Investigation of Weisskopf-Ewing approximation for the determination of ( n,p ) cross sections using the surrogate reaction technique

Abstract

The present study explores the limitations of the surrogate reaction method for determining the $(n,p)$ cross sections for the target nuclei in the mass region $A\ensuremath{\approx}50$ for the neutron energies 1--20 MeV. In the past few years there have been several experimental attempts for determining the $(n,p)$ and $(n,xp)$ cross sections using the surrogate reaction method. But this method has not been benchmarked with the experimentally well-known $(n,p)$ cross sections. The surrogate reaction method with Weisskopf-Ewing approximation may help in providing good constraints for the cross-section data, but this approximation has not been validated yet for $(n,p)$ reactions. In this paper, we have examined the validity of the Weisskopf-Ewing approximation for the $(n,p)$ reactions and also check the sensitivity of the surrogate reaction results with respect to the compound nucleus spin distribution. We have simulated the cross sections obtained through the surrogate reaction method for $n+^{48}\mathrm{Ti}, n+^{53}\mathrm{Cr}, n+^{56}\mathrm{Fe}$, and $n+^{59}\mathrm{Co}$ reactions for the different schematic spin distributions of the compound nucleus and studied the effect of assuming the validity of the Weisskopf-Ewing approximation. It has been observed that the proton decay probabilities of the compound nucleus for the $(n,p)$ channel are strongly spin dependent, therefore the Weisskopf-Ewing approximation is violated. We have also observed that the cross sections obtained using the Weisskopf-Ewing approximation show clear dependence on the spin distribution of the compound nucleus. It has also been observed that, due to the large pre-equilibrium contributions in the $(n,p)$ reactions at higher neutron energies, the use of the surrogate reaction method for the neutron energies greater than $\ensuremath{\approx}15$ MeV may not be suitable. It is concluded that the surrogate reaction method relying solely on the Weisskopf-Ewing approximation is not sufficient for determining the $(n,p)$ cross sections for the target nuclei in mass range $A\ensuremath{\approx}50$ and further development and exploration of the surrogate technique is required.