Approximate Symmetries in the Interacting Boson Model……………………37-42 Dennis Bonatsos
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Arxiv:2010.09509V2 [Hep-Ph] 2 Apr 2021 in Searches for CLFV Or LNV, Incoming Muons Are the Source of Both the Μ → E Signal and the RMC Back- Ground
FERMILAB-PUB-20-525-T The high energy spectrum of internal positrons from radiative muon capture on nuclei Ryan Plestid1, 2, ∗ and Richard J. Hill1, 2, y 1Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506, USA 2Theoretical Physics Department, Fermilab, Batavia, IL 60510,USA (Dated: April 5, 2021) The Mu2e and COMET collaborations will search for nucleus-catalyzed muon conversion to positrons (µ− ! e+) as a signal of lepton number violation. A key background for this search is radiative muon capture where either: 1) a real photon converts to an e+e− pair “externally" in surrounding material; or 2) a virtual photon mediates the production of an e+e− pair “internally”. If the e+ has an energy approaching the signal region then it can serve as an irreducible background. In this work we describe how the near end-point internal positron spectrum can be related to the real photon spectrum from the same nucleus, which encodes all non-trivial nuclear physics. I. INTRODUCTION Specifically, on a nucleus (e.g. aluminum), the reaction µ− + [A; Z] ! e+ + [A; Z − 2] ; (1) Charged lepton flavor violation (CLFV) is a smok- ing gun signature of physics beyond the Standard Model becomes a viable target for observation (see also [7]). (SM) and is one of the most sought-after signals at the While neutrinoless double beta (0νββ) decay is often intensity frontier [1–4]. Important search channels in- touted as the most promising direction for the discovery volving the lightest two lepton generations are µ ! 3e, of LNV, there do exist extensions of the SM that predict µ ! eγ, and nucleus-catalyzed µ ! e [1–6]. -
The Interacting Boson Model
The interacting boson model P. Van Isacker, GANIL, France Dynamical symmetries of the IBM Neutrons, protons and F-spin (IBM-2) T=0 and T=1 bosons: IBM-3 and IBM-4 Symmetries in N~Z nuclei (III), Valencia, September 2003 The interacting boson model • Nuclear collective excitations are described in terms of N s and d bosons. • Spectrum generating algebra for the nucleus is U(6). All physical observables (hamiltonian, transition operators,…) are expressed in terms of the generators of U(6). • Formally, nuclear structure is reduced to solving the problem of N interacting s and d bosons. Symmetries in N~Z nuclei (III), Valencia, September 2003 Justifications for the IBM • Bosons are associated with fermion pairs which approximately satisfy Bose statistics: (0) ( 2) S + = a a+ ¥ a + Æ s+ , D+ = a a+ ¥ a + Æ d +  j ( j j )0 m  jj '( j j' )m m j jj ' • Microscopic justification: The IBM is a truncation and subsequent bosonization of the shell model in terms of S and D pairs. • Macroscopic justification: In the classical limit (N Æ ∞) the expectation value of the IBM hamiltonian between coherent states reduces to a liquid-drop hamiltonian. Symmetries in N~Z nuclei (III), Valencia, September 2003 Algebraic structure of the IBM • The U(6) algebra consists of the generators U(6) = s +s,s+ d ,d + s,d + d , m,m' = -2, ,+2 { m m m m' } K • The harmonic oscillator in 6 dimensions, +2 + + H = ns + nd = s s +  dm dm = C1[U(6)] ≡ N m = -2 • …has U(6) symmetry since "gi ŒU(6) : [H,gi ]= 0 • Can the U(6) symmetry be lifted while preserving the rotational -
EVE Xe ISOTOPES by the FRAMEWORK of IBA Đsmail Maraş , Ramazan Gümüş and Nurettin Türkan Celal
