Phenomenological approach affecting of (n, p) reaction cross sections via 14.5-MeV neutrons

Abstract

A new systematic formula is suggested to evaluate the (n, p) reaction cross sections at neutron energy of 14.5 MeV based upon the reaction’s Q-value dependence, explicit symmetry breaking, and shell effects. The measured data for the (n, p) reaction cross sections have been gathered from the available literature, and then, it was analyzed for isotopes having 3 ≤ Z ≤ 83. It has been noted that the plot of σ(n,p) against $$\left( {{Z \mathord{\left/ {\vphantom {Z {A^{{{ 3\mathord{\left/ {\vphantom { 32}} \right. \kern-0pt} 2}}} }}} \right. \kern-0pt} {A^{{{ 3\mathord{\left/ {\vphantom { 32}} \right. \kern-0pt} 2}}} }}} \right)$$ , $$\left( {{{\left( {N - Z + 1} \right)} \mathord{\left/ {\vphantom {{\left( {N - Z + 1} \right)} {A^{{{ 4\mathord{\left/ {\vphantom { 43}} \right. \kern-0pt} 3}}} }}} \right. \kern-0pt} {A^{{{ 4\mathord{\left/ {\vphantom { 43}} \right. \kern-0pt} 3}}} }}} \right)$$ and $$\left( {N/Z \cdot A^{{{ 2\mathord{\left/ {\vphantom { 23}} \right. \kern-0pt} 3}}} } \right)$$ is more efficient in determining the (n, p) reaction cross sections, as the reaction Q-value is related to values of σ(n,p) too, which has been adequately represented and compared to other terms such as Sp, Sn, and Sα separation energies. The odd–even effects investigated in the cross sections of odd-mass nuclei are higher than those of their neighboring even–even nuclei close to magic numbers. The estimates of the current formula are compared with the experimental data gathered from the literature, and they are found to be in good agreement.