Mass-number and excitation-energy dependence of the spin cutoff parameter

Abstract

The spin cutoff parameter determining the nuclear level density spin distribution $\ensuremath{\rho}(J)$ is defined through the spin projection as ${\ensuremath{\langle}{J}_{z}^{2}\ensuremath{\rangle}}^{1/2}$ or equivalently for spherical nuclei, ${(\frac{\ensuremath{\langle}J(J+1)\ensuremath{\rangle}}{3})}^{1/2}$. It is needed to divide the total level density into levels as a function of $J$. To obtain the total level density at the neutron binding energy from the $s$-wave resonance count, the spin cutoff parameter is also needed. The spin cutoff parameter has been calculated as a function of excitation energy and mass with a super-conducting Hamiltonian. Calculations have been compared with two commonly used semiempirical formulas. A need for further measurements is also observed. Some complications for deformed nuclei are discussed. The quality of spin cut off parameter data derived from isomeric ratio measurement is examined.