Proton capture reactions and nuclear structure Proton capture reactions and nuclear structure Protonvangstreacties en kernstructuur (met een samenvat ting in het Nederlands) PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Rijksuniversiteit te Utrecht, op gezag van de rector magnificus prof. dr. J.A. van Ginkel, volgens besluit van het College van Decanen in het openbaar te verdedigen op woensdag 18 oktober 1989 des namiddags te 12.45 uur door Sybren Wouter Kikstra geboren op 14 augustus 1962 te Almelo PROMOTOR: PROF. DR. C. VAN DER LEUN Dit werk is een onderdeel van het onderzoeksprogramma van de "Stichting voor Fundamenteel Onderzoek der Materie" (FOM), die financieel gesteund wordt door de "Nederlandse Organisatie voor Wetenschappelijk Onderzoek" (NWO). Adagio cuUbilr — Ludwig van Beethoven Contents 1 Introduction 9 1.1 Historical notes 9 1.2 Proton capture reactions 10 1.3 Resonant absorption 11 1.4 Summary 11 2 Resonant absorption by the lowest two T = 3/2 levels of 9Be 15 2.1 Introduction 15 2.2 Experimental 16 2.3 Measurements and data analysis 18 2.4 Results 20 2.5 Theory and discussion 22 2.5.1 The Ex = 14.393 MeV, J*;T = 3/2"; 3/2 level 24 2.5.2 The Ex = 16.975 MeV, J*;T = 1/2"; 3/2 level 25 3 Superallowed 42Sc(/?+)42Ca decay 31 3.1 Introduction 31 3.2 The 41Ca(n,7)42Ca measurements 32 3.3 The 41Ca(p,7)42Sc measurements 32 3.3.1 Experimental 32 42 3.3.2 Determination of 5p( Sc) 35 3.3.3 Levels of 42Sc 38 3.4 The 42Sc->42Ca superallowed ft value 41 4 Investigation of the 40Ca level scheme 51 4.1 Introduction 51 4.2 Experimental 52 39 4.3 The K+p resonances for Ep = 0.3-2.9 MeV 53 4.3.1 Measurements 53 4.3.2 Analysis 53 4.3.3 Results and discussion 60 Contents 4.4 Gamma-ray spectra 65 4.4.1 Measurements 65 4.4.2 Analysis 65 4.4.3 Results and discussion 70 4.5 Shell model calculations 81 4.5.1 Introduction 81 4.5.2 The WBMB interaction 83 4.5.3 Calculations 83 4.5.4 Results and discussion 85 4.6 Summary and conclusions 91 Statistical nuclear spin assignments 95 5.1 Introduction 95 5.2 Average spins 95 5.3 Weighted averages 99 5.4 Chi-squared tests 102 5.4.1 Resonances 102 5.4.2 Bound states 108 5.5 New assignments 109 5.6 Summary and conclusion 109 Appendix 113 Samenvatting 115 Nawoord 117 Curriculum vitae 119 Chapter 1 Introduction In this thesis experimental studies are described of the structure of some atomic nuclei. Where possible, an attempt has been made to interpret the results of the measurements in terms of existing models. The 40Ca and 42Sc nuclides were excited by bombarding 39K and 41Ca targets, respectively, with low energy protons (Ep = 0.3-3.0 MeV), that were produced by the Utrecht 3 MV Van de GraafF accelerator. From the measured energy and intensity of the 7-rays created in the subsequent decay of the nuclei, accurate information was obtained on the existence and properties of their excited states. The nuclear reactions of this type are referred to as proton-capture or (p,7) reactions. In addition, properties of two levels at high excitation energy of the 9Be nucleus were investigated. These levels were excited by the resonant absorption of 7-rays from the nB(p,7)12C reaction. The above, essentially independent investigations are described in chapters 2-5 of this thesis in the style presently required by the international physics journals, i.e. rather concisely. The purpose of the rest of this introduction is to provide the reader with some background information which may be considered 'common knowledge' in publications. We will start with some historical notes, proceed with a short discussion of the merits of capture reactions and resonant absorption in nuclear spectroscopy, and finally give some details specific to the above mentioned subjects of this thesis. 1.1 Historical notes The discovery by Pose [1] in 1929 of a resonant effect in the bombardment of a thin aluminum foil with a-particles from a radioactive source, marks the start of the exploitation of resonances in capture reactions for obtaining data on properties of nuclear energy levels. In 1935, resonances in the yield of a proton induced reaction were observed by Hafstadt and Tuve [2] who used a 10 Introduction Van de Graaff accelerator, and narrow (few keV) separated (p,7) resonances were first measured with a Geiger Miiller counter by Tangen [3] during world war II. Giant steps forward in the detection techniques were made around 1955, when the high efficiency Nal detectors became generally available, and again in 1966 with the introduction of high-resolution semiconductor detectors of the Ge(Li) type. Presently, Ge and Ge(Li) detectors are used, often surrounded by a scintillator which is effective in the reduction of the counting of unwanted background radiation [4,5]. Nal detectors are still in use when energy resolution is less important than efficiency [6]. The importance of the developments in computer facilities and data acquisition techniques hardly needs mentioning. 