The Strutinsky method and its foundation from the Hartree-Fock-Bogoliubov approximation at finite temperature

Abstract

Strutinsky's shell-correction method is investigated in the framework of the microscopical Hartree-Fock-Bogoliubov method at finite temperature (HFBT). Applying the Strutinsky energy averaging consistently to the normal and abnormal density matrices and to the entropy, we define a self-consistently averaged HFBT system as the solution of a variational problem. From the latter we derive the generalized Strutinsky energy theorem and the explicit expressions for the shell correction of a statistically excited system of BCS quasiparticles. Using numerical results of HF calculations, we demonstrate the convergence of the Strutinsky expansion and estimate the validity of the practical shell-correction approach. We also discuss the close connections of the Strutinsky energy averaging with semiclassical expansions and their usefulness for solving the average nuclear self-consistency problem. In particular we argue that the Hohenberg-Kohn theorem should hold for the averaged HFBT system and we thus provide a justification of the use of semiclassical density functionals.

From finite nuclei to the nuclear liquid drop: Leptodermous expansion based on self-consistent mean-field theory

“…According to the Strutinsky Energy Theorem [18][19][20][21], the energy per nucleon can be decomposed into an average part (smoothly depending on the number of nucleons) and the shellcorrection term that fluctuates with particle number reflecting the non-uniformities (bunchiness) of the single-particle level distribution:…”

“…Note that these are drawn from smoothed energies (i.e., after subtraction of the shell corrections). The remaining fluctuations are due to higher-order shell effects [20,21] which cannot be accounted for by the generalized Strutinsky procedure. The construction (17a) of the effective surface energy amplifies those residual fluctuations dramatically; it is only by virtue of the smoothed energy that one can see any clear trend.…”

Surface symmetry energy of nuclear energy density functionals

“…The characterization in terms of "bulk" and "local" is not very precise and somehow arbitrary; it has its origin in the macroscopic-microscopic approach, which offers a description in terms of a macroscopic liquid drop (whose properties change smoothly as a function of nucleon numbers) and shell correction that oscillates rapidly with shell filling [16][17][18][19]. In the context of DFT, the binding energy of a nucleus of mass A and neutron-excess I = (N −Z)/A can be split into a smooth function of I and A, and a fluctuating shell correction term by means of the Strutinsky energy theorem [16,[20][21][22][23]. This theorem, together with the shell-correction method, offers a formal framework to link the self-consistent DFT with macroscopicmicroscopic models which often provide useful insights in terms of the liquid drop (or droplet) model and shell effects.…”

Semiclassical Description of Nuclear Bulk Properties

“…They certainlyjnust be nonlocal, since the shell effects contained in T q(r) and J q (r) are not local, but global properties of the nucleusT 3 This problem can be overcome by averaging out the shell effects and expressing the average of the energy by a.functional of the average densities o q (r) . This can be justified by means of Strutinsky*s energy averaging method 21 which, in fact, allows to decompose the exact HF energy in a rather unique way into an average and a fluctuating ("shell-correction") part 21 23 it has been checked that the missing higher order terms in eq. (2.14) are negligible for all practical purposes.…”