, the electron and the measured atom, respectively.

A more detailed description of the working principle of the Penning trap can be found in [42] and [43].

4.3.3 Cooling and isobaric purification In order to decrease their motional amplitudes, the ions are cooled, which results in smaller orbits centered in the trap. In this manner, inhomogeneities of the magnetic field and anharmonicities of the electric quadrupole field will have less impact on the measurement. Cooling is done by inserting a buffer gas into the trap, which gives rise to a viscous drag force

F = −δmv . (4.20)

The damping parameter δ describes the effect of the buffer gas. The ions lose energy through collisions with the gas atoms, leading to a damping of the axial and the cyclotron motion. However, this also causes the radius of the magnetron motion to increase, since the Lorentz force FL = q · v × B decreases (Fig. 4.8). Therefore, after some cooling time all ions will be lost as their magnetron radius increases until they hit the trap electrodes. However, as described above, by coupling the cyclotron and magnetron motions with a driving quadrupole field at ω+ + ω−, the unstable magnetron motion can be converted into cyclotron motion, which in turn is cooled away, as it is stable. Since the reduced cyclotron frequency is typically about three orders of magnitude larger than the magnetron frequency, the cyclotron motion is cooled away faster than the magnetron radius expands, leading to a centering of the ions, Fig 4.9. Since, unlike the magnetron frequency, the cyclotron frequency ωc = ω+ + ω− is mass dependent, this centering is mass selective. When the trap is opened, only 4.3 Penning traps 23

8 Counts 6

0 0 200 400 600 800 1000 Time of Flight (µs)

6 on resonance off resonance 5 A 4 B

3 Counts 2

0 0 200 400 600 800 1000 Time of Flight (µs)

550 B 500

s) 450 µ

400

350

300 Time of Flight (

250 A 200 -6 -4 -2 0 2 4 6 ν RF-1222225 (Hz)

Figure 4.7: Time-of-Flight spectrum from a measurement of 88Rb+ with 600 ms excitation time. The top ﬁgure shows all recorded ions versus their detection times. In the middle, only ions on resonance and oﬀ resonance are marked separately. The bottom panel shows the resulting resonance spectrum. The corresponding regions in the two lower panels are marked ’A’ and ’B’, respectively. 24 Experimental methods

Figure 4.8: Motion of ions in the trap without (left) and with (right) buffer gas. The magnetron motion has a larger radius than the cyclotron motion and is centred around the centre of the electric field. The reduced cyclotron motion is centred around the magnetic field lines.

Figure 4.9: Motion of ions in the trap with buﬀer gas and ωc-excitation 4.3 Penning traps 25

1400

1200 Nb Mo 1000 Zr

800

Counts 600

400

200 Y 0 -150 -100 -50 0 50 100 150 200 ν RF-1064800 (Hz)

Figure 4.10: Cooling resonance spectrum for A = 101 isobars produced in ﬁssion reactions those centred ions will be ejected. An example of a cooling resonance spectrum from the JYFLTRAP puriﬁcation trap is shown in Fig. 4.10.

Inserting buffer gas into the Penning trap reduces the possible storage time of the ions. Charge exchange with impurities in the gas will neutralise the ions of interest. In addition, molecules can be formed. Therefore, noble gases with high ionisation energies are used. The collisions with the gas atoms also change the ions’ orbit, and thus the frequency as they will be in a different field region. This reduces the mass resolving power of the trap. To achieve cooling, the buffer gas atoms have to be lighter than the ions to be cooled, or the distortions of the ions’ path will be too great for any net cooling effect. The method of buffer gas cooling in Penning traps was first described in [44].

4.3.4 Decay spectroscopy with pure samples

A common problem in decay spectroscopy is the high background; the ion species of interest makes up only a small fraction of the sample, especially as one moves away from stability. If the daughter nucleus is radioactive, its decay will contribute to the background as well. A solution to this problem is to use a Penning trap for isobaric or even isomeric purification to produce a pure sample. If the sample is initially pure, even a daughter nucleus of similar half-life as the parent can be accounted for, as it is possible to fit a decay curve with two decay parameters if the composition of the initial sample, i.e. the pure sample after the trap, is known. However, the background due to the decay of the daughter nucleus will increase over time as more and more activity is accumulated and decays back to stability. Tape stations are therefore regularly used in decay spectroscopy, where the ions are implanted on a movable tape and, after some measurement time, can be transported away from the detectors. This was done at JYFLTRAP to study the decay of several neutron-rich even zirconium isotopes [9]. A problem in using this technique is the usually small transmission efficiency of Penning traps compared to the large statistics needed for decay spectroscopy. 26 Experimental methods

Trapmagnet

MCP/ FC FC

Beam Switchyard RFQcooler/buncher Crossbeam ionsource

Figure 4.11: The JYFLTRAP setup

4.3.5 JYFLTRAP The JYFLTRAP triple trap setup consists of a linear Paul trap to cool and bunch the beam and a double Penning trap system for isobaric puriﬁcation and precision mass measurement. The layout is shown in Fig. 4.11 and will be discussed brieﬂy in the following.

RFQ cooler/buncher The beam from IGISOL has an emittance of about 13 π-mm-mrad and an energy spread of less than 100 eV. In order to improve the overall beam quality, a RFQ cooler/buncher is located after the bending magnet and the electrostatic beam switchyard. The potential in the cooler and the cooling/bunching principle are depicted in Fig. 4.12. The net eﬀect of this treatment is a reduced transverse emittance of ∼ 3 π-mm-mrad at 38 keV and a decreased energy spread of ∼ 1 eV of the beam. Also, the initially continuous beam can be bunched by collecting ions in the cooler for a certain time and releasing them in bunches. The cooling process is independent of the chemical properties of the ions, only the radio frequency has to be adjusted depending on the mass of the ions. The pressure in the cooler is typically of the order of 10−2 mbar. The RFQ cooler/buncher is described in detail in [45].

The double Penning trap setup The Penning trap at the IGISOL facility consists of two cylindrical Penning traps housed in the warm bore of a superconducting 7 T magnet. The magnet has two homogeneous field regions of 1 cm3 each. The electrode configuration of the first trap is shown in Fig. 4.13; the configuration of the second trap is identical except for the diaphragm. Placing both traps in the same magnet avoids the problem of having to transport the ions through strong magnetic field gradients between the traps. The disadvantage, however, is that no pumping is possible between the traps, and the pressure especially in the precision trap is harder to control. The whole trap is kept on a high voltage (HV) platform to decelerate the incoming beam, the HV usually being 30 kV. A description of the technical details of the IGISOL Penning trap is given in [46].

The buﬀer gas for the ﬁrst trap is fed directly into the trap structure through a hole in one of the electrodes. The traps are separated by a 5 cm long diaphragm of 2 mm inner diameter. Vacuum pumps are placed at both ends of the magnet. Because of this setup, it is not possible to directly 4.3 Penning traps 27

0 20 40 cm Injection Extraction

V HV platform

0 z

VZ Accumulate

Release

Figure 4.12: Sketch of the IGISOL RFQ cooler/buncher

Ring

Endcap 1stcorrection Diaphragm Beam 2ndcorrection

Gasfeeding

Figure 4.13: Electrode conﬁguration of the JYFLTRAP puriﬁcation trap 28 Experimental methods

measure the pressure inside the traps, only in the gas feeding line. From the width of the cooling resonance spectra and the shape of the time-of-flight resonance spectrum the pressure can to some extent be deduced. The first trap contains helium buffer gas at a pressure of about 10−5–10−4 mbar and is used for cooling and isobaric mass separation. The potential well has a depth of 100 V. The resulting magnetron frequency for these voltages is ν− = 1700 Hz. A mass resolving power of 145000 can be reached, which is sufficient for isobaric purification, as shown in Fig. 4.10. The second trap is operated in vacuum ( < 10−8 in the extraction line) for precision mass measurements. The depth of the capturing potential is 10 V.

4.3.6 ISOLTRAP The ISOLTRAP setup is the pioneer Penning trap experiment from which JYFLTRAP and other experiments were derived. It consists of the same basic elements as the JYFLTRAP setup, namely a RFQ cooler/buncher, and two Penning traps, one for isobaric puriﬁcation and one for precision measurements. These are aligned vertically due to space constraints in the experimental hall. Contrary to the JYFLTRAP setup, the Penning traps are on ground voltage. The setup is shown in Fig. 4.14

The RFQ cooler/buncher The RFQ cooler/buncher [47] is located on a 60 kV high-voltage platform, corresponding to the high voltage of the ISOLDE target. It is filled with helium buffer gas at a pressure of ≈ 5 · 10−6 mbar outside the electrodes. After being extracted in bunches from the RFQ and the HV platform, the ions are decelerated by pulsing an electrode down from 60 kV to about 3 kV. The ions are then deflected vertically, towards the Penning traps. The need to pulse the ions’ energy down before guiding them to the traps means that beam tuning through the traps can only be done with bunched ions rather than in continuous mode, which results in a difficult optimisation procedure and mass dependent tuning due to the mass dependent flight time to the pulsed drift tubes.

The Penning traps The first of the two Penning traps [43] is a cylindrical Penning trap, similar to the ones employed at JYFLTRAP. It is housed in the warm bore of a 4.7 T magnet and is filled with helium buffer gas at a pressure of ≈ 2 · 10−6mbar in the beam line. A typical purification cycle consists of 5–15 ms magnetron excitation at the magnetron frequency ν− = 304 Hz, followed by around 100 ms of quadrupole excitation. The depth of the trapping potential is 100 V, though the actual quadrupolar field has a depth of 10 V; the ions are cooled down to the quadrupole potential through collisions with the buffer gas.

The precision trap is housed in a separate 5.9 T magnet. While this complicates tuning further, as the ions have to be injected into a second magnetic field, it does enable differential pumping between the traps and thereby improved vacuum in the precision trap. Inside the trap, very good vacuum conditions with pressures of < 10−8 mbar can be reached. The trap is a hyperbolical Penning trap, resulting in a better field definition compared to a cylindrical electrode structure. The magnet has shim coils at room temperature, allowing fine-tuning of the homogeneity of the field. The depth of the trap potential is 10 V, resulting in a magnetron frequency of ν− = 1078 Hz. The ring electrode itself is at -10 V, meaning that the ions with a typical energy of a few eV, do not have sufficient energy to be transferred to ground potential without additional acceleration. 4.3 Penning traps 29

Figure 4.14: Sketch of the ISOLTRAP triple trap setup 30 Experimental methods 5 Precision mass measurements at JYFLTRAP

5.1 Evaluation of the statistical uncertainties

A time-of-flight resonance spectrum is obtained by scanning through a range of frequencies and recording the time of the ions’ detection by the MCP. For each measured frequency point the average time of flight is calculated as the mean of the distribution of all recorded ions. The deviation of the ion distribution is taken as the uncertainty of this average value. From the resulting resonance curves the cyclotron frequency of the examined species can be determined by fitting the theoretical line shape [41], using each point’s time-of-flight uncertainty for weighting. The Levenberg-Marquardt fitting routine is used, adopted to fit the theoretical time-of-flight resonance shape. The fit yields the centre frequency, its uncertainty and the reduced χ2. For χ2 > 1, the fit uncertainty is multiplied with the square root of the reduced χ2.

To determine the mass of a nuclide the magnetic field in the trap has to be known. To this end, a time-of-flight resonance spectrum of a different nuclide of well-known mass has to be taken, so that the ratio of the two frequencies, and hence the ratio of the masses, can be obtained. For precise measurements it is important to determine the resonance frequency of the reference ion before and after the measurement of the nuclide of interest. In this manner, time-dependent fluctuations, e.g. of the magnetic field, can be averaged, 1 m − m ν (νref,1 + νref,2) r = meas e = ref = 2 (5.1) mref − me νmeas νmeas for singly-charged ions. If the time between measurements and reference measurements varies, an interpolation rather than averaging is necessary. In practice, this means that the examined species and the reference are usually measured alternatingly, starting and ending with the reference mass. This also means, however, that the frequency ratios derived from subsequent measurements are not independent, as they are calculated using a common reference measurement. This has to be considered when calculating the uncertainty of the average frequency ratio for one nuclide. The uncertainty of one individual frequency ratio as calculated in Eq. 5.1, is given by

2 2 1 2 δνref,1 δνref,2 2 (νref,1 + νref,2) δr = + + · δνmeas . (5.2) s 2ν 2ν ν2 meas meas meas The weight of this one ratio when calculating the average of a set of measurements is then 2 1/(δri) wi = 2 (5.3) i 1/(δri) and the average is given by P r = ri · wi. (5.4) i X 31 32 Precision mass measurements at JYFLTRAP

The uncertainty of the average of the frequency ratios of a set of N frequencies of the nuclide of interest and N + 1 reference frequencies can now be calculated using the uncertainties of the determined frequencies.

w 2 δr = 1 · δν (5.5) 2ν ref,1 " meas,1 − N 1 w w 2 + i + i+1 · δν2 2ν 2ν ref,i+1 i=1 meas,i meas,i+1 X 2 1/2 w 2 N ν + ν + N δν + ref,i ref,i+1 w · δν 2ν ref,N+1 2ν2 i meas,i  meas,N i=1 meas,i ! X  A similar procedure is applied to Qβ measurements, where the mother and daughter nuclides are measured alternatingly, and the Q-value resulting from one measurement is given by

1 (νdaughter,i + νdaughter,i+1) Q = 2 − 1 (m − m ) (5.6) i ν daughter e mother,i The advantage of directly measuring the Q-value is that the uncertainty of the mass of the daughter nucleus, which serves as reference, scales with ν daughter − 1 νmother which is ≪1, as the masses are very close.

5.2 Systematic uncertainties

In addition to the statistical uncertainty and the uncertainty of the mass of the reference ion, three sources of systematic errors have to be taken into account in the calculation of the final uncertainty: the count rate effect due to a high number of ions in the trap, the fluctuations of the magnetic field and electronics, and a mass-dependent uncertainty due to imperfections in the electric quadrupolar field.

5.2.1 Count rate Large numbers of ions in the trap, especially of different species, can cause the observed resonance frequency to shift, as described in [48]. This shift is assumed to be caused by Coulomb interactions. If all ions in the trap have the same mass, no shift is expected. If different masses are introduced, the respective resonance frequencies are predicted to be lowered and shifted closer to each other. It is therefore important to keep the number of ions in the precision trap low, and to account for any remaining shifts in the analysis. Where sufficient statistics are available, a count rate class analysis is conducted as described in [49] and shown in Fig. 5.1. The available data set is split into groups depending on the number of detected ions. For each of these groups the resonance frequency is determined by fitting the theoretical line shape. A linear fitting routine is used to extrapolate the frequency to 0.6 ions in the trap, accounting for the 60% efficiency of the detector. Figure 5.1 shows two examples of count rate class analyses conducted this way. As can be seen, in the upper part the extrapolation seems quite reliable and the fitted frequencies line up nicely, though the resonance frequency increases with the count rate, rather than decrease as predicted in [48]. The lower plot, however, illustrates a problem regularly encountered in count rate class analyses at JYFLTRAP. 5.2 Systematic uncertainties 33

The scatter of the individual fitted frequencies is considerable, and, looking at the first two classes only, the slope might as well be negative. Indeed, in about 30% of all cases, the slope is found to be negative rather than positive as in Fig. 5.1. This behaviour might be explained by the gradient of the magnetic field in the precision trap. It has been observed that a larger axial amplitude leads to a higher frequency, i.e. the magnetic field increases in the axial direction, while larger radii lead to lower frequencies, i.e. the field decreases in the azimuthal direction. Rather than being caused by different ion species in the trap, the count rate effect might thus be caused by ions of the same species in different positions with different magnetic field strengths. The direction of the frequency shift thus depends on the shape of the ion cloud, which in turn depends on the conditions in the purification trap and on the transfer between the traps. Such a scenario would also explain why a count rate class effect is often observed even if only one stable ion species is present in the trap. This somewhat random behaviour is one reason why this analysis method is not always used. Another reason are low statistics. When the total number of ions collected for a resonance spectrum is too low to split into groups, the maximum number of detected ions per cycle is limited in the analysis, and the remaining systematic uncertainty is estimated based on the count rate class analysis of the spectra with sufficient statistics. The resulting uncertainty is quadratically added to the final averaged frequency ratio, as the effect is expected to cause an offset which will not average out with an increasing number of measurements.

5.2.2 Fluctuations There are various reasons for the cyclotron frequency to fluctuate. One is the fluctuation of the magnetic field due to the variation of the temperature in the experimental hall. This effect is shown in Fig. 5.2. The frequency shift due to a change in temperature can be quite large, but, as can be seen in Fig. 5.2, the variation is slow, and this drift is accounted for by taking reference measurements before and after each measurement, and by keeping the acquisition time for one resonance spectrum below about one hour. However, the high-voltage cage in which the trap is located has been covered in thermoplastic foil, to try to reduce the fluctuations of the temperature. There are, however, also fluctuations on a shorter time scale, e.g. of power supplies. These residual fluctuations appear to be completely random. They are therefore expected to average out over the course of several measurements. The size of the fluctuations is estimated based on the behaviour of the reference frequencies with time, and the average offset between consecutive references. The resulting uncertainty in terms of a frequency shift is added to each determined cyclotron frequency, and hence the impact on the final value decreases with an increasing number of measurements.

5.2.3 Mass-dependent uncertainties A misalignment of the magnetic and electric fields, or inhomogeneities in the electric quadrupole field, can cause the cyclotron frequency of one ion species to shift relative to that of another. The bigger the mass difference, the larger this shift. This effect was investigated by comparing 132 the resonance frequencies of O2 molecules and Xe. The measured cyclotron frequencies were 132 νc(O2) = (3358937.32 ± 0.05) Hz and νc( Xe) = (814609.991 ± 0.018) Hz, leading to a mass ratio 132 of r = νc( Xe) = 0.242520153(5). The tabulated value is r = 0.242520137(2). The resulting exp νc(O2) AME mass dependent uncertainty is

rexp − rAME −10 = 7 · 10 · (A − Aref ) . rAME This value might, however, underestimate the actual effect for lower masses. The frequency shift is accounted for by multiplying this uncertainty by the difference in mass number between the reference and the measured nuclide and quadratically adding it to the uncertainty of the final average 34 Precision mass measurements at JYFLTRAP

0.400

0.350

0.300

0.250 -959951 (Hz) c ν 0.200

0.150 fitted frequencies extrapolated frequency 0.100 0 1 2 3 4 5 6 average number of detected ions per bunch 0.550

0.500

0.450

0.400

0.350

0.300

-959951 (Hz) 0.250 c ν 0.200

0.150

0.100 fitted frequencies extrapolated frequency 0.050 0 1 2 3 4 5 6 average number of detected ions per bunch

Figure 5.1: Two examples of count rate class analyses for 112Tc. The extrapolated value is at 0.6 ions in the trap, corresponding to a 60% detection eﬃciency of the MCP. 5.3 Results 35

0.40 24.7 Frequency Temperature 0.35

0.30 24.6 C)

0.25 o

0.20 24.5

0.15 Temperature (

Frequency - 1887196 (Hz) 0.10 24.4

0.05

0.00 24.3 12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00 26.11. 26.11. 27.11. 27.11. 27.11. 27.11. 28.11. 28.11. 28.11. Time

Figure 5.2: Fluctuation of temperature and cyclotron frequency of 57Fe. frequency ratio.

5.3 Results

The work presented here was conducted using the IGISOL fission ion guide, with a cyclotron beam of 25–30 MeV protons at an intensity of 5–10 µA. Most of the data in this work has been previously published, [6, 20, 21, 27], and details of the analysis can be found in those references. In addition, previously unpublished measurements of 102−110Mo and 100−105Zr, done in June 2005, were included. The systematic uncertainties of these measurements, as discussed above, are 0.04 Hz for both the count rate effect and the fluctuations. The number of measurements and the excitation times are given in table 5.1. The reference was 97Zr, as with the already published data for zirconium and molybdenum [6], and it was therefore possible to obtain an average frequency ratio and an average mass excess. The obtained frequency ratios νc,ref and mass excess values are given in table 5.2. νc,meas 36 Precision mass measurements at JYFLTRAP

Table 5.1: Overview of the nuclides studied in June 2005. Given are the number N of resonance spectra taken, excitation time, the half-life, spin, and parity as listed in the AME03 [28]. ’#’ denotes estimated values, and ’()’ uncertain spin and/or parity. π Nucleus N TRF [ms] T1/2 I 100Zr 4 800 7.1 s 0+ 101Zr 4 800 2.3 s 3/2+ 102Zr 4 800 2.9 s 0+ 103Zr 4 800 1.3 s (5/2−) 104Zr 4 400 1.2 s 0+ 105Zr 4 400 600 ms 102Mo 4 800 11.3 min 0+ 103Mo 4 800 67.5 s (3/2+) 104Mo 4 800 60 s 0+ 105Mo 4 800 35.6 s (5/2−) 106Mo 4 800 8.73 s 0+ 107Mo 4 800 3.5 s (7/2−) 108Mo 4 400 1.09 s 0+ 109Mo 4 400 530 ms 7/2−# 110Mo 5 200 300 ms 0+ 5.3 Results 37

Table 5.2: Obtained frequency ratios x for the singly charged positive ions relative to the reference mass, and resulting mass excess values ME in keV.

ref νc Isotope Reference meas ME (JYFL) [keV] ME (AME03) [keV] Diﬀ νc 85Br 88Rb 0.965237440(37) −78575.4 ± 3.5 −78610 ± 19 −34.6 86Br 88Rb 0.977334856(38) −75632.3 ± 3.5 −75640 ± 11 −7.7 87Br 88Rb 0.988731283(39) −73892 ± 4 −73857 ± 18 35 88Br 88Rb 1.000145235(39) −70716 ± 4 −70730 ± 40 −14 89Br 88Rb 1.011550223(40) −68275 ± 4 −68570 ± 60 −295 90Br 88Rb 1.022977586(41) −64001 ± 4 −64620 ± 80 −619 91Br 88Rb 1.034388086(43) −61108 ± 4 −61510 ± 70 −402 92Br 88Rb 1.045822783(82) −56233 ± 7 −56580 ± 50 −347 94Rb 88Rb 1.068422547(45) −68564 ± 5 −68553 ± 8 11 95Rb 88Rb 1.079829822(38) −65935 ± 4 −65854 ± 21 81 96Rb 88Rb 1.091260919(41) −61355 ± 4 −61225 ± 29 130 97Rb 88Rb 1.102670725(65) −58519 ± 6 −58360 ± 30 159 95Sr 97Zr 0.979449067(132) −75121 ± 13 −75117 ± 7 5 96Sr 97Zr 0.989792213(134) −72924 ± 13 −72939 ± 27 −15 97Sr 97Zr 1.000159088(133) −68586 ± 13 −68788 ± 19 −203 98Sr 97Zr 1.010501790(136) −66429 ± 13 −66646 ± 26 −217 99Sr 97Zr 1.020863862(70) −62523 ± 7 −62186 ± 80 338 100Sr 97Zr 1.031212498(86) −59831 ± 9 −60220 ± 130 −389 95Y 97Zr 0.979381343(69) −81235 ± 7 −81207 ± 7 28 96Y 97Zr 0.989732208(70) −78341 ± 7 −78347 ± 23 −6 96Ym 97Zr 0.989749280(69) −76800 ± 7 −77206 ± 21 −406 97Y −76125 ± 8 −76258 ± 12 −133 97Ym 97Zr 1.000082958(74) −75458 ± 8 −75590 ± 12 −132 98Y 97Zr 1.010436763(88) −72299 ± 12 −72467 ± 25 −168 99Y 97Zr 1.020773794(73) −70654 ± 8 −70201 ± 24 453 100Y 97Zr 1.031129407(121) −67332 ± 12 −67290 ± 80 42 100Ym 97Zr 1.031131010(125) −67187 ± 12 −67090 ± 220 97 101Y 97Zr 1.041473324(78) −65065 ± 8 −64910 ± 100 155 98Zr 97Zr 1.010337145(135) −81292 ± 13 −81287 ± 20 5 99Zr 97Zr 1.020696482(138) −77633 ± 13 −77768 ± 20 −135 100Zr 97Zr 1.031029154(56) −76381 ± 6 −76604 ± 36 −223 101Zr 97Zr 1.041383548(57) −73169 ± 6 −73457 ± 31 −288 102Zr 97Zr 1.051719824(58) −71593 ± 6 −71742 ± 51 −150 103Zr 97Zr 1.062080443(59) −67818 ± 6 −68372 ± 109 −554 104Zr 97Zr 1.072422363(60) −65732 ± 6 −66341 ± 401 −609 105Zr 97Zr 1.082788496(67) −61460 ± 7 −62364 ± 401 −904 100Nb 100Nbm 0.999996640(83) −79802 ± 20 −79939 ± 26 −137 100Nbm 97Zr 1.030994733(22) −79488 ± 10 −79471 ± 28 17 101Nb 102Ru 0.990294436(39) −78883 ± 5 −78942 ± 19 −59 102Nb 97Zr 1.051667579(28) −76309 ± 10 −76350 ± 40 −41 102Nbm 102Nb 1.000000983(77) −76216 ± 20 −76220 ± 50 −4 103Nb 102Ru 1.009961485(41) −75020 ± 5 −75320 ± 70 −300 104Nb 97Zr 1.072354888(30) −71823 ± 5 −72220 ± 100 −397 105Nb 102Ru 1.029641706(42) −69907 ± 5 −70850 ± 100 −943 106Nb 102Ru 1.039493991(43) −66195 ± 5 −67100 ± 200 −905 107Nb 102Ru 1.049333291(84) −63715 ± 9 −64920 ± 400 −1205 102Mo 97Zr 1.051587093(57) −83574 ± 6 −83557 ± 21 17 38 Precision mass measurements at JYFLTRAP

ref νc Isotope Reference meas ME (JYFL) [keV] ME (AME03) [keV] Diﬀ νc 103Mo 97Zr 1.061934753(58) −80970 ± 6 −80847 ± 61 123 104Mo 97Zr 1.072260324(59) −80359 ± 6 −80329 ± 54 31 105Mo 97Zr 1.082612522(60) −77345 ± 6 −77338 ± 71 8 106Mo 97Zr 1.092944645(61) −76144 ± 6 −76255 ± 18 −111 107Mo 97Zr 1.103303130(62) −72562 ± 7 −72943 ± 162 −381 108Mo 97Zr 1.113641805(65) −70769 ± 7 −71303 ± 196 −534 109Mo 97Zr 1.124005948(71) −66676 ± 7 −67245 ± 298 −569 110Mo 97Zr 1.134348347(82) −64547 ± 8 −65456 ± 401 −909 106Tc 102Ru 1.039351332(46) −79736 ± 5 −79775 ± 13 −39 107Tc 105Ru 1.019137991(80) −78743 ± 9 −79100 ± 150 −357 108Tc 105Ru 1.028699157(81) −75916 ± 9 −75950 ± 130 −34 109Tc 105Ru 1.038248172(90) −74276 ± 10 −74540 ± 100 −264 110Tc 105Ru 1.047813645(87) −71028 ± 9 −70960 ± 80 68 111Tc 105Ru 1.057366451(100) −69018 ± 11 −69220 ± 110 −202 112Tc 102Ru 1.098383006(58) −65250 ± 6 −66000 ± 120 −750 106Ru 105Ru 1.009528321(80) −86310 ± 9 −86322 ± 8 −12 107Ru 105Ru 1.019085671(79) −83856 ± 9 −83920 ± 120 −64 108Ru 105Ru 1.028619965(80) −83655 ± 9 −83670 ± 120 −15 109Ru 105Ru 1.038182111(82) −80732 ± 9 −80850 ± 70 −118 110Ru 105Ru 1.047721142(84) −80067 ± 9 −79980 ± 50 87 111Ru 105Ru 1.057287033(88) −76778 ± 10 −76670 ± 70 108 112Ru 105Ru 1.066831083(88) −75624 ± 10 −75480 ± 70 144 113Ru 105Ru 1.076402249(119) −71819 ± 12 −72200 ± 70 −381 114Ru 105Ru 1.085950928(126) −70212 ± 13 −70530 ± 230 −318 115Ru 120Sn 0.958523298(62) −66071 ± 8 −66430 ± 130 −359 108Rh 120Sn 0.899973318(61) −84924 ± 8 −85020 ± 110 −96 108Rhm 120Sn 0.899972299(88) −85037 ± 10 −85080 ± 40 −43 109Rh 120Sn 0.908312639(60) −85018 ± 7 −85011 ± 12 7 110Rh 120Sn 0.916673797(61) −82674 ± 7 −82780 ± 50 −106 111Rh 120Sn 0.925017220(61) −82311 ± 8 −82357 ± 30 −46 112Rh 120Sn 0.933381862(62) −79577 ± 8 −79740 ± 50 −163 113Rh 120Sn 0.941729225(63) −78774 ± 8 −78680 ± 50 94 114Rh 120Sn 0.950097168(65) −75672 ± 8 −75630 ± 110 42 115Rh 120Sn 0.958450190(65) −74236 ± 8 −74210 ± 80 26 116Rh 120Sn 0.966822543(69) −70642 ± 8 −70740 ± 140 −98 117Rh 120Sn 0.975178272(79) −68904 ± 9 −68950 ± 500 −46 118Rh 120Sn 0.983554346(213) −64894 ± 24 −65140 ± 500 −246 112Pd 120Sn 0.933321426(62) −86327 ± 8 −86336 ± 18 −9 113Pd 120Sn 0.941686037(62) −83597 ± 8 −83690 ± 40 −93 114Pd 120Sn 0.950027102(62) −83497 ± 8 −83497 ± 24 0 115Pd 120Sn 0.958394697(122) −80434 ± 14 −80400 ± 60 34 115Pdm 120Sn 0.958395480(121) −80347 ± 14 −80310 ± 60 37 116Pd 120Sn 0.966740203(63) −79838 ± 8 −79960 ± 60 −122 117Pd 120Sn 0.975110888(66) −76430 ± 8 −76530 ± 60 −100 118Pd 120Sn 0.983460297(66) −75398 ± 8 −75470 ± 210 −72 119Pd 120Sn 0.991836131(73) −71415 ± 9 −71620 ± 300 −205 120Pd 120Sn 1.000186128(81) −70317 ± 10 −70150 ± 120 167 5.4 Discussion 39

