Fixed-J level densities beyond spin cut-off approximation

It is well known that the expression for fixed-J level density I-l(E, J) = -I(E) partial derivative/partial derivative M I(M\E)\(M=J+1/2) reduces to familiar Bethe's formula provided the conditional M-distribution I(MIE) is approximated by a Gaussian form, so called spin cut-off approximation (M is the z-component of total angular momentum J and E is the excitation energy). After a detailed analysis, we find that the Bethe's formula which overestimates I-l(E, J) at high J values, in particular near the yrast line, can be significantly improved by including a few higher-order moment terms in a suitable expansion for I(M\E) with the lowest-order term to be a Gaussian, e.g., Edgeworth expansions. We also find that, except at very low excitation energies, reasonable values (close to exact) of the moments of I(M\E) can easily be obtained when multiple Laplace-back transform of the partition function for grand canonical ensemble is evaluated within the saddle point approximation. Furthermore, we study the effects of shell structure as well as residual interaction on the excitation energy dependence of these moments.