Kosai Tanabe

Phase transitions along and off the yrast line

Abstract The characteristics of deformed nuclei along and off the yrast line are investigated using a model based on the cranked temperature-dependent (or thermal) Hartree-Fock-Bogoliubov approximation. The behaviour of free energies indicates that phase transitions exist even in a finite nuclear system. Besides the superconducting phase and the normal phase, there appears a gapless superconducting phase in the transient region between the two phases. A new type of phase is predicted to occur in the high-energy and low-spin region with the spontaneous breakdown of the three-dimensional rotation symmetry, and characterized by the “bidirectional alignment of spins”. In addition three different types of backbending are also predicted.

The Thermal Linear Response Theory for the Dissipative High Spin Quantum States

The thermal linear response theory with the inclusion of the non· Markovian effect is formulated based on the thermal cranked Hartree·Fock·Bogoliubov (THFB) theory. We propose the proper strength function which is suitable to be compared with y-ray spectra from giant resonances at high spin and high temperature. A clarification is given of the relation between the stability condition of the THFB solution and the equation in the thermal random phase approximation (TRPA).

Shape coexistence at high spins in 158Er and 160Yb predicted by the self-consistent calculation☆

Abstract The self-consistent calculation based on the cranked Hartree-Fock-Bogoliubov approximation is performed to study the evolution of nuclear shapes at high spins for the nuclei 158 Er and 160 Yb. Strong quadrupole-pairing interaction reproduces the sharp backbending well without introducing the core moment-of-inertia. The coexistence of the prolate and the oblate deformations is predicted at very high spins I ⪆ 50 in both nuclei.

g-Factors and backbending along the yrast in Er isotopes from A = 158 to 170

Abstract g-factors and energy levels are described in the framework of a self-consistent cranked HFB calculation for the Er isotopes with mass number A = 158–170. We show that the backbending behavior and the g-factor, which is a measure of spin-alignment, are sensitive to the gradual change of Fermi surface in the vi 13 2 level.

Quantum number projection at finite temperature via thermofield dynamics

Applying thermofield dynamics, we reformulate the exact quantum number projection in the finite-temperature Hartree-Fock-Bogoliubov theory. Explicit formulas are derived for the simultaneous projection of particle number and angular momentum, in parallel to the zero-temperature case. We also propose a practical method for the variation-after-projection calculation, by approximating entropy consistently with the Peierls inequality. Using quantum number projection in finite-temperature mean-field theory will be useful for studying the effects of quantum fluctuations associated with the conservation laws on thermal properties of nuclei.

The explicit determination of the linear boson transformation coefficients

The problem of determining the wavefunction is solved for the boson Bogoliubov transformation. The method of series expansion is applied to derive the general expression for the coefficients which connect the new Fock states of an arbitrary number of quasiparticles with the states before the transformation.

New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation

We formulate a new Bardeen-Cooper-Schrieffer (BCS)-type theory at finite temperature, by deriving a set of variational equations of the free energy after the particle-number projection. With its broad applicability, this theory can be a useful tool for investigating the pairing phase transition in finite systems with the particle-number conservation. This theory provides effects of the symmetry-restoring fluctuation (SRF) for the pairing phenomena in finite fermionic systems, distinctively from those of additional quantum fluctuations. It is shown by numerical calculations that the phase transition is compatible with the conservation in this theory, and that the SRF shifts up the critical temperature (T{sup cr}). This shift of T{sup cr} occurs due to reduction of degrees-of-freedom in canonical ensembles, and decreases only slowly as the particle-number increases (or as the level spacing narrows), in contrast to the conventional BCS theory.

Thermal high spin giant dipole resonance in Er isotopes

Abstract The thermal RPA calculations based on the thermal cranked Hartree-Fock-Bogoliubov enemble are carried out for the giant dipole resonance excited on the thermal high spin states. The dynamical strength function is adopted as a quantity comparable with experimental data. According to the location of the Fermi surface the resonance components differ from those expected in the classical picture.

On the variational derivation of the thermal RPA equation

Abstract By applying the variational principle to the grand potential including residual two-body interactions, the thermal random-phase-approximation (TRPA) equation is derived without recourse to the linearization ansatz. The relation of the TRPA equation to the stability condition of the thermal Hartree-Fock-Bogoliubov (THFB) solution is elucidated.

Effects of particle-number conservation on heat capacity of nuclei

By applying the particle-number projection to the finite-temperature Bardeen-Cooper-Schrieffer (BCS) theory, the S-shaped heat capacity, which has recently been claimed to be a fingerprint of the superfluid-to-normal phase transition in nuclei, is reexamined. It is found that the particle-number (or number-parity) projection gives S shapes in the heat capacity of nuclei that look qualitatively similar to the observed ones. These S shapes are accounted for as effects of the particle-number conservation on the quasiparticle excitations and occur even when we keep the superfluidity at all temperatures by assuming a constant gap in the BCS theory. The present study illustrates significance of the conservation laws in studying phase transitions of finite systems.