Table 5.3: Previous measurements of strontium. Isotope Method Result Reference 95 Sr β-endpoint Qβ = 6082 ± 10 Blönnigen(1984) [50] 95 Sr β-endpoint Qβ = 6052 ± 25 Mach(1990) [51] 95Sr Penning trap ME = −75109±9 Raimbault-Hartmann(2002) [52] 96 Sr β-endpoint Qβ = 5332 ± 30 Peuser(1979) [53] 96 Sr β-endpoint Qβ = 5413 ± 22 Decker(1980) [54] 96 Sr β-endpoint Qβ = 5345 ± 50 Graefenstedt(1987) [55] 96 Sr β-endpoint Qβ = 5354 ± 40 Mach(1990) [51] 97 Sr β-endpoint Qβ = 7452 ± 40 Blönnigen(1984) [50] 97 Sr β-endpoint Qβ = 7480 ± 18 Gross(1992) [56] 98 Sr β-endpoint Qβ = 5821 ± 10 Blönnigen(1984) [50] 98 Sr β-endpoint Qβ = 5815 ± 40 Graefenstedt(1987) [55] 99 Sr β-endpoint Qβ = 8030 ± 80 Iafigliola(1984) [57] 99 Sr β-endpoint Qβ = 8360 ± 75 Graefenstedt(1987) [55] 100 Sr β-endpoint Qβ = 7520 ± 140 Iafigliola(1984) [57] 100 Sr β-endpoint Qβ = 7075 ± 100 Graefenstedt(1987) [55]

5.4 Discussion

5.4.1 Comparison to previous data The new mass values for the technetium, ruthenium, rhodium and palladium isotopes have been compared to previous measurements in [20], those of bromine and rubidium in [21], and niobium and yttrium in [27]. Such a comparison for the new strontium, zirconium and molybdenum masses is presented here.

Strontium

The previous measurements of the strontium isotopes are listed in Table 5.3, and depicted in Fig. 5.3 together with the new values. 95Sr has been previously measured in two β-endpoint measurements, [50, 51]. If the mass of the daughter nucleus 95Y is taken from this work, neither one agrees with our new value. However, the mass of 95Sr has also been measured at ISOLTRAP [52] with a precision better than the value presented here. The new JYFLTRAP value agrees with the ISOLTRAP value.

The mass of 96Sr has been measured by four diﬀerent groups using β-endpoint measurements [53, 54, 55, 51]. Only the result by Decker et al. [54] agrees with the new value; this is also the measurement on which the AME03 value is based. All other results give to high a binding energy. This is also the case for the two previous measurements of 97Sr [50, 56], and those of 98Sr [50, 55], though the result by Graefenstedt et al. [55] almost agrees with the new value if the mass of the daughter nucleus 98Y is taken from this work.

The two previous mass measurements of 99Sr [57, 55] differ greatly, the AME03 value being based on the result by Iafigliola et al. [57] . Even though the resulting mass given in the AME03 differs from our value by almost 380 keV, using the mass of the daughter nucleus 99Y given here reduces the discrepancy between our value and the β-endpoint result to about 100 keV. 100Sr was measured by the same groups as 99Sr, again with greatly differing results. In this case, the AME03 value is based on the measurements by Graefenstedt et al. [55]. Our value, however, confirms the result by Iafigliola et al. [57]. 40 Precision mass measurements at JYFLTRAP

150 Sr95 Sr96 Sr97 100

-50

-100

ME(AME)-ME (keV) -150

-200

-250 JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) Mach(1990) Mach(1990) Gross(1992) Mach(1990)* Mach(1990)* Gross(1992)* Decker(1980) Peuser(1997) Decker(1980)* Peuser(1997)* Blonnigen(1984) Blonnigen(1984) Raimbault(2002) Blonnigen(1984)* Blonnigen(1984)* Graefenstedt(1987) Graefenstedt(1987)*

Sr98 Sr99 Sr100 400

200

-200 ME(AME)-ME (keV)

-400 JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) Iafigliola(1984) Iafigliola(1984) Iafigliola(1984)* Iafigliola(1984)* Blonnigen(1984) Blonnigen(1984)* Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987)* Graefenstedt(1987)* Graefenstedt(1987)*

Figure 5.3: Strontium: Comparison between previous literature values and the values presented in this work. For the literature values that were given as a reaction or decay Q-value, the mass excess of the daughter is taken from the AME03, or, when marked with an asterisk (*), from this work. 5.4 Discussion 41

Zr98 Zr99 Zr100 Zr101 Zr102 Zr103 Zr104 Zr105 400

200

-200

-400

ME(AME)-ME (keV) -600

-800

-1000 Blair(1969) JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) Gross(1992) Gross(1992) Gross(1992)* Keyser(1980) Keyser(1980)* Graefenstedt(1987) Graefenstedt(1987b) Graefenstedt(1987b) Graefenstedt(1987b)* Graefenstedt(1987b)*

Figure 5.4: Zirconium: Comparison between previous literature values and the values presented in this work. For the literature values that were given as a reaction or decay Q-value, the mass excess of the daughter is taken from the AME03, or, when marked with an asterisk (*), from this work.

Zirconium Fig. 5.4 shows the results of the previous measurement, which are listed in Table 5.4, and the new values, given in Table 5.2. The mass of 98Zr has previously been measured by Blair et al. [58] in a (t,p) reaction. This results agrees very well with the value presented here. 99−103Zr were previously studied in β-endpoint measurements. 99,101Zr were measured by Gross et al. [56], in both cases the AME03 value is based on those values. However, both results give too light a mass compared to our new value. The same is true for the results that Graefenstedt et al. obtained for 100,102,103Zr [60, 55]. Again, for all three isotopes, the AME03 value is based on these measurements. 101Zr was also studied by Keyser et al. [59], a measurement which agrees nicely with the value presented here. 104,105Zr had not previously been measured, the masses given in the AME03 are based on extrapolations. Both masses are underestimated.

Molybdenum For each isotope the previous measurements, given in Table 5.5, and the value measured at JYFLTRAP, as listed in Table 5.2, are compared in Fig. 5.5. The mass of 102Mo has previously been measured both in a (t,p) reaction [61] and in a β-endpoint measurement [62]. Both results agree with each other and with our result. 103,104,105Mo have all been studied by Graefenstedt et al. [60]. For 103Mo their result gives too large a mass, for the other two isotopes, the masses agree with the results 42 Precision mass measurements at JYFLTRAP

Table 5.4: Previous measurements of zirconium. Isotope Method Result Reference 98 Zr (t,p) Q(t,p) = 3508 ± 20 Blair(1969) [58] 99 Zr β-endpoint Qβ = 4559 ± 15 Gross(1992) [56] 100 Zr β-endpoint Qβ = 3335 ± 25 Graefenstedt(1987) [55] 101 Zr β-endpoint Qβ = 5780 ± 120 Keyser(1980) [59] 101 Zr β-endpoint Qβ = 5485 ± 25 Gross(1992) [56] 102 Zr β-endpoint Qβ = 4605 ± 30 Graefenstedt(1987) [55] 103 Zr β-endpoint Qβ = 6945 ± 85 Graefenstedt(1987) [55]

Table 5.5: Previous measurements of molybdenum. Isotope Method Result Reference 102Mo (t,p) Q = 5034 ± 20 Casten(1972) [61] 102 Mo β-endpoint Qβ = 3508 ± 20 Jokinen(1995) [62] 103 Mo β-endpoint Qβ = 3750 ± 60 Graefenstedt(1987) [60] 104 Mo β-endpoint Qβ = 2155 ± 40 Graefenstedt(1987) [60] 104 Mo β-endpoint Qβ = 2155 ± 40 Jokinen(1995) [62] 105 Mo β-endpoint Qβ = 4950 ± 45 Graefenstedt(1987) [60] 106 Mo β-endpoint Qβ = 3510 ± 45 Graefenstedt(1987) [60] 106 Mo β-endpoint Qβ = 3520 ± 17 Gross(1992) [63] 106 Mo β-endpoint Qβ = 3520 ± 17 Jokinen(1995) [62] 107 Mo β-endpoint Qβ = 6160 ± 60 Graefenstedt(1989) [64] 108 Mo β-endpoint Qβ = 5135 ± 60 Gross(1992) [63] 108 Mo β-endpoint Qβ = 5120 ± 40 Jokinen(1995) [62] 108Mo ESR ME = −70830 ± 200 Matoˇs(2004) [65] 109Mo ESR ME = −66650 ± 230 Matoˇs(2004) [65] 110Mo ESR ME = −64780 ± 250 Matoˇs(2004) [65] 5.4 Discussion 43

200 Mo102 Mo103 Mo104 Mo105

150

100

0 ME(AME)-ME (keV)

-50

-100 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) Casten(1972) Jokinen(1995) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987)

Mo106 Mo107 Mo108 Mo109 Mo110 200

-200

-400

-600 ME(AME)-ME (keV)

-800

-1000 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) Gross(1992) Gross(1992) Matos(2004) Matos(2004) Matos(2004) Gross(1992)* Jokinen(1995) Jokinen(1995) Jokinen(1995)* Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987)*

Figure 5.5: Molybdenum: Comparison between previous literature values and the values presented in this work. For the literature values that were given as a reaction or decay Q-value, the mass excess of the daughter is taken from the AME03, or, when marked with an asterisk (*), from this work. 44 Precision mass measurements at JYFLTRAP

500

-500

-1000

-1500

ME(JYFL)-ME(HFB2) (keV) Sr -2000 Y Zr Nb Mo -2500 56 57 58 59 60 61 62 63 64 65 66 67 68 Neutron number N

Figure 5.6: Comparison to the HFB2 model predictions. presented here. 106Mo, too, was measured by Graefenstedt et al., and also by Gross et al. [63] and Jokinen et al. [62], with all results agreeing with each other. However, our new value suggest the nuclide is less bound by about 110 keV.

Graefenstedt et al. also studied 107Mo. If the mass of the daughter nucleus 107Tc is taken from the AME03, the resulting mass value diﬀers from our value by about 400 keV. If, however, the mass of 107Tc is taken from this work, the corrected mass value agrees with our value. The mass value of 108Mo given in the AME03 is based on extrapolation, which results in too small a mass by about 500 keV, even though the nuclide has previously been measured by Gross et al. [63] and Jokinen et al. [62]. Both these measurements yield mass values in agreement with our value. More recently, 108Mo has been studied using the ESR storage ring at GSI in isochronous mode [65]. This measurement, too, agrees with ours. During the same ESR campaign the masses of 109,110Mo were measured, with both results agreeing with the ones presented here. The AME03 mass values for both isotopes are based on extrapolations. As in the case of 108Mo, these extrapolations overestimate the binding.

5.4.2 Comparison to global models In [20, 21] the measured mass values of the isotopes of bromine, rubidium, technetium, ruthenium, rhodium and palladium have been compared to a selection of mass model predictions. The same is done here for the measured isotopes of strontium, yttrium, zirconium, niobium and molybdenum. Additional data is taken from the AME03 to extend the comparison for all elements to N = 56. They are compared to the HFB-2 (Fig. 5.6), and HFB-9 (Fig. 5.7), the HFBCS-1 (Fig. 5.8), the FRDM (Fig. 5.9), the ETFSI-1 (Fig. 5.10) and ETFSI-2 (Fig. 5.11), the two versions of the model by Duﬂo and Zuker (Figs. 5.12 and 5.13), and the KTUY mass formula (Fig. 5.14). 5.4 Discussion 45

1000

500

-500

-1000

-1500

ME(JYFL)-ME(HFB9) (keV) Sr Y -2000 Zr Nb Mo -2500 56 57 58 59 60 61 62 63 64 65 66 67 68 Neutron number N

Figure 5.7: Comparison to the HFB9 model predictions.

1000

500

-500

ME(JYFL)-ME(HFBCS1) (keV) -1000 Y Zr Nb Mo -1500 56 57 58 59 60 61 62 63 64 65 66 67 68 Neutron number N

Figure 5.8: Comparison to the HFBCS-1 model predictions. 46 Precision mass measurements at JYFLTRAP

1500

1000

500

-500

-1000 Sr ME(JYFL)-ME(FRDM) (keV) Y -1500 Zr Nb Mo -2000 56 57 58 59 60 61 62 63 64 65 66 67 68 Neutron number N

Figure 5.9: Comparison to the FRDM model predictions.

500

-500

-1000

Sr ME(JYFL)-ME(ETFSI1) (keV) -1500 Y Zr Nb Mo -2000 56 57 58 59 60 61 62 63 64 65 66 67 68 Neutron number N

Figure 5.10: Comparison to the ETFSI-1 model predictions. 5.4 Discussion 47

1000

500

-500

Sr ME(JYFL)-ME(ETFSI2) (keV) -1000 Y Zr Nb Mo -1500 56 57 58 59 60 61 62 63 64 65 66 67 68 Neutron number N

Figure 5.11: Comparison to the ETFSI-2 model predictions.

1400

1200

1000

800

600

400

200

0 Sr -200 Y

ME(JYFL)-ME(Duflo-Zuker96) (keV) Zr -400 Nb Mo -600 56 57 58 59 60 61 62 63 64 65 66 67 68 Neutron number N

Figure 5.12: Comparison to the 10 parameter Duﬂo-Zuker model predictions. 48 Precision mass measurements at JYFLTRAP

1200

1000

800

600

400

200

-200 Sr -400 Y

ME(JYFL)-ME(Duflo-Zuker95) (keV) Zr -600 Nb Mo -800 56 57 58 59 60 61 62 63 64 65 66 67 68 Neutron number N

Figure 5.13: Comparison to the 28 parameter Duﬂo-Zuker model predictions.

3000

2500

2000

1500

1000

500

ME(JYFL)-ME(KTUY) (keV) -500 Sr Y -1000 Zr Nb Mo -1500 56 57 58 59 60 61 62 63 64 65 66 67 68 Neutron number N

Figure 5.14: Comparison to the KTUY model predictions. 5.4 Discussion 49

16 Br Mo 15 Nb Pd Rb 14 Rh Ru Sr Tc 13 Y Zr 12 (MeV) 2n S 11

8 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Neutron number

Figure 5.15: Two-neutron separation energy S2n as a function of N.

It is interesting to note that all models seem to underbind the lighter nuclides, while overbinding the heavier ones (except for the two ETFSI calculations, which, at higher masses, tend to underestimate the binding again). All models change from less bound to more strongly bound than our mass values around N ≈ 59. As was the case for the isotopes from technetium to palladium [20], the KTUY calculation gives far too low masses for the heavier nuclides compared here, with discrepancies of over 2.5 MeV. Both the calculations by Duﬂo and Zuker, as well, already in this region show the trend towards too large binding, which was also observed in the region from technetium to palladium, there especially in technetium. The HF based models all do comparatively well between N = 60 and N = 68, where the older HFB-2 seems to agree better than the newer HFB-9. All three models, however, seem to have problems reproducing the odd-even staggering. All in all, it seems that in the mass region examined here, none of the models yields the reliable predictions that would be needed for calculations of the astrophysical r-process.

5.4.3 Study of systematic trends Two-neutron separation energy

The two-neutron separation energy S2n = −ME(A, Z) + ME(A − 2,Z) + 2 · ME(n), ME(n) being the mass excess of the neutron, can be viewed as an indicator of major structural change and shell closures. Fig. 5.15 shows the two-neutron separation energy for all data included in this work. For the two isotopes closest to stability the needed mass excesses for the (A − 2) isotopes are taken from the AME03. The change in shell structure at N = 60 is clearly visible, especially around the 50 Precision mass measurements at JYFLTRAP

semi-magic zirconium. Another startling feature is the very smooth behaviour between technetium and palladium, which has been discussed in [20]. A diﬀerent way of presenting the two-neutron separation energy is as a function the proton number Z, as shown in Fig. 5.16. In this ﬁgure, the change in structure is even more obvious, with an inver- sion of the two-neutron separation energies of N = 60 and N = 62 at Z = 40 in the even-N nuclei. The pronounced shell gap between N = 56 and N = 58 steadily decreases towards lower Z, i.e. more neutron-rich nuclei. In the odd-N nuclei the lines marking N = 59 and N = 61 are completely inverted up to Z = 42, where normal ordering is again established.

Due to the strikingly smooth behaviour of the two-neutron separation energy in the technetium, ruthenium, rhodium and palladium isotopes, a simplified liquid drop model equation was fitted to the values in [20]. For the even-even nuclei, this was compared to the E2 transition energy from the lowest excited 2+ state to the 0+ ground state, as shown again in Fig. 5.17. According to the microscopic calculations of Ref. [66], for even-even nuclei the shape change in the case of axial deformation from prolate to oblate is predicted to occur at N = 66 for ruthenium and N = 68/70 for palladium in good agreement with the energies of the first 2+ states. For ruthenium, the decrease in the S2n value (relative to the fit) beyond N = 66 coincides with the appearance and lowering of the oblate minimum. For palladium, the situation in light of the model calculation is quite different. Coexistence of two shapes close in energy and weakening deformation (β2 = −0.19, +0.14) eventually seem to lead to stronger two-neutron binding. A weakening of the deformation at N = 74 is also supported by the increase in the energy of the first 2+ state to nearly 450 keV. Therefore, it can be concluded that rather small changes in nuclear structure are visible in the ground state binding if the masses are known to a precision of significantly better than 100 keV.

It is also interesting to compare the two-neutron separation energy to the changes in the mean-square charge radii, Fig. 5.18. The charge radii are taken from [67, 68, 69]. A strong increase of the charge radius is observed at N = 60. This eﬀect is strongest for yttrium, for which also the changes in the two-neutron separation energy are most pronounced.

Neutron separation energy

As stated in chapter 2, the neutron separation energy Sn = −ME(A, Z) + ME(A − 1,Z) + ME(n) can give a clue as to the path of the r-process, which is assumed to proceed where Sn ≤ 3 MeV. As can be seen in Fig. 5.19 this limit has not yet been reached in this work, though 92Br comes close. Due to the odd-even staggering, however, this means that the masses of at least two more bromine isotopes further from stability will have to be measured in order to actually reach the r-process path.

Valence proton-neutron interactions

In order to isolate the average empirical proton-neutron interaction energy, δVpn has been deﬁned as a double diﬀerence of masses. For even-even nuclei, the average interaction of the last two neutrons with the last two protons is given by

1 δV ee(Z, N) = ([B(Z, N) − B(Z, N − 2)] − [B(Z − 2, N) − B(Z − 2, N − 2)]) . (5.7) pn 4 For nuclei with odd proton number and even neutron number, the interaction strength of the last proton with the last two neutrons is

1 δV oe(Z, N) = ([B(Z, N) − B(Z, N − 2)] − [B(Z − 1, N) − B(Z − 1, N − 2)]) , (5.8) pn 2 5.4 Discussion 51

16 N = 56 N = 62 15 N = 54

14 N = 58

12 (MeV) 2n S 11 N = 70 N = 72 N = 64 10 N = 66 N = 68 9 N = 60 8 36 38 40 42 44 46 Proton number Z 16 N = 59 N = 61 15 N = 63 N = 57 14 N = 55

12 (MeV) 2n S 11

10 N = 69 N = 73 N = 65 9 N = 59

8 36 38 40 42 44 46 Proton number Z

Figure 5.16: Two-neutron separation energy S2n as a function of Z for even-N (top) and odd-N (bottom) nuclei. 52 Precision mass measurements at JYFLTRAP

300 550 Ru Ru 200 Pd Pd 500 100 0 450

-100 400 -200 -fit (keV) 350 E2 (keV) 2n -300 S -400 300 -500 250 -600 -700 200 60 62 64 66 68 70 72 74 Neutron number

Figure 5.17: Two-neutron separation energy relative to the function given in [20] plotted with the E2 transition energy. 5.4 Discussion 53

Sr 2 Y Zr 1.8 )

2 1.6

(fm β = 0.3 1.4 2 β β 2 = 0.2 2 = 0.4

N-50,N 1.2 > 2

δ 1

0.8 β 0.6 2 = 0.1

Sr 16 Y Zr Nb 15 Mo

13 (MeV) 2n S 12

54 56 58 60 62 64 66 68 Neutron number

Figure 5.18: Two-neutron separation energies and relative mean-square charge radii < δ2 >N−50,N for the strontium, yttrium and zirconium isotopes around N = 60. Droplet model isodeformation lines [68] for yttrium are shown dashed. 54 Precision mass measurements at JYFLTRAP

6.5

5.5

5 (MeV) n S 4.5

3.5

3 49 51 53 55 57 59 61 63 65 67 69 71 73 N (odd) Br Nb Rb Ru Tc Zr Mo Pd Rh Sr Y

8.5

7.5

7 (MeV) n S 6.5

5.5

5 50 52 54 56 58 60 62 64 66 68 70 72 74 N (even) Br Nb Rb Ru Tc Zr Mo Pd Rh Sr Y

Figure 5.19: Neutron separation energy Sn for odd (a) and even (b) neutron numbers. 5.4 Discussion 55

600 even Z, even N Kr Sr 550 Zr Mo Ru 500 Pd

450

(keV) 400 pn V δ 350

300

250

200 52 54 56 58 60 62 64 66 68 70 Neutron number N

ee Figure 5.20: Average empirical proton-neutron interaction energy δVpn for even-even nuclei.

and similarly for even-Z–odd-N nuclei. δVpn eﬀectively cancels out other interactions to second order and isolates that of the last valence protons and neutrons. Larger values of δVpn are expected if the last protons and neutrons are ﬁlling similar orbits. The δVpn values calculated from the masses presented in this work, and including the krypton masses measured recently at ISOLTRAP [70], are shown in Figs. 5.20, 5.21 and 5.22, where the thin lines mark the old values based on the AME03, and the thick lines mark the new values based on the masses given in this work.

eo Brenner et al. [71] report several anomalies in the region covered here. The sudden increase of δVpn at 101Zr has not been conﬁrmed by our measurements. The other anomalies listed in [71] concern the oe 101 99 101 δVpn of Nb, Y and Y. It seems, however, that niobium and yttrium have been mislabelled in the relevant plot (Fig. 4 in [71]), and also the aforementioned anomalies are interchanged, i.e. they 99 101 103 101 concern Y, Nb and Nb. The sharp peak of δVpn at Nb is even more pronounced using the new data, with 101Nb lying higher and 103Nb lying lower than before. A similar discontinuity had been observed for 99Y and 101Y, with a sudden decrease at 99Y and a sharp increase towards 101Y. This anomaly has now been replaced by a relatively smooth behaviour. In addition, a sudden drop at 115Pd has disappeared in the new values. The odd palladium isotopes, as well, now follow a smoother trend. Such a smooth behaviour is also observed for rhodium, and for the heavier ruthenium and technetium isotopes.

Since δVpn is largest when the last protons and neutrons are filling orbits with large spatial overlap, ee it depends on the fractional filling of the neutron and proton shells [72]. In Fig. 5.23, δVpn is plotted as a function of both N and Z and the fractional filling of the shells Z = 28–50 and N = 50–82. According to the δVpn scheme, the largest values are expected along the diagonal where the fractional filling are similar. This is not the case in this region. + + Cakirli et al. [72] pointed out a correlation between δVpn and R4/2 = E(41 )/E(21 ), which is considered to be a measure of collectivity and is plotted in Fig. 5.24. Clearly, collectivity increases abruptly in zirconium and strontium between N = 58 and N = 60, whereas molybdenum displays a smoother 56 Precision mass measurements at JYFLTRAP

800 Kr even Z, odd N Sr 700 Zr Mo Ru 600 Pd

500

(keV) 400 pn V δ 300

200

100

0 51 53 55 57 59 61 63 65 67 69 71 Neutron number N

eo Figure 5.21: Average empirical proton-neutron interaction energy δVpn for even Z – odd N nuclei.

800 Br odd Z, even N Rb 700 Y Nb Tc 600 Rh

500

(keV) 400 pn V δ 300

200

100

0 52 54 56 58 60 62 64 66 68 70 Neutron number N

oe Figure 5.22: Average empirical proton-neutron interaction energy δVpn for odd Z – even N nuclei. 5.4 Discussion 57

f_n 0.06 0.13 0.19 0.25 0.31 0.38 0.44 0.5 0.56 0.63

46 1 1 2 2 0.82

44 21122 0.73

42 4412 0.64 Z f_p 40 4213 0.55

38 4 2 0.45

36 3 3 0.36

52 54 56 58 60 62 64 66 68 70 N 1 350-400 keV 2 400-450 keV 3 450-500 keV 4 500-580 keV

ee Figure 5.23: δVpn against N and Z. The fractional ﬁlling of the main shells is given on the top and right axis, respectively.

