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The $\Theta_{eff}/\Theta_{rig}$ parameter of the spin distribution of thelevel density was determined for 61 nuclei covering the mass range of 44 to200. The experimental isomeric cross-section ratios for 25 isomeric pairs werecompared with the model calculation to find the best fit to the experimentaldata. The model calculations were carried out with the TALYS code using theBSFG model for the level density. The reduced $\chi ^2$ values were calculatedto describe the deviation of the experimental data from the model calculation.An $\eta_d $ was introduced calculating the $\Theta_{eff}/\Theta_{rig}$ valuefrom the low energy discrete levels of the nucleus. The $\eta /\eta_d $ valuesseem 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 excitationenergy in the continuum, indicating that $\eta $ is independent of theexcitation energy. The mass number and (N-Z) dependence of the $\eta $ valueswere studied. The $\eta $ values for the nuclei with odd mass number show anexponential decrease as a function of A or (N-Z). The $\eta $ values for theodd-odd type of nuclei appear to be constant, near one, up to the mass number110 or (N-Z) of 13. Above these values, the $\eta $ values show exponentialdecrease. The $\eta $ values for even-even type nuclei decrease exponentiallyup to A equal to 142 or (N-Z) equal to 20. The values are lower than those forthe nearby odd-odd type nuclei. The $\eta $ values increase for nuclei with Abetween 142 and 156 and (N-Z) between 20 and 28, and they finally reach thevalue of odd-odd type systematics.

nuclear physics a

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