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Register a new userFinite-temperature mean-field approximations for shell model Hamiltonians: the code HF-SHELL
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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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The advent of nucleon-nucleon potentials derived from chiral perturbation theory, as well as the so-called V-low-k approach to the renormalization of the strong short-range repulsion contained in the potentials, have brought renewed interest in realistic shell-model calculations. Here we focus on calculations where a fully microscopic approach is adopted. No phenomenological input is needed in these calculations, because single-particle energies, matrix elements of the two-body interaction, and matrix elements of the electromagnetic multipole operators are derived theoretically. This has been done within the framework of the time-dependent degenerate linked-diagram perturbation theory. We present results for some nuclei in different mass regions. These evidence the ability of realistic effective hamiltonians to provide an accurate description of nuclear structure properties.
The aim of this work is to present an overview of the derivation of the effective shell-model Hamiltonian and decay operators within many-body perturbation theory, and to show the results of selected shell-model studies based on their utilisation. More precisely, we report some technical details that are needed by non-experts to approach the derivation of shell-model Hamiltonians and operators starting from realistic nuclear potentials, in order to provide some guidance to shell-model calculations where the single-particle energies, two-body matrix elements of the residual interaction, effective charges and decay matrix elements, are all obtained without resorting to empirical adjustments. On the above grounds, we will present results of studies of double-beta decay of heavy-mass nuclei where shell-model ingredients are derived from theory, so to assess the reliability of such a way to shell-model investigations. Attention will be also focussed on the relevant aspects that are connected to the behavior of the perturbative expansion, whose knowledge is needed to establish limits and perspectives of this approach to nuclear structure calculations.
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.
The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interactions approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow Shell Model (GSM) provides such a framework as it is capable of describing resonant and non-resonant many-body states on equal footing. To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the $psdf$ shell model space. The resulting interaction is expected to describe nuclei with $5 leqslant A leqslant 12$ at the $p-sd$-shell interface. The optimized one-body potential reproduces nucleon-$^4$He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the Helium, Lithium, and Beryllium isotopes up to $A=9$. A very good agreement with experiment was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the $psd$ region of the nuclear chart.
We present an approach to derive effective shell-model interactions from microscopic nuclear forces. The similarity-transformed coupled-cluster Hamiltonian decouples the single-reference state of a closed-shell nucleus and provides us with a core for the shell model. We use a second similarity transformation to decouple a shell-model space from the excluded space. We show that the three-body terms induced by both similarity transformations are crucial for an accurate computation of ground and excited states. As a proof of principle we use a nucleon-nucleon interaction from chiral effective field theory, employ a $^4$He core, and compute low-lying states of $^{6-8}$He and $^{6-8}$Li in $p$-shell model spaces. Our results agree with benchmarks from full configuration interaction.
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