3.4

3.2

2.8

2.6

2.4 E4/E2 2.2

2 Sr 1.8 Zr Mo 1.6 Ru Pd 1.4 56 58 60 62 64 66 68 N

+ + Figure 5.24: E(41 )/E(21 ) for strontium, zirconium, molybdenum, ruthenium and palladium. 58 Precision mass measurements at JYFLTRAP

Table 5.6: Comparison of δVpn and R4/2 for nuclides with corresponding numbers of valence proton and neutron particles or holes. δVpn (keV) R4/2 pair p-h p-p/h-h p-h p-p/h-h 110Ru - 112Ru 447.0(37) 444.5(41) 2.757 2.723 110Pd - 116Pd 370.2(41) 438.0(47) 2.462 2.578 112Pd - 114Pd 391.5(45) 403.5(41) 2.533 2.563 96Zr - 94Sr 550.7(21) 540.5(21) 1.571 2.564 98Zr - 96Sr 441.2(48) 376.5(47) 1.507 2.199

behaviour, as was the case for the two-neutron separation energy. In the palladium isotopes, R4/2 is almost constant.

Cakirli et al. state that nuclei in the particle-particle (p-p) region (lower left corner of Fig. 5.23) and hole-hole (h-h) region (upper right corner of Fig. 5.23) both δVpn and R4/2 will be larger than for corresponding nuclei in the particle-hole (p-h) region (upper left corner of Fig. 5.23). In the limited dataset discussed here, only ﬁve such pairs can be compared. These are listed in Table 5.6 For the two palladium pairs the observation by Cakirli et al. holds, and the h-h nuclides have larger collectivity and larger valence proton-neutron interaction than the corresponding p-h nuclides. For the ruthenium pair the values are almost equal. For the two strontium-zirconium pairs, however, this simple model does not hold. While R4/2 is still larger for the p-p nuclides than for the p-h nuclides, δVpn shows the opposite behaviour.

An interesting application of the δVpn scheme is the extrapolation of unknown mass values. δVpn can be approximated by ∂2B δV (Z, N) ≈ , (5.9) pn ∂Z∂N the mixed partial derivative of the binding energy. While it was seen in section 5.4.2 that the absolute binding energies predicted by current global models are rather unreliable when moving away from stability, this second derivative can be expected to be better reproduced, as the pairing only weakly aﬀects δVpn[73]. Thus, if three masses are known, and δVpn can be calculated from model binding energies, it is possible to use Eq. 5.7 to extrapolate the fourth mass. For a sample of the models examined in section 5.4.2, δVpn was calculated and compared to experimental values (including [70]), Figs. 5.25–5.29. All these models display discrepancies for strontium, zirconium and molybdenum around N = 60. The values for ruthenium and palladium are better reproduced, especially by the HBF-9 calculations. It is worth of notice that the deviations are in all cases below 300 keV. This is a considerable improvement over the agreement of the absolute binding energies from which the δVpn are calculated. To test the mass prediction power of these δVpn values, the binding energies of 110Mo, 114Ru, and 120Pd were calculated using Eq. 5.7. The binding energies were taken from this work, except for those of 120,122Cd which were taken from the AME03. The results are presented in Fig. 5.30. The models mostly give too large a binding energy, only in the case of 114Ru does the HFB-9 result in a slightly low binding energy. The ETFSI-2 calculation agrees remarkably well with the experimental value for 120Pd. Compared to the often large discrepancies found for the calculated absolute binding energies in section 5.4.2, the extrapolations based on δVpn are far closer to the experimental values. This is, however, not surprising, since three of the four input parameters in Eq. 5.7 are taken directly from experiment, and the fourth value, the actual δVpn, is usually around 500 keV. Another drawback is that each further step away from stability increases the uncertainty considerably. 5.4 Discussion 59

-50

-100 (HFB9-exp) (keV)

pn -150 V δ

-200

-250 52 54 56 58 60 62 64 66 68 70 Neutron number N

Kr Sr Zr Mo Ru Pd

ee Figure 5.25: δVpn , HFB-9 for even-even nuclei.

150

100

-50

-100

(FRDM-exp) (keV) -150 pn V δ -200

-250

-300 52 54 56 58 60 62 64 66 68 70 Neutron number N

Kr Sr Zr Mo Ru Pd

ee Figure 5.26: δVpn , FRDM for even-even nuclei. 60 Precision mass measurements at JYFLTRAP

100

-50 (DuZu-exp) (keV) pn V δ -100

-150 52 54 56 58 60 62 64 66 68 70 Neutron number N

Kr Sr Zr Mo Ru Pd

ee Figure 5.27: δVpn , Duﬂo-Zuker (28 parameters) for even-even nuclei.

150

100

-50

(ETFSI-exp) (keV) -100 pn V δ -150

-200

-250 52 54 56 58 60 62 64 66 68 70 Neutron number N

Kr Sr Zr Mo Ru Pd

ee Figure 5.28: δVpn , ETFSI-2 for even-even nuclei. 5.4 Discussion 61

150

100

-50

(KTUY-exp) (keV) -100 pn V δ -150

-200

-250 52 54 56 58 60 62 64 66 68 70 Neutron number N Kr Sr Zr Mo Ru Pd

ee Figure 5.29: δVpn , KTUY for even-even nuclei.

350 Mo110 Ru114 Pd120 300 250 200 150 100 50

BE(model) - BE(exp.) (keV) 0 -50 Exp. Exp. Exp. KTUY KTUY KTUY FRDM FRDM FRDM HFB-9 HFB-9 HFB-9 ETFSI-2 ETFSI-2 ETFSI-2 Duflo-Zuker Duflo-Zuker Duflo-Zuker

Figure 5.30: Extrapolated binding energies using theoretical δVpn values, relative to the JYFLTRAP value. Note that larger values mean larger binding and smaller mass. The larger uncertainties for 120Pd are due to the larger uncertainties of the binding energies of 120,122Cd from the AME03 used to calculate this value. 62 Precision mass measurements at JYFLTRAP

1.4

1.2

(MeV) 0.8 exp ν ∆ 0.6

0.4

0.2 50 55 60 65 70 N Br Rb Y Nb Tc Rh Kr Sr Zr Mo Ru Pd

Figure 5.31: Neutron odd-even staggering three-point indicator ∆ν as a function of neutron number N (N odd).

Odd-even staggering A measure of the empirical pairing gap can be obtained from the three-point expression π ∆(3)(n) = n [B(n − 1) + B(n + 1) − 2B(n)] , (5.10) 2

n where πn = (−1) is the number parity, B is the (negative) binding energy, and n is the number of particles, either Z or N, while the other one is kept constant. Fig. 5.31 shows the odd-even staggering as a function of neutron number for odd N, calculated according to 1 ∆(3)(N) = − [B(Z, N − 1) + B(Z, N + 1) − 2B(Z, N)] . ν 2 For ruthenium, rhodium and palladium and for the heavier molybdenum isotopes the pairing gap is relatively smooth, and its increase with increasing Z is visible, with the even-Z elements having a larger pairing gap. The sudden change at N = 60 in zirconium and yttrium clearly shows as a sharp peak at N = 59 and equally sharp decrease at N = 60. In strontium, niobium and molybdenum this eﬀect is also present, albeit less pronounced. This peak shows that the indicator ∆ν breaks down at this point, since the neighbouring even-N nuclides used in deriving ∆ν have diﬀerent deformations. 6 Spectroscopy at ISOLTRAP

The aim of this project is to install a tape station on top of the ISOLTRAP setup (Fig. 4.14). This will, on the one hand, enable background-free decay spectroscopy with isobarically and even isomerically pure samples, and on the other hand, it will assist precision mass measurements by allowing the determination of the measured species, especially in the case when only one of two or more isomeric states is observed in the trap. Using ISOLTRAP, a mass separation of about 100 keV can be reached, depending on the excitation time, which in turn depends on the half-life of the studied nuclide, and a ratio of contamination to ion-of-interest of up to 103 can be tolerated. While the mass resolution of the GPS/HRS together with the RILIS laser ion source theoretically provides isotopically pure beams, contaminations due to surface ionisation can still cause problems. Using ISOLTRAP for puriﬁcation would therefore be feasible for mass numbers with large contaminations and for elements which cannot currently be ionised using RILIS. An example of the former is the region around neutron-rich mercury, thallium and lead, where contamination due to francium ions is a problem, as can be seen in Fig. 6.1. Thallium has 81 protons, thus the ground state should be formed by one proton hole in one of the close-lying h11/2s1/2d3/2 orbits below the Z = 82 shell gap. For even-A–odd-N isotopes beyond A = 206 this hole can couple to a neutron in one of the 208 g9/2d3/2i11/2 orbits and thus form the low-lying states. Pb is doubly magic, and therefore the low- lying nuclear structure of the heavier isotopes should be governed only by valence neutrons above N = 126. In higher-lying states excitation of protons across Z = 82 may take place. However, data on these nuclides is scarce, partly due to contamination problems. Trap-assisted spectroscopy would enable the study of the evolution of single-particle states with an increasing number of protons, thus shedding light on the little-known interaction between proton holes and neutrons around Z = 82 and N = 126.

6.1 Current situation

A picture of the upper part of the current ISOLTRAP setup, including the magnet for the precision trap and the extraction beamline is shown in Fig. 6.2. The beamline ends in a double cross in which the channeltron detector is housed. Alternatively, an MCP detector can be inserted. The electrode structure as reproduced in the ion-optical simulation program SIMION is shown in Fig. 6.3.

6.2 Designing the new extraction beamline in SIMION

Since the ring electrode is at -2.5 V when the ions are ejected and the tape is on ground, the ions do not have suﬃcient energy to reach the tape. Therefore, one of the electrodes in the drift section must be switched down. For this, the long drift tube before the valve was chosen, as it is the longest electrode, so the ions’ time of ﬂight through the electrode will be long enough for switching (around 6 µs).

The new geometry is limited by space constraints, as the crane bridge in the ISOLDE hall leaves only little space in the vertical, and the platform on which the precision trap is located gives a horizontal limit. Considering these limitations, three sets of three electrodes and one drift tube were added to the SIMION ion-optical bench, which will still leave ample room for the crane to pass above the

63 64 Spectroscopy at ISOLTRAP

Figure 6.1: Yields at ISOLDE for mercury, thallium and francium using a uranium-carbide target and the RILIS. The neutron-rich yields of the francium surface-ions are measured, the RILIS yields for mercury and thallium are estimates. Using a quartz transfer line should reduce the francium contamination suﬃciently to enable puriﬁcation even of mercury.

Figure 6.2: The upper magnet and the extraction beamline of ISOLTRAP. The aluminium tube is part of the temperature stabilisation system. 6.3 Construction of the new detection setup 65

Figure 6.3: The ISOLTRAP extraction reproduced as a SIMION ion-optical bench as currently implemented. On the left is the hyperbolical precision trap, on the right hand side the Channeltron detector. A valve is located where the red cross is.

Figure 6.4: SIMION, simulation of the new geometry. The black lines mark the paths of a sample of ions being ejected from the trap. new setup. The tape is located in a second, specially designed cross. With this design, ions of mass number A = 85 are in the pulsed tube about 405 µs after being extracted from the trap, depending on the applied voltages. Pulsing the tube by 200 V results in the detection of all ions, as can be seen in Fig. 6.4. A larger voltage diﬀerence might, however, be needed to prevent the ions from diﬀusing out of the tape during transportation.

Testing the Channeltron in the new geometry. The Channeltron was placed in the new geometry, removing the drift tube in the double cross above the lower valve. The channeltron will be located 44 mm lower than previously. It is, however, still possible to detect the ions after adjusting the electrode voltages. Instead of using the three new electrodes before the Channeltron as an einzel lens, the ﬁrst two of these together with the previous drift tube can also be tuned as an einzel lens. The geometry including the Channeltron is shown in Fig. 6.5.

6.3 Construction of the new detection setup

In order to avoid having to construct a complicated beamline and support structure for the tape station, it was decided to keep the tape station in air and have a diﬀerential pumping section mounted 66 Spectroscopy at ISOLTRAP

Figure 6.5: SIMION ion-optical bench of the new ISOLTRAP extraction geometry with the Chan- neltron. on the main beamline where the tape is entering the cross. The tape station and detectors can then be placed lower, since the space above the trap is very limited due to the hall’s bridge crane, as mentioned above. The tape station could also be placed on a separate table, simplifying construction and access. The detectors should, however, still be as close as possible to the implantation point, in order to reduce transport time and minimise the decay of short-lived nuclei. The new setup will consist of two parts: a lower stage to replace the current Channeltron section, and an upper part for the tape, as was already implemented in the simulations. Each part needs access through various flanges to connect all needed devices. Between the two parts there will be a CF 100 valve to separate the high-vacuum (better than 10−8 mbar) lower part from the tape station, where the vacuum is expected to be considerably worse, of the order of a few 10−5 mbar. The design of both new chambers and the valve between them are shown in Fig. 6.6. The complete design of the new setup on the platform is shown in Fig. 6.7. The lower cross is mounted at an angle to enable access to the liquid helium filling valve. The actual tape station is placed below the three detectors. The design of the upper cross is specialised. It is shorter than a normal cross to fit at the end of the beamline. It will also provide mounting for the differential pumping chamber, see section 6.3.1. In addition, it will be possible to mount a MCP for tuning purposes.

6.3.1 Diﬀerential pumping section The slit setup to bring the tape from vacuum to air is based on the one developed at GSI, Fig. 6.8. To accommodate two slits for the tape (into the vacuum and back out again) in a similar setup, the slits are rotated by 90◦ relative to the original slit, Fig. 6.9. The outer dimensions are identical, so the original chamber design, shown in Fig. 6.10, can be used.

6.4 Status

Some parts of the beamline have already been manufactured. Figure 6.11 shows the lower cross with the extension piece. The extension has been modified by adding a connection piece for the pressure gauges. Several flanges with electrical feedthroughs have been designed. These are shown in Fig. 6.12, attached to the lower cross and the upper part. The upper part has not yet been modified to allow connection of the differential pumping section. A proposal has been submitted to the ISOLDE and Neutron Time-of-Flight Committee to perform mass measurements followed by β- and γ-decay studies on isobarically pure beams of neutron-rich mercury and thallium isotopes. 6.4 Status 67

Figure 6.6: Design of both new crosses and the two valves after the ISOLTRAP precision trap, seen from two perspectives. 68 Spectroscopy at ISOLTRAP

Figure 6.7: The trap and the detector/tape station table with three germanium detectors. 6.4 Status 69

Figure 6.8: Diﬀerential pumping/slit system to guide the tape into vacuum developed by Wilfried H¨uller at GSI. 70 Spectroscopy at ISOLTRAP

Figure 6.9: The inner part of the pumping section. 6.4 Status 71

Figure 6.10: Diﬀerential pumping/slit system developed by Wilfried H¨uller, outer chamber which will house the part in Fig. 6.9

Figure 6.11: The lower cross with the extension piece to enable the connection of a pump and pressure gauges. 72 Spectroscopy at ISOLTRAP

Figure 6.12: Lower cross, extension piece and upper part with flanges and electronic feedthroughs. The upper part has not yet been modified to add the flange for the differential pumping section. 7 Summary and outlook

All in all, 73 nuclear masses measured with the JYFLTRAP Penning trap mass spectrometer were presented in this work. Being located in a region of the nuclear chart portraying various shape changes, these mass values can help considerably improve the current knowledge of nuclear structure. The reached precision enables mapping of even relatively minor trends on the mass surface. The found discrepancies between the new results and the literature values showed in many cases, e.g. niobium and technetium, systematic trends. As the parameters of the mass models were fitted to this wrong input data, wrong model predictions are to be expected, and are indeed observed. This, in turn, can lead to wrong prediction for astrophysical processes. The mass measurement campaign initiated in this work is still being continued with mass measurements towards lighter nuclei around the N = 50 shell closure. So far, several neutron-rich isotopes of germanium, gallium, arsenic, sele- nium and nickel have been measured. At ISOLTRAP, neutron-rich krypton, copper and zinc isotopes have been measured. Combined, these precision data yield a new picture of the mass surface in this region of the nuclear chart. In the near future, this region will be further extended by measuring isotopes of heavier fission products at JYFLTRAP. In addition, several nuclides with unresolved isomeric states presented in this work may be revisited using a new technique for isomeric cleaning employing a Ramsey excitation [74] recently developed and tested at JYFLTRAP. Figure 7.1 shows a cleaning spectrum of 115Sn and 115In (∆m ≈ 500 keV or 4.5 Hz) from an offline ion source. The dipole excitation frequency was applied as two time-separated fringes of 10 ms with a waiting time of 80 ms in between. After the excitation, the non-excited ions were transferred back into the first trap, while the ions in resonance had too large a cyclotron radius to pass the 2 mm diaphragm separating the traps. Thus, a clean sample can be obtained even for ion species with mass differences too small for purification in the first trap. The resulting, clean time-of-flight resonance spectra are shown in Fig. 7.2. In order to improve the accuracy and precision of JYFLTRAP a carbon cluster source has been designed and will be installed for offline studies. This will lead to a better understanding of the systematic uncertainties encountered. In particular the mass dependent uncertainty can be remeasured by comparing carbon clusters of various sizes. The count rate effect, too, can be studied systematically in such a way. Another important factor is the timing of the potential wall between the two Penning traps. Its opening time must correspond exactly (within a few hundred ns) to the flight time of the ions in order for the ions to have as low a kinetic energy as possible upon entering the second trap. Any nonlinearities and irregularities of the voltage switches could thus be examined.

The design of a new decay spectroscopy setup after ISOLTRAP commenced in 2005. This effort is being continued and will provide a possibility for background free spectroscopy. The tape will be guided out of the vacuum through a differential pumping section to a separate measurement station, increasing the flexibility in setting up different detectors. The first parts have been manufactured by the workshop of the University of Mainz. A proposal for measurements in the region of neutron-rich mercury and thallium has been submitted.

73 74 Summary and outlook

180 Sn Sn Sn Sn 160

140

120

100

Counts 80 4.5 Hz 60 In In 40 In

0 934900 934910 934920 934930 ν + (Hz)

Figure 7.1: ν+ scan in the precision trap using the Ramsey excitation method.

115In 115Sn 500 400 (a) s 300 µ

500 400 300 (b) time-of-flight / 500 400 300 (c) -2 0 2 4 6 8 10 Quadrupole frequency - 935100 Hz / Hz

Figure 7.2: Time-of-ﬂight resonance spectra of 115Sn and 115In, the shaded areas represent the ions in resonance (arb. scales). In the top panel, no additional cleaning in the precision trap was used. In the other panels, Ramsey cleaning was used. In the middle panel, the dipole excitation was set 115 to the reduced cyclotron frequency ν+ of Sn, thus removing it from the trap and leaving a clean sample of 115In. Finally, in the bottom panel, 115In was removed, and 115Sn measured. A Analysis programs

A.1 Frequency calibration and contaminations

Unwanted contamination in the traps can often be hard to identify. If, however, a resonance frequency can be determined, it is possible to calculate the atoms and molecules that would have a corresponding resonance frequency. To this end, a program was written in C++ which, based on the AME03 [28] mass table, combines atomic masses and compares them to the observed one. No additional information about chemistry is included. The number of atoms in the molecule can be specified, as can be an uncertainty for the center frequency. The same program also serves to calibrate the timings and frequencies relevant for JYFLTRAP. Any molecule can be given, and the program will return the cyclotron frequencies in both traps, the reduced cyclotron frequency in the precision trap, which is needed for isomeric cleaning, and the transfer times between the cooler and purification trap, and between the purification and precision trap. To simplify the input, carbon clusters can be specified in multiples of 12C. A graphical user interface was written using GTKmm, as seen in Fig. A.1.

A.2 Data ﬁtting

In order to determine the ions’ cyclotron frequency from a time-of-flight resonance spectrum, the theoretical line shape is fitted to the measured data points. This is done by the Levenberg-Marquardt method, a nonlinear least-squares fitting routine. The original code was taken from the Numerical Recipes in C [75] and adopted to fit the theoretical time-of-flight resonance shape. Based on this fitting routine, two separate programs were developed to analyse data from JYFLTRAP. The program used in this work is command line based, reading in an ASCII input file. In the input file it is possible to limit the used data according to different criteria. The recorded ion bunches can be sorted depending on the total number of ions recorded. This can be used to limit the minimum and maximum ions per bunch which will be included in the analysis and to do a count rate class analysis [49]. For the count rate class analysis, an additional linear fitting routine is used to extrapolate the frequency to a specified ion number, depending on the assumed efficiency of the extraction and the detector. A second way of limiting the used data is to limit the time-of-flight window during which ions have to arrive at the detector. This has to be done after sorting the recorded bunches according to the ion number, so that the total number of ions in the trap is used for the count rate class analysis. Setting a time-of-flight window can be used to reduce the background and enhance the time-of-flight effect.

Several resonance spectra of the same ion species can be specified in the input file and will be handled by the program without having to restart it. All the spectra taken during a run can thus be fitted at the same time. The program will output ASCII files giving the fitted parameters and the frequencies, and plots of all fitted spectra, all count rate class analyses, and the fitted frequencies versus time. Thus, it is possible to quickly get a good overview of the data. Since the input file is saved as well, modification and re-fitting can easily be done. A graphical user interface was written in Python to generate the input file for the fitting program, see Fig. A.2.

75 76 Analysis programs

Figure A.1: A calculator for frequencies and timings and for determining contaminations from measured frequencies. A.2 Data ﬁtting 77

Figure A.2: A GUI for the ﬁtting program. 78 Analysis programs

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[75] http://www.nrbook.com/a/bookcpdf.html. PHYSICAL REVIEW LETTERS week ending PRL 96, 042504 (2006) 3 FEBRUARY 2006

First Precision Mass Measurements of Refractory Fission Fragments

U. Hager,1 T. Eronen,1 J. Hakala,1 A. Jokinen,1,* V.S. Kolhinen,2 S. Kopecky,1 I. Moore,1 A. Nieminen,1 M. Oinonen,3 S. Rinta-Antila,1 J. Szerypo,2 and J. Aÿsto¨1 1Department of Physics, University of Jyva¨skyla¨, P.O. Box 35 (YFL), FIN-40014, Finland 2Sektion Physik, University of Munich (LMU), Am Coulombwall 1, D-85748 Garching, Germany 3Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FIN-00014, Finland (Received 15 April 2005; published 1 February 2006) Atomic masses of 95–100Sr, 98–105Zr, and 102–110Sr have been measured with a precision of 10 keV employing a Penning trap setup at the IGISOL facility. Masses of 104;105Zr and 109;110Mo are measured for the first time. Our improved results indicate significant deviations from the previously published values deduced from beta end point measurements. The most neutron-rich studied isotopes are found to be significantly less bound (1 MeV) compared to the 2003 atomic mass evaluation. A strong correlation between nuclear deformation and the binding energy is observed in the two-neutron separation energy in all studied isotope chains.

DOI: 10.1103/PhysRevLett.96.042504 PACS numbers: 21.10.Dr, 07.75.+h, 27.60.+j

Accurate knowledge of masses of radioactive isotopes is Jyva¨skyla¨ [1]. Ions of interest were produced in a fission important not only in nuclear physics but in several other reaction of natural uranium induced by proton bombard- areas of physics, such as the element synthesis in the ment at 25 MeV. Yields of studied nuclei varied from a few Universe and studies of fundamental interactions and sym- thousands of ions=s down to 100 ions=s for the most metries. Within nuclear physics, masses and binding en- exotic ones. After acceleration to 30 keV and mass sepa- ergies are sensitive probes to explore the evolution of ration, ions are injected into a gas-filled radio frequency nuclei far from the valley of stability, including shell quadrupole cooler (RFQ) [4] where interactions between structure, pairing, and spin-orbit coupling. Until now there the ions and buffer gas atoms effectively cool the ion has been a significant lack of accurate and reliable data on ensemble. In addition to cooling, the RFQ is used to collect masses of neutron-rich nuclei. The purpose of this Letter is and store the ions, which can be released as narrow to demonstrate that for the first time the accurate measure- bunches, typically of the order of 10–20 s. A cooled ment of masses of exotic neutron-rich nuclei can be per- and bunched ion cloud can be easily transported to the formed in a universal way employing a combination of the injection of a Penning trap. ion guide isotope separator on-line (IGISOL) method [1] The Penning trap system at IGISOL consists of a puri- and Penning trap technique. fication and a measurement trap. The two traps are housed In this Letter, we present results on the first precision within the warm bore of a 7 T superconducting magnet that measurement of the masses of neutron-rich Sr, Zr, and Mo has two homogeneous regions of 1cm3 volume separated isotopes. These studies are motivated by earlier gamma and by 20 cm in the center of the magnet. The first trap used for B laser spectroscopy experiments that observed a shape tran- the isobaric purification has a homogeneity B better than sition between N 58 and 60. In our first, medium- 10ÿ6, and the second trap, called a precision trap, better resolution study of neutron-rich Zr isotopes with a purifi- than 10ÿ7. Both traps are of a cylindrical type. cation Penning trap [2], this change of shape was observed The trapping of ions is accomplished by a combination to result in a large local increase in the two-neutron sepa- of a homogenous magnetic field and a static electric quad- ration energy. Whether this behavior extends to the neigh- rupole field. Solving the equation of motion [5] for an ion boring strontium and molybdenum isotopes was studied in in the trap results in three different eigenmotions: one axial this work with a significantly better mass resolution than and two radial motions, the latter corresponding to mag- previously available. netron and reduced cyclotron motions with angular fre- Earlier information of some masses measured in this quencies !ÿ and !, respectively. The sum of these two work had been deduced from beta-decay end point ener- frequencies correspond to the true cyclotron frequency gies; see discussion in Ref. [2,3]. As shown by this work qB those measurements lead to large systematic errors due to !c ! !ÿ : (1) an inadequate knowledge of the decay schemes and com- m plex spectra. Such erroneous data are serious problems in The purification trap uses a buffer gas cooling technique developing theoretical mass models for neutron-rich nuclei which employs helium as buffer gas with a pressure of far from stability. 10ÿ4 mbar. Isobaric purification is performed by first in- The mass measurements described in this Letter were creasing the ions’ magnetron radius beyond the 1 mm performed at the IGISOL facility at the University of radius of a narrow channel located between the two traps.

This is done by applying a dipole electric field at the [mass excess ME ÿ82946:6 2:8 keV, [3] ] pro- magnetron frequency. Following this, a mass-selective duced on-line in the fission reaction. For each frequency quadrupole excitation at the true cyclotron frequency is the time of flight was calculated from the average of the applied which converts the magnetron motion to reduced distribution. The resulting average time of flight versus cyclotron motion thus increasing the kinetic energy of the frequency distribution was then fitted to obtain the true excited ions. Because the first trap is filled with buffer gas, cyclotron frequency !c of the measured ion. the fast reduced cyclotron motion is cooled via ion-atom An empirical estimate for the statistical uncertainty did collisions. Only those ions with the true cyclotron fre- not exceed a few times 10ÿ8 for each measurement. quency are centered and extracted, resulting in an iso- Therefore, the largest contribution to the total uncertainty topically clean ion bunch. By choosing an appropriate originates from systematic effects. The uncertainty due to excitation time and amplitude, it is possible to achieve a magnetic field fluctuations was deduced using all measure- mass resolving power of up to 106 [2,6,7]. Figure 1 shows ments of 97Zr performed during the run. From this data set, an example of an isobaric purification scan for A the fluctuation of the cyclotron frequency due to magnetic 101 ions. field variations resulted in an uncertainty of about 4 The isobarically clean sample is injected to the precision 10ÿ8 of the frequency ratio x !c;ref , corresponding to !c;meas trap, which operates under vacuum. There the ions are first about 4 keV in this mass region. given some magnetron radius, typically 0.5 to 1 mm with a Another possible source of error arising from the mass dipole excitation, using the phase-locking technique [8]. dependence was estimated from an off-line measure- Following this, a quadrupole excitation with a duration of ment by comparing the frequencies measured for 132Xe 400 ms was used. The radial energy is converted to axial xexpÿxAME and O2 ions. The uncertainty was found to be energy when the ions leave the high magnetic field. xAME 7 10ÿ10 m ÿ m , with x being the frequency ratio Because of the large energy ratio, 106, between the two ref AME calculated using the tabulated values from Ref. [3]. radial motions, a significant reduction of the time of flight (TOF) to the ion detector is observed when the ions have been excited with their true cyclotron frequency. The detection of the resonance frequency is based on the time-of- flight technique [9]. The comparison between the cyclotron frequency of an unknown species with the frequency of a well-known reference ion will allow a precise mass determination via the following relation

!c;meas mmeas mref ÿ me me: (2) !c;ref Figure 2 illustrates TOF spectra obtained for the reference ion 97Zr and for the most neutron-rich isotopes measured, 100Sr, 105Zr, and 110Mo. During a week long measurement campaign, the masses of 98–105Zr, 95–100Sr, and 102–110Mo were measured. In all cases the reference frequency was obtained from 97Zr

FIG. 2. TOF resonances measured for the reference ion 97Zr and the most exotic isotope of each isotopic chain studied in this work. The modest asymmetries observed, and well reproduced in FIG. 1. Isobaric purification scan for fission products at mass the fit, are due to a residual reduced cyclotron motion resulting A 101. from the incomplete radial cooling in the purification trap.