Mathematical and Computational Applications , Vol. 15, No. 1, pp. 79-88, 2010. © Association for Scientific Research THE IVESTIGATIO OF EVE-EVE 114-120 Xe ISOTOPES BY THE FRAMEWORK OF IBA Đsmail Maraş 1*, Ramazan Gümüş 2 and Nurettin Türkan 3,4 1Celal Bayar University, Faculty of Arts and Science, Manisa, Turkey [email protected] 2Celal Bayar University, Institute of Science, Manisa, Turkey [email protected] 3University of Wisconsin, Department of Physics, 53715 Madison, WI, USA 4Bozok University, Faculty of Arts and Science, 66200 Yozgat, Turkey [email protected] Abstract- In this work, the ground state, quasi beta and quasi gamma band energies of 114,116,118,120 Xe isotopes have been investigated by using the both (IBM-1 and IBM-2) versions of interacting boson model (IBM). In calculations, the theoretical energy levels have been obtained by using PHINT and NP-BOS program codes. The presented results are compared with the experimental data in respective tables and figures. At the end, it was seen that the obtained theoretical results are in good agreement with the experimental data. Key Words- Interacting Boson Model, Even-Even Xe, Band Energies (Ground State, Quasi Beta and Quasi Gamma Band). 1. ITRODUCTIO One of the most remarkable simplicities of atomic nuclei is that the thousands of 2-body nucleonic interactions in a nucleus can be reduced to and simulated by a 1-body potential [1]. This is done with the interacting boson model (IBA) [2], which is a useful model to formalize description of symmetry in nuclei. This model (IBA) has a U(6) group structure leading to sub-groups chains denoted by U(5), SU(3) and O(6), which describe vibrational, axially symmetric rotational and γ-soft rotational nuclei. -
Generalized Interacting Boson Model and the Collective Behaviour in Nuclei
PramS.a, Vol. 17, No. 5, November 1981, pp. 381-387. © Printed in India Generalized interacting boson model and the collective behaviour in nuclei M SUGUNA, R D RATNA RAJU and V K B KOTA* Theoretical Group, Department of Physics, Andhra University, Waltair 530 003, India *Department of Physics and Astronomy, University of Rochester, Rochester, New York, USA *Permanent Address: Physical Research Laboratory, Ahmedabad 380 009, India MS received 9 May 1981 ; revised 3 October 1981 Abstract. The effect of including the high spin bosons on the manifestation of collec- tive behaviour in nuclei is examined by plotting the B(E2; 2+ ~ 0+) rates as a function of neutron number for various values of )/, where ~ is the highest angular momentum of the bosons included in the calculation. B(E2; 2+ ~ 0 +) values of a large number of nuclei in various regions of the nuclear periodic table are calculated with a single value for the effective charge in the generalized scheme. Irreducible representations of SU(3) contained in the symmetric partition [N] of U(15) are worked out for integers N upto N = 15, to enable the explicit inclusion of the g boson into calculations. The experimentally observed odd-K bands in 284U and 184W are described as a direct conse- quence of the g boson. Keywords. Generalized interacting boson model; irreducible representations; sym- metric partitions; g boson. 1. Introduction The interacting boson model 0~M) of Arima and Iachello (1976, 1978) describes the collective properties of nuclei by considering pairs of protons and neutrons coupled to S = 0 and J -----L = 0, and 2. -
Investigation of Shape Coexistence in Te Isotopes
Investigation of shape coexistence in 118-128Te isotopes H. Sabria1, Z. Jahangirib, M. A. Mohammadia a Department of Physics, University of Tabriz, Tabriz 51664, Iran. b Physics Department, Payame Noor University, Tehran 19395-4697, Iran. 1 Corresponding Author E-mail: [email protected] 1 Abstract In this paper, we have considered the interplay between phase transitions and configuration mixing of intruder excitations in the 118-128Te isotopes. A transitional interacting boson model Hamiltonian in both IBM-1 and IBM-2 versions which are based on affine SU (1,1) Lie Algebra are employed to describe the evolution from spherical to deformed gamma unstable shapes along the chain of Te isotopes. The excitation energies, B(E0) and B(E2) transition rates are rather well reproduced in comparison with experimental counterparts when the weight of SO(6) limit is increased in Hamiltonian. Also our results show obvious relations between the configuration mixing ratio and quadrupole, hexadecapole and hexacontatetrapole deformation values in this isotopic chain. Keywords: intruder states; Interacting Boson Model (IBM); infinite dimensional algebra; energy levels; B(E0) and B(E2) transition probabilities. PACS: 21.60.Fw; 21.10.Re; 27.60.+j 1. Introduction Shape coexistence has been observed in many mass regions throughout the nuclear chart and has become a very useful paradigm to explain the competition between the monopole part of the nuclear effective force that tends to stabilize the nucleus into a spherical shape, in and near to shell closures, and the strong correlations (pairing, quadrupole in particular) that favors the nucleus into a deformed shapes in around mid-shell regions [1-15]. -
