Bose–Einstein Statistics

The properties of the ideal Bose gas are calculated from the integral equations for the energy and the number of particles as a function of the temperature and chemical potential. It is shown that the integral equations break down below the Einstein temperature that corresponds to the transition to the low-temperature state. The lowest single-particle energy level must be treated explicitly to get the proper equations. With the inclusion of the lowest single-particle energy level, the low-temperature behavior is calculated. The occupation of the lowest level becomes comparable to the total number of particles in the system below the Einstein temperature, and equal to the total number of particles at zero temperature. A numerical solution to the properties of the Bose gas is discussed, and the detailed calculations are assigned to the problems at the end of the chapter.

Rotational behavior of thermally excited 56Fe, 58Fe and 60Fe isotopes

Thermal and rotational behaviors of neutron rich fp-shell isotopes such as [Formula: see text], [Formula: see text] and [Formula: see text] were analyzed microscopically within the framework of statistical theory of hot rotating nuclei (STHRN) for the angular momentum range (0–15)[Formula: see text] at excitation energy above 4[Formula: see text]MeV. Pair-breaking phenomenon and band-crossing phenomenon of Fe isotopes were discussed with and without the inclusion of BCS pairing. The STHRN method with BCS effect was extended to the Fe isotopes to determine the critical temperature [Formula: see text], where the pair-breaking phenomenon takes place and it is found to occur below [Formula: see text][Formula: see text]MeV. The observation of band-crossing phenomenon above the [Formula: see text] was explained without considering the effect of BCS pairing. The single particle energy levels were engendered from triaxially deformed Nilsson Hamiltonian. The outcomes of the present investigation on moment of inertia (MOI), back-bending phenomenon, spin cutoff parameter show a strong evidence of band-crossing phenomenon and it eventually led to a shape transition from spherical to noncollective oblate. Moreover, attention on separation energy of protons and neutrons reveals that the neutron pairs are responsible for band-crossing. STHRN method was able to reproduce results in good agreement with experiments and comparable with other theories such as projected shellmodel (PSM) and shellmodel Monte Carlo (SMMC) method.

Evolution of nuclear spin-orbit splittings with Skyrme functional SAMi-T

A new Skyrme functional has been developed with tensor term guided by ab initio relativistic Brueckner-Hartree-Fock (RBHF) studies on neutron-proton drops. Instead of extracting information on the tensor force from experimental single-particle energy splittings, the RBHF calculations do not contain beyond mean-field effects such as particle-vibration coupling and therefore the information on the tensor force can be obtained without ambiguities. The new functional gives a good description of nuclear ground-state properties aswell as various giant resonances. The description for the evolution of single-particle energy splittings is also improved by the new functional.

Description of nuclei with magic number Z (N) = 6

Encouraged by the evidence for Z = 6 magic number in neutron-rich carbon isotopes, we have performed relativistic mean-field plus BCS calculations to investigate ground state properties of entire chains of isotopes (isotones) with Z (N) = 6 including even and odd mass nuclei. Our calculations include deformation, binding energy, separation energy, single particle energy, root mean squared radii, along with charge and neutron density profile, etc., and are found to be an excellent match with latest experimental results demonstrating Z = 6 as a strong magic number. N = 6 is also found to have a similar kind of strong magic character.

Shape coexistence and parity doublet in Zr isotopes

The ground and excited states properties of Zr isotopes are studied from proton to neutron drip lines using the relativistic (RMF) and nonrelativistic (SHF) mean-field formalisms with Bardeen–Cooper–Schrieffer (BCS) and Bogoliubov pairing, respectively. The well-known NL3* and SLy4 parameter sets are used in the calculations. We have found spherical ground and low-lying large deformed excited states in most of the isotopes. Several couples of Ωπ = 1/2± parity doublets configurations are noticed, while analyzing the single-particle energy levels of the large deformed configurations.