042504-2 PHYSICAL REVIEW LETTERS week ending PRL 96, 042504 (2006) 3 FEBRUARY 2006

A large number of ions in the precision trap can cause mental values for 104;105Zr, as well as 109;110Mo, are the measured cyclotron frequency to shift due to ion-ion obtained for the first time. Published data with similar interactions in the trap. In order to reduce this effect, the precision are available only for a very few other mass count rate was kept below 20 ions per bunch after purifi- chains of neutron-rich nuclei. These are Rb and Sr isotopes cation. When necessary, the beam intensity was reduced studied at the ISOLTRAP facility of CERN [10]. Figure 3 by inserting slits of variable opening before the RFQ. displays the difference between the AME2003 values [3] The count rate effect was carefully examined using 58Ni and this experiment for all studied isotopes. With the ions. For the count rates used in this experiment, a maxi- exception of 99Sr, the data show that neutron-rich Sr, Zr, mum uncertainty of 0:1Hzon the measured frequency and Mo nuclei are significantly less bound than the tabu- was deduced, corresponding to 9 10ÿ8 in the frequency lated values in AME2003. The experimental values for the ratio x. most neutron-rich isotopes studied differ by as much as The obtained frequency ratios x and the corresponding 1 MeV from the extrapolated values in Ref. [3]. mass excess values are given in Table I. The uncertainty of A detailed comparison of the new experimental values the reference ion 97Zr does not affect the uncertainty of the with the predictions of different mass models will be done frequency ratio x, but only that of the resulting mass in a forthcoming paper. For a recent evaluation, see excess. For Zr isotopes the presented results up to 104Zr Ref. [11]. Using the new data, it is instructive to study agree reasonably well with our previous experiment that the evolution of the two-neutron separation energy as a only employed the less accurate purification trap [2]. It is function of the neutron number. The experimental data worth noticing that the mass excess of ÿ75123 10 keV (Fig. 4) indicate a dramatic change in behavior for Sr and 95 obtained for Sr agrees well with the value of ÿ75117 Zr isotopes between N 58 and 60 which coincides with 7 keV given in AME2003. This value in turn is primarily the known change of structure (deformation). The same based on the high-accuracy measurement at ISOLTRAP effect is still observable in the Mo isotope chain, thanks to [10]. the current precise data. The very smooth, almost linear The data in Table I represent the first direct mass measurement of these refractory-element isotopes. The experi-

TABLE I. Obtained frequency ratios x with statistical and systematic uncertainties and resulting mass excess values ME in keV. The systematic error is obtained as the quadratic sum of the count rate and the magnetic ﬁeld related uncertainties.

Isotope x !c;ref ME [keV] !c;meas 102Mo 1:0515 871 4 2:2 9:910ÿ8 ÿ83 570 10 103Mo 1:061 934 81 2:3 9:910ÿ8 ÿ80 965 10 104Mo 1:072 260 38 1:7 9:910ÿ8 ÿ80 354 10 105Mo 1:082 612 57 1:9 9:910ÿ8 ÿ77 341 10 106Mo 1:092 944 70 2:0 9:910ÿ8 ÿ76 139 10 107Mo 1:103 303 20 2:3 9:910ÿ8 ÿ72 556 10 108Mo 1:113 641 90 2:4 9:910ÿ8 ÿ70 760 10 109Mo 1:124 006 02 7:5 9:910ÿ8 ÿ66 670 12 110Mo 1:134 348 35 24:9 9:910ÿ8 ÿ64 547 24 98Zr 1:010 337 15 2:9 9:910ÿ8 ÿ81 291 10 99Zr 1:020 696 54 10:6 9:910ÿ8 ÿ77 627 13 100Zr 1:031 029 22 3:0 9:910ÿ8 ÿ76 376 10 101Zr 1:041 383 61 3:3 9:910ÿ8 ÿ73 164 10 102Zr 1:051 719 85 2:1 9:910ÿ8 ÿ71 590 10 103Zr 1:062 080 43 2:5 9:910ÿ8 ÿ67 819 10 104Zr 1:072 422 41 4:3 9:910ÿ8 ÿ65 728 10 105Zr 1:082 788 40 9:0 9:910ÿ8 ÿ61 469 12 95Sr 0:979 449 05 3:1 9:910ÿ8 ÿ75 123 10 96Sr 0:989 792 20 3:0 9:910ÿ8 ÿ72 926 10 97Sr 1:000 159 07 2:9 9:910ÿ8 ÿ68 587 10 98Sr 1:010 501 76 2:9 9:910ÿ8 ÿ66 431 10 FIG. 3. Comparison of measured mass excess (ME) to 99Sr 1:020 863 85 2:2 7:310ÿ8 ÿ62 524 7 AME2003 [3]. Error bars in the reference line correspond to 100Sr 1:031 212 53 4:5 9:310ÿ8 ÿ59 828 10 AME2003 errors. Uncertainties in the experimental values are of the order of the size of the symbol; see Table I.

042504-3 PHYSICAL REVIEW LETTERS week ending PRL 96, 042504 (2006) 3 FEBRUARY 2006

the universality of the IGISOL technique, more than 200 atomic masses of neutron-rich nuclei between Ni and Ce can be measured in the near future with a relative accuracy 10ÿ7. This will provide an important contribution to the theoretical development of mass models and a pivotal role in providing data for r-process calculations. It will be particularly challenging to extend these experiments towards the neutron number N 70 at which major changes in the nuclear structure are predicted to occur [18,19]. This work was has been supported by the European Union within the NIPNET RTD project under Contract No. HPRI-CT-2001-50034 and by the Academy of Fin- FIG. 4. Two-neutron separation energies. Filled symbols are land under the Finnish Center of Excellence Programme from this measurement and open symbols are taken from 2000–2005 (Project No. 44875). A. J. is indebted to finan- AME2003 [3]. cial support from the Academy of Finland (Project No. 46351). behavior of the experimental curves beyond N 60 indicates stability in the structure of these nuclei. This is in accordance with the prediction in the liquid drop model *Electronic address: [email protected].fi context, where this behavior is produced by the asymmetry [1] J. Aÿsto¨, Nucl. Phys. A693, 477 (2001). term only [12,13]. [2] S. Rinta-Antila, S. Kopecky, V.S. Kolhinen, J. Hakala, We compare our results with a recent successfully tested J. Huikari, A. Jokinen, A. Nieminen, and J. Aÿsto¨, Phys. microscopic model, the Hartree-Fock-Bogoliubov (HFB) Rev. C 70, 011301 (2004). plus particle-number projection mass model [Ref. [14] ]. [3] G. Audi, O. Bersillon, J. Blachot, and A. H. Wapstra, Nucl. The newest parameter set of this model (termed HFB-8) is Phys. A729, 3 (2003). determined by optimizing the fit to the full data set of the [4] A. Nieminen, J. Huikari, A. Jokinen, J. Aÿsto¨, P. Camp- 2149 measured masses with N;Z 8 (both spherical and bell, and E. C. A. Cochrane, Nucl. Instrum. Methods Phys. deformed) of Ref. [3]. The corresponding root mean square Res., Sect. A 469, 244 (2001). [5] L. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 error is 0.635 MeV for this data set. For the Sr, Zr, and Mo (1986). nuclei studied in this work the model produces an excellent [6] V.S. Kolhinen, T. Eronen, J. Hakala, A. Jokinen, S. Ko- agreement for isotopes with neutron numbers N>60. pecky, S. Rinta-Antila, J. Szerypo, and J. Aÿsto¨, Nucl. Below this value, only Mo isotope masses agree well Instrum. Methods Phys. Res., Sect. B 204, 502 (2003). with the model, but Sr and Zr isotopes near the semimagic [7] V.S. Kolhinen et al., Nucl. Instrum. Methods Phys. Res., Z 40, N 56 are not in agreement with the data. In Sect. A 528, 776 (2004). most models, above N 60 these nuclei become prolate [8] K. Blaum, G. Bollen, F. Herfurth, A. Kellerbauer, H.-J. and well deformed. For Sr and Zr nuclei this is also con- Kluge, M. Kuckein, S. Heinz, P. Schmidt, and L. Schweik- firmed by the experiments [15,16]. However, in the HFB-8 hard, J. Phys. B 36, 921 (2003). model at N 66 and 68, Mo isotopes are already predicted [9] M. Ko¨nig, G. Bollen, H.-J. Kluge, T. Otto, and J. Szerypo, Int. J. Mass Spectrom. Ion Processes 142, 95 (1995). to be oblate. This seems to lead to an underestimation of [10] H.Raimbault-Hartmann et al., Nucl. Phys. A706, 3 (2002). the two-neutron binding energy. [11] D. Lunney, J. Pearson, and C. Thibault, Rev. Mod. Phys. Any major change in nuclear structure would introduce a 75, 1021 (2003). deviation from a smooth trend in two-neutron separation [12] R. Fossion, C. Coster, J. Garcia-Ramos, T. Werner, and energies [12]. Therefore, it will be important to study these K. Heyde, Nucl. Phys. A697, 702 (2002). nuclei in another theoretical context which at the same [13] P. Mo¨ller, J. Nix, W. Myers, and W. Swiatecki, At. Data time treats both excited structures as well as binding en- Nucl. Data Tables 59, 185 (1995). ergies. This allows inclusion of mixing of different struc- [14] M. Samyn, S. Goriely, M. Bender, and J. Pearson, Phys. tures and intruder states. Such a development is underway Rev. C (to be published). for the Sr, Zr, and Mo isotopes employing the IBM ap- [15] W. Urban et al., Nucl. Phys. A689, 605 (2001). [16] P. Campbell et al., Phys. Rev. Lett. 89, 082501 (2002). proach [17]. [17] J. Garcia-Ramos, K. Heyde, R. Fossion, V. Hellemans, In summary, precise data on the masses of 23 neutron- and S. D. Baerdemacker, Eur. Phys. J. A 26, 221 (2005). rich Sr, Zr, and Mo isotopes have been presented for the [18] N. Schunck, J. Dudek, A. Gozdz, and P. Regan, Phys. first time. A significant deviation has been observed in Rev. C 69, 061305(R) (2004). comparison with the recent mass evaluation. Taking into [19] F. Xu, P. Walker, and R. Wyss, Phys. Rev. C 65, 021303(R) account the yield distribution of proton-induced fission and (2002).

042504-4 PHYSICAL REVIEW C 75, 064302 (2007)

Precision mass measurements of neutron-rich Tc, Ru, Rh, and Pd isotopes

U. Hager,* V.-V. Elomaa, T. Eronen, J. Hakala, A. Jokinen, A. Kankainen, S. Rahaman, S. Rinta-Antila, A. Saastamoinen, T. Sonoda, and J. Ayst¨ o¨ Department of Physics, University of Jyvaskyl¨ a,¨ P.O. Box 35 (YFL), FIN-40014 Jyvaskyl¨ a,¨ Finland (Received 18 October 2006; revised manuscript received 30 November 2006; published 4 June 2007)

The masses of neutron-rich 106−112Tc, 106−115Ru, 108−118Rh, and 112−120Pd produced in proton-induced ﬁssion of uranium were determined using the JYFLTRAP double Penning trap setup. The measured isotopic chains include a number of previously unmeasured nuclei. Typical precisions on the order of 10 keV or better were achieved, representing a factor of 10 improvement over earlier data. In many cases, signiﬁcant deviations from the earlier measurements were found. The obtained data set of 39 masses is compared with different mass predictions and analyzed for global trends in the nuclear structure.

DOI: 10.1103/PhysRevC.75.064302 PACS number(s): 27.60.+j, 21.10.Dr, 21.60.−n, 25.85.Ge

I. INTRODUCTION neutron capture process (r-process) is assumed to proceed here, producing more than half the nuclei heavier than iron Precision mass measurements in nuclear physics made existing in the universe today [11]. The relevant part of the possible by the introduction of Penning trap mass spectrometry assumed r-process path is shown in Fig. 1. The resulting are becoming an important tool for probing nuclear structure abundances depend on the masses and the β-decay half-lives effects far from stability [1]. In particular, mass differences of the nuclides. Hence, to reliably model the r-process path, can be important sources of information on nuclear structure the half-lives, branching ratios, and masses of neutron-rich effects caused by shell closures and changing pairing energies. nuclei far from stability are needed, preferably up to the The former manifests itself, for example, in large changes point where the neutron-separation energy S is smaller than in the two-neutron separation energy S along an isotopic N 2N ∼3 MeV. Often, precise mass measurements of these nuclei chain. One recently studied example is the appearance of a are not possible because of short half-lives and low production neutron subshell found at N = 60 in the zirconium region. rates. It is important to map the nuclear chart as far as A jump of the two-neutron separation energy is observed at possible in order to improve nuclear structure calculations and N = 59 because of the sudden onset of large ground state enable reliable extrapolations toward the region of interest. In deformations [2,3]. In recent years, the neutron-rich region particular, possible indications of a quenching of the N = 82 between A = 100 and A = 130 has been subject to intense shell could significantly influence the predicted r-process path. studies of excited states via spectroscopic methods because The half-lives of the neutron-rich isotopes studied in this work of the various shape transitions from strongly deformed have recently been measured [13], pointing out the need for zirconium [4] toward ruthenium [5] and palladium [6,7], improved mass values in the region. which possess features pointing to triaxial as well as to oblate The IGISOL facility provides the possibility of producing deformed structures. Shapes and properties of neutron-rich radioactive nuclides with little sensitivity to chemistry, there- nuclei in this region have been theoretically investigated in fore allowing access even to refractory elements. Together Ref. [8]. Above this region, it has been suggested more recently with the Penning trap setup, precision mass measurements of that the N = 82 shell closure might weaken or be quenched far a broad range of nuclei become feasible. from stability. This quenching has been predicted by models, In continuation of the previous work done in this region of and weak experimental indication has been found [9]. − the nuclear chart, as mentioned above, the masses of 112 120Pd, Since the structural changes of neutron-rich nuclei above − − − 108 118Rh, 106 115Ru, and 106 112Tc were measured. This paper the deformed zirconium region and well below the spherical examines these masses for systematic effects and compares 132Sn are slow and weak with the changing proton and neutron them with a selection of mass models. numbers, it is of interest to find out how sensitively these changes could be probed with the presently available high δm −7 precision in mass measurements ( m < 10 ). Often, different structures coexist and compete for the lowest energy [8], and II. EXPERIMENTAL METHODS even a small discontinuity in the systematics, if measurable, The data presented in the following were taken using may suggest a change in the structure. This was successfully the JYFLTRAP Penning trap setup installed at the IGISOL shown by the work performed on neutron-deficient Pb isotopes (Ion Guide Isotope Separator On-Line) facility in Jyvaskyl¨ a,¨ at the ISOLTRAP facility at CERN [10]. Finland. A schematic layout of the JYFLTRAP setup is shown Another reason for interest in this region of the nuclear in Fig. 2, and it is described in Refs. [2] and [15]. A more chart is its importance to stellar nucleosynthesis, as the rapid detailed description of the working principle of the Penning trap can be found in Ref. [16]. To produce the nuclei of interest, a thin (10 mg/cm2) target *[email protected].fi of natural uranium was bombarded with typically 25 MeV

FIG. 1. Path of the r-process in the region examined in this work. The thick squares mark the assumed path of the r-process [12], the black filled boxes mark stable nuclei, the filled dark grey boxes were previously studied at JYFLTRAP [2], and the filled light grey boxes denote masses measured in the present work. Crosses mark the heaviest isotope of each element with known half-lives [13,14]. protons from the JYFL K130 cyclotron. The intensity of the ions’ cyclotron frequency proton beam was nominally 5 µA. The fission products recoil out of the target and are stopped in helium gas at a pressure of 1 q νc = B (1) about 200 mbar. Because of charge exchange processes with 2π mion the gas, the ions will end up being mainly singly charged. q m B They are then transported with the helium flow out of the (charge ,mass ion, magnetic field ) is used to convert the chamber and accelerated to 30 kV potential. After extraction, magnetron motion into cyclotron motion, which results in a a55◦ bending magnet provides a mass resolving power of gain in radial energy of those ions of the corresponding mass, as 500, sufficient to select ions of only one mass number. Typical the reduced cyclotron frequency is about three orders of magni- yields for the nuclei studied in this experiment ranged from tude higher than the magnetron frequency. This increase in en- 100 to 10000 ions/s. Further details on the IGISOL facility can ergy is detected by measuring the time of flight to a Microchan- be found in Ref. [17]. nel plate (MCP) detector. By scanning through different ν To improve the overall beam quality, the ions are injected quadrupole excitation frequencies RF, a time-of-flight spectrum for the ion species in question can be obtained. Figure 3 into a radio frequency quadrupole (RFQ) cooler/buncher, 120 placed on a high-voltage platform at 30 kV, where they are shows a cyclotron resonance spectrum of Pd obtained in this decelerated and cooled by collisions with helium buffer gas manner. [18]. The ions are then released as bunches and transferred The magnetic field can be determined by measuring a reference ion of well-known mass. Since the charge state of into the Penning trap setup on the same high-voltage platform + consisting of two cylindrical Penning traps housed in the warm all ions examined was 1, the mass is given by bore of a superconducting magnet of 7 T. The magnet has νref two homogeneous field regions of 1 cm3 located 20 cm apart m = c (m − m ) + m , (2) meas meas ref e e from each other. The first trap contains helium buffer gas at νc a pressure of a few times 10−5 mbar and is used for cooling where νref,νmeas are cyclotron frequencies of the reference and isobaric mass separation [19]. The incoming ion beam c c and measured ions; and m ,m , and m are masses of from the RFQ cooler is captured and cooled in collisions ref e meas the reference ion, the electron, and the measured atom. To with the buffer gas. An electric dipole excitation is used to account for drifts of the magnetic field strength, reference mea- increase the radii of all ions. Afterward, an electric quadrupole surements were taken before and after each measurement; the excitation is employed to mass-selectively center the ions averaged frequency is then used as the reference. This method of the wanted species. These are then transferred through a cannot, however, compensate for short-term fluctuations of the 5 cm long 2 mm diaphragm into the second trap, which is − field. operated in high vacuum (p<10 8 mbar) for the precision mass measurement. After the ions from the purification trap are captured, the magnetron radius is increased by a phaselocked 600 dipole excitation to ensure identical conditions during each 550 cycle [20]. Then a phaselocked quadrupole excitation at the

s) 500 µ

450 -5 -8 10 mbar 10 mbar 400 7Tmagnet -3 350 10 mbar MCP Time of Flight ( Transfer line detector RFQ cooler 300 IGISOL Purification Precision beam trap trap 250 −15 −10 −5 0 5 10 15 800 V ν 30 kV RF−895960 (Hz) -Accumulation 97 V -Cooling -Isobaric -Mass 120 = separation measurement FIG. 3. Cyclotron resonance spectrum of Pd (T1/2 500 ms) taken with 200 ms excitation time. Solid line represents the ﬁt to the FIG. 2. Schematic layout of the JYFLTRAP setup. data points.

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Because of the Fourier transformation of the exciting time. When measuring radioactive isotopes, the excitation time quadrupole wave, the cyclotron resonance will get narrower as is often limited by the half-life of the species. the quadrupole excitation time in the precision trap increases, ∝ 1 ν T . The full width at half maximum (FWHM) at a III. DATA ANALYSIS AND RESULTS quadrupole excitation time of 800 ms is about 1.1 Hz. The FWHM does not, however, solely determine the precision A. Analysis methods which can be reached; this also depends on the collected Table I gives an overview of the nuclides studied in this statistics. One therefore has to ﬁnd a compromise between work. For each run, the measured nuclides and the used the length of each cycle, which is dominated by the duration references are given; half-lives and isomeric states of these of the quadrupole excitation in the precision trap, the time nuclei are listed together with the applied excitation times used to take one resonance spectrum, and the number of for the measurement in the precision trap, and the number of measurements that can be done during the available beam measurements done.

TABLE I. Overview of nuclides studied in this work. Given are the run date, reference nuclide, number N of resonance spectra taken, excitation time, half-life, and spin and parity, and the excitation energy, half-life, and spin and parity of known isomers with T1/2 > 10 ms as listed in the AME03 [14]. # denotes estimated values, and ( ) uncertain spin and/or parity.

π Nucleus Run Reference NTRF (ms) T1/2 I Isomer

π Eexc (keV) T1/2 I

106Tc Feb 06 102Ru 3 800 35.6 s (1,2) 107Tc Jan 05 105Ru 5 400 21.2 s (3/2−) 108Tc Jan 05 105Ru 5 400 5.17 s (2)+ 109Tc Jan 05 105Ru 5 400 860 ms 3/2−# 110Tc Jan 05 105Ru 5 400 920 ms (2+) 111Tc Jan 05 105Ru 4 200 290 ms 3/2−# 112Tc Feb 06 102Ru 4 200 290 ms 2−# 106Ru Jan 05 105Ru 5 400 373.59 d 0+ 107Ru Jan 05 105Ru 5 400 3.75 m (5/2)+ 108Ru Jan 05 105Ru 5 400 4.55 m 0+ 109Ru Jan 05 105Ru 5 400 34.5 s 5/2+# 110Ru Jan 05 105Ru 5 400 11.6 s 0+ 111Ru Jan 05 105Ru 4 400 2.12 s (5/2+) 112Ru Jan 05 105Ru 5 400 1.74 s 0+ 113Ru Jan 05 105Ru 5 400 800 ms (5/2+) 130(18)a 510 ms (11/2−) 114Ru Jan 05 105Ru 5 200 530 ms 0+ 115Ru May 06 120Sn 4 300 740 ms 108Rh May 05 120Sn 3 1600 16.8 s 1+ −60(110) 6.0 min (5)(+#) 109Rh May 05 120Sn 4 1600 80 s 7/2+ 110Rh May 05 120Sn 4 1200 28.5 s (>3)(+#) −60(50) 3.2 s 1+ 111Rh May 05 120Sn 4 1200 11 s (7/2+) 112Rh May 05 120Sn 4 1200 3.4 s 1+ 330(70) 6.73 s >3 113Rh May 05 120Sn 4 800 2.80 s (7/2+) 114Rh May 05 120Sn 3 800 1.85 s 1+ 200(150) 1.85 s (4,5) 115Rh May 05 120Sn 4 800 990 ms 7/2+# 116Rh May 05 120Sn 5 400 680 ms 1+ 200(150) 570 ms (6−) 117Rh May 05 120Sn 4 300 440 ms 7/2+# 118Rh May 05 120Sn 1 200 310 ms (4–10)(+#) 112Pd May 05 120Sn 4 1600 21.03 h 0+ 113Pd May 05 120Sn 5 1600 93 s (5/2+) 81.1(3) 300 ms (9/2−) 114Pd May 05 120Sn 5 800 2.42 m 0+ 115Pd May 05 120Sn 5 800 25 s 5/2+# 89.18(25) 50 s 11/2−# 116Pd May 05 120Sn 6 1600 11.8 s 0+ 117Pd May 05 120Sn 4 1600 4.3 s (5/2+) 203.2(3) 19.1 ms 11/2−# 118Pd May 05 120Sn 5 800 1.9 s 0+ 119Pd May 05 120Sn 5 400 920 ms 120Pd May 05 120Sn 5 200 500 ms 0+

a The estimate originally given in Ref. [21]is99

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TABLE II. Overview of results. Second column gives the ratio of the reference frequency to the frequency of the isotope of interest. Third column gives the mass excess (ME) calculated from this ratio. Fourth column gives the mass value from the AME03, and last column the difference between the new result and the tabulated value (AME03 − JYFLTRAP). All systematic uncertainties are included.

ref νc Nucleus meas ME (keV) AME03 ME (keV) Diff. (keV) νc 106Tc 1.039351332(46) −79736 ± 5 −79775 ± 13 −39 107Tc 1.019137991(85) −78743 ± 9 −79100 ± 150 −357 108Tc 1.028699156(86) −75916 ± 9 −75950 ± 130 −34 109Tc 1.038248173(95) −74276 ± 10 −74540 ± 100 −264 110Tc 1.047813648(93) −71028 ± 10 −70960 ± 80 68 111Tc 1.057366451(100) −69018 ± 11 −69220 ± 110 −202 112Tc 1.098383006(58) −65250 ± 6 −66000 ± 120 −750 106Ru 1.009528319(87) −86311 ± 9 −86322 ± 8 −11 107Ru 1.019085672(85) −83856 ± 9 −83920 ± 120 −64 108Ru 1.028619965(85) −83655 ± 9 −83670 ± 120 −15 109Ru 1.038182111(88) −80732 ± 10 −80850 ± 70 −118 110Ru 1.047721142(89) −80067 ± 10 −79980 ± 50 87 111Ru 1.057287033(95) −76778 ± 10 −76670 ± 70 108 112Ru 1.066831082(94) −75624 ± 10 −75480 ± 70 144 113Ru or 113Rum 1.076402249(119) −71819 ± 12 −72200 ± 70 −387 114Ru 1.085950928(126) −70213 ± 13 −70530 ± 230 −317 115Ru 0.958523298(61) −66071 ± 8 −66430 ± 130 −359 108Rh 0.899972299(126) −85037 ± 15 −85080 ± 40 −43 108Rhm 0.899973318(109) −84924 ± 13 −85020 ± 110 −96 109Rh 0.908312639(60) −85018 ± 8 −85011 ± 12 7 110Rh or 110Rhm 0.916673797(60) −82674 ± 8 −82780 ± 50 −106 111Rh 0.925017220(61) −82311 ± 8 −82357 ± 30 −46 112Rh or 112Rhm 0.933381862(62) −79577 ± 8 −79740 ± 50 −163 113Rh 0.941729225(63) −78774 ± 8 −78680 ± 50 94 114Rh or 114Rhm 0.950097168(65) −75672 ± 8 −75630 ± 110 42 115Rh 0.958450190(65) −74236 ± 8 −74210 ± 80 26 116Rh or 116Rhm 0.966822543(70) −70642 ± 9 −70740 ± 140 −98 117Rh 0.975178272(79) −68904 ± 10 −68950 ± 500 −46 118Rh 0.983554346(213) −64894 ± 24 −65140 ± 500 −246 112Pd 0.933321426(62) −86327 ± 8 −86336 ± 18 −9 113Pd 0.941686037(62) −83597 ± 8 −83690 ± 40 −93 114Pd 0.950027102(62) −83497 ± 8 −83497 ± 24 0.3 115Pd 0.958394697(122) −80434 ± 14 −80400 ± 60 34.2 115Pdm 0.958395480(121) −80347 ± 14 −80310 ± 60 36.7 116Pd 0.966740203(63) −79838 ± 8 −79960 ± 60 −122 117Pd 0.975110888(66) −76430 ± 8 −76530 ± 60 −100 118Pd 0.983460297(66) −75398 ± 8 −75470 ± 210 −72 119Pd 0.991836131(73) −71415 ± 9 −71620 ± 300 −205 120Pd 1.000186128(81) −70317 ± 10 −70150 ± 120 167

