Phenomenological analysis of high energy nuclear reaction

Cross-section of reaction, namely the probability of production of new isotopes by high energy nuclear reaction was investigated. Product nuclei (Ap, Zp) distribute widely in a Z-N plane. A semi-empirical formula for the product nuclei was given by Rudstam. It was found that sigma (Zp) for a constant Ap showed gaussian distribution. The present study was made for obtaining a simple empirical formula expressed with Δ Z = Z sub(OR) - Z sub(O β), width (R) of Gaussian distribution and the maximum value h = sigma (Z sub(OR)) of sigma, where Z sub(OR) is a value of Z on a line of constant A sub(p) in a Z-N plane giving the maximum value of sigma, and Z sub(o β) is the intersection of the line of constant A sub(p) and β stable line. The dependence of Δ Z, R and h on A sub(p), Z sub(p), E, and the mass number A sub(t) and the atomic number Z sub(t) of target nuclei were investigated, clear correlation of A sub(p) and Δ Z was observed for various A sub(t). The dependence of R on A sub(p) was also seen. The values of h depend largely on the incident energy E. The effects of even or odd A sub(p) on h and R were seen owing to precise investigation. Two formulas of sigma were obtained in the present study, which corresponded to Δ A(= A sub(t) - A sub(p)) >= 3 and Δ A < 3. (Kato, T.)