FIXED-J LEVEL DENSITIES BEYOND SPIN CUTOFF 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) re duces to familiar Bethe's formula provided the conditional M-distribut ion 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 pa rticular near the yrast line, can be significantly improved by includi ng 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 expansion s. We also find that, except at very low excitation energies, reasonab le values (close to exact) of the moments of I(M\E) can easily be obta ined when multiple Laplace-back transform of the partition function fo r grand canonical ensemble is evaluated within the saddle point approx imation. Furthermore, we study the effects of shell structure as well as residual interaction on the excitation energy dependence of these m oments.