The mass excesses (ME) obtained in the measurements are Prior to May 2005, it was not possible to record individual listed in Table II, giving also the frequency ratio, the AME03 ion bunches at JYFLTRAP. Instead, the average number of [14] tabulated value, and finally the differences between the detected ions was kept below two per bunch during the results presented here and the AME03 values. measurement. Since May 2005, single bunches were recorded, In addition to the statistical uncertainties and the un- and the number of detected ions could be chosen in the certainty of the reference ion [105Ru: ME = (−85928 ± analysis; i.e., cycles with too high a number of detected ions 3) keV, 120Sn: ME = (−91105.1 ± 2.5) keV, 102Ru: ME = were discarded. Where sufficient statistics were available, (−89098 ± 2) keV], three sources of systematic errors were a count rate class analysis was conducted as described in taken into account in the calculation of the uncertainties: the Ref. [22], extrapolating the frequency to 0.6 ions in the trap count rate effect due to a high number of ions in the trap [22], due to the MCP detection efficiency of 60% at 30 keV. The the fluctuations of the magnetic field, and a mass-dependent resulting systematic uncertainty on the other measurements uncertainty caused by imperfections in the electric quadrupolar was estimated based on that analysis and on the maximum field. count rate allowed in the analysis; for the first run in January

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05 the uncertainty due to the count rate effect was estimated TABLE III. Previous measurements of technetium. to be 0.05 Hz (≈5keVforA = 100); for the run in May 05, 0.04 Hz (limited to three ions in the trap); in February 06, Isotope Method Result Reference

0.03 Hz (limited to three ions in the trap); and in May 106 Tc β-endpoint Qβ = 6547 ± 11 Groß(1992) [23] 06, 0.01 Hz (limited to two ions in the trap). The resulting 107 Tc β-endpoint Qβ = 4820 ± 85 Graefenstedt(1989) [24] uncertainty was added to the final averaged frequency ratio. 108 Tc β-endpoint Qβ = 7720 ± 50 Graefenstedt(1989) [24] The observed resonance frequency has been found to 109 Tc β-endpoint Qβ = 6315 ± 70 Graefenstedt(1989) [24] fluctuate with the temperature in the experimental hall. However, this variation is slow, and the drift is accounted for by taking reference measurements before and after each Graefenstedt et al. [24] by measuring the β-endpoint energy. measurement, and by keeping the acquisition time for one Those measurements were also adopted to the AME03. For resonance spectrum short, typically less than 30 min. The re- 108Tc, the value agrees with our data; for the two other isotopes, maining short-term fluctuations of the magnetic field and other the new values indicate that these nuclei are less bound. In the fluctuations, e.g., of power supplies, were estimated based case of 109Tc, using our mass excess of the daughter rather on the behavior of the reference measurements. Since these than the AME03 one in calculating the mass excess from the fluctuations are expected to be random, the corresponding Qβ values slightly decreases the discrepancy. uncertainty is added to each determined cyclotron frequency, 110,111,112Tc were previously measured at IGISOL by a and hence their impact on the final value decreases with an β-endpoint measurement. These values were never published increasing number of measurements. In January 05, these because of problems in the interpretation of the feeding of fluctuations were estimated to be 0.05 Hz; in May 05, 0.03 Hz; excited states. However, the results were adopted in the AME. in February 06, 0.01 Hz; and in May 06, 0.02 Hz. For 110Tc, that value agrees with the new result; for 111Tc, Finally, the mass-dependent uncertainty was derived from the new mass excess is ∼200 keV larger. The AME03 mass a measurement in which the measured resonance frequency 112 129 excess for Tc differs from our value by as much as 750 keV. of O2 molecules was compared with that of Xe and was × −10 This shows that the decision not to publish the old results was deduced to be 7 10 per mass unit difference between the well founded, and indeed the feeding to excited states was nucleus of interest and the reference. This uncertainty was underestimated. added to the uncertainty of the final average frequency ratio. It is worth noting that during the measurement of 106Tc, impurities in the precision trap were observed, similar to B. Results and comparison with earlier data effects from decays in the trap. Since the half-life of 106Tc is more than 40 times longer than the storage time in the 1. Technetium trap, this was not expected. The contamination was, however, For each individual isotope, the previous measurements clearly related to the technetium, as revealed by a mass (given in Table III) and the value measured at JYFLTRAP scan in the purification trap. No explanation has yet been (Table II) are compared in Fig. 4. found. Of the measured technetium isotopes, only 107Tc has a known isomeric state. However, as this state is very short- lived [184(3) ns], it does not need to be considered in the 2. Ruthenium analysis. The β-endpoint energy of 106Tc was measured by For 113Ru, the isomeric state [21] poses a problem to the Groß et al. [23]. The value disagrees with the one presented mass measurement. Since the applied excitation time (400 ms, in this work. 107−109Tc have previously been measured by Table I, corresponding to a FWHM of ≈2 Hz) was not

Tc106 Tc107 Tc108 Tc109 Tc110 Tc111 Tc112 200 40 0 20 -200 0 FIG. 4. Technetium: Comparison between -400 previous literature values and values presented -20 in this work. For the literature values given as a

ME(AME)-ME (keV) -600 reaction or decay Q value, the mass excess of -40 the daughter is taken from the AME03, or, when ∗ -800 marked with an asterisk ( ), from this work. Note the different scale for 106Tc. JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) Gross(1992) Gross(1992)* Graefenstedt(1989) Graefenstedt(1989) Graefenstedt(1989) Graefenstedt(1989)* Graefenstedt(1989)* Graefenstedt(1989)*

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TABLE IV. Previous measurements of ruthenium.

Isotope Method Result Reference

106Ru 104Ru(t,p)106Ru Q = 5892 ± 20 Casten(1972) [25] β-endpoint Qβ = 39.2 ± 0.3 Agnew(1950) [26] 107 Ru β-endpoint Qβ = 2900 ± 135 Graefenstedt(1989) [24] β-endpoint Qβ = 3140 ± 300 Pierson(1962) [27] 108 Ru β-endpoint Qβ = 1355 ± 90 Graefenstedt(1989) [24] β-endpoint Qβ = 1380 ± 80 Jokinen(1992) [28] β-endpoint Qβ = 1350 ± 60 Jokinen(1994) [29] β-endpoint Qβ = 1315 ± 100 Pierson(1962) [27] 109 Ru β-endpoint Qβ = 4160 ± 65 Graefenstedt(1989) [24] 110Ru Penning trap ME =−80010 ± 70 Kolhinen(2003) [15] β-endpoint Qβ = 2810 ± 50 Jokinen(1991) [30] 111Ru Penning trap ME =−76670 ± 70 Kolhinen(2003) [15] 112Ru Penning trap ME =−75480 ± 70 Kolhinen(2003) [15] β-endpoint Qβ = 4520 ± 80 Jokinen(1991) [30] 113Ru Penning trap ME =−71690 ± 80 Kolhinen(2003) [15] 114 Ru β-endpoint Qβ = 6120 ± 200 Jokinen(1994) [29]

sufficient to separate the ground and excited states (99– 110,111,112Tc, these measurements were not published because 160 keV or about 1.2 Hz), only one state of 113Ru was observed, of uncertainties in the interpretation of feeding to excited and it could not be determined which state was measured or states. whether the observed resonance corresponds to a mixture of nuclei of both states. The previous measurements conducted for the ruthenium 3. Rhodium isotopes are listed in Table IV and plotted in Fig. 5 together 108,110,112,114,116Rh all have isomeric states according to the with the new values given in Table II. AME03 [14]. For 108,110Rh, the isomeric excitation energies For 106,107,108Ru, all measurements agree rather well. given in Ref. [14] are negative. Since the data presented 106Ru has been measured in a (t,p) reaction [25], all other here do not allow spin assignment, the state with the higher measurements were β-endpoint measurements. 109Ru has binding energy will naturally be referred to as the ground state, been measured by Graefenstedt et al. [24]inthesame regardless of which state in Ref. [14] it might correspond to. measurement as 108Ru; however, this value disagrees with the Only for 108Rh were two resonances observed. To separate the new one by ∼120 keV. 110Ru has been determined both by a isomeric ground and excited states in 108Rh, an excitation time β-endpoint measurement [30] and by using the JYFLTRAP of 1.6 s was applied. It was thereby possible to resolve both purification trap [15]. While the β-endpoint measurement states, as shown in Fig. 6. disagrees slightly with the value presented in this work, the old The excitation energy is given in the AME03 as JYFLTRAP measurement and the present one agree. Similarly, (−60 ± 110) keV; this work found an excitation energy of the previous JYFLTRAP measurement and the present one 113.0(7.5) keV (no systematic uncertainties included), and as agree reasonably well for 111,112,113Ru. In all three cases, stated above, the state with the higher binding energy is listed the new mass excesses are smaller. This discrepancy might be as the ground state in Table II. due to the count rate effect, as discussed in Sec. III, since the Measuring two masses this close together introduces method used in Ref. [15] depends on having a large number additional uncertainties, as the purification in the first trap of ions in the trap, and all fission products with the same cannot separate the states and hence both can be present in the mass number were in the trap simultaneously. The ratio of precision trap at the same time. An additional uncertainty of the nuclide of interest to all other nuclides—and hence the 0.1 Hz, corresponding to a relative uncertainty of ∼10−7 was frequency shift—directly reflects the relative production cross therefore added to the frequencies of both states. This number section of that nuclide. Since the production decreases when was estimated from an offline study of a similar case. going farther from stability, that ratio becomes less favorable The heavier isotopes 110,112,114,116Rh are also known to have and hence the shift larger. isomeric states. Considering that in the case of 108Rh two The β-endpoint measurements done for 112,114Ru [30] both isomeric states differing by about 100 keV could be resolved suggest heavier masses than the values presented in this work. using an excitation time of 1.6 s, and given the excitation times The AME03 value for 114Ru is derived from that work; and the isomeric excitation energies from Table I, one would however, for better systematic agreement, the original value expect the isomer of 112Rh and maybe that of 114Rh to be was increased by 1 MeV in the compilation. The AME03 resolved if the relative production rate was on the order of values for 113,115Ru are based on unpublished β-endpoint 15% or larger, as it was for 108Rh. However, only a single- measurements conducted at IGISOL. As with the case of peak resonance was observed for either case, and it cannot

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200 Ru106 Ru107 Ru108 Ru109

100

-100

ME(AME)-ME (keV) -200

-300 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) FIG. 5. Ruthenium: Comparison between pre- Agnew(1950) Casten(1972) Pierson(1962) Pierson(1962) Jokinen(1992) Jokinen(1994) Pierson(1962)* Jokinen(1992)* Jokinen(1994)* vious literature values and values presented in this work. For the literature values that were given as Graefenstedt(1987) Graefenstedt(1989) Graefenstedt(1989) Graefenstedt(1989)* Graefenstedt(1989)* a reaction or decay Q value, the mass excess of 400 the daughter is taken from the AME03, or, when Ru110 Ru111 Ru112 Ru113 Ru114 Ru115 marked with an asterisk (∗), from this work. ‘#’ 200 denotes extrapolated values. 0

-200

-400

-600

ME(AME)-ME (keV) -800

-1000 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(1995) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(1995)# AME(1995)# AME(1995)# Jokinen(1991) Jokinen(1991) Jokinen(1991) Jokinen(1991)* Jokinen(1991)* Jokinen(1991)* Kolhinen(2003) Kolhinen(2003) Kolhinen(2003) Kolhinen(2003) be concluded whether the measured mass value applies to the For 110,116Rh, the isomeric states could not be resolved with ground or the excited isomeric state. the excitation times used. It could therefore be possible that the observed resonance is either the ground or the excited state, or a superposition of both. 550 The previous measurements of the rhodium isotopes are listed in Table V, and depicted in Fig. 7 together with the new

s) values.

µ 500 The AME03 values for 108,109Rh agree with the values 109 450 presented in this work. Rh has been previously measured in two different reactions: (t,α)[31] and (d,3He) [32]; both 110 400 values agree with each other and with our value. Rh has been previously measured by a β-endpoint measurement [34], Time of Flight ( 350 which disagrees with the new value, and by employing the JYFLTRAP purification trap [33]. The latter measurement 111 300 agrees with the new measurement, as is the case for Rh. The 112 −3 −2 −1 0 1 2 previous measurements of Rh diverge, the value presented ν −995727 (Hz) in this work lies between the β-endpoint measurement [35] RF and the old JYFLTRAP measurement [33]. The discrepancy FIG. 6. Resonance spectrum of 108Rh and 108mRh. The excitation between the old and new JYFLTRAP values is probably again time was 1.6 s, and the solid line represents the fit to the data points. due to the count rate effect in the old measurements. The same 114 113 The left minimum corresponds to the excited isomeric state, the right is true for Rh. For Rh, the new value is just outside the 115 one to the ground state, and the vertical lines mark the fitted resonance error bars of the older JYFLTRAP measurement. For Rh frequencies. and 116Rh, however, both JYFLTRAP measurements agree;

064302-7 U. HAGER et al. PHYSICAL REVIEW C 75, 064302 (2007)

TABLE V. Previous measurements of rhodium.

Isotope Method Result Reference

108 Rh β-endpoint Qβ = 4505 ± 105 Graefenstedt(1989) [24] 109Rh 110Pd(t,α)109Rh Q = 9206 ± 25 Flynn(1982) [31] 110Pd(d,3He)109Rh Q =−5134 ± 5 Kaffrell(1987) [32] 110Rh Penning trap ME =−82640 ± 70 Kolhinen(2003) [33] β-endpoint Qβ = 5400 ± 100 Pinston(1970) [34] 111Rh Penning trap ME =−82240 ± 70 Kolhinen(2004) [33] 112Rh Penning trap ME =−79480 ± 40 Kolhinen(2004) [33] β-endpoint Qβ = 6200 ± 500 Ayst¨ o(1988)¨ [35] 113Rh Penning trap ME =−78680 ± 80 Kolhinen(2004) [33] 114Rh Penning trap ME =−75530 ± 60 Kolhinen(2004) [33] β-endpoint Qβ = 6500 ± 500 Ayst¨ o(1988)¨ [35] 115Rh Penning trap ME =−74210 ± 80 Kolhinen(2004) [33] β-endpoint Qβ = 6000 ± 500 Ayst¨ o(1988)b¨ [36] 116Rh Penning trap ME =−70640 ± 100 Kolhinen(2004) [33] β-endpoint Qβ = 8000 ± 500 Ayst¨ o(1988)¨ [35] the β-endpoint results [35,36] agree in the case of 115Rh, but Figure 9 shows the results of the previous measurement, they give too small a mass for 116Rh. The AME03 values for which are listed in Table VI, and the new values, given in 117Rh and 118Rh are based on extrapolations. Table II. 112Pd was previously measured by a β-endpoint measurement [39] and by a (t,p) reaction [25]; both values agree with 4. Palladium the value presented in this work. The β-endpoint energies of 113,114,115,116Pd have been 113,115,117 The studied Pd isotopes all have isomeric states. measured by Fogelberg et al. [37]. Except for 115Pd, the values 113,117 However, those of Pd are short-lived compared to the suggest a lower mass than the values presented in this work. storage time in the trap. Therefore, the determined mass The values for 114,115Pd agree within uncertainties. The mass 115 value corresponds to the ground state. The isomer of Pd, of 114Pd has also been measured by Jokinen et al. [29], also by on the other hand, has a half-life longer than that of the ground a β-endpoint measurement. The same holds for 116,118,120Pd. state (see Table I). Using an excitation time of 2 s, it was Except for 120Pd, these measurements agree with our new possible to separate both states. The resulting spectrum is values. shown in Fig. 8(a). From this it was possible to determine an abundance ratio of ground state to excited state of 1:2, and therefore to determine the masses of both states even from IV. DISCUSSION measurements done with 800 ms excitation, see Fig. 8(b).Asin the case of 108,108mRh, an additional uncertainty of 0.1 Hz was The atomic masses of 39 neutron-rich nuclides between added. The isomeric excitation energy of 88(14) keV derived Z = 43–46 and N = 62–74 were measured with high pre- from the determined mass excesses agrees with the directly cision, including previously unmeasured nuclides, reducing measured isomeric transition energy of 89.18(25) keV [37,38]. considerably the uncertainties of these mass values. These

TABLE VI. Previous measurements of palladium.

Isotope Method Result Reference

112Pd 110Pd(t,p)112Pd Q = 5659 ± 20 Casten(1972) [25] β-endpoint Qβ = 299 ± 20 Nussbaum(1955) [39] 113 Pd β-endpoint Qβ = 3340 ± 35 Fogelberg(1990) [37] 114Pd 116Cd(14C,16O) 114Pd Q = 2497 ± 29 Cohler(1984) [40] 114 Pd β-endpoint Qβ = 1414 ± 30 Fogelberg(1990) [37] β-endpoint Qβ = 1451 ± 25 Jokinen(1994) [29] 115 Pd β-endpoint Qβ = 4584 ± 50 Fogelberg(1990) [37] 116 Pd β-endpoint Qβ = 2607 ± 30 Fogelberg(1990) [37] β-endpoint Qβ = 2620 ± 100 Jokinen(1994) [29] 118 Pd β-endpoint Qβ = 4100 ± 200 Jokinen(1994) [29] β-endpoint Qβ = 4000 ± 200 Koponen(1989) [41] 120 Pd β-endpoint Qβ = 5500 ± 100 Jokinen(1994) [29]

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400 Rh108 Rh109 Rh110 Rh111 Rh112 300 200 100 0 -100

ME(AME)-ME (keV) -200 -300 -400

FIG. 7. Rhodium: Comparison between pre- JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) Flynn(1982) Aysto(1988)

AME(1995)# AME(1995)# vious literature values and values presented in Aysto(1988)* Kaffrell(1987) Pinston(1970)

Kolhinen(2003) Kolhinen(2004) Kolhinen(2004) this work. For the literature values that were given as a reaction or decay Q value, the mass Graefenstedt(1989) excess of the daughter is taken from the AME03, ∗ 1500 or, when marked with an asterisk ( ), from this Rh113 Rh114 Rh115 Rh116 Rh117 Rh118 work. ‘#’ denotes extrapolated values.

1000

500

0 ME(AME)-ME (keV)

-500 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(1995) AME(2003) Aysto(1988) Aysto(1988) AME(1995)# AME(1995)# AME(1995)# AME(2003)# AME(2003)# Aysto(1988)* Aysto(1988)* Aysto(1988b) Kolhinen(2004) Kolhinen(2004) Kolhinen(2004) Kolhinen(2004) precision data allow us to take a critical look at various mass The r-process path is assumed to lie at SN 3 MeV. Although models as well as studies of systematic trends as a probe for this limit could not be reached in this experiment, the new data possible structural changes with proton and neutron number. will allow more precise extrapolations toward the r-process Of special interest for the r-process path is the neutron sep- path. The lowest neutron separation energies determined from 112 aration energy SN =−ME(A, Z) + ME(A − 1,Z) + ME(n). the new data are 4281(16) keV for Tc, 3930(14) keV

600 550 550 500 s) s) µ 500 µ 450 450 400 400 Time of Flight ( Time of Flight ( 350 350 300 300 −2 −1 0 1 2 −4 −2 0 2 4 ν ν RF−935029 (Hz) RF−935029 (Hz)

FIG. 8. Resonance spectra of 115Pd and 115mPd with excitation times of (a) 2 s and (b) 800 ms. Solid line represents the ﬁt to the data points, vertical lines mark the ﬁtted resonance frequencies. Excitation energy is 89.18(25) keV.

064302-9 U. HAGER et al. PHYSICAL REVIEW C 75, 064302 (2007)

400 Pd112 Pd113 Pd114 Pd115 Pd116 Pd117 Pd118 Pd119 Pd120 300 200 100

0 FIG. 9. Palladium: Comparison between -100 previous literature values and values presented in this work. For the literature values that were -200 ME(AME)-ME (keV) given as a reaction or decay Q value, the mass -300 excess of the daughter is taken from the AME03. -400 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) AME(2003)# Cohler(1984) Casten(1972) Jokinen(1994) Jokinen(1994) Jokinen(1994) Jokinen(1994) Koponen(1989) Fogelberg(1990) Fogelberg(1990) Fogelberg(1990) Fogelberg(1990) Nussbaum(1955) for 113Ru, 4061(26) keV for 118Rh, and 4088(12) keV for situation regarding the two-neutron separation energy of 119Pd. neutron-rich nuclides from strontium to palladium. In particular, in this section we present the observed data in The two-neutron separation energies for technetium, ruthe- the form of two-neutron separation energies to explore the nium, rhodium, and palladium nuclei as a function of neutron structural features due to the changing number of valence number display a smooth behavior as compared to the neutrons. kink observed at N = 58–60 for strontium, zirconium, and In the following discussion the measured mass values of molybdenum nuclei. In this region, these nuclei, in particular 110,112,114,116Rh and 113Ru are assumed to correspond to their strontium and zirconium, become strongly prolate deformed. ground states. On the other hand, a smooth behavior is expected from a spherical liquid-drop model prediction ﬁrst introduced in the form of a semiempirical mass model by von Weizsacker¨ [42]. 120 A. Systematics However, we do observe a singular exception, Pd, which does not seem to follow the general trend, though only a precise As stated in the Introduction, the two-neutron separation mass measurement of 121Pd and 119Rh could decide whether =− + − + energy S2N ME(A, Z) ME(A 2,Z) 2[ME(n)] can this is a more general feature indicating major structural be viewed as an indicator of major structural change and shell change. closures. The two-neutron separation energies calculated from The observed structureless behavior on the MeV energy the masses presented in this work are plotted in Fig. 10 together scale of Fig. 10 indicates only small structural changes within with the values tabulated in the AME03 mass tables. the set of studied isotopes. However, the high precision of the An irregularity in the tabulated AME03 values occurring measured masses allows a search for weaker effects in the form = at neutron number N 69 in technetium and ruthenium is of local correlations within the nuclear many-body system removed by our measurements. For a more global view, [43]. To further explore small deviations from the general Fig. 11 combines the data from this work, the previous JYFLTRAP data [2], and AME03 values to show the updated

16 Rh Pd Pd Tc Ru Rh Pd Ru 15 Rh 15 Tc Ru Mo Tc 14 Sr 14 Rh Zr Ru 13 Pd 13 (MeV) 2N 12 (MeV) S

2N Tc S 12 11

10 11 Mo Sr Zr 9 54 56 58 60 62 64 66 68 70 72 74 10 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Neutron number Neutron number FIG. 11. Two-neutron separation energy, values taken from this FIG. 10. Two-neutron separation energy. Thick lines represent work, from an earlier JYFLTRAP measurement [2], and from the results from this work, thin ones those from AME03. AME03.

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0.4 1200 Pd Tc Rh 1000 Ru 0.3 Ru Rh Tc 800 Pd

0.2 600 400

-fit (MeV) 0.1 200 2N S 0 0

ME(JYFL)-ME(HFB9) (keV) -200 -0.1 -400 -600 62 64 66 68 70 72 74 62 63 64 65 66 67 68 69 70 71 72 73 74 Neutron number Neutron number N

FIG. 12. Two-neutron separation energy, relative to the function FIG. 15. Comparison between the values presented in this work given in the text [Eq. (3)]. and the values predicted by the HFB-9 calculations.

300 550 1200 Ru Ru Tc 200 Pd Pd 500 1000 Ru 100 Rh 800 Pd 0 450 600 -100 400 400 -200 -fit (keV) 350 200 E2 (keV) 2N -300 S 0 -400 300 -500 -200 250 ME(JYFL)-ME(HFBCS1) (keV) -600 -400 -700 200 -600 60 62 64 66 68 70 72 74 62 63 64 65 66 67 68 69 70 71 72 73 74 Neutron number Neutron number N

FIG. 13. Two-neutron separation energy relative to the function FIG. 16. Comparison between the values presented in this work given in the text and E2 transition energy. and the values predicted by the HFBCS1 calculations.

800 400 Tc Tc 600 Ru 200 Ru Rh Rh 400 Pd 0 Pd 200 -200 0 -400 -200 -600 -400 -600 -800 ME(JYFL)-ME(FRDM) (keV) ME(JYFL)-ME(HFB2) (keV) -800 -1000

-1000 -1200 62 63 64 65 66 67 68 69 70 71 72 73 74 62 63 64 65 66 67 68 69 70 71 72 73 74 Neutron number N Neutron number N

FIG. 14. Comparison between the values presented in this work FIG. 17. Comparison between the values presented in this work and the values predicted by the HFB-2 calculations. and the values predicted by the FRDM calculations.

064302-11 U. HAGER et al. PHYSICAL REVIEW C 75, 064302 (2007)

200 1000 Tc Tc Ru Ru 0 Rh 800 Rh Pd Pd -200 600

-400 400

-600 200

-800 0

ME(JYFL)-ME(ETFSI1) (keV) -200 -1000 ME(JYFL)-ME(Duflo-Zuker95) (keV) -400 -1200 62 63 64 65 66 67 68 69 70 71 72 73 74 62 63 64 65 66 67 68 69 70 71 72 73 74 Neutron number N Neutron number N

FIG. 18. Comparison between the values presented in this work FIG. 20. Comparison between the values presented in this work and the values predicted by the ETFSI-1 calculations. and the values predicted by Duﬂo and Zuker using 28 parameters.

The energy of the first excited 2+ level for even-even smooth behavior shown in Fig. 10,theS2N data were fitted using the function isotopes of palladium and ruthenium [44] is examined for possible correlations with the two-neutron separation energy Z2 in Fig. 13. According to the microscopic calculations of f (Z,A) = a + Z(Z − 1)A−4/3b + c, (3) A(A − 2) Ref. [8], for even-even nuclei the shape change in the case of axial deformation from prolate to oblate is predicted to resembling the Weizsacker¨ semiempirical mass formula [42], occur at N = 66 for ruthenium and N = 68/70 for palladium with the first term corresponding to the asymmetry term, in good agreement with the energies of the first 2+ states. and the second one to the Coulomb term. The resulting fit For ruthenium, the decrease in the S value (relative to = = = 2N parameters are a 104(5) MeV, b 3.1(3) MeV, and c the fit) beyond N = 66 coincides with the appearance and − 15.6(5) MeV, underlining the importance of the asymmetry lowering of the oblate minimum. For palladium, the situation term in this mass region. In Fig. 12, the two-neutron separation in light of the model calculation is quite different. Coexistence energies are plotted relative to this fit. Conclusions are difficult of two shapes close in energy and weakening deformation to draw from this plot because the observed small, 50– (β2 =−0.19, +0.14) eventually seem to lead to stronger 100 keV, fluctuations are influenced, for example, by changes two-neutron binding. A weakening of the deformation at in the orbital energies of the valence neutrons. However, it is N = 74 is also supported by the increase in the energy of the interesting to observe that the reduced two-neutron binding first 2+ state to nearly 450 keV. Therefore, we can conclude = is near its maximum near the N 66 midshell where the that rather small changes in nuclear structure are visible in the maximum deformation is known to occur. For further insight ground state binding if the masses are known to a precision into this observation, we restrict ourselves in the following of significantly better than 100 keV. For more quantitative to even-even nuclei, because in these nuclei the ground state conclusions, a more detailed theoretical treatment is needed. assignment for the measured masses is unambiguous.

