Mass distributions are normally obtained from measurements, but models can be used to fill gaps that are too large for linear interpolation. A variable number of

Gaussian functions can be used to represent the mass distributions of different fission reactions and neutron energies, from Th to Es (Z = 90-99) and for excitation energies < 20 MeV (e. g., Figs. 9 and 10). Thus, the sum of 2 to 5 Gaussian functions can be fitted to the experimental chain yield data [Y(A)] of products from the fission of these nuclei, using the method of least squares. The Gaussian functions can then be characterised against mathematical functions of the atomic numbers (ZF), mass numbers (Af), and excitation energies (E*) of the fissioning nuclei. Reciprocal variance weighting is used in both types of calculation, and the resulting functions provide a means of determining complete mass distributions for fissioning nuclei.

The central Gaussian curve is not needed to represent chain yields from spontaneous fission reactions (SF), in agreement with experimental observations that show the valley yields from spontaneous fission to be more than an order-of-magnitude less than those from thermal-neutron induced fission reactions. Furthermore, one Gaussian curve per peak can be adopted to represent the chain-yield data reasonably well for both 14 MeV neutron-induced fission and thermal-neutron induced fission of the heavier actinides (ZF > 94). Other modifications can be made to improve the chain-yield representations: for example, fission of heavier actinides — modify the peak Gaussian functions to include an exponential drop in Y(A) for AH < 130 and in the complementary range for the light peak (these modified peak functions are then renormalized to achieve a 200% sum for all yields).

Equations have also been developed to calculate the uncertainties in fission yields obtained from these model estimates. Uncertainties in the calculated yields can be estimated from the following empirical equation proposed for the percentage uncertainty (PER):

PER = (25) exp{-0.25[lnY(A)]}

with an estimated range of uncertainty of Y(A)/(l + PER/100) to Y(A)(l + PER/100).

Most experimental chain yields fall within the estimated range of uncertainties, implying that most of the calculated chain yields should be reliable.

Many of the measured chain yields have fine structure that cannot be fully reproduced by summing smooth Gaussian functions (Figs. 9 and 10), although complementary single Gaussian curves can represent the experimental data reasonably well for high excitation energies and ZF > 94. Thus, an empirical multi­Gaussian model has been successfully developed to calculate the chain yields [Y(A)] of fission reactions, with a nuclear charge [ZF ] from 90 to 99 and excitation energy E* < 20 MeV. There are many other features of these mass distribution curves that will not be considered in any further detail within this review.

A A

Fig. 9. Various Gaussian curves fitted to mass distributions of fission processes: thermal-neutron fission of 239Pu, 242mAm and 249Cf, and spontaneous fission of 252Cf