Experimental differential cross sections, level densities, and spin cutoffs as a testing ground for nuclear reaction codes

Proton double-differential cross sections from ${}^{59}\mathrm{Co}(\alpha ,p){}^{62}\mathrm{Ni}$, ${}^{57}\mathrm{Fe}(\alpha ,p){}^{60}\mathrm{Co}$, ${}^{56}\mathrm{Fe}({}^7\mathrm{Li},p){}^{62}\mathrm{Ni}$, and ${}^{55}\mathrm{Mn}({}^6\mathrm{Li},p){}^{60}\mathrm{Co}$ reactions have been measured with 21-MeV $\alpha$ and 15-MeV lithium beams. Cross sections have been compared against calculations with the empire reaction code. Different input level density models have been tested. It was found that the Gilbert and Cameron [A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43, 1446 (1965)] level density model is best to reproduce experimental data. Level densities and spin cutoff parameters for ${}^{62}\mathrm{Ni}$ and ${}^{60}\mathrm{Co}$ above the excitation energy range of discrete levels (in continuum) have been obtained with a Monte Carlo technique. Excitation energy dependencies were found to be inconsistent with the Fermi-gas model.

Figure 1

Angular distribution of outgoing protons from the ${}^{59}\mathrm{Co}(\alpha ,p)$ reaction.

Figure 2

Experimental proton and neutron differential cross sections versus empire calculations with different input level density models. The neutron differential cross section values are from Ref. [15]. Left panel: ${}^{59}\mathrm{Co}(\alpha ,p)$ (points) with $E_{\alpha }=21$ MeV and ${}^{59}\mathrm{Co}(\alpha ,n)$ (squares) with $E_{\alpha }=17.6$ MeV. Right panel: ${}^{56}\mathrm{Fe}({}^7\mathrm{Li},xp)$ with $E_{{}^7\mathrm{Li}}=15$ MeV. Dashed lines are original calculations. Solid lines are original calculations scaled to match experimental points in the discrete level region.

Figure 3

Experimental proton differential cross sections versus empire calculations with different input level density models. Left panel: ${}^{57}\mathrm{Fe}(\alpha ,p)$ with $E_{\alpha }=21$ MeV. Right panel: ${}^{55}\mathrm{Mn}({}^6\mathrm{Li},xp)$ with $E_{{}^6\mathrm{Li}}=15$ MeV.

Figure 4

Experimental proton differential cross sections (points) versus empire calculations using the Fermi-gas model with two spin cutoff parameters according to Eqs. (3) (bottom line) and (2) (top line).

Figure 5

Shaded areas: Level densities and spin cutoff functions obtained from Monte Carlo simulations for ${}^{60}\mathrm{Co}$ and ${}^{62}\mathrm{Ni}$ nuclei. Lines: Calculations according to Fermi-gas formula with spin cutoff expressions (3) (bottom lines) and (2) (top lines).

Figure 6

Experimental proton spectrum obtained with 18-MeV $\alpha$ beam in Ref. [17] (points). Empire calculations using the Fermi-gas model with two spin cutoff parameters according to expressions (3) (bottom line) and (2) (top line).