Systematics of nuclear charge distribution in fission the Z_P model

Abstract

An extension of the conventional Z_P model has been used with data for ten fission reactions and the method of least-squares for derivation of parameters that describe the nuclear charge-distributions. Data for light and heavy fission products for each reaction were treated together by consideration of the complementarity of average mass numbers of precursors (A′_L+A′_H=A_F). This treatment gave calculated yields that are essentially equal for complementary elements (Z_L+Z_H=Z_F). The parameters determined,$\bar \sigma Z$, the Gaussian dispersion width parameter, a linear function of Δ_Z=|Z_P-A′(Z_F/A_F)|, Z_P being the Z at maximum of the curve, and$\overline {EOZ}$ and$\overline {EON}$, the even-odd proton and neutron yield enhancement factors, represented most data (A_H⋟130–150 and the complementary light A's) moderately well, better than did oscillating functions of$\bar \sigma Z$ and Δ_Z. The$\bar \sigma Z$ values were found to be approximately constant (0.48 to 0.62) and, generally, to increase with the average number of neutrons emitted,$\bar v, (\partial \bar \sigma Z/\partial \bar v \cong 0.04)$. The Δ_Z values at A′=140 were in the range of 0.42 to 0.50, and the slopes, ∂Δ_Z/∂A′_H, ranged from 0.0 to 0.03. The$\overline {EOZ}$ factor was found to be several times larger than the$\overline {EON}$ factor and to decrease with increasing excitation energy and with A and/or Z of the fissioning nucleus, as has been reported previously. The adequacy of the Z_P model for representation of data and for prediction of yields in the high-yield mass-number regions mentioned above are discussed, and the large uncertainties that are involved in extrapolating the model to near symmetric or to very asymmetric mass and charge divisions are pointed out.