Nuclear shape transitions at finite temperature

Abstract

Changes in shape in Mg are studied at T&0 both in finite-temperature mean-field calculations and in the exact canonical ensemble. With increasing temperature the canonical ensemble average of the rotational energy spectrum tends toward a more equispaced harmonic spectrum. This deformed to spherical transition gives rise to a peak in the specific heat which is also seen in finitetemperature Hartree-Fock approximation albeit at a slightly higher temperature. The canonical ensemble average of the quadrupole moment does not, however, appear to vanish at the critical temperature as is the case in the finite-temperature Hartree-Fock approximation.

Landau-Ginzburg method applied to finite fermion systems: Pairing in nuclei

“…) and without finite size corrections (∆ L ) can easily be obtained from from equations (31) and (20). In spite of the simplicity of the pairing calculation(the density of states and the pairing interaction are assumed to be constant) and the difficulties with the continuum contribution (for 208 P b) the value of the discontinuity calculated with or without finite size corrections is in reasonable agreement with the empirical value for the three heavier nuclei.…”

“…In the latter case this evidence for a second order transition which probably is shape related [19]. From the spectra of four even-even nuclei 20 Ne, 48 Ca, nuclei. This suggests that a pairing transition takes place in these nuclei.…”

“…This issue, particularly in deformed systems, has been clouded by the fact that finite temperature mean field calculations have suggested that this phase transition is simply due to a drastic change of shape [19]. The deformed-to-spherical shape transition seen in these calculations is not seen in exact canonical calculations [20,21,22,23] and may be an artifact of the finite temperature mean field approximation and also depends on the volume of the system [24,25]. In spite of the fact that the canonical partition function above the critical temperature is dominated by the single particle degrees of freedom a few collective states still contribute and are extremely important in calculation of shape dependent parameters.…”

“…This suggests that a pairing transition takes place in these nuclei. In the case of 20 Ne such is not the case and the transition may be shape related.…”

Anatomy of nuclear shape transition in the relativistic mean field theory

“…It is then found that the shape transition temperature is noticeably higher. Except for some calculations in the s-d shell nuclei [12,13], nearly all the calculations have been done for nuclei in the rare-earth region; it is found that the deformation undergoes a sudden collapse at the shape transition temperature. Grossly, one understands the dissolution of the deformation with temperature in these nuclei from the following: shell structure leads to the population of the deformation-driving states, the so-called intruder states producing the static ground state deformation; their depopulation with gradual heating restores the spherical symmetry.…”