Anatomy of nuclear shape transition in the relativistic mean field theory

Abstract

A detailed microscopic study of the temperature dependence of the shapes of some rare-earth nuclei is made in the relativistic mean field theory. Analyses of the thermal evolution of the single-particle orbitals and their occupancies leading to the collapse of the deformation are presented. The role of the nonlinear σ−field on the shape transition in different nuclei is also investigated; in its absence the shape transition is found to be sharper. The understanding of the mean field shape evolution with temperature has been attempted in a macroscopic approach [3,4] generally referred to as the Landau theory of phase transitions.They have also been studied in microscopic framework like finite-temperature non-relativistic Hartree-Fock [5,6] and Hartree-Fock-Bogoliubov (HFB) approaches [7][8][9] with the pairingplus-quadrupole (P+Q) interaction. The shape transition temperature is found to be in the domain of ∼ 1.0 to 1.8 MeV for the rare-earth nuclei. Here the model Hamiltonian is simplistic, the model space is small, an inert core is assumed and moreover, the role of the Coulomb field is taken into consideration in an effective manner. Recently, we have studied [10,11] this same phenomenon in the framework of relativistic mean field theory (RMF).Here the model space is sufficiently large, all the nucleons are treated on equal footing and the Coulomb interaction is properly accounted for. 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.The aim of the present paper is to analyse in more microscopic details the collapse of the deformation with temperature. In doing so, we also explore whether the sudden collapse observed in the rare-earth nuclei is universal or system-specific. The stability towards the deformed ground state for the axially symmetric nuclei that we consider is given by the

Liquid-gas phase transition in infinite and finite nuclear systems

“…Phase transitions are normally signaled by peaks in the heat capacity with rise in temperature. Theoretical models of different genres, such as the microcanonical [14] or the canonical [15] description of multifragmentation, the lattice-gas model [4,13,16], or even the microscopic treatment in a relativistic [17] or a nonrelativistic [3] Thomas-Fermi framework support such a structure in the heat capacity. A clear idea about the subtle details of the liquid-gas phase transition in finite nuclei, however, has not emerged yet.…”

Reappraisal of the limit on the variation inαimplied by the Oklo natural fission reactors

“…Even at excitation energies much higher than that of |i , central densities ρ 0k are unchanged [51,53], which means that the equivalent sharp radii R k , defined so that 4π 3 R 3 k ρ k0 is equal to the volume integral of ρ k , are also unchanged. This assumption, coupled with the fact that the quadrupole shape parameters β 2k of |i can be constrained by reference to existing studies [54][55][56] of 150 Sm (see following paragraph), and the relation…”

“…For temperatures up to 0.75 MeV, corresponding to an average excitation energy in 150 Sm exceeding the energy of |i , the reported quadrupole deformation parameter β 2 increases very slightly, due to the weakening of pairing correlations, as the temperature increases [55,56] (β 2 denotes the common value of β 2p and β 2n ). Similar behavior is observed for 164 Er in a finite temperature Hartree-Fock Bogoliubov calculation [57], which also uses a realistic effective interaction (the D1S Gogny force) and a large configuration space.…”

Atomic parity nonconservation, neutron radii, and effective field theories of nuclei

“…[33,34]. The calculations presented here have been carried out by expanding the fermionic wave functions and the bosonic fields in 12 and 20 oscillator shells, respectively.…”

“…The analysis of the data of a clean measurement by Wood et al [39] of the amplitude of the parity nonconserving transition between the 6s and 7s states of 133 Cs, the only naturally occurring cesium isotope, established a value of Q exp W = −72.06(28) exp (34) theor for the weak charge of this element [15]. This experimentally extracted result differed by 2.5 σ from the standard model prediction with radiative corrections of Q SM W = −73.20 ± 0.13 [Ref.…”