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Register a new userVariational approximations to exact solutions in shell-model valence spaces: calcium isotopes in the pf-shell
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We study the performance of self-consistent mean-field and beyond-mean-field approximations in shell-model valence spaces. In particular, Hartree-Fock-Bogolyubov, particle-number variation after projection and projected generator coordinate methods are applied to obtain ground-state and excitation energies for even-even and odd-even Calcium isotopes in the pf-shell. The standard (and non-trivial) KB3G nuclear effective interaction has been used. The comparison with the exact solutions -- provided by the full diagonalization of the Hamiltonian -- shows an outstanding agreement when particle-number and angular-momentum restorations are performed and both quadrupole and neutron-neutron pairing degrees of freedom are explicitly explored as collective coordinates.
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A systematic shell model description of the experimental Gamow-Teller transition strength distributions in $^{42}$Ti, $^{46}$Cr, $^{50}$Fe and $^{54}$Ni is presented. These transitions have been recently measured via $beta$ decay of these $T_z$=-1 nuclei, produced in fragmentation reactions at GSI and also with ($^3${He},$t$) charge-exchange (CE) reactions corresponding to $T_z = + 1$ to $T_z = 0$ carried out at RCNP-Osaka.The calculations are performed in the $pf$ model space, using the GXPF1a and KB3G effective interactions. Qualitative agreement is obtained for the individual transitions, while the calculated summed transition strengths closely reproduce the observed ones.
We report in this paper a study in terms of the nuclear shell model about the location of the calcium isotopes drip line. The starting point is considering the realistic two-body potential derived by Entem and Machleidt within chiral perturbation theory at next-to-next-to-next-to-leading order (N3LO), as well as a chiral three-body force at next-to-next-to-leading order (N2LO) whose structure and low-energy constants are consistent with the two-body potential. Then we construct the effective single-particle energies and residual interaction needed to diagonalize the shell-model Hamiltonian. The calculated two-neutron separation energies agree nicely with experiment until 56Ca, which is the heaviest isotope whose mass has been measured, and do not show any sign of two-neutron emission until 70Ca. We discuss the role of the choice of the model space in determining the neutron drip line, and also the dependence of the results on the parameters of the shell-model Hamiltonian.
Based on the realistic nuclear force of the high-precision CD-Bonn potential, we have performed comprehensive calculations for neutron-rich calcium isotopes using the Gamow shell model (GSM) which includes resonance and continuum. The realistic GSM calculations produce well binding energies, one- and two-neutron separation energies, predicting that $^{57}$Ca is the heaviest bound odd isotope and $^{70}$Ca is the dripline nucleus. Resonant states are predicted, which provides useful information for future experiments on particle emissions in neutron-rich calcium isotopes. Shell evolutions in the calcium chain around neutron numbers textit{N} = 32, 34 and 40 are understood by calculating effective single-particle energies, the excitation energies of the first $2^+$ states and two-neutron separation energies. The calculations support shell closures at $^{52}$Ca (textit{N} = 32) and $^{54}$Ca (textit{N} = 34) but show a weakening of shell closure at $^{60}$Ca (textit{N} = 40). The possible shell closure at $^{70}$Ca (textit{N} = 50) is predicted.
The lightest Xenon isotopes are studied in the framework of the Interacting Shell Model (ISM). The valence space comprises all the orbits lying between the magic closures N=Z=50 and N=Z=82. The calculations produce collective deformed structures of triaxial nature that encompass nicely the known experimental data. Predictions are made for the (still unknown) N=Z nucleus 108-Xe. The results are interpreted in terms of the competition between the quadrupole correlations enhanced by the pseudo-SU(3) structure of the positive parity orbits and the pairing correlations brought in by the 0h11/2 orbit. We have studied as well the effect of the excitations from the 100-Sn core on our predictions. We show that the backbending in this region is due to the alignment of two particles in the 0h11/2 orbit. In the N=Z case, one neutron and one proton align to J=11 and T=0. In 110-Xe and 112-Xe the alignment begins in the J=10 T=1 channel and it is dominantly of neutron neutron type. Approaching the band termination the alignment of a neutron and a proton to J=11 and T=0 takes over. In a more academic mood, we have explored the role of the isovector and isoscalar pairing correlations on the structure on the yrast bands of 108-Xe and 110-Xe and examined the role of the isovector and isoscalar pairing condensates in these N~Z nuclei.
We present the code HF-SHELL for solving the self-consistent mean-field equations for configuration-interaction shell model Hamiltonians in the proton-neutron formalism. The code can calculate both ground-state and finite-temperature properties in the Hartree-Fock (HF), HF+Bardeen-Cooper-Schrieffer (HF+BCS), and the Hartree-Fock-Bogoliubov (HFB) mean-field approximations. Particle-number projection after variation is incorporated to reduce the grand-canonical ensemble to the canonical ensemble, making the code particularly suitable for the calculation of nuclear state densities. The code does not impose axial symmetry and allows for triaxial quadrupole deformations. The self-consistency cycle is particularly robust through the use of the heavy-ball optimization technique and the implementation of different options to constrain the quadrupole degrees of freedom.
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