1.2 Proton capture reactions Proton capture resonance reactions are an excellent tool for nuclear structure investigations. Firstly, the reaction process is very well understood. Provided that the reaction proceeds through separated resonances, which is the case when the bombarding energy is not too high, the compound system has a well-defined angular momentum and the unquestioned single-level Breit-Wigner theory may be applied. Secondly, the electromagnetic interaction is the best understood of all four fundamental interactions; the results of electromagnetic theory and experiment agree on the 1 ppm level. The strength of the electromagnetic in- teraction is ideal; it is sufficiently large to cause easily observable effects of the charge and current distribution in the nucleus, and small enough, compared to the strong interaction, to validate the application of perturbation theory for the analysis of the observed effects. The above considerations imply that the results of the measurements are model-independent, and consequently the data may be treated statistically. The availability, in most cases, of a variety of resonances with different spins and parities favourably distinguishes the (p,7) reaction from e.g. thermal neu- tron capture. Specific bound states may thus be excited with different intensities at different (p,7) resonances, which is especially advantageous in the identifica- tion and disentanglement of close doublets [4]. It should be mentioned, however, that the (p,7) and (n,7) reactions are complementary in that there are no p- and sd-shell nuclei which can be studied in both reactions. Another advantage of (p,7) reactions is the possibility to measure the lifetimes of nuclear excited states from the observed Doppler shifts of the energies of 7-rays emitted by the recoiling final nucleus [4,5]. The power of (p,7) reactions in combination with a good detector system was beautifully demonstrated in the study by Endt et al. [7] of 26A1, which is now by far the best known nucleus in the sd-shell. The data are ideally suited Resonant absorption 11 for tests of chaos theory (see e.g. [8]), for which complete (no missing levels) and pure (correct spin assignments) data are of utmost importance. The availability of complete and pure information has prompted the study of a new method for the assignment of nuclear level spins, which is discussed in chapter 5 of this thesis. For further reading the reader is referred to refs. [9-11]. 1.3 Resonant absorption As was first shown in 1957 [12,13], it is feasible to use proton capture resonances as a source of tuneable monoenergetic 7-rays to excite nuclear levels. A 7- ray energy slightly higher than the excitation energy of the level is needed to compensate for the recoil energy losses at emission and absorption. The angle dependence of the Doppler shift provides the energy tuneability for obtaining a resonant dip in the transmission cross section, which contains the nuclear structure information. In the first experiments a level was 'self-excited' by the Doppler-shifted decay 7-rays of that same level. The feasibility of 'cross excitation' of a level in one nucleus by a 7-ray from another nucleus was first demonstrated by Sparks et al. [14]. The resonant absorption method is reviewed in ref. [15]. 1.4 Summary Chapter 2 describes an investigation of the lowest two T = 3/2 levels of 9Be. As shown schematically in fig. 1.1, these levels were excited by 7-rays arising from broad resonances in the nB(p,7)12C reaction. The results of the measurements are interpreted by a comparison to the analogue /?-decay of 9Li and to shell model calculations. The basic idea behind the experiments presented in chapter 3 is contained in the following equations + Trip = m42Sc + Sp, and thus Tl = ~ ' «ca Sn — Sp + mp — mn, where m denotes the mass in energy units, and 5n and Sp are the neutron separation energy in 42Ca and the proton separation energy in 42Sc, respectively. Fig. 1.2 illustrates the situation in the form of simplified level schemes. The total decay energy of the superallowed 0+ —• 0+ /?+ transition between the ground states of 42Sc and 42Ca was thus determined accurately by measure- 42 42 ments in Utrecht of Sp of Sc and in Oak Ridge of Sa of Ca. The results were 12 Introduction f,x(MeV) f,T £x (MeV) (MeV) 18.83 .