0 Tc 900 Ru Tc 800 Ru -200 Rh Pd 700 Rh Pd 600 -400 500 -600 400 300 -800 200 100

ME(JYFL)-ME(ETFSI2) (keV) -1000 0 ME(JYFL)-ME(Duflo-Zuker96) (keV) -100 -1200 -200 62 63 64 65 66 67 68 69 70 71 72 73 74 62 63 64 65 66 67 68 69 70 71 72 73 74 Neutron number N Neutron number N

FIG. 19. Comparison between the values presented in this work FIG. 21. Comparison between the values presented in this work and the values predicted by the ETFSI-2 calculations. and the values predicted by Duﬂo and Zuker using ten parameters.

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2500 However, both versions seem to have problems reproducing Tc Ru the odd-even effect, especially in technetium. Palladium as 2000 Rh well seems to present a problem in both calculations. Except Pd for these problems, however, the HFB-9 calculations seem to 1500 describe the general trends in this mass region rather well. The HFBCS-1 calculations also represent the data quite well up to 1000 N = 70 (Fig. 16); from there on, they clearly overestimate the binding strength. 500 The FRDM model appears to underestimate the binding energies around A = 110, see Fig. 17. For heavier masses, ME(JYFL)-ME(KTUY) (keV) 0 the agreement is fairly good, but the overall trend in the model indicates that when going even farther from stability, -500 62 63 64 65 66 67 68 69 70 71 72 73 74 the binding energies might be overestimated. Neutron number N Both ETFSI versions strongly underestimate the binding in this mass region; the ETFSI-1 calculation, Fig. 18, is slightly FIG. 22. Comparison between the values presented in this work better for N<70; while ETFSI-2, Fig. 19, comes closer to and the values predicted by the KTUY05 formula. the measured masses for N>70. The Duflo-Zuker calculation with 28 parameters (Fig. 20) describes the data better than the one with ten parameters (Fig. 21). Still, the pairing in rhodium poses a problem, as B. Comparison to mass model predictions well as the values for N = 73. Also, both models increasingly The measured ME values were compared with those diverge from the measured values as one moves outward from obtained by a number of mass models: the Hartree-Fock- β stability. This might make extrapolations based on either Bogoliubov model versions HFB-2 and HFB-9 [45], the finite model unreliable, systematically overestimating the binding range droplet model (FRDM) [46], the calculations done by energy. Duflo and Zuker using both the formula with 28 parameters The KTUY predictions do not agree with the new data at from 1995 and the one using ten parameters from 1996 [47], all, except for the lightest rhodium and palladium isotopes, see and the KTUY05 [48] formula. The selection of these models Fig. 22. All other binding energies are overestimated, indicat- was based on Ref. [49], which discusses the applicability of ing that this model is not a good basis for further extrapolations these models to astrophysical calculations. In addition, the ex- in this mass region. It is interesting to note, however, that tended Thomas-Fermi plus Strutinsky integral (ETFSI) model in a different mass region recently studied with JYFLTRAP, [50], which is another microscopic-macroscopic approach, and namely, the neutron-rich rubidium and bromine isotopes, the the Hartree-Fock + BCS (HFBCS) mass model [51]were KTUY model is in relatively good agreement with the data included in the comparison. [52]. The selected models cover a wide variety of different All in all, the most reliable model in this part of the nuclear approaches to mass modeling. The HFB models are completely chart seems to be HFB-9, though the problem seen in the microscopic, deriving the properties of the nucleus from palladium isotopes would need to be solved. The inability of internucleonic forces with free parameters which are fitted the examined models to reproduce the experimental data might to the data. Since these calculations become very demanding in part be explained by the previous lack of precise mass data in when many nucleons are involved, a simpler microscopic- this region, in particular where model parameters are derived macroscopic approach was explored, using shell-model cor- from a fit to the data. rections on derivatives of the liquid-drop model [42]. One of these models is the FRDM, in which the macroscopic part is V. CONCLUSIONS based on the droplet model with modifications to take into In conclusion, 39 masses were measured, four of them for account the finite range of the nuclear forces and to allow the first time. For most nuclei, the precision of the mass proton and neutron distributions to separate. The microscopic value could be significantly improved. The fine structure shell corrections are calculated using the Strutinsky method. of the mass surface in the form of two-neutron separation The KTUY calculations are a variant of the macroscopic- energies was shown to be sensitive to small changes in nuclear microscopic models, calculating a general trend and fluc- deformation. While it was not possible to reach the assumed tuations about this trend. The calculations of Duflo and path of the astrophysical r-process, the new values can help Zuker lie between the macroscopic-microscopic and a purely test and improve model calculations, and therefore decrease microscopic approach. They do not employ explicit nucle- the uncertainties of the extrapolations toward the r-process onic interactions, but rather they assume smooth effective path. interactions. The Hamiltonian is then split into monopole and multipole terms, which are parametrized. When comparing the HFB-2 calculation to the data ACKNOWLEDGMENTS presented in this work in Fig. 14, it seems to generally underestimate the binding energies, whereas the HFB-9 values This work has been supported by the Academy of Fin- (Fig. 15) are centered around the values presented in this work. land under the Finnish Centre of Excellence Programme

064302-13 U. HAGER et al. PHYSICAL REVIEW C 75, 064302 (2007)

2000–2005 (Project No. 44875, Nuclear and Condensed Excellence Programme 2006–2011 (Nuclear and Accelerator Matter Physics Programme at JYFL) and the Finnish Centre of Based Physics Programme at JYFL).

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064302-14 PRECISION MASS MEASUREMENTS OF NEUTRON-RICH ... PHYSICAL REVIEW C 75, 064302 (2007)

[49] J. M. Pearson and S. Goriely, Nucl. Phys. A777, 623 (2006). [51] F. Tondeur, S. Goriely, J. M. Pearson, and M. Onsi, Phys. Rev. [50] S. Goriely, in Proceedings of the International Con- C 62, 024308 (2000). ference on Capture Gamma-Ray Spectroscopy and Re- [52] S. Rahaman, U. Hager, V.-V. Elomaa, T. Eronen, J. Hakala, lated Topics, edited by S. Wender (AIP, New York, A. Jokinen, A. Kankainen, P. Karvonen, I. Moore, H. Pentilla¨ 2000). et al., Eur. Phys. J. A 32, 87 (2007).

064302-15 Eur. Phys. J. A 32, 87–96 (2007) THE EUROPEAN DOI 10.1140/epja/i2006-10297-y PHYSICAL JOURNAL A Regular Article – Nuclear Astrophysics

Precise atomic masses of neutron-rich Br and Rb nuclei close to the r-process path

S. Rahamana, U. Hager, V.-V. Elomaa, T. Eronen, J. Hakala, A. Jokinen, A. Kankainen, P. Karvonen, I.D. Moore, H. Penttilä, S. Rinta-Antila, J. Rissanen, A. Saastamoinen, T. Sonoda, and J. Ayst¨¨ o Department of Physics, P.O. Box 35 (YFL), FIN-40014 University of Jyväskylä, Finland

Received: 18 October 2006 / Revised: 26 February 2007 Published online: 3 April 2007 – c Societ`a Italiana di Fisica / Springer-Verlag 2007 Communicated by W. Henning

Abstract. The Penning trap mass spectrometer JYFLTRAP, coupled to the Ion-Guide Isotope Separator On-Line (IGISOL) facility at Jyväskylä, was employed to measure the atomic masses of neutron-rich 85–92Br and 94–97Rb isotopes with a typical accuracy less than 10 keV. Discrepancies with the older data are discussed. Comparison to different mass models is presented. Details of nuclear structure, shell and subshell closures are investigated by studying the two-neutron separation energy and the shell gap energy.

PACS. 21.10.Dr Binding energies and masses – 27.50.+e 59 ≤ A ≤ 89 – 27.60.+j 90 ≤ A ≤ 149 – 07.75.+h Mass spectrometers

1 Introduction Additional motivation for this work derives from the rapid neutron capture process (r-process) on heavy ele- Nuclei with masses A ∼ 100 have received a consider- ments. The r-process is considered to be responsible for able interest in recent years both theoretically as well as the synthesis of the heavy elements beyond iron (Z ≥ 26) experimentally. Reasons for this interest stem from shell and approximately half of all nuclear species in nature closure effects at N = 50, the subshell closure at N =56 are produced via this process. In a good approximation and an onset of large deformation for the nuclei with the neutron capture reactions proceed in a (n,γ) ↔ (γ,n) N ≥ 60. A systematic study of the properties of a se- equilibrium, fixing the r-process reaction path at rather ries of neutron-rich isotopes of rubidium, strontium, zirco- low neutron separation energies of about 2 to 3 MeV [6]. nium and molybdenum reveals a rapidly changing behav- The majority of nuclei in the r-process path are not ior in nuclear structure in the region of neutron number accessible experimentally, therefore the theoretical calcu- 58 ≤ N ≤ 61. This behavior has been studied experi- lations involve extensive extrapolations in the direction of mentally using several methods employing β-decay [1], γ- heavier and more neutron-rich isotopes. For reliable nu- ray measurements [2], collinear laser spectroscopy [3] and cleosynthesis calculations, nuclear masses (or the neutron most recently direct mass measurements [4]. The defor- separation energy Sn), half-lives and beta-decay Q values mation effect is dominant in the strontium and zirconium are important parameters [7]. To first order, the values of isotope chains where the onset of deformation is charac- Sn determine the r-process path and the values of the half- terized by a breaking of a smooth trend of two-neutron lives determine the shape of the abundance curve. Thus separation energies. the nuclear mass is one of the important nuclear parame- Systematic theoretical calculations employing the ters for the r-process calculations. Hartree-Fock-Bogoliubov (HFB) model predict that the The study of nuclear properties via precision atomic strontium, zirconium and molybdenum nuclei with N ≤ mass measurements of exotic nuclei is an important part 58 are nearly spherical in shape whereas those with of the JYFLTRAP setup at the Ion-Guide Isotope Sepa- N ∼ 60 prefer a highly deformed prolate shape [5]. The rator On-Line (IGISOL) facility [8] in Jyväskylä. So far, JYFLTRAP precise experimental observations indicate neutron-rich isotopes of Ga, Ge, As, Se, Br, Rb, Sr, Y, this occurrence [4]. Extension of this knowledge of defor- Zr, Mo, Tc, Ru, Rh and Pd have been investigated [4,9– mation changes towards the lower-Z region is of particu- 12]. Two r-process paths calculated by using the canonical lar interest in the present study of rubidium and bromine model [13,14] and the neutron-rich nuclei investigated at isotopes. JYFLTRAP are shown in fig. 1. Some of the investigated nuclei at JYFLTRAP are directly recline on the r-process a e-mail: [email protected] paths. In this paper experiments on neutron-rich Rb and 88 The European Physical Journal A

-5 -8 60 10 mbar 10 mbar Stable JYFLTRAP 7Tmagnet 55 24 3 -3 10 mbar MCP TN= 1.5 GK,n = 10 / cm Transfer line detector 28 3 TN= 1.0 GK,n = 10 / cm RFQ cooler Purification Precision 50 IGISOL beam trap trap

45 30 kV 800 V -Accumulation 40 97 V -Isobaric -Mass -Cooling and bunching separation measurement

proton number 35 Fig. 2. A schematic drawing of the JYFLTRAP setup. The main components are the RFQ cooler and buncher and two 30 cylindrical Penning traps. The Penning traps are inside a single 7 T superconducting solenoid. A microchannel plate (MCP) 25 detector is placed at the end of the setup which is at ground 40 45 50 55 60 65 70 75 80 85 potential. neutron number

Fig. 1. The neutron-rich nuclei (empty circles) investigated Table 1. The excitation time used for Br and Rb isotopes at JYFLTRAP and the two r-process paths [13,14] at two dif- for the mass measurements is indicated. 88Rb was used as a ferent temperatures and neutron densities. The rubidium and reference ion. Measurements were performed in July 2005. bromine isotopes studied in this article are indicated by ﬁlled grey circles. Measured isotopes Excitation time (ms) 85–90Br 800 Br isotopes around the mass region A ∼ 100 will be pre- 91Br 400 sented and discussed. The masses of Br and Rb isotopic 92Br 150 chains were previously measured employing β-decay end- 94Rb 800 point energies and using a dipole mass spectrometer, re- 95Rb 300 spectively. Recently, ISOLTRAP [15] has also measured 96–97Rb 150 masses of neutron-rich Kr isotopes up to 95Kr.

first trap, called the purification trap is filled with helium 2 Experimental setup and procedure gas at a pressure of about 10−5 mbar and is dedicated to 2.1 JYFLTRAP isobaric cleaning using a mass selective buffer gas cooling technique [21]. The second trap, the precision trap, has a −8 JYFLTRAP [16] is an ion trap experiment for cooling, residual pressure of about 10 mbar. It is used for high- bunching, isobaric purification and precision mass mea- precision mass measurements using the time-of-flight ion surements of radioactive ions produced at the IGISOL fa- cyclotron resonance technique [22]. cility. In this work radioactive nuclides were produced in The cooled and bunched ions from the RFQ buncher a proton-induced fission reaction by bombarding a thin were captured in the purification Penning trap and fur- (15 mg/cm2) natural uranium target with a 30 MeV pro- ther cooled by the collisions with helium atoms, finally ton beam of average intensity of 7 μA from the Jyväskylä being stored at the axial potential mimima of the trap. K-130 cyclotron. The production rates of the studied nu- Possible isobaric contaminations were removed by apply- clides varied from 10000 ions/s to 100 ions/s for the ing successive RF dipole and quadrupole excitations in the most exotic isotope. The ions were extracted from the presence of the helium gas. As a result, the ions of interest gas cell by helium gas flow into a differential pumping were centered when the applied quadrupole excitation fre- stage where they were accelerated to 30 keV and mass- quency was close to the ion cyclotron frequency. A cycle separated with a 55◦ dipole magnet. The ions were trans- time of about 400 ms was used in the purification trap and ported to the JYFLTRAP setup where they were effi- a mass resolving power of about 105 was reached with this ciently cooled and cleaned from possible isobaric con- configuration. taminants before their mass was measured. To perform The isobarically purified and cooled ions were trans- this process JYFLTRAP consists of two main compo- ported to the precision trap. RF dipole excitation at the nents as shown in fig. 2, a helium-filled RFQ cooler and ion’s magnetron frequency (ν−) was applied in order to en- buncher [17–19] and two cylindrical Penning traps in one hance the magnetron radius employing the phase-locking 7 T superconducting magnet. technique [23]. The RF quadrupole excitation was then The ions delivered to the RFQ cooler and buncher were applied at the sum frequency νc = ν+ + ν− to convert cooled, accumulated and finally bunched at a low kinetic the slow magnetron motion to the reduced cyclotron mo- energy with an emittance of 3 π-mm-mrad (measured at tion with a higher radial energy. νc and ν+ are the cy- 38 keV) [20]. These ion bunches were transported to the clotron and reduced cyclotron frequency of the ions respec- Penning trap system. The traps are placed in the homo- tively. The excitation time varied from 150 ms to 800 ms geneous regions of the magnet separated by 20 cm. The (see table 1). Finally, the ions were ejected from the trap. S. Rahaman et al.: Precise atomic masses of neutron-rich Br and Rb nuclei close to the r-process path 89

550 The drift of the magnetic ﬁeld was taken into account by the linear interpolation of the reference cyclotron 500 frequencies measured before and after the cyclotron frequency measurement of the ion of interest. As the mea- 450 surement time increases the reliability of this linear in-

m terpolation decreases because of the short-term magnetic-

/s 400 field fluctuation due to external influences as for example, temperature, pressure and the presence of ferromagnetic materials near the superconducting magnet [24]. 30 min- 350 utes of accumulation time for each file ensure the reliabil- mean TOF ity of the measurement. The cyclotron frequency of the ref- 300 erence ions was plotted as a function of time. Two consec- 97Rb + utive reference frequencies were not deviated by each other 250 more than 50 mHz. Experimental study showed that this -20 -16 -12 -8 -4 0 4 8 12 16 20 fluctuation is random and a deviation of 50 mHz was de- excitation frequency - 1108427 / Hz rived from the plot. This uncertainty was added quadratically to the statistical uncertainty of each measured fre- Fig. 3. Time-of-flight (TOF) resonance of 97Rb+ ions mea- quency. A mass-dependent systematic error on the order sured at JYFLTRAP. The line shows a fit to the data points of 10−10/u was derived from the off-line measurement by using the theoretically expected line shape. The excitation time 129 comparing the frequencies of Xe and O2 ions. This un- used for this isotope is 150 ms. certainty was added to the final average frequency ratio of each nuclei. If the ions stored in the trap have equal mass, the They drift towards the microchannel plate (MCP) detec- driving field will act on the center of mass of all ions and tor through a set of drift tubes where a strong magnetic- there will be no frequency shift [25]. However, some of field gradient exists. Here the ions experience a force which the investigated nuclei had very short half-lives, for exam- converts the radial kinetic energy of the ions into longitu- ple 97Rb (T = 170 ms). Therefore the decay products dinal energy additional to the 30 keV acceleration from the 1/2 and the ions created by charge exchange processes were a high-voltage platform to the ground potential where the source of the contaminating ions. In order to correct for MCP is situated. As a result an ion which was in resonance this the center value of the cyclotron frequency is plot- with the applied excitation quadrupole field moves faster ted as a function of the number of detected ions and the towards the detector than an ion which was off resonance. data is fitted by a linear function and extrapolated to the By measuring the time of flight as a function of the ap- observed 0.6 ion (detector efficiency 60%), equivalent to plied excitation frequency, the cyclotron frequency ν was c one ion in the trap [24]. The detected number of ions was determined. A typical time-of-flight resonance spectrum kept below 2 to 3 ions per bunch to minimize this shift. is shown in fig. 3. This spectrum yields the ion cyclotron One example, in the case of the 96Rb measurement the frequency 1 q amount of cyclotron frequency shift was 3.6 mHz/ion. In νc = B, (1) the case of the other nuclei the size of the frequency shift 2π m werevariedfrom0to8mHz/ion. The uncertainties at the where B is the magnetic field, m is the mass and q the extrapolated point (0.6 ion) were found to be a factor of charge state of the ion. To calibrate the magnetic field, the two times larger than at 2 ions per bunch. In the cases ref cyclotron frequency (νc ) of a precisely known reference where the ion class analysis was not possible due to the mass (mref ) was measured. The atomic mass of the ion of lower number of ions, the uncertainty of the frequency interest was then determined using the equation was increased manually to an average value. This average value was determined from the cases in which the ion class · − m = r (mref me)+me, (2) analysis was applied successfully.

ref where r = νc /νc is the frequency ratio and me is the electron mass. 3Results

The results of the mass measurements for 85–92Br and 2.2 Evaluation of uncertainties 94–97Rb performed at JYFLTRAP are summarized in table 2 and discussed in sects. 3.1 and 3.2. The cyclotron The dominating systematic uncertainties in the cyclotron frequency ratio of each isotope is given with respect to frequency determination are the uncertainties due to the cyclotron frequency of the 88Rb reference isotope. The magnetic-field fluctuations and the mass difference be- mass of 88Rb is known with an uncertainty of 160 eV [26]. tween the reference ion and the ion of interest. A shift The uncertainty of all the investigated isotopes reached a of the center value of the cyclotron frequency due to con- level below 10 keV. In table 2 the column MEex presents taminating ions in the trap is a further possible source of the measured JYFLTRAP mass excess with the final un- systematic error. certainty. The uncertainty contains the statistical and 90 The European Physical Journal A

Table 2. Results from the analysis of 85–92Br and 94–97Rb measured at JYFLTRAP. The measured average frequency ratio r and its uncertainty is presented. T1/2 represents the beta-decay half-life of the studied nuclei. ME ex represents the experimental mass excess obtained from the cyclotron frequency ratio. MElit are the AME03 values [26]. The last column gives the diﬀerence between the AME03 and JYFLTRAP values Δ = ME lit − ME ex.

ref νc Nucleus T Frequency ratio (r)= MEex /keV MElit /keV Δ /keV 1/2 νc 85Br 2.87 min 0.965 237 440(37) −78575.4(35) −78610(19) −34.6 86Br 55.10 s 0.977 334 856(38) −75632.3(35) −75640(11) −7.7 87Br 55.70 s 0.988 731 283(39) −73892(4) −73857(18) 35 88Br 16.30 s 1.000 145 235(39) −70716(4) −70730(40) −14 89Br 4.40 s 1.011 550 223(40) −68275(4) −68570(60) −295 90Br 1.90 s 1.022 977 586(41) −64001(4) −64620(80) −619 91Br 640 ms 1.034 388 086(43) −61108(4) −61510(70) −402 92Br 343 ms 1.045 822 783(82) −56233(7) −56580(50) −347 94Rb 2.69 s 1.068 422 547(45) −68564(5) −68553(8) 11 95Rb 377 ms 1.079 829 822(38) −65935(4) −65854(21) 81 96Rb 199 ms 1.091 260 919(41) −61355(4) −61225(29) 130 97Rb 170 ms 1.102 670 725(65) −58519(6) −58360(30) 159 all known systematic uncertainties. All previous measure- value −73892(4) keV diﬀers by 2 standard deviations from ments of Br masses were extracted from the endpoint en- the value of −73857(18) keV adopted in the AME03 mass ergy of the beta spectrum. In the case of the Rb isotopes a table. dipole mass spectrometer and a Penning trap were used up to 94Rb. For heavier Rb isotopes masses were previously 99 measured up to Rb but with moderate precision only. 3.1.4 88Br

3.1 85–92Br isotopes The endpoint energy of a beta spectrum has been determined in coincidence with cascade γ transitions to the 85 88 3.1.1 Br ground state of Kr [27]. An average Qβ = 8970(130) keV − 85 and a mass excess value of 70730(120) keV was derived. Earlier, the mass of Br has been primarily derived It was also investigated by M. Groß et al. [28] yielding al- from the beta-decay study of K. Aleklett et al. [27]. most the same mass excess value. The JYFLTRAP value A beta spectrum yielded Qβ = 2870(19) keV and a − − 70716(4) keV is in good agreement with the previous val- massexcessof 78600(20) keV. The adopted value in ues. 88Br has an isomeric state at an energy of 272.7 keV the AME03 is −78610(19) keV. The JYFLTRAP value − with a half-life of 5.4 μs. The ground-state mass measure- 78575.4(35) keV diﬀers by 35 keV or 2 standard devi- ment will not be aﬀected by such a short-lived isomeric ations from the adopted value. state since it will decay before reaching the Penning trap system. 3.1.2 86Br

The mass of this nucleus was deduced from its 3.1.5 89Br beta decay studied by K. Aleklett et al. [27]. A Q value of 7620(60) keV and a mass excess value β Spectroscopic investigations of 89Br nuclei have been per- −75640(60) keV were derived from the beta spectrum formed extensively by P. Hoﬀ et al. [29] in 1981 using a gated by the 2751 keV transition which depopulates molecular ion 27Al89Br+. The endpoint energy was de- the level at 4316 keV in 86Kr. M. Groß et al. [28] rived from the observed beta spectra in coincidence with also studied this nucleus in 1992 and extracted a selected γ transitions in 89Kr having an energy more mass excess of −75636(12) keV. The JYFLTRAP value than 4 MeV and possessing strong β branches. An av- −75632.3(35) keV is in good agreement with the value of erage Q = 8140(140) keV leads to a mass excess value −75640(11) keV adopted in AME03. β of −68690(150) keV. M. Groß et al. [28] also investigated the beta endpoint energy of 89Br. Our measured value 3.1.3 87Br −68275(4) keV diﬀers by 295 keV or 5 standard deviations from the value adopted in AME03. This deviation is re- The previous mass excess value of 87Br has been extracted duced to 100 keV taking into account the 89Kr mass value from the beta endpoint energy [27,28]. The JYFLTRAP measured recently at ISOLTRAP [15] (see table 3). S. Rahaman et al.: Precise atomic masses of neutron-rich Br and Rb nuclei close to the r-process path 91

Table 3. The Q-value of the Br isotopes from the Penning 3.2 94–97Rb isotopes mass measurements (this work and [15]) is indicated. 3.2.1 94Rb Isotopes Q-value from trap Q-value Difference mass measurement from AME03 Q − Q trap AME03 The mass of 94Rb was measured with the Orsay double- Q (keV) Q (keV) (keV) trap AME03 focusing mass spectrometer in 1982 and again in 1986 85Br 2905(4) 2870(19) −35 with better accuracy [31,32]. In the 1982 run inconsis- 86Br 7632(4) 7626(11) −6 tencies arose in the evaluation of 94Rb. This finally lead 87Br 6817(5) 6852(18) 35 to the suggestion of the existence of two short-lived iso- 88Br 8975(5) 8962(40) −13 mers, however this was not confirmed by any other ex- 89Br 8261(4) 8160(30) −101 periment. Finally, it was confirmed that the 94Rb beam 90Br 10959(4) 10350(80) −609 was contaminated. Other direct mass measurements took 91Br 9867(5) 9800(40) −67 place at the Prism mass spectrometer (PMC) consistent 92Br 12536(8) 12205(50) −331 with the Orsay measurements [33]. The mass of 94Rb was also determined at ISOLDE using the Penning trap mass spectrometer with an uncertainty of 9 keV [34]. The 3.1.6 90Br JYFLTRAP value −68564(5) keV is in excellent agreement with all previous measurements. The mass excess value of 90Br was determined from the endpoint energy of a beta spectrum by P. Hoff et al. [29]. The beta spectrum observed in coincidence with 3.2.2 95Rb 90 the 3231 keV γ transition of Kr yielded an average Qβ of 9800(400) keV and a mass excess of −65400(400) keV. An- In our experiment the mass excess of 95Rb was measured other experiment by M. Groß et al. on the beta endpoint to be −65935(4) keV. The value agrees within the uncer- energy provided a mass excess value of −64660(80) keV. tainties with the 1982 and 1986 measurements of the Or- The JYFLTRAP value −64001(4) keV differs by 619 keV say groups. The new value differs slightly from the adopted from the value adopted in the AME03 mass table. The value in the AME03 and disagrees with G.D. Alkhazov et difference of nearly 8 standard deviations can be due to al. by 150 keV [33]. various reasons. Firstly, a low-statistics beta spectrum can easily yield a MeV error in an endpoint energy determination. Secondly, the energy levels of 90Kr are poorly known. 3.2.3 96Rb Recently, the measured mass value of the 90Kr did not improve the observed deviation as indicated in table 3. Our measured mass excess of 96Rb, −61355(4) keV agrees within the error with the value of G. Audi et al. from 1982. However, it differs significantly from the measurement of 3.1.7 91Br G.D. Alkhazov et al. and the adopted value in the AME03. 96Rb seems less bound than the AME03 value indicates. 96 The mass value of 91Br has been determined at the An isomeric state in Rb is predicted by AME2003 [26] ISOLDE II mass separator by studying the endpoint en- to lie at (0±200 keV) with a half-life > 1(±200) ms. Since ergy of the beta spectrum measured by M. Graefenstedt no other resonance was observed within a scan range of et al. in 1989 [30]. The beta spectrum observed in co- 200 keV, our measured mass excess value could be either incidence with a set of gated γ transitions was obtained ground state or isomeric state. giving an average Qβ of 9790(100) keV and a mass value of −61565(115) keV. M. Groß et al. deduced a mass excess value of −61545(75) keV from the beta endpoint energy. 3.2.4 97Rb The JYFLTRAP value, −61108(4) keV differs from this value by as much as 400 keV. Considering the new mass The measured mass excess of 97Rb, −58519(6) keV lies value of the 91Kr this deviation is reduced to 67 keV tab- within the uncertainty of the 1986 value. However, it dif- ulated in table 3. fers from the AME03 value by 159 keV corresponding to 5 standard deviations. The AME03 value is influenced also by the measurement of G.D. Alkhazov et al., which differs 3.1.8 92Br by 290 keV from the JYFLTRAP value.

