Microscopic study of spin cut-off factors of nuclear level densities

Abstract

Level densities and spin cut-off factors have been investigated within the microscopic approach based on the BCS Hamiltonian. In particular, the spin cut-off parameters have been calculated at neutron binding energies over a large range of nuclear mass using the BCS theory. The spin cut-off parameters σ 2 (E) have also been obtained from the Gilbert and Cameron expression and from rigid body calculations. The results were compared with their corresponding macroscopic values. It was found that the values of σ 2 (E) did not increase smoothly with A as expected based on macroscopic theory. Instead, the values of σ 2 (E) show structure reflecting the angular momentum of the shell model orbitals near the Fermi energy.

Cross section of reaction 181 Ta(p,nγ) 181 W and the influence of the spin cut-off parameter on the cross section

“…2. The formation cross section of each energy level was calculated by using various spin cut-off parameters σ: 4.65 [9], 6.06 [15] and 6.75 [15] for target 181 Ta at Ep=6.5 MeV, 8.5 MeV.…”

Angular momentum dependence of the nuclear level-density parameter aroundZ~50

“…[6] pointed out they are the first ones to calculate the level-density parameter a(E) and the spin cut-off parameter for a large number of nuclei using a realistic microscopic approach. The calculations were carried out at excitation energies of neutron resonance reactions.…”

“…There have been many attempts (e.g., Refs. [2][3][4][5][6][7][8][9][10]) to refine the knowledge of these parameters, as there could be large uncertainties in reaction cross-section calculations due to variations in these parameters. Most of the earlier attempts have been concentrated on low excitation energy and the low-spin region because the relevant, accurate, and extensive experimental data (from s-wave neutron resonance spacing and density of low-lying discrete states in the excitation energy region below approximately 8 MeV) are available in this region.…”

“…Spin distribution of nuclear levels has been calculated [5] microscopically using random-phase and static-path approximations (RPA-SPA) without the assumption of individual random spin vectors. Also, the spin cut-off parameter was calculated [6] at neutron binding energies over a large range of nuclear masses using the BCS theory. The work presented in Ref.…”

“…The work presented in Ref. [6] has been accomplished using realistic values of single-particle energies k and their corresponding magnetic quantum number m k . It was found that the values of this parameter do not increase smoothly with A as expected from the Fermi-gas model.…”