4 Muon Capture on the Deuteron 7 4.1 Theoretical Framework
February 8, 2008 Muon Capture on the Deuteron The MuSun Experiment MuSun Collaboration model-independent connection via EFT http://www.npl.uiuc.edu/exp/musun V.A. Andreeva, R.M. Careye, V.A. Ganzhaa, A. Gardestigh, T. Gorringed, F.E. Grayg, D.W. Hertzogb, M. Hildebrandtc, P. Kammelb, B. Kiburgb, S. Knaackb, P.A. Kravtsova, A.G. Krivshicha, K. Kuboderah, B. Laussc, M. Levchenkoa, K.R. Lynche, E.M. Maeva, O.E. Maeva, F. Mulhauserb, F. Myhrerh, C. Petitjeanc, G.E. Petrova, R. Prieelsf , G.N. Schapkina, G.G. Semenchuka, M.A. Sorokaa, V. Tishchenkod, A.A. Vasilyeva, A.A. Vorobyova, M.E. Vznuzdaeva, P. Winterb aPetersburg Nuclear Physics Institute, Gatchina 188350, Russia bUniversity of Illinois at Urbana-Champaign, Urbana, IL 61801, USA cPaul Scherrer Institute, CH-5232 Villigen PSI, Switzerland dUniversity of Kentucky, Lexington, KY 40506, USA eBoston University, Boston, MA 02215, USA f Universit´eCatholique de Louvain, B-1348 Louvain-la-Neuve, Belgium gRegis University, Denver, CO 80221, USA hUniversity of South Carolina, Columbia, SC 29208, USA Co-spokespersons underlined. 1 Abstract: We propose to measure the rate Λd for muon capture on the deuteron to better than 1.5% precision. This process is the simplest weak interaction process on a nucleus that can both be calculated and measured to a high degree of precision. The measurement will provide a benchmark result, far more precise than any current experimental information on weak interaction processes in the two-nucleon system. Moreover, it can impact our understanding of fundamental reactions of astrophysical interest, like solar pp fusion and the ν + d reactions observed by the Sudbury Neutrino Observatory. -
Status of the Alcap Experiment
Status of the AlCap experiment R. Phillip Litchfield∗† UCL E-mail: [email protected] The AlCap experiment is a joint project between the COMET and Mu2e collaborations. Both experiments intend to look for the lepton-flavour violating conversion m + A ! e + A, using ter- tiary muons from high-power pulsed proton beams. In these experiments the products of ordinary muon capture in the muon stopping target are an important concern, both in terms of hit rates in tracking detectors and radiation damage to equipment. The goal of the AlCap experiment is to provide precision measurements of the products of nuclear capture on Aluminium, which is the favoured target material for both COMET and Mu2e. The results will be used for optimising the design of both conversion experiments, and as input to their simulations. Data was taken in December 2013 and is currently being analysed. 16th International Workshop on Neutrino Factories and Future Neutrino Beam Facilities - NUFACT2014, arXiv:1501.04880v1 [physics.ins-det] 20 Jan 2015 25 -30 August, 2014 University of Glasgow, United Kingdom ∗Speaker. †On behalf of the AlCap Collaboration © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ Status of the AlCap experiment R. Phillip Litchfield 1. Muon to electron conversion and the motivation for AlCap The term ‘muon to electron conversion’ refers to processes that cause the neutrinoless decay of a muon into an electron, specifically those in which the muon is the ground-state orbit of an atomic nucleus.1 In this case the conservation of momentum and energy can be achieved by coherent interaction on the nucleus, i.e. -
Interacting Boson Model of Collective Octupole States (I)
