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

The spin cutoff parameter determining the nuclear level density spin distribution $\rho \left(J\right)$ is defined through the spin projection as ${\langle J_z^2\rangle }^{1/2}$ or equivalently for spherical nuclei, ${\left(\frac{\langle J(J+1)\rangle }{3}\right)}^{1/2}$. 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.

Figure 1

Comparison of experimental spin cutoff parameters from Refs. [2, 23] with calculations based on different models: Rigid-body, Al-Quarishi [8], Egidy2009 [9], microscopical calculations from this work. Error bars for experimental points are typically 15% in ${\sigma }^2$.

Figure 2

Comparison of present (microscopic) calculations of ${\sigma }^2$ with those of Ref. [4] [Eq. (58)] at 6 MeV of excitation energy.