Comparison of shell model results for some properties of even-even Ge isotopes

Abstract

In this work we examine two recent effective shell model interactions, JUN45 and JJ4B, that have been proposed for use in the f 5/2 , p 3/2 , p 1/2 , g 9/2 model space for both protons and neutrons. We calculate a number of quantities that did not enter into the fits undertaken to fix the parameters of both interactions. In particular we consider static quadrupole moments (Q's) of excited states of the even-even 70−76 Ge isotopes, as well as the B(E2) values in these nuclei. (We have previously studied 70 Zn isotopes using JJ4B.) Some striking disagreements between the JUN45 prediction and the experimental results had already been noted for the quadrupole moments of the 2 + 1 states of these nuclei. We investigate whether these discrepancies also occur for the JJ4B interaction. Subsequently, we also apply both interactions to calculate the Q's of some more highly excited states and compare the two sets of predictions regarding the nature of the nuclear states under consideration. In order to gain insight into these more complex large-scale shell-model calculations, we examine the corresponding and much simpler single-j shell model calculations in the g 9/2 neutron shell.PACS numbers:

The 76Se Gamow–Teller strength distribution and its importance for stellar electron capture rates

“…The effective interactions and single-particle energies are those of Menendez et al (RG interaction, [18]) and of Honma et al (JUN45 interaction, [19]). The Jun45 interaction has been used very recently to study the collective properties of Ge isotopes [20]. We note that all model spaces are free of spurious center-of-mass excitations.…”

Measurements ofg(41+,22+)in70,72<

“…[2] to include g factors. In addition, it discusses for each state the detailed shell-model wave functions and also the average occupation numbers of protons and neutrons in each shell-model orbital.…”

“…Large-scale shell-model calculations [2] had been carried out for 70,72,74,76 Ge using the p 3/2 , f 5/2 p 1/2 and g 9/2 model space for both protons and neutrons and two interactions, JUN45 [3] and JJ4B [32].…”

Consequences of omitting spin-orbit partner configurations forB(E2)values and quadrupole moments in nuclei

“…We give ratios with and without the f 5/2 orbit removed. It should be pointed out that we previously performed calculations in Ge isotopes [5]. These calculations used a space consisting of the f 5/2 , p 3/2 , p 1/2 , and g 7/2 orbitals for both protons and neutrons.…”

“…Comparing the results that are obtained with the two interactions with each other and with the measured values acts as a check, both on the quality of each interaction and on the appropriateness of the shell model space that is used. In the Ge calculations [5] it was thought that the specific truncated shell-model space contributed more than the interaction details to the discrepancies with the experimental data. In [5] the large-scale shell-model wave-functions were very fractionated indicating the need to take collective effects and effective charges into account.…”