Mass number and excitation energy dependence of the $Θ_{eff}/Θ_{rig}$ parameter of the spin cut-off factor in the formation of an isomeric pair

Abstract: The $\Theta_{eff}/\Theta_{rig}$ parameter of the spin distribution of the level density was determined for 61 nuclei covering the mass range of 44 to 200. The experimental isomeric cross-section ratios for 25 isomeric pairs were compared with the model calculation to find the best fit to the experimental data. The model calculations were carried out with the TALYS code using the BSFG model for the level density. The reduced $\chi ^2$ values were calculated to describe the deviation of the experimental data from the model calculation. An $\eta_d $ was introduced calculating the $\Theta_{eff}/\Theta_{rig}$ value from the low energy discrete levels of the nucleus. The $\eta /\eta_d $ values seem to be independent of the mass number, their average value near to one. The $\eta /\eta_d $ values also seem to be independent of the average excitation energy in the continuum, indicating that $\eta $ is independent of the excitation energy. The mass number and (N-Z) dependence of the $\eta $ values were studied. The $\eta $ values for the nuclei with odd mass number show an exponential decrease as a function of A or (N-Z). The $\eta $ values for the odd-odd type of nuclei appear to be constant, near one, up to the mass number 110 or (N-Z) of 13. Above these values, the $\eta $ values show exponential decrease. The $\eta $ values for even-even type nuclei decrease exponentially up to A equal to 142 or (N-Z) equal to 20. The values are lower than those for the nearby odd-odd type nuclei. The $\eta $ values increase for nuclei with A between 142 and 156 and (N-Z) between 20 and 28, and they finally reach the value of odd-odd type systematics.