An empirical correlation formula of spontaneous fission half-lives

A simple empirical correlation formula has been proposed separately for the spontaneous fission half-lives data with the nuclides in the range of Pu ∼ Fm and in the wider range of Th ∼ 104. Its functional form was derived on the basis of Swiatecki's correlation formula, in which the spontaneous fission half-lives were expressed as a function of the usual fissionability parameter (Z2/A) and the mass deviation (δM) of the experimental mass from Green's mass formula. The correlation functions proposed in the present work are of the form log10T =c1 + c2 (1-X) δM + c3 + Δ for the nuclides in the wider range of Th ∼ 104. Here T, δM and X are the spontaneous fission half-lives measured in years, the mass deviation in MeV, and the fissionability parameter, respectively. The values of δM and X are calculated by using the original and the revised Myers- Swiatecki mass formulas and also by using the Seeger-Perisho mass law. The parameters of c1, c2, c3, and Δ were determined by following an iterative least-square procedure. For 19 even-even, 7 odd-A, 2 odd-odd nuclides in the range of Pu ∼ Fm, the correlation formula with the best fitness was found to be log10T = - 347.032X - 19.020 (1-X) δM + 288.894 + Δ (4.451 for odd-A nuclides and 3.520 for odd-odd nuclides) with the weighted variance of 0.796, by using the original Myers-Swiatecki mass formula. For 26 even-even, 8 odd-A, 2 odd-odd nuclides in the wider range of Th ∼ 104, the correlation formula with the best fitness was found to be log10T 2821.608(1-X)3 - 25.285(1-X) δM - 18.949 + Δ (3.725 for odd-A nuclides and 3.363 for odd-odd nuclides) with the weighted variance of 0.604, by using the revised Myers-Swiatecki mass formula. Both correlation function forms do not seem to be very successful, when the X- and δM-values are calculated by using the Seeger-Perisho mass law. In their mass law the fissionability parameters (X) are extremely close together for a given element. (author)