Our measured mass excess value of −56233(7) keV diﬀers from the AME03 value by 350 keV. The AME03 value is 4 Discussion based on the previous measurements by M. Graefenstedt et al. in 1989 [30] and M. Groß et al. in 1992 [28]. The large The masses of neutron-rich Br and Rb isotopes have been diﬀerence of 7 standard deviations cannot be understood measured by direct means using the Penning trap tech- but could have similar origins as discussed before for 90Br. nique with accuracies better than 10 keV. Discrepancy 92 The European Physical Journal A

200 150 94 95 96 97 85 86 87 88 Rb Rb Rb Rb Br Br Br Br 150

100 100 keV

TRAP) / keV 50 AP) /

TR 50 0

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(2003)

(2005) (2005) (2005)

(2005)

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t (1978) β (1992) (1992) β

L L L

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t (1978)

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Alekl Fig. 6. Experimental mass excess of Rb isotopes relative to

JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP 85–88 the AME03 values. The filled circles indicate the double fo- Fig. 4. Experimental mass excess of Br isotopes relative cusing spectrometer experiment of G. Audi et al. (1982) [31] to the AME03 values. The filled circles indicate beta-decay and (1986) [32], the ISOLTRAP experiment of H. Raimbault- experiments of K. Aleklett et al. (1979) [27] and M. Groß et al. Hartmann et al. (2002) [34] and the dipole mass spectrometer. (1992) [28]. The filled squares are the values from JYFLTRAP. of G.D. Alkhazov et al. (1989) [33]. The filled squares are the values from JYFLTRAP. 89 90 91 92 800 Br Br Br Br

600 keV

)/ their predictive power for the region far from stability,

400 where mass values are required for example to calculate TRAP

200 the r-process path. For comparison, we have chosen ﬁve

leading nuclear-mass models generally used in the liter- ME(JYFL 0 )- ature [35,36] that have reliably reproduced the known

-200 masses. The Finite-Range Droplet Model (FRDM) by Peter ME(AME03 -400 M¨oller et al. [37], belongs to a microscopic and macro-

-600 scopic (mic-mac) type of calculation. This model contains

two parts, a macroscopic part (based on the liquid-drop

1992) 1992) 1992)

1992)

(2005)

(1989)

(2005)

(1989)

(2003) (2003) (2003) model) and a microscopic part (single-particle model). In

f (1981)

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Hoff (1981)

Hof the macroscopic part the binding energy is a smooth func-

AME (2003) AME

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FL tion of proton number Z and neutron number N, derived

JYFLTR

JY JY

raefenstedt

raefenstedt G G from the liquid-drop model. Microscopic effects are ob- Fig. 5. Experimental mass excess of 89–92Br isotopes relative tained from a deformed single-particle model. The mass to the AME03 values. The filled circles indicate beta-decay excess values calculated according to this model have the experiments of P. Hoff et al. (1981) [29], M. Graefenstedt et al. largest deviations for both isotope chains investigated in (1989) [30] and M. Groß et al. (1992) [28]. The filled squares this work as shown in figs. 7 and 8. No significant odd-even are the values from JYFLTRAP. staggering is observed in this region. The Hartree-Fock-Bogoliubov model (HFB-9) [38] is with the older values as discussed in sect. 3 and sum- classified as fully microscopic, since the model is based on marized in figs. 4, 5 and 6 indicated deviations from the an effective two-body (nucleon-nucleon) interaction. This previous values of up to 600 keV. The shortest-lived iso- also includes pairing energy. The advantage of this model tope measured has a half-life of 170 ms (97Rb). The new is that it permits one to derive all properties of the nucleus JYFLTRAP data provides significant improvements in the from internucleonic forces. A drawback of this model is knowledge of experimental masses. In the following we will that it generally does not succeed in calculating odd nuclei use these data to highlight possible shell structure effects which is an inconvenience for astrophysics. The odd-even far from stability by viewing the systematics of the two staggering is clearly overestimated in this model and can neutron-separation energies and by comparing the results be seen for Br and Rb isotopes shown in figs. 7 and 8. with a few selected mass models. The Extended Thomas-Fermi and Strutinsky Integral (ETFSI) model [39,40] adopted a semi-classical approximation to the Hartree-Fock method which includes full 4.1 Comparison with mass models Strutinsky shell corrections. They extend Thomas-Fermi calculations to be available for a Skyrme-type (zero-range) It is necessary to compare the models with experimen- interaction and a delta-function pairing force incorporat- tal data for their further development and to improve ing a full Strutinsky integral. Mass excess values calcu- S. Rahaman et al.: Precise atomic masses of neutron-rich Br and Rb nuclei close to the r-process path 93

800 17 600 16

e 400 15

l)/k

d 200 14

E 0 13

/MeV

)-M -200 12

S R -400 11

F 10 Y -600

(J Sr Zr Mo E -800 9

M 8 Rb -1000 Br Br Kr -1200 7 48 49 50 51 52 53 54 55 56 57 49 51 53 55 57 59 61 63 65 67 neutron number neutron number Fig. 7. Comparison of Br mass excess values from JYFLTRAP Fig. 9. Experimental two-neutron separation energy (S2n) and calculated values from ﬁve leading mass models. plotted as a function of the neutron number. Empty diamonds connected with dashed lines present the values cited 2000 in the Atomic Mass Evaluation 2003 [26]. Full circles connected with solid line indicate the new and previous [4] ex- 1500 perimental values from JYFLTRAP (Br, Rb, Sr, Zr and Mo) 1000 and ISOLTRAP (Kr) [15].

500

E(Model) / keV 0 9.5

-500 TRAP) - M 8.5 -1000

E(JYFL M 7.5 -1500 Rb -2000 6.5 48 50 52 54 56 58 60 62

/MeV neutron number

n S 5.5 Fig. 8. Comparison of Rb mass excess values from JYFLTRAP and calculated values from five leading models. The AME03 tabulated mass values are used for N = 48–55 to see an en- 4.5 larged region. 3.5 lated according to this model are better relative to the 2.5 previous two models for the isotopes studied in this work. 50 51 52 53 54 55 56 57 58 59 60 Odd-even staggering is observed but less than that of the neutron number HFB-9 model. Fig. 10. One-neutron separation energy (Sn) plotted as a func- Another mass model [41] called KTUY also has two tion of the neutron number. The filled symbols indicate the ex- parts and belongs to the mic-mac family. The macroscopic perimental values from JYFLTRAP (Br, Rb) and ISOLTRAP part is a smooth function of Z and N based on the liquid- (Kr) [15]. Empty diamonds present the values cited in the drop model including an average pairing energy. The mi- Atomic Mass Evaluation 2003 [26]. croscopic part calculates the intrinsic shell energy and the average deformation energy of a deformed nucleus employing a single-particle potential. The mass excesses from this itly. This model starts with an assumption that there ex- model agree reasonably well with the JYFLTRAP exper- ists an effective interaction (pseudopotential) which makes imental values both for Br and Rb. For the heaviest Rb the HF calculation possible. Finally, it can be written isotopes, however, a large difference of nearly 1 MeV is as an effective Hamiltonian which contains two parts, observed. Only small odd-even staggering is noticed for a monopole term and a multipole term. The monopole N = 50–53 in the Br isotope chain and for N = 50–57 calculations are purely HF-type based on single-particle in the Rb isotope chain. It is of interest to note that properties while the multipole term acts as a residual in- the KTUY model fails completely in predicting masses teraction and the calculation goes beyond HF. The mass of neutron-rich Tc-Pd isotopes as shown by another study excess for Rb isotopes does not differ significantly for lower performed recently at JYFLTRAP [12]. neutron number but it starts to differ for higher neutron The Duflo and Zuker mass model [42] is more funda- number. For example, this model has a 1 MeV discrep- mental than the mic-mac approach but it is not yet fully ancy compared to experiment at N = 59. The odd-even microscopic since no nucleonic interaction appears explic- staggering is noticed for N = 50–53 for the Br isotope 94 The European Physical Journal A

Fig. 11. Shell gap as a function of the proton number for neutron numbers N0 = 50 and 56. Left side plots are calculated using two-neutron separation energies and right side plots are calculated using neutron separation energies. The filled circles indicate the JYFLTRAP values and the empty circles are taken from the AME03 mass table. The theoretical values are indicated by the symbols shown in figures. chain and for N = 50–55 for the Rb isotope chain but is the ground state. This effect is also visible for Sr and for comparably smaller than for other models. Rb at N = 58 to 60. A similar trend continues in the case of the Mo isotopes that are less deformed than the Zr isotopes at these neutron numbers. This phenomenon 4.2 Two-neutron separation energies and the shell gap has been interpreted by K. Heyde et al. as due to a coexistence of different shapes at low energies [43]. However, Figure 9 displays the two-neutron separation energies no such conclusion can yet be drawn for the Kr and Br (S2n) of neutron-rich Br, Kr, Sr, Zr and Mo isotopes chains due to the lack of experimental data in this region. derived from the mass excess values measured by the JYFLTRAP and ISOLTRAP setups [4,15]. The data is Figure 10 shows the experimental neutron separation energies for Br, Rb and Kr. The experimental neutron complemented by the values from the AME03 [26]. 91 The occurrence of nuclear shell effects is clearly ob- capture Q-value for Br is 3.20(1) MeV. The value clearly served as a function of neutron number. The main shell indicates that the investigated nuclei are very close to the closure at N = 50 manifests itself in a steep decrease of r-process path. Our new mass values in this region will substantially help to improve the theoretical predictions S2n values for all nuclei with N =51andN = 52. A similar change of the slope is observed at the N = 56 neutron and the network calculations of the r-process path. subshell closure. This change of the slope is most promi- Large shell gaps are a predominant feature of magic nent for Zr due to the fact that Z = 40 is a semi-magic nuclei. In the language of the shell model, such magic- proton number. At N = 59 for Zr isotopes the change in number nuclei have a closed-shell structure leading to their the slope of the S2n curve shows very clearly a sudden pronounced stability. This phenomenon is well understood phase transition from a spherical to a deformed shape of for the ground states of nuclei close to the valley of β- S. Rahaman et al.: Precise atomic masses of neutron-rich Br and Rb nuclei close to the r-process path 95 stability. However, the situation seems to be quite different shell gap values are in a poor agreement with the experi- for highly unstable nuclei. One example is that of abnor- mental results. mal neutron to proton number ratios. Several theoretical More exotic Rb and Br isotopes will be measured in calculations and experimental results have shown indica- the future to gain a comprehensive understanding of the tions of a quenching of the N0 = 20 shell in neutron-rich shell effects at lower-Z regions. To complete the shell gap isotopes [44–46]. Also the N0 = 50 shell gap has been plots towards the lower-Z region for N0 = 50, future predicted by different mass models [47,48] to be reduced JYFLTRAP experiment will aim to measure the masses towards Z ∼ 28. This phenomenon has been explained by of the neutron-rich isotopes further down towards Z = 28. refs. [44,49] and can be understood from a single-particle spectrum. In the case of nuclei far from the stability line, This work has been supported by the TRAPSPEC Joint Re- the single-particle spectrum is wider, therefore for these search Activity project under the EU 6th Framework program nuclei the neutron pairing energy will be enhanced and, “Integrating Infrastructure Initiative - Transnational Access”, as a result, the shell gaps are weakened. Contract Number: 506065 (EURONS) and by the Academy The shell gap energy (Δ(N0)) can be calculated by of Finland under the Finnish center of Excellence Program using the one- or two-neutron separation energies 2006-2011 (Nuclear and Accelerator Based Physics Program at JYFL and project numbers 202256 and 111428). Δ(N0)2n = S2n(Z, N0) − S2n(Z, N0 + 2) (3) and Δ(N0)1n = Sn(Z, N0) − Sn(Z, N0 +1), (4) References where N0 defines the magic neutron number. Figure 11 displays two regions of interest regarding the present work 1. S. Rinta-Antila, T. Eronen, V.-V. Elomaa, U. Hager, J. Hakala, A. Jokinen, P. Karvonen, H. Penttilä, J. Rissanen, and other recent data. The JYFLTRAP values from this ¨ work, previous work and the new ISOLTRAP values for T. Sonoda, A. Saastamoinen, J. Aystö, Eur. Phys. J. A 31, 1 (2007). Kr are included in this plot [4,10,15]. Our Δ(N ) data 0 2n 2. H.B. Ding, S.J. Zhu, J.H. Hamilton, A.V. Ramayya, J.K. for Z =35atN = 50 confirm the data that showed a 0 Hwang, K. Li, Y.X. Luo, J.O. Rasmussen, I.Y. Lee, C.T. clear trend towards the shell quenching as predicted by Goodin, X.L. Che, Y.J. Chen, M.L. Li, Phys. Rev. C 74, several models. At N0 =56andZ = 40 an enhanced 054301 (2006). shell gap energy is observed as expected because of both 3. P. Campbell, H.L. Thayer, J. Billowes, P. Dendooven, neutron and proton subshell closures. When comparing K.T. Flanagan, D.H. Forest, J.A.R. Griffith, J. Huikari, the N0 =50andN0 = 56 shell gaps (calculated according A. Jokinen, R. Moore, A. Nieminen, G. Tungate, S. to eq. (3)) the effect for N0 = 56 is more pronounced. Zemlyanoi, J. Ayst¨¨ o, Phys. Rev. Lett. 89, 082501 (2002). The gap is reduced by about a factor of two from Z =40 4. U. Hager, T. Eronen, J. Hakala, A. Jokinen, S. Kopecky, to Z = 35. On the contrary, the change in the Δ(N0)1n I. Moore, A. Nieminen, S. Rinta-Antila, J. Ayst¨¨ o, V.S. shell gap energies are considerably smaller. For N0 =56 Kolhinen, J. Szerypo, M. Oinonen, Phys. Rev. Lett. 96, no essentials reduction of the shell gap is observed down 042504 (2006). to Z = 35. 5. A. Kumar, M.R. Gunye, Phys. Rev. C 32, 2116 (1985). A large scattering of the shell gap values calculated by 6. K. Langanke, G. Martinez-Pinedo, Rev. Mod. Phys. 75, different models is observed for the N0 = 50 shell closures. 819 (2003). The Δ(N0 = 50)2n data is reasonably well reproduced by 7. J.J. Cowan, F.K. Thielemann, J.W. Truran, Phys. Rep. KTUY, FRDM, ETFSI models whereas no or only weak 208, 267 (1991). reduction is given by the Duflo and Zucker and HFB-9 8. J. Ayst¨¨ o, Nucl. Phys. A 693, 477 (2001). models. None of the models can reproduce the observed 9. A. Jokinen, T. Eronen, U. Hager, I. Moore, H. Penttilä, S. ¨ shell gap energies at N = 56. Rinta-Antila, J. Aystö, Int. J. Mass Spectrom. 251,204 (2006). 10. A. Jokinen et al., in preparation. 11. J. Hakala et al., in preparation. 5 Conclusions 12. U. Hager et al., submitted to Phys. Rev. C. 13. P.A. Seeger, W.A. Fowler, D.D. Clayton, Astrophys. J. The masses of 85–92Br and 94–97Rb isotopes have been Suppl. 11, 121 (1965). measured in the neighborhood of the r-process path with −8 14. V. Bouquelle, N. Cerf, M. Arnould, T. Tachibana, S. a relative precision of about 10 . A significant deviation Goriely, Astron. Astrophys. 305, 1005 (1996). is observed compared to the older data for Br isotopes. 15. P. Delahaye, G. Audi, K. Blaum, F. Carrel, S. George, The model mass excess values have an offset with the F. Herfurth, A. Herlert, A. Kellerbauer, H.-J. Kluge, D. JYFLTRAP mass excess values of about 400 keV for the Lunney, L. Schweikhard, C. Yazidjian, Phys. Rev. C 74, Br isotopes (see fig. 7). On the other hand, the model mass 034331 (2006). excess values diverge with the increasing neutron number 16. V.S. Kolhinen, T. Eronen, U. Hager, J. Hakala, A. Jokinen, for the Rb isotopes (see fig. 8). The neutron capture Q- S. Kopecky, S. Rinta-Antila, J. Szerypo, J. Ayst¨¨ o, Nucl. value of 91Br indicates that this isotope might directly lie Instrum. Methods Phys. Res. A 528, 776 (2004). on the r-process path. A reduced shell gap energy is ob- 17. A. Jokinen, J. Huikari, A. Nieminen, J. Ayst¨¨ o, Nucl. Phys. served at Z = 35 compared to Z = 40. The theoretical A 701, 577 (2002). 96 The European Physical Journal A

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U. Hager ∗ A. Jokinen V.-V. Elomaa T. Eronen J. Hakala A. Kankainen S. Rahaman J. Rissanen I. D. Moore S. Rinta-Antila A. Saastamoinen T. Sonoda J. Ayst¨o¨

Department of Physics, University of Jyv¨askyl¨a, P.O. Box 35 (YFL), Fin-40014

Abstract

The atomic masses of neutron-rich 95−101Y and 101−107Nb produced in proton- induced fission of uranium were determined using the JYFLTRAP double Penning trap setup. Accuracies of better than 10 keV could be reached for most nuclides. The masses of 106,107Nb were measured for the first time. The energies of the isomeric states in 96Y and 100Y were measured as 1541(10) keV and 145(15) keV. The niobium isotopes appear to be systematically less bound than the values given in the latest Atomic Mass Evaluation. The new data lie in a region of the nuclear chart characterised by the transition from spherical to strongly deformed shapes. These structural changes are explored by studying different systematic trends. The data are also compared to several model predictions to test their ability to reproduce the structural changes along the isotopic chains of yttrium and niobium.

Key words: Y and Nb isotopes, Mass measurement, Penning trap, N = 60 PACS: 27.60.+j, 21.10.Dr, 21.60.-n

1 Introduction

The neutron-rich region around A ≈ 100 has been studied extensively due to the shape transition and the shape coexistence around Z = 40 and N = 60, see [1] and references therein. While the ground states of the strontium and zirconium isotopes below N ≈ 60 appear to be only weakly deformed or nearly spherical, the heavier isotopes display a mainly axially symmetric deformed

∗ Corresponding author. Email address: [email protected] (U. Hager).

Preprint submitted to Elsevier Science 18 June 2007 shape. The molybdenum isotopes, on the other hand, are found to be triaxial [2]. Lhersonneau et al. [3] noted that nuclei with N ≥ 60 have large ground state quadrupole deformations, while the intermediate N = 59 isotones of strontium, yttrium and zirconium still have nearly spherical ground states. This rapid change is explained by unusually large deformations on the one hand and a strong subshell closure on the other hand. In laser spectroscopic studies the shape change in strontium [4] was observed in the form of a sudden increase of the mean-square charge radii at N = 60. Subsequent studies found a similar feature in the neutron-rich zirconium isotopes [5] and, more recently, in the neutron-rich yttrium isotopes [6]. Recently, precision mass measurements of neutron-rich strontium, zirconium and molybdenum isotopes were conducted at JYFLTRAP [7], where the sudden shape change in zirconium around N = 60 was confirmed by the evolution of the two-neutron separation energy along the isotopic chain. In strontium a similar change was observed, albeit less pronounced, molybdenum displayed a smoother behaviour. In this work, the masses of the neutron-rich isotopes of the odd-Z elements yttrium and niobium are studied, filling the gaps in that previous study. The level schemes of several of the nuclides included in this work were recently measured by Luo et al. [8], who found the quadrupole deformation in this region to decrease with increasing Z, and proposed a transitional character for niobium with regard to the triaxial deformation. The ground state of 97Y is given by Lhersonneau et al. [9] as a one-quasiproton 98 + state πp1/2. The isomeric state in Y was found to be a 5 (πg9/2,νs1/2) state + [10]. Luo et al. [8] assigned π5/2 [422], derived from πg9/2, to the ground-state 99,101 band heads in Y. This points to the role of the πg9/2 level in the onset of deformation, when at N = 60 it becomes the ground state rather than the isomeric band head. The g9/2 level is also important in the neutron-rich niobium isotopes. In [11], the exchange of the positions of the p1/2 and g9/2 quasiparticles in the N = 58 isotones is pointed out, making the 9/2+ excited state in 97Y the ground state in 99Nb, where the 1/2− state is an excited state. In 100Nb, the 1+ ground state is predicted to be spherical and based on the + (πg9/2,νg7/2) quasiproton-quasineutron configuration [12], and the 5 isomeric 101,105 state is in a (πg9/2,νs1/2) configuration. The ground-state bands in Nb are in a π5/2+[422] configuration [8]. These configurations underline the role of the g9/2 proton orbital in the evolution of the deformation of the neutron-rich yttrium and niobium isotopes. A closer look at the existing data reveals the sudden change of deformation to be limited to nuclei with proton numbers Z between 38 and 41 and neutron numbers close to N = 60. This is often explained in terms of the interaction between proton and neutron configurations with large spatial overlap [13,14]. For N < 56, the neutrons occupy orbits connected to the d5/2 single-particle level, and the protons are successively filling the 2p-1f shell. For larger neutron numbers, the neutrons occupy orbits having high angular momenta, i.e. g7/2 and h11/2. At large deformations, these orbits have considerable overlap with the proton orbits derived from the g9/2 single-particle level. The correlation

2 between the relevant neutron and proton orbits drives the nucleus to large deformations for nuclides with Z = 38 – 41 and N ≥ 60. For larger proton numbers, the situation becomes even more complex with the mixing of many configurations and less pronounced axial deformation. Due to the competing configurations in this region, the nuclear shapes tend to be γ-soft or even triaxial, and no sudden shape changes similar to the one in the N = 60 region have been observed [15]. In this work the masses of 95−101Y and 101−107Nb, including those of the isomeric states 96,97,100Ym and 100,102,104Nbm, were measured using the JYFLTRAP Penning trap setup. The data are compared to the previous measurements which are mainly based on β-endpoint studies. These are known to suffer from large systematic uncertainties, especially if the decay levels involved are unknown and hence possible feeding to excited states cannot be properly accounted for. The new mass data are also compared to several global mass models. Such comparisons can reveal the different strengths and weaknesses in the different models. These, in turn, can give an indication as to the un- derlying physics. Additionally, systematic trends are discussed, e.g. the two- neutron separation energy, which is a good indicator of structural change in this neutron-rich region.

2 Experimental setup

The data were obtained using the JYFLTRAP Penning trap setup installed at the IGISOL (Ion Guide Isotope Separator On-Line) facility in Jyväskylä, Finland. The radioactive nuclides were produced in the proton-induced fission of uranium. The 30 MeV protons were delivered by the JyväskyläK-130 cyclotron, and the target was a thin (10 mg/cm2) target of natural uranium. The reaction products were stopped in helium at a pressure of about 200 mbar, transported with the helium flow out of the chamber and accelerated to 30 keV and mass separated by a 55◦ bending magnet, providing a mass resolving power of 500, sufficient to select ions of only one mass number. Typical yields for the nuclei studied in this experiment range from 100 to 10000 ions/second. Further details on the IGISOL facility can be found in [16]. The ions were then injected into a radio frequency quadrupole-cooler/buncher (RFQ) [17], placed on a 30 kV high-voltage platform, where they were accumulated and extracted as short bunches to be injected into the first of two cylindrical Penning traps housed in the warm bore of a 7 T superconducting magnet, placed on the same 30 kV high voltage platform, Fig. 1. This purification trap, used for isobaric purification, contained helium gas at a pressure of a few times 10−5 mbar [18]. The pure ion sample was transferred into the second trap for precision mass measurement. The ions’ radius was first increased by a phaselocked [19] dipole excitation at the mass independent magnetron frequency. A quadrupole

3 10mbar10mbar-5-8 7Tmagnet 10mbar-3 MCP Transferline detector RFQcooler IGISOL PurificationPrecision beam traptrap

30kV 800V -Accumulation 97V -Cooling -Isobaric-Mass separationmeasurement Fig. 1. Schematic layout of the JYFLTRAP setup. excitation was then used to increase the energy of the ions of the correspond- 1 q ing mass, according to ν = 2π m B. Upon extraction from the magnetic field, the ions’ magnetic moment couples to the gradient of the magnetic field, and the radial energy is converted into axial energy. Thus, the ions in resonance with the quadrupole excitation will be accelerated, which can be observed by comparing the time of flight of the ions to a MCP detector. A time-of-flight cyclotron resonance spectrum thus obtained for 99Y is shown in Fig. 2. Fig- ure 2(a) shows the distribution of counts relative to the time of flight for all detected ions. The thick vertical lines mark the region which was included in the analysis, the peak at about 100 µs is due to decay in the trap, with the β-particles ionising light impurities in the trap, and is therefore discarded. The shaded grey area marks the ions with high radial energy, leading to a short time of flight. Figure 2(b) shows at which frequencies these on-resonance ions were detected. As there is only one peak visible in this figure, there was one ion species in the trap with a resonance frequency in the scanned range. Fig- ure 2(c) shows the resulting time-of-flight cyclotron resonance spectrum of 99Y with 600 ms excitation time.