Nuclear Physics A472 (1987) 61-84 North-Holland, Amsterdam INTERACTING BOSON MODEL OF COLLECTIVE OCTUPOLE STATES (I). The rotational limit J. ENGEL’ and F. IACHELLO A. W. Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06.511, USA Received 5 March 1987 Abstract: We discuss the problem of describing low-lying collective negative-parity states within the framework of the interacting boson model. We suggest that a simultaneous description of quadrupole and octupole states in nuclei be done in terms of the group U(16), which includes f- and p-bosons in addition to the usual d- and s-bosons. We analyze the dynamical symmetries associated with the rotational limit of this model and discuss their classical (large-N) analogs. We conclude with a preliminary application of the model to the radium isotopes. 1. Introduction Low-lying collective nuclear states are dominated by the occurrence of quadrupole vibrations and deformations. Their properties can be described in terms of shape variables, aZcL (CL= 0, kl, *2), ref ‘) or alternatively in terms of interacting s- and d-bosons with Jp = O+ and Jp = 2+ respectively ‘). The role played by d-bosons is easily understood since they can be thought of as a quantization of the variables (yzcI. The introduction of s-bosons is less obviously necessary and arose from a study of the underlying microscopic structure which led to an interpretation of bosons in terms of nucleon pairs ‘). It reflects the existence in nuclei of a pairing interaction in addition to the quadrupole interaction. An important consequence of the introduc- tion of s-bosons is that it facilitates phenomenological descriptions of spectra. -
Subject Categories and Scope Descriptions Co Q
International Nuclear Information System (INIS) • LU Q CD XA0202260 D) c CO IAEA-ETDE/TNIS-2 o X LU CO -I—• SUBJECT CATEGORIES AND SCOPE DESCRIPTIONS CO Q ETDE/INIS Joint Reference Series No. 2 CT O c > LU O O E "- =3 CO I? O cB CD C , LU • CD 3 CO -Q T3 CD >- c •a « C c CD o o CD «2 i- CO .3-3/33 CO ,_ CD a) O % 3 O •z. a. Renewable energy technologies • Radiation protection • Energy storage, conversion, and consumption Radioactive waste management • Energy policy • Radiation effects on living organisms • Fossil fuels INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, JULY 2002 ETDE/INIS Joint Reference Series No. 2 SUBJECT CATEGORIES AND SCOPE DESCRIPTIONS INTERNATIONAL ATOMIC ENERGY AGENCY VIENNA, JULY 2002 SUBJECT CATEGORIES AND SCOPE DESCRIPTIONS IAEA, VIENNA, 2002 IAEA-ETDE/INIS-2 ISBN 92-0-112902-5 ISSN 1684-095X © IAEA, 2002 Printed by the IAEA in Austria July 2002 PREFACE This document is one in a series of publications known as the ETDE/INIS Joint Reference Series. It defines the subject categories and provides the scope descriptions to be used for categorization of the nuclear literature for the preparation of INIS input by national and regional centers. Together with volumes of the INIS Reference Series and ETDE/INIS Joint Reference Series it defines the rules, standards and practices and provides the authorities to be used in the International Nuclear Information System. A list of the volumes published in the IMS Reference Series and ETDE/ENIS Joint Reference Series can be found at the end of this publication. -
Phase Diagram of the Proton-Neutron Interacting Boson Model
PHYSICAL REVIEW LETTERS week ending VOLUME 93, NUMBER 21 19 NOVEMBER 2004 Phase Diagram of the Proton-Neutron Interacting Boson Model J. M. Arias,1 J. E. Garcı´a-Ramos,2 and J. Dukelsky3 1Departamento de Fı´sica Ato´mica, Molecular y Nuclear, Facultad de Fı´sica, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain 2Departamento de Fı´sica Aplicada, Universidad de Huelva, 21071 Huelva, Spain 3Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain (Received 2 June 2004; revised manuscript received 3 September 2004; published 15 November 2004) We study the phase diagram of the proton-neutron interacting boson model with special emphasis on the phase transitions leading to triaxial phases. The existence of a new critical point between spherical and triaxial shapes is reported. DOI: 10.1103/PhysRevLett.93.212501 PACS numbers: 21.60.Fw, 05.70.Fh, 21.10.Re, 64.60.Fr Quantum phase transitions (QPT) have become a sub- IBM-1 there are three dynamical symmetries: SU(5), ject of great interest in the study of several quantum O(6), and SU(3). These correspond to well-defined nu- many-body systems