Finite-temperature mean-field approximations for shell model Hamiltonians: the code HF-SHELL

Abstract

We present the code HF-SHELL for solving the self-consistent mean-field equations for configurationinteraction shell model Hamiltonians in the proton-neutron formalism. The code can calculate both zero-and finitetemperature properties in the Hartree-Fock (HF), HF+ Bardeen-Cooper-Schrieffer (HF+BCS) and the Hartree-Fock-Bogoliubov (HFB) mean-field approximations. Particlenumber 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.

Zero-pairing and zero-temperature limits of finite temperature Hartree-Fock-Bogoliubov theory

“…Oxygen isotopes are described as having an inert core of 16 O, implying that the protons play no role and that 18 O, 19 O, 22 O and 26 O possess 2, 3, 6 and 10 active valence neutrons, respectively. The working equations are solved on the basis of the HF-SHELL code [6]. In the present context, virtually all sd-shell nuclei exhibit a deformed mean-field minimum and several of them are triaxial [11].…”

“…In Eqs. (3) and (4), the uppercase Tr indicates a many-body trace over Fock space, while the lower case tr will be used to indicate traces over the one-body Hilbert space 6. A partition function associated with D can be defined but it is not equal to Z given that the derivatives of the latter do not satisfy thermodynamic consistency relations[4,6].…”

State densities of heavy nuclei in the static-path plus random-phase approximation

“…For the finite-temperature HFB, we calculate the self-consistent HFB solution at each temperature using the code of Ref. [57], together with the particlenumber-projected partition function using the method of Ref. [58].…”

“…We gratefully acknowedge W. Ryssens for the use of the HF-SHELL code [57] in the calculation of the HFB state densities, and for providing the parameters of the CI shell model interaction used in this work. We also thank G.…”

Symmetry-projected variational calculations with the numerical suite TAURUS I. Variation after particle-number projection

“…While being powerful tools, all those codes have the common feature that they were written and optimized specifically for energy density functionals and can not handle natively general Hamiltonian such as the ones constructed from Effective Field Theory (EFT) [29][30][31][32][33] or commonly used in shell-model calculations [34][35][36][37]. On that note, we remark that a valence-space finite-temperature HFB solver was recently proposed [38].…”