E. Boeker

FBCS for odd nuclei and the inverse gap equations: Application to N = 50 isotones

Abstract The single-quasiparticle descriptions of odd superfluid nuclei by BCS theory and by particle number projection methods are compared with the exact lowest-seniority shell model. The purpose is to trace systematic inadequacies of the inverse-gap-equations (IGE) method to extract single-particle energies from spectroscopic data on odd nuclei and to improve that method by using number projection techniques. The IGE method yields too large a spacing of single-particle energies especially near closed subshells and also the force strengths are not correctly given in general. A similar method based on particle number projection leads to correct results. A conventional two-quasiparticle BCS calculation of the spectra of even nuclei with parameters obtained by the IGE method leads to other results than when for both the odd and the even nuclei a number-conserving description is used. In the former approximation particle-hole like states are relatively too high and particle-particle or hole-hole like states too low in energy, which may strongly influence the configuration mixing. As a practical application the spectra and a few other spectroscopic properties of the even single-closed-shell nuclei with 50 neutrons are calculated.

Comparison between the bcs and the FBCS formalisms as approximations to the low-seniority shell model

Abstract A discussion is given of the discrepancies between the wave functions of single-closed-shell nuclei as obtained from the BCS formalism and those from the FBCS formalism. Sources of these discrepancies for the ground states are made clear and demonstrated by simple examples. The difference between the BCS and FBCS two-quasiparticle spectra may especially become large when the number of particles corresponds to a closed subshell structure and if subshells of low degeneracy occur near the Fermi level. As an illustration the states of the even N = 50 nuclei are calculated in both approximations and compared to those of the exact V ≦ 2 shell model. Particle number projection is the main effect in improving spectra. The parameters ua, va which minimize the ground state energy were found to be not the most suitable to calculate excited states.

A particle-quasiparticle description of 112, 114, 116Sb

Abstract A simple description of the even Sb isotopes, for which no calculations have been published earlier, is that of a proton coupled to a number projected neutron quasiparticle wave function, assuming a Z = N = 50 core. We performed such a calculation for 112, 114, 116 Sb, for which nuclei sufficient experimental information is available. The spectra and transition rates were calculated in shell-model spaces consisting of five and eight Subshells and using a Gaussian Serber force. The shell-model parameters were derived from experimental data of the adjacent nuclei. A large number of low-lying levels, their branching ratios and half-lives were calculated. Reasonable agreement with experimental data is obtained. The calculated magnetic moments of the isomeric 8 − states do not show the experimental trend however. Spectroscopic factors for the ( 3 He, d) reaction on 115 Sn are predicted. Their experimental determination would be another helpful test of the interpretations given.

Pairing correlations in excited states of superfluid nuclei

Abstract Extended gap equations are used to improve the pair distributions in excited states of superfluid nuclei. So one may obtain a better approximation of the low-seniority shell model, for energies and wave functions without any increase of computational labour. The reduction of pairing in excited states becomes more important as the number of quasiparticles increases, and yields changes in excitation energies which may be as large as 400 keV for three-quasi-particle states. Calculations have been performed for the Sn ( Z = 50) isotopes and the N = 50 isotones.

EXACT AND APPROXIMATE ANGULAR MOMENTUM PROJECTION FOR LIGHT NUCLEI.

Abstract The Peierls-Yoccoz angular momentum projection method is applied to axially symmetric Hartree-Fock wave functions for several sd-shell nuclei. Excitation energies, rms radii and B (E2; 2 + → 0 + ) values are calculated and compared with the results of two different approximation methods. This is also done for some 12 C wave functions considered earlier. A discussion of the accuracy of these approximations is given. An approximate formula for the B (E2; 2 + → 0 + ) value is presented, which gives much better agreement with the exact angular momentum projection results than the formula from the Bohr-Mottelson model.

The particle-phonon model and particle-core model for 63Cu

Abstract The accuracy of the particle-phonon and particle-core models in describing the properties of 63 Cu is studied. From the measured properties of the low-lying levels, adopted values and uncertainties are deduced, which are used to obtain the model parameters by fitting procedures. The influence of a change in the excitation energy of the ( 3 2 ) 2 − level is investigated. It is seen that the particle-phonon model cannot reproduce the properties of 63 Cu as good as the particle-core model, although the former has a much larger configuration space. The quadrupole moment of the 62 Ni 2 + core state in the particle-core model is calculated as +25 e · fm 2 .

Iinelastic electron scattering calculations on N = 50 isotones

Abstract The first excited 2 + , 3 − and 4 + levels in 88 Sr, 90 Zr and 92 Mo are described by the seniority υ = 2 shell model and by the two-quasiparticle BCS model. In both models the DWBA cross sections for inelastic electron scattering are calculated. It appears that both models often give the same cross sections, the overall normalisation being then the difference. The agreement with the experimental data for 90 Zr and 92 Mo for the shell model case is much better than for the BCS model.

Electron scattering on odd-mass nuclei described by particle-phonon and particle-core models: Application to 63Cu

Abstract Some odd-mass nuclei are described well by particle-phonon and particle-core coupling models. With a few assumptions, and introducing effective operators in the formula of the differential cross section for electron scattering in the Born approximation, the form factors are calculated in a rather simple way. In the case of 63 Cu, it becomes clear that measurements of the inelastic form factors can be a sharp test on these coupling models.