Back-shifted Fermi Gas Model Research Articles

Level density parameters of47Ti and50V

The energy distribution of the protons andα-particles from the reactions47Ti(α, α′),47Ti(α, p) and50V(p, α) was measured in the angular range from 60° to 150°. The energies of the incoming particles were 15.35 MeV forα-particles and 13.85 MeV for protons. The results can be described in the frame of the statistical model of the nuclear reactions. The level density parameters could be determined by comparing the experimental data with the theoretical results. The values for the backshifted Fermi gas model are47Ti:a=6.6±0.6MeV−1,Δ=−0.5±0.3 MeV50V:a=6.3±0.6 MeV−1,Δ=−1.0±0.3 MeV.

Level Densities from Excitation Functions of Isolated Levels

Thick-target excitation functions were measured for the reactions ${\mathrm{Co}}^{59}(p,{\ensuremath{\alpha}}_{0}){\mathrm{Fe}}^{56}$, ${\mathrm{Co}}^{59}(p,{\ensuremath{\alpha}}_{1}){\mathrm{Fe}}^{56}$, ${\mathrm{Co}}^{59}(p,{\ensuremath{\alpha}}_{2}){\mathrm{Fe}}^{56}$, ${\mathrm{Mn}}^{55}(p,{\ensuremath{\alpha}}_{0}){\mathrm{Cr}}^{52}$, ${\mathrm{Mn}}^{55}(p,{\ensuremath{\alpha}}_{1}){\mathrm{Cr}}^{52}$, and ${\mathrm{Ni}}^{62}(p,{\ensuremath{\alpha}}_{0}){\mathrm{Co}}^{59}$ at two or more angles for proton bombarding energies 6-13.5 MeV. The ${\mathrm{Fe}}^{56}(\ensuremath{\alpha},{p}_{0}){\mathrm{Co}}^{59}$ reaction was studied at $\ensuremath{\alpha}$-particle bombarding energies of 12-18.5 MeV. These measurements were used to determine the parameters in three different level-density formulas which were thought to be reasonable candidates to describe the level densities of the residual nuclei. In addition, the experimental values of the cross sections to isolated levels were used in conjunction with available values of the level width $\ensuremath{\Gamma}$ from cross-section fluctuation measurements to determine level densities of compound nuclei at about 20-MeV excitation energy. The absolute values and energy dependence of the nuclear level density in the excitation energy range 0-20 MeV investigated for several nuclei agree with a back-shifted Fermi gas model. The constant-temperature model gives a reasonable fit to the level density in the energy range 0-10 MeV but fails at higher excitation energies. The conventional shifted Fermi gas model does not reproduce the energy dependence and absolute values of the various experimental level densities for any value of the level-density parameter $a$.

Die energieabhängigkeit der niveaudichte im bereich der kernmassen A = 30–65

The available information on the level density at low excitation energy and at the neutron binding energy is combined to determine experimentally both the level density parameter a and the energy shift Δ between the actual groound state and the fictive ground state of the Fermi gas model. Contrary to the widely used shifted Fermi gas model, it is found that the Δ-values for doubly even nuclei are approximately zero, and that the fictive ground states of odd-mass and odd nuclei are negative by about one and two times the pairing energy Δ as determined from odd-even mass differences. The changes introduced into statistical model-calculations by using the back-shifted Fermi gas model instead of the conventionally shifted Fermi gas model are discussed.