Modified Hartree-Fock-Bogoliubov at finite temperature

Abstract

The modified HFB (MHFB) theory at finite temperature is derived, which conserves the unitarity relation of the particle-density matrix. This is achieved by constructing a modified quasiparticle-density matrix, where the fluctuation of the quasiparticle number is microscopically built in. This matrix can be directly obtained from the usual quasiparticle-density matrix by applying the secondary Bogoliubov transformation, which includes the quasiparticle occupation number. It is shown that, in the limit of constant pairing parameter, the MHFB theory yields the previously obtained modified BCS (MBCS) equations. It is also proved that the modified quasiparticle RPA, which is based on the MBCS quasiparticle excitations, conserves the Ikeda sum rule. The numerical calculations of the pairing gap, heat capacity, level density, and level density parameter within the MBCS theory are carried out for ${}^{120}$Sn. The results show that the superfluid - normal phase transition is completely washed out. The applicability of the MBCS up to a temperature as high as $T\sim$ 5 MeV is analyzed in detail.

24 pages, 9 figures (JPEG format), to be published in Physical Review C

References in corpus (9)

• Exact solution of the nuclear pairing problem
• Signature of a Pairing Transition in the Heat Capacity of Finite Nuclei
• Pairing-correlations and particle-number projection methods
• Renormalized QRPA and double beta decay: a critical analysis of double Fermi transitions
• Single- and double-beta decay Fermi-transitions in an exactly solvable model
• Self consistent random phase approximation within the O(5) model and Fermi transitions
• Temperature dependent BCS equations with continuum coupling
• Fully-Renormalized QRPA fulfills Ikeda sum rule exactly
• Double-beta decay matrix elements for Ge-76

Cited by in corpus (16)

• Pairing phase transition: A Finite-Temperature Relativistic Hartree-Fock-Bogoliubov study
• Pairing effect on the giant dipole resonance width at low temperature
• Exact and approximate ensemble treatments of thermal pairing in a multilevel model
• Pairing within the self-consistent quasiparticle random-phase approximation at finite temperature
• Pairing reentrance in hot rotating nuclei
• Shear-Viscosity to Entropy-Density Ratio from Giant Dipole Resonances in Hot Nuclei
• Canonical and microcanonical ensemble descriptions of thermal pairing within BCS and quasiparticle RPA
• Anti-bubble effect of temperature \& deformation: a systematic study for nuclei across all mass regions between A $=$ 20$-$300
• Thermodynamic properties of hot nuclei within the self-consistent quasiparticle random-phase approximation
• Thermodynamics of small superconductors with fixed particle number
• Effects of thermal shape fluctuations and pairing fluctuations on the giant dipole resonance in warm nuclei
• Giant dipole resonance in ${}^{201}$Tl at low temperature
• Improved treatment of blocking effect at finite temperature
• Test of modified BCS model at finite temperature
• On the test of the modified BCS at finite temperature
• Reply to comment ``On the test of the modified BCS at finite temperature''