3 Data analysis

Table 1 lists the nuclides measured in this work, with 100,102,104Nb taken from [20]. The reference nuclides are given in Table 2. The resonance frequencies of the reference mass and of the nuclide of interest are measured alternatingly, the resonance frequency is extracted by ﬁtting the theoretical line shape [21], and two subsequent reference frequencies are interpolated to account for long-term drifts of the magnetic ﬁeld. Since the charge state of all ions examined was +1, the unknown mass is given by

ref νc mmeas = meas (mref − me)+ me , (1) νc

4 25 140

120 20 100

15 80

60 Counts 10 40 Counts in resonance 5 20

0 0 -9 -6 -3 0 3 6 9 0 100 200 300 400 500 600 700 800 900 ν RF-1086180 (Hz) Time of flight (µs) (a) (b)

500

450 s)

µ 400

350

300 Time of flight ( 250

200 −9 −6 −3 0 3 6 9 ν RF−1086180 (Hz) (c)

Fig. 2. The figures show (a) all detected ions and their time of flight, (b) only the ions with high radial energy and thus short time of flight (as marked in (a)) as a function of the excitation frequency, and (c) is the resulting time-of-flight resonance spectrum for 99Y, using an excitation time of 600 ms. A more detailed explanation is given in the text.

ref meas νc , νc are the cyclotron frequencies of the reference ion (interpolated) and the measured ion, respectively, mref , me, and mmeas denote the masses of the reference ion, the electron, and the measured atom, respectively. Apart from the uncertainty of the reference masses, 2.8 keV for 97Zr and 2 keV for 102Ru, three systematic uncertainties were taken into account in the analysis: In an ideal Penning trap, the measured resonance frequency is inversely proportional to the mass. In the real trap, however, a slight offset of 7 · 10−10 per mass unit difference between the compared masses was found. This shift was accounted for by quadratically adding this uncertainty multiplied by the difference in mass number between the reference and the measured nucleus to the uncertainty of the final average for each studied nucleus. Large numbers of ions in the trap can cause the frequency to shift. At the time the yttrium isotopes were measured, it was not possible to record individual cycles, but rather an average over ten cycles was taken. It was therefore not possible to determine the number of ions in the trap at one time. To minimize

5 Table 1 Overview of the nuclides studied in this work. Given are the number N of resonance spectra taken, excitation time, the half-life, spin, and parity. Also given are the excitation energy, half-life, and spin and parity of known isomers with T1/2 > 150 ms as listed in the NUBASE evaluation [22]. ’#’ denotes estimated values, and ’()’ uncertain spin and/or parity. Isomer π π Nucleus N TRF [ms] T1/2 I Eexc [keV] T1/2 I 95Y 6 400 10.3 min 1/2− 96Y 5 1 400 5.34 s 0− 1140(30) 9.6 s (8)+ 97Y 4 2 400 3.75 s (1/2−) 667.51(23) 1.17 s (9/2)+ 98Y 2 600 548 ms (0)− 410(30) 2.0 s (5+, 4−) 99Y 5 400 1.47 s (5/2+) 100Y 10 400, 600 3 735 ms 1−, 2− 200#(200#) 940 ms (3,4,5)+# 101Y 5 400 426 ms (5/2+) 100Nb 7 800 1.5 s 1+ 470(40) 2.99 s 5+ 101Nb 3 600 7.1 s (5/2#)+ 102Nb 3 800 1.3 s 1+ 130(50) 4.3 s high 103Nb 3 600 1.5 s (5/2+) 104Nb 3 800 4.9 s (1+) 220(120) 940 ms high 105Nb 3 600 2.95 s 5/2+# 106Nb 4 600 920 ms 2+# 107Nb 2 200 300 ms 5/2+# 1 The isomeric state was measured separately 6 times. 2 The measured state was actually the isomeric state. The ground state mass was then calculated using the literature value for the excitation energy. 3 Five spectra were taken with 400 ms excitation time, and ﬁve with 600 ms. frequency shifts, the count rate was kept low (≤ 2 ions on average) already during the measurement. As a remaining conservative uncertainty an additional 0.05 Hz (≈ 5 · 10−8 or 5 keV for A = 100) was added to the uncertainty of the frequencies when calculating the average frequency ratio. When the niobium isotopes were measured, individual cycles were recorded, and, where suﬃcient statistics were available, a count rate class analysis was conducted [23] 1 , and the frequency shift inferred based on those results. The count rate of all measurements was then limited to three ions in the analysis. Therefore,

1 In the count rate class analysis all recorded ions were included when dividing the data into classes, not just the ones in the time-of-ﬂight window marked in Fig. 2(a).

6 300

250 Isomeric state 200

150 Ground state Counts 100

0 -20 -10 0 10 20 ν RF-1120336 (Hz) Fig. 3. Cooling resonance from the purification trap of 96Y and 96Ym with 60 ms excitation time. The two states are clearly separated. the additional uncertainty was smaller than for the yttrium isotopes. The effect, based on the conducted count rate class analyses and accounting for three ions in the trap, was 0.025 Hz. To compensate for short-term fluctuations of the magnetic field and of the electronics, the fluctuation of the references from one measurement to the next was examined. The average discrepancy was found to be of the order of 0.05 Hz for the yttrium isotopes and 0.025 Hz for niobium, probably due to optimised timings and potentials. Since these fluctuations are assumed to be random, this value was quadratically added to the statistical uncertainty of each measured frequency; its influence decreases with an increasing number of measurements for the nuclide.

3.1 Isomeric states of yttrium

Several of the studied isotopes have isomeric states. These states, as listed in the Nubase evaluation [22], are given in Table 1. The isomeric state in 96Y has large enough an excitation energy to be separated already in the puriﬁcation trap, as shown in Fig. 3. It was therefore possible to study both states independently.

For 97Y, the isomeric state was dominant, see Fig. 4, so the quadrupole frequency in the purification trap was chosen to obtain only this state. A time- of-flight resonance spectrum is shown in Fig. 5, confirming that indeed a clean sample was injected into the precision trap. The mass of the isomeric state was measured and the ground state mass was obtained using the isomeric excitation energy measured by γ-spectroscopy.

7 120 Counts

100

40 Counts in resonance 20

440 420 s) µ 400 380 360 340 Time of flight ( 320 ToF 300 Fit -10 -5 0 5 10 ν RF-1108656 (Hz)

Fig. 4. A time-of-flight cyclotron resonance spectrum of 97Y and 97Ym with 400 ms excitation time. The top panel shows the counts when setting a gate on the ions with highest radial energy, i.e. shortest time of flight, similar to Fig. 2(a). The quadrupole frequency in the purification trap was set to the cyclotron frequency of the ground state.

In the case of 98Y only one resonance was observed. Since laser spectroscopic studies of this nuclide conﬁrmed a higher production cross section for the ground state [6], it was concluded that indeed the ground state mass was measured. It is possible that a slight contamination due to the excited isomeric state was present, see Fig. 6. This possible contamination was, however, by far too small for reliable ﬁtting of two resonances. A conservative systematic uncertainty of 0.1 Hz (≈ 10−7) was added to account for frequency shifts caused by the isomeric contamination.

The heaviest yttrium isotope with a known isomeric state is 100Y. Both states were observed in the trap. It was, however, not possible to completely sepa-

8 500 35 450 30

400

s) 25 µ

20 350

Time of flight ( 300 Counts in resonance 10

250 5

200 0 -8 -6 -4 -2 0 2 4 6 8 -8 -6 -4 -2 0 2 4 6 8 ν ν RF-1108653 (Hz) RF-1108653 (Hz) (a) (b)

Fig. 5. (a) A time-of-flight cyclotron resonance spectrum of 97Ym with 400 ms excitation time. Shown in (b) are the counts when setting a gate on the fast ions, similar to Fig. 2(a). The quadrupole frequency in the purification trap was set to favour the isomeric state. rate them, as shown in Fig. 7. To verify that indeed two states are present, an on-resonance count rate spectrum was obtained by gating on the time of flight for fast ions, see Fig. 8. Figure 8(a) shows all detected ions and their time of flight. In Fig. 8(b) only fast ions are counted, showing the frequencies at which ions in the trap were in resonance with the excitation frequency. Clearly, two peaks are visible. Since having both species in the trap simultaneously can introduce systematic shifts of the resonance frequencies, an additional uncertainty of 0.1 Hz (≈ 10 keV) was added to the final value.

3.2 Isomeric states of niobium

The isomeric states of 100,102,104Nb are discussed in detail in [20]. In 100Nb, the isomeric state was found to be dominant (≈ 85%). The relative intensity of the ground state could be doubled by a longer storage time (4 s) in the purification trap before purification. The enhancement of the ground state relative to the excited isomeric state can be due to two reasons: either the ground state is the longer-lived state, contradicting the assignments given in Table 1, or the 100 enhancement is due to the decay of Zr (T1/2 = 7.1 s), which is produced more than twice as much as 100Nb and decays exclusively to the ground state of 100Nb. The authors of [20] point out that previous β-decay studies confirm the ground state to be the 1+ state, and the isomeric state the high-spin state. The ground state of 102Nb is produced more strongly than the isomeric state. A longer waiting time in the purification trap removed the isomeric state completely. The feeding from the decay of 102Zr is negligible in this case, as the production of 102Zr is far lower than that of 102Nb. This means that the

9 30 12 25 10 20 8

15 6 Counts

4 10 Counts in resonance

2 5

0 0 0 200 400 600 800 1000 -8 -6 -4 -2 0 2 4 6 8 ν Time of flight (µs) RF-1097292 (Hz) (a) (b)

500

450 s)

µ 400

350

300 Time of flight ( 250

200 −9 −6 −3 0 3 6 9 ν RF−1097292 (Hz) (c)

Fig. 6. (a) shows all counts vs time of flight for a measurement of 98Y with 600 ms excitation time. The peak at about 100 µs arising from decay in the trap is larger since the storage time is about the same as the half-life of 98Y. The vertical lines mark the time-of-flight window where the ions have the highest radial energy, used to obtain the count spectrum shown in (b). As can be seen in (b), there is a possible slight contamination due to the isomeric state seen as a peak at lower frequencies. (c) shows the corresponding time-of-flight resonance spectrum.

450 s)

µ 400

350 Time of flight (

300

−9 −6 −3 0 3 6 9 ν RF−1075272 (Hz)

Fig. 7. A time-of-ﬂight cyclotron resonance spectrum of 100Y and 100Ym with 600 ms excitation time. The vertical lines mark the ﬁtted resonance frequencies .

10 25 14

12 20

10 15 8 Counts 6 Counts 10

4 5 2

0 0 0 100 200 300 400 500 600 700 800 900 −8 −6 −4 −2 0 2 4 6 8 ν Time of flight (µs) RF−1075272 (Hz) (a) (b)

Fig. 8. Time-of-ﬂight measurements of 100Y and 100Ym with 600 ms excitation time. The peak in (a) at about 100 µs is again caused by ionisation due to decay. The vertical lines mark the time-of-ﬂight window where the ions have a high radial energy, used to obtain the count spectrum shown in (b). The lines are drawn to guide the eye.

380 360 340 320 s) µ 300 280 260

Time of flight ( 240 220 200 180 -15 -10 -5 0 5 10 15 ν RF-1004823 (Hz) Fig. 9. A time-of-ﬂight cyclotron resonance spectrum of 107Nb with 200 ms excitation time. The line represents the ﬁt.

ground state is the longer lived state, contradicting the literature values in Table 1. In the case of 104Nb, only one state was observed, even after 4 s additional waiting. The observed state must therefore be the longer lived one, which, according to Table 1 is the 1+ ground state. None of the heavier niobium isotopes have known isomeric states. Figure 9 shows a time-of-ﬂight resonance spectrum for 107Nb.

11 Table 2 ref νc Reference nuclides (Ref., all singly-charged), obtained frequency ratios meas for the νc singly-charged ions, and resulting mass excess values (ME) in keV. The difference between the new value and the AME03 value (Diff.) is given in the last column. ’#’ marks values based on extrapolation. ref νc Isotope Ref. meas ME (JYFL) [keV] ME (AME03) [keV] Diff. [keV] νc 95Y 97Zr 0.979381343(69) −81235 ± 7 −81207 ± 7 28 96Y 97Zr 0.989732208(70) −78341 ± 7 −78347 ± 23 −6 96Ym 97Zr 0.989749280(69) −76800 ± 7 −77206 ± 21 −406 97Y −76125 ± 8 −76258 ± 12 −133 97Ym 97Zr 1.000082958(74) −75458 ± 8 −75590 ± 12 −132 98Y 97Zr 1.010436763(88) −72299 ± 12 −72467 ± 25 −168 99Y 97Zr 1.020773794(73) −70654 ± 8 −70201 ± 24 453 100Y 97Zr 1.031129407(121) −67332 ± 12 −67290 ± 80 42 100Ym 97Zr 1.031131010(125) −67187 ± 12 −67090# ± 220# 97 101Y 97Zr 1.041473324(78) −65065 ± 8 −64910 ± 100 155 100Nb∗ 100Nbm 0.999996640(83) −79802 ± 20 −79939 ± 26 −137 100Nbm∗ 97Zr 1.030994733(22) −79488 ± 10 −79471 ± 28 17 101Nb 102Ru 0.990294436(39) −78883 ± 5 −78942 ± 19 −59 102Nb∗ 97Zr 1.051667579(28) −76309 ± 10 −76350 ± 40 −41 102Nbm∗ 102Nb 1.000000983(77) −76216 ± 20 −76220 ± 50 −4 103Nb 102Ru 1.009961485(41) −75020 ± 5 −75320 ± 70 −300 104Nb∗ 97Zr 1.072354888(30) −71823 ± 5 −72220 ± 100 −397 105Nb 102Ru 1.029641706(42) −69907 ± 5 −70850 ± 100 −943 106Nb 102Ru 1.039493991(43) −66195 ± 5 −67100# ± 200# −905 107Nb 102Ru 1.049333291(84) −63715 ± 9 −64920# ± 400# −1205 ∗ Taken from [20]

4 Results

The results are listed in Table 2 together with the values as listed in the AME03 [24]. The results for the niobium isotopes 100,102,104Nb are taken from [20]. The mass of the ground state of 97Y is calculated from the mass value of the isomeric state using the literature value of the excitation energy, Eexc = 667.51(23) keV.

12 Table 3 Previous measurements of yttrium. Isotope Method Result Reference 95Y (t,α) Q = 8294 ± 20 Flynn(1983) [26] 95 Y β Qβ = 4445 ± 5 Decker(1980) [27] 95 Y β Qβ = 4417 ± 10 Bloennigen(1984) [28] 96 Y β Qβ = 7120 ± 50 Decker(1980) [27] 96 Y β Qβ = 7079 ± 15 Bloennigen(1984) [28] 96 Y β Qβ = 7030 ± 70 Graefenstedt(1987) [29] 96 Y β Qβ = 7067 ± 30 Mach(1990) [30] 96 m Y β Qβ = 8237 ± 21 Gross(1992) [31] 97 Y β Qβ = 6702 ± 25 Bloennigen(1984) [28] 97 Y β Qβ = 6645 ± 70 Graefenstedt(1987) [29] 97 Y β Qβ = 6689 ± 13 Gross(1992) [31] 98 Y β Qβ = 8780 ± 30 Bloennigen(1984) [28] 98 Y β Qβ = 8840 ± 55 Graefenstedt(1987) [29] 98 Y β Qβ = 8963 ± 41 Mach(1988) [32] 98 Y β Qβ = 8830 ± 17 Gross(1992) [31] 99 Y β Qβ = 7605 ± 60 Graefenstedt(1987) [29] 99 Y β Qβ = 7568 ± 14 Gross(1992) [31] 100 Y β Qβ = 7920 ± 100 Iaﬁgliola(1984) [25] 100 Y β Qβ = 9310 ± 70 Graefenstedt(1987) [29] 101 Y β Qβ = 8545 ± 90 Gross(1992) [31]

In the following, the results given in Table 2 are compared in detail to previously measured values, and to the value given in the AME03 [24].

4.0.1 Yttrium

The previous measurements of the yttrium isotopes are listed in Table 3, and depicted in Fig. 10 together with the new values. The value obtained by Iafigliola et al. [25] for 100Y is not included in the figure due to considerable discrepancy. 95Y was previously measured by Flynn et al. [26] in a (t, α) reaction. The resulting mass value agrees with our value. The isotope was also studied by two groups employing β-endpoint measurements. The first of these measurements

13 200 Y95 Y96 Y96m Y97

100

-100

-200 ME(AME)-ME (keV) -300

-400 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) Flynn(1983) Mach(1990) Gross(1992) Gross(1992) Decker(1980) Decker(1980) Bloennigen(1984) Bloennigen(1984) Bloennigen(1984) Graefenstedt(1987) Graefenstedt(1987)

500 Y98 Y99 Y100 Y101 400

300

200

100

ME(AME)-ME (keV) -100

-200

-300 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) Mach(1988) Gross(1992) Gross(1992) Gross(1992) Gross(1992)* Gross(1992)* Bloennigen(1984) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987)* Graefenstedt(1987)*

Fig. 10. Comparison between previous literature values and the values presented in this work for the yttrium isotopes. For the literature values that were given as a reaction or decay Q-value, the mass excess of the daughter is taken from the AME03, or, when marked with an asterisk (*), from [7].

14 by Decker et al. [27] disagrees slightly with the result presented here, while the other [28] agrees. All other isotopes were studied only in β-endpoint measurements. The mass of 96Y was determined by four groups [27–30]. They all agree with this work. However, the previous measurement of the isomeric state disagrees with ours, the diﬀerence being ≈ 400 keV. Thus, the resulting excitation energy of 1541 ± 10 disagrees signiﬁcantly with the literature value of 1140 ± 30 [24]. All three measurements of 97Y give too low a mass by over 100 keV. In the case of 98Y, as well, three of the four measurements yield too high a binding energy [28,29,31]. The value by Mach et al. [32], however, agrees with our result. Both previous measurements of 99Y diverge considerably from our resulting mass value, which is smaller by over 400 keV. Taking the mass value for the daughter nucleus 99Zr from a previous JYFLTRAP measurement [7] worsens the situation. Possibly the feeding to a higher lying state remained unobserved in the β-decay spectroscopy. The new mass value of 100Y agrees with the AME03 value which is based on the measurement by Graefenstedt et al. [29]. If, however, the mass of the daughter 100Zr is again taken from [7], there is a discrepancy of over 200 keV, suggesting the Qβ-value to be incorrect. The same holds true for 101Y, where the AME03 value, based on Gross et al. [31], while giving too high a mass, is still in better agreement with our result than the original Qβ-value with the daughter taken from [7].

4.0.2 Niobium

Fig. 11 compares the results of the previous measurements, listed in Table 4, and our new values, given in Table 2. The masses of the niobium isotopes up to 105Nb have previously been determined from β-endpoint measurements conducted by Graefenstedt et al. [29]. In addition, the β-decay of 101Nb has been studied by Gross et al. [31], and the mass of 100Nbm was measured in a (t,3He) reaction. For all isotopes except 100,101Nb, the molybdenum daughter nuclei have previously been measured using JYFLTRAP [7]. However, only in the cases of 103,104Mo is the discrepancy between those values and the AME03 values large enough to signiﬁcantly alter the calculated mass excesses of the niobium isotopes. All β-endpoint measurements, except the one for 100Nbm, yield too large a binding energy. In the cases of 100Nb, 100Nbm, 102Nb and 102Nbm, the results agree with each other within uncertainties, while for 101Nb, they slightly dis- agree. For the heavier isotopes this discrepancy becomes more pronounced. Using the mass of the daughter nucleus given in [7] for 103Nb and 104Nb slightly increases this divergence. The old mass value of 105Nb diﬀers from our value by almost 1 MeV. 106Nb and 107Nb have not previously been measured, their respective AME03 values are based on extrapolation. Following the trend in the

15 100 Nb100 Nb100m Nb101 Nb102 Nb102m

-50

-100 ME(AME)-ME (keV) -150

-200 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) Gross(1992) Ajzenberg(1979) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987)*

400 Nb103 Nb104 Nb105 Nb106 Nb107 200 0 -200 -400 -600

ME(AME)-ME (keV) -800 -1000 -1200 JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP JYFLTRAP AME(2003) AME(2003) AME(2003) AME(2003) AME(2003) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987) Graefenstedt(1987)* Graefenstedt(1987)*

Fig. 11. Comparison between previous literature values and the values presented in this work for the niobium isotopes. For the literature values that were given as a reaction or decay Q-value, the mass excess of the daughter is taken from the AME03, or, when marked with an asterisk (*), from [7].

16 Table 4 Previous measurements of niobium. Isotope Method Result Reference 100 Nb β Qβ = 6245 ± 25 Graefenstedt(1987) [29] 100 m Nb β Qβ = 6745 ± 75 Graefenstedt(1987) [29] 100Nbm (t,3He) Q = −6690 ± 30 Ajzenberg-Selove(1979) [33] 101 Nb β Qβ = 4590 ± 30 Graefenstedt(1987) [29] 101 Nb β Qβ = 4569 ± 18 Gross(1992) [31] 102 Nb β Qβ = 7210 ± 35 Graefenstedt(1987) [34] 102 m Nb β Qβ = 7335 ± 40 Graefenstedt(1987) [34] 103 Nb β Qβ = 5530 ± 30 Graefenstedt(1987) [29] 104 Nb β Qβ = 8105 ± 90 Graefenstedt(1987) [34] 104 m Nb β Qβ = 8320 ± 80 Graefenstedt(1987) [34] 105 Nb β Qβ = 6485 ± 70 Graefenstedt(1987) [29] lighter isotopes, this extrapolation considerably underestimates both masses.

5 Discussion

5.1 Comparison to mass models

Since yttrium is known to undergo structural changes around N = 60, the measured mass values of the yttrium isotopes are compared to the predictions made by a selection of mass models to find out how well the models reproduce these features. The selected models cover a range of different approaches. The HFB-9 model is based on a mean field approach, and it is the most fundamental of the models considered here [35], while the FRDM (Finite Range Droplet Model) [36] represents the microscopic-macroscopic models, grafting shell model corrections onto the liquid-drop model. The model by Duflo and Zuker [37] separates the Hamiltonian into monopole and multipole terms, while the KTUY [38] mass formula separates global trends and fluctuations about them. The ETFSI-2 (extended Thomas-Fermi plus Strutinski integral) [39] calculations are based on density functional calculations. As can be seen in Fig. 12 all models underbind the lighter yttrium isotopes, while yielding too high a binding energy for the more neutron-rich nuclei. The transition happens between N = 58 and N = 60. It seems, therefore, that none of the models examined here correctly describes the observed structural changes in yttrium.

17 1500

1000

500

-500

-1000

-1500

ME(JYFL)-ME(model) (keV) HFB-9 FRDM -2000 Duflo-Zuker95 KTUY ETFSI-2 -2500 56 57 58 59 60 61 62 Neutron number N Fig. 12. Comparison of the experimental yttrium masses to model predictions. It should be noted, however, that all the models ﬁt several parameters to experimental data. Thus, the observed deviations from the new measurements, similar in all models, might be due to wrong input data used for the ﬁtting of the model parameters rather than the physics of the models. An example of systematically wrong input data are the niobium masses presented in this paper, and also the new mass values for strontium, zirconium and molybdenum [7], which, too, display a systematic divergence from the old values. The trend observed for the yttrium isotopes largely continues for the niobium isotopes, Fig. 13, with most models predicting too large a binding energy beyond N = 60. The ETFSI-2 model, however, shows a fairly good agreement. The HFB-9 predictions display strong odd-even staggering. It is interesting to note that for the heavier niobium isotopes the FRDM and the ETFSI-2 models show better agreement with the new data than the AME03 values.

5.2 Two-neutron separation energy

For neutron-rich nuclides, a good indicator of structural changes is the two- neutron separation energy S2n = −ME(A, Z)+ME(A−2, Z)+2·ME(n). The two-neutron separation energy for the neutron-rich isotopes between strontium and molybdenum is plotted in Fig. 14, using the results from this work and from [7], together with the relative mean-square charge radii δhr2i for strontium, yttrium and zirconium, taken from [4–6]. The kink in the two-neutron separation energy observed in zirconium around N = 60 was already discussed in [7]. The new data, however, show that this eﬀect is even more pronounced in yttrium. This is reﬂected in the charge radii, where both elements display a steep increase from N = 59 to N = 60, a feature that is clearly stronger in

18 2500 HFB-9 FRDM 2000 Duflo-Zuker95 KTUY 1500 ETFSI-2

1000

500

-500

ME(JYFL)-ME(model) (keV) -1000

-1500

-2000 56 57 58 59 60 61 62 63 64 65 66 Neutron number N Fig. 13. Comparison of the experimental niobium masses to model predictions. Additional data from [24] were used to extend the comparison to N = 56. yttrium than in zirconium. Unfortunately, at this point no data regarding the charge radii of niobium are available. When plotting the two-neutron separation energy as a function of proton number Z, shell gaps and structural changes become very obvious, since a smooth behavior would result in parallel lines for diﬀerent neutron numbers N. Figure 15 shows that this is not the case in this region. The sub shell gap at N = 56 becomes narrower when going further from stability, while the gap at N = 54 widens. The two-neutron separation energies of the isotones of N = 60 and N = 62 are inverted at Z = 40, while those of N = 59 and N = 60 are inverted up to Z = 41 with a big gap between N = 57 and N = 59 at Z = 40. In these ﬁgures the greatest deviation from the expected smooth trend is seen in zirconium around N = 60. For Z ≥ 42, on the other hand, the isotone lines run almost parallel, indicating the stability of the structure in these nuclides.

5.3 Valence proton-neutron interactions

Another interesting parameter used to analyse nuclear structure is the average empirical proton-neutron interaction energy δVpn, which, for nuclei with oe odd proton number and even neutron number, is given by δVpn (Z,N) = 1 2 ([B(Z,N) − B(Z,N − 2)] − [B(Z − 1,N) − B(Z − 1,N − 2)]), and is shown in Fig. 16. Brenner et al. [41] report several anomalies in the region covered here, namely concerning 101Nb, and 99Y and 101Y. It seems, however, that niobium and yttrium have been mislabelled in the relevant plot (Fig. 4 in [41]), and also the aforementioned anomalies are interchanged, i.e. they con- 99 101 103 101 cern Y, and Nb and Nb. The sharp peak of δVpn at Nb is even more

19 Sr 2 Y Zr 1.8 )

2 1.6

(fm β = 0.3 1.4 2 β β 2 = 0.2 2 = 0.4

N-50,N 1.2 > 2

δ 1

0.8 β 0.6 2 = 0.1

Sr 16 Y Zr Nb 15 Mo

13 (MeV) 2n S 12

54 56 58 60 62 64 66 68 Neutron number Fig. 14. Two-neutron separation energies (bottom) for strontium, yttrium, zirconium, niobium and molybdenum, and relative mean-square charge radii (top) for the strontium, yttrium and zirconium isotopes around N = 60, droplet model isodeformation lines [6] for yttrium are shown dashed. pronounced using the new data, with 101Nb lying higher and 103Nb lying lower than before. A similar discontinuity had been observed for 99Y and 101Y, with a sudden decrease at 99Y and a sharp increase towards 101Y. This anomaly has now been replaced by a relatively smooth behaviour.

6 Conclusions

The masses of 19 neutron-rich isotopes of yttrium and niobium were measured with great precision, in most cases with a relative uncertainty of better than

20 16 N = 56 N = 62 15 N = 54

14 N = 58

12 (MeV) 2n S 11 N = 70 N = 72 N = 64 10 N = 66 N = 68 9 N = 60 8 36 38 40 42 44 46 Proton number Z

16 N = 59 N = 61 15 N = 63 N = 57 14 N = 55

12 (MeV) 2n S 11

10 N = 69 N = 73 N = 65 9 N = 59

8 36 38 40 42 44 46 Proton number Z

Fig. 15. Two-neutron separation energy as a function of proton number Z for nuclides around N = 60 and Z = 40. The errorbars are smaller than the symbols. Additional data were taken from [7,15,24,40].

21 800 Y Nb 700

600

500

(keV) 400 pn V δ 300

200

100

0 57 59 61 63 Neutron number N

Fig. 16. The empirical proton-neutron interaction energy δVpn for yttrium and niobium. The thick lines are calculated using the mass values from this work, the thin ones are from the AME03. 10−7. These new data complete the earlier work done at JYFLTRAP around Z = 40 and N = 60 [7]. The shape change that was observed in zirconium at N = 60 in that earlier work could be confirmed also in yttrium. Niobium and molybdenum, on the other hand, display a different behaviour. Here the change is far smoother with the heavier isotopes being triaxially deformed. The many isomeric states found in the isotopes studied in this work presented a challenge. However, in most cases it was possible to separate the different states. Combined with previous measurements conducted at JYFLTRAP, these new precision data remap the mass surface in this region of the nuclear chart. They provide new information on nuclear structure and serve as a benchmark for mass predictions. The measured masses can provide reliable input for mass models to improve their predictive power towards the astrophysical r-process path.

Acknowledgements

This work has been supported by the Academy of Finland under the Finnish Centre of Excellence Programme 2000-2005 (Project No. 44875, Nuclear and Condensed Matter Physics Programme at JYFL) and the Finnish Centre of Excellence Programme 2006-2011 (Nuclear and Accelerator Based Physics Programme at JYFL).

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