in condensed matter, quantum optics, clear shapes: spherical, deformed -unstable, and prolate ultracold quantum gases, and nuclear physics. QPT are axial deformed, respectively. The structure of the IBM-1 structural changes taking place at zero temperature as a Hamiltonian allows to study systematically the transition function of a control parameter (for a recent review, see from one shape to another. There were some pioneering [1]). Examples of control parameters are the magnetic works along these lines in the 1980s [10–12], but it has field in spin systems, quantum Hall systems, and ultra- been the recent introduction of the concept of critical cold gases close to a Feshbach resonance, or the hole- point symmetry that has recalled the attention of the doping in cuprate superconductors. -
Description of Transitional Nuclei in the Sdg Boson Model
UM-P-91/102 . Description of transitional nuclei in the sdg boson model V.-S. Lac and S. Kuyucak School of Physics, University of Melbottrne, Parkville, Victoria 3052, Australia Abstract We study the transitional nuclei in the framework of the sdg boson model. This extension is necessitated by recent measurements of E2 and E4 transitions in the Pt and Os isotopes which can not be explained in the sd boson models. We show how 7-unstable and triaxial shapes arise from special choices of sdg model Hamiltonians and discuss ways of limiting the number of free parameters through consistency and coherence conditions. A satisfactory description of E2 and E4 properties is obtained for the Pt and Os nuclei, which also predicts dynamic shape transitions in these nuclei. \V ' i 1. Introduction Description of transitional nuclei has been one of the most challenging tasks for collective models of nuclei. A complicating feature of these nuclei is the triaxial nature of their energy surface which is neither 7-rigid as in the Davydov-Filippov model *) nor 7-unstable as in the Wilets-Jean model 2), but rather 7-soft which necessitates introduction of more elaborate geometric models such as the Generalized Collective Model3). More recently, the interacting boson model (IBM)4) has provided a very simple description for the transitional nuclei based on the 0(6) limit and its perturbations 5-6). The 0(6) limit had been especially successful in explaining the E2 transitions among the low-lying levels of the Pt isotopes 5_6). Its main shortcomings are (i) the energy surface is 7-unstable which leads to too much staggering in the quasi-7 band 7), (ii) the quadrupole moments vanish 8), (iii) the B(E2) values fall off too rapidly due to boson cut-off 9), (iv) it fails to describe the E4 properties 10-18). -
Radiative Muon Capture on Carbon, Oxygen and Calcium
TRI-PP -90-21 May 1990 Radiative muon capture on carbon, oxygen and calcium D.S. Armstrong/") S. Ahmad/6) R.A. Burnham/C) T.P. Gorringe.W M.D. Hasinoff, A.J. Larabee<e>, and C.E. Waltham University of British Columbia, Vancouver, B.C., Canada V6T 2A6 G. AzuelosO, J.A. Macdonald, T. Numao and J-M. Poutissou TRIUMF, Vancouver, B.C., Canada VST 2A3 M. Blecher and D.H. Wright'^ Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 E.T.H. Clifford^) and J. Summhammer*1' TRIUMF and University of Victoria, Victoria, B.C., Canada V8W 2Y2 P. Depommier and R. Poutissou Universile de Montreal, Montreal, P.Q., Canada II3C 3J7 H. Mes National Research Council of Canada, Ottawa, Canada KlA OR6 B.C. Robertson Queen's University, Kingston, Ontario, Canada K7L 3N6 The photon energy spectra from radiative muon capture on 12C,16 O and 40Ca have been measured using a time projection chamber as a pair spec- trometer. The branching ratio for radiative muon capture is sensitive to <7P, the induced pseudoscalar coupling constant of the weak interaction. Ex- pressed in terms of the axial-vector weak coupling constant ga, values of 40 16 ffp/So = 5.7 ± 0.8 and gp/ga = 7.3 ± 0.9 are obtained for Ca and O respectively, from comparison with phenomenological calculations of the nu- clear response. From comparison with microscopic calculations, values of {oT 4 Ca 16 and 12 gp/ga = 4.6± 1.8, 13.6 +}|, and 16.2 ±J$ ° . °. C, respec- •:« tively are obtained.