Local even–odd effect based on the number of configurations of pre-formed and formed fragmentations in a fissioning nucleus

The present paper proposes a modeling of the local even–odd effect based on the number of configurations in a nucleus undergoing fission at two stages along its fission path. One is the fissioning nucleus stage just after passing through the outer saddle point when the fragments are considered as pre-formed and the intrinsic energy is not yet shared. The other stage is at the end of the fission path when the scission is imminent. Then the intrinsic energy is already partitioned and the fragments are completely formed. The probability that a pre-formed fragmentation arrives at the end of the fission path (i.e. at scission) when the fragmentation is completely formed is expressed by the ratio of the number of configurations of the formed fragmentation to the one of pre-formed fragmentation. The local even–odd effect is defined as half of the difference between these normalized ratios corresponding to even-Z and odd-Z fragmentations.Both numbers of configurations in the fissioning nucleus, in which the fragments are pre-formed and completely formed, are calculated using level densities described by the constant temperature function (justified by the small values of the intrinsic energy before scission).The obtained local even–odd effect results describe well the experimental data, including the increase at asymmetry values corresponding to fragmentations in which one of the fragments is magic or double magic (i.e. fragmentations in which ZH=50ZH=50 and/or NH=82NH=82 and very asymmetric fragmentations in which ZL=28ZL=28).