Equilibrium and pre-equilibrium processes in the ${}^{55}\mathrm{Mn}$(${}^6\mathrm{Li}$,$\mathit{xp}$) and ${}^{57}\mathrm{Fe}$($\alpha$,$\mathit{xp}$) reactions

Spectra of outgoing neutrons and protons from the ${}^6\mathrm{Li}$ $+$ ${}^{55}\mathrm{Mn}$ reaction and protons from the $\alpha$ $+$ ${}^{57}\mathrm{Fe}$ reaction have been measured with beams of 15-MeV ${}^6\mathrm{Li}$ ions and 30-MeV $\alpha$ particles. These reactions proceed through the same ${}^{61}\mathrm{Ni}$ nucleus at the same excitation energy, thus allowing the difference in reaction mechanisms to be studied. It is shown that spectra from the first reaction measured at backward angles are due to emission from a traditional compound nucleus reaction, in which the intermediate nucleus has reached statistical equilibrium; the spectra from the second reaction contain a significant fraction of pre-equilibrium emission at all angles. Level density parameters of the residual nucleus ${}^{60}\mathrm{Co}$ have been obtained from the first reaction. Both emission spectra and angular distributions have been measured for the second reaction. It was found that the pre-equilibrium component exhibits a forward-peaked angular distribution, as expected, but with a steeper slope than predicted and with an unusual slight rise at angles above ${120}^{°}$. The backward-angle rise is explained qualitatively by the dominance of the multistep compound mechanism at backward angles.

Figure 1

Angular dependence of elastically scattered $\alpha$ particles. Points show the experimental data scaled to the calculation. Error bars due to counting statistics are less than the size of the points. The line shows the results of calculations with the optical model potential N-9401 from the ripl-2 database [5].

Figure 2

(a) Proton and (b) neutron evaporation spectra from the ${}^6\mathrm{Li}$ $+$ ${}^{55}\mathrm{Mn}$ reaction. The points are experimental data taken at $157{}^{°}$ for the lower proton energies and ${150}^{°}$ for the higher proton energies. The neutron data points are an average of measurements at $125{}^{°}$ and $140{}^{°}$. The lines are the result of empire calculations with Gilbert-Cameron (top curve) and HF-BCS (bottom curve) input level density models. Experimental cross sections are multiplied by $4\pi$ sr to compare with the calculated, angle-integrated spectrum.

Figure 3

Proton evaporation spectrum from the ${}^3\mathrm{He}$ $+$ ${}^{58}\mathrm{Fe}$ reaction. The points show the ${157}^{°}$ data from Ref. [3] normalized to $4\pi$ sr, and the line shows the angle-integrated results of empire calculations using the Gilbert-Cameron level-density model with the parameters from Ref. [10].

Figure 4

Proton experimental spectra from the $\alpha$ $+$ ${}^{57}\mathrm{Fe}$ reaction measured at laboratory angles of ${30}^{°}$, ${45}^{°}$, ${70}^{°}$, ${90}^{°}$, ${104}^{°}$, ${120}^{°}$, ${135}^{°}$, ${150}^{°}$, and ${160}^{°}$ (from top to the bottom). The four backward-angle spectra are scaled down for better visualization.

Figure 5

Angle-integrated proton spectrum from the $\alpha$ $+$ ${}^{57}\mathrm{Fe}$ reaction. The points show the experimental data, while the lines are the results of calculations using the empire and talys codes. The curves labeled pre-equilibrium also include contributions from the equilibrium or compound component.

Figure 6

Angular distribution of outgoing protons from different energy intervals. The points show the experimental results from the ${}^{57}\mathrm{Fe}$($\alpha$,$\mathit{xp}$) reaction, and the lines are from the calculations with the code talys.

Figure 7

Energy spectrum of outgoing protons from the ${}^{57}$ Fe($\alpha$,$\mathit{xp}$) reaction measured at a laboratory angle of ${160}^{°}$. The points show the data, and the line is the compound nucleus reaction component calculated in the talys code.

Figure 8

Experimental angular distribution of pre-equilibrium outgoing protons with energies greater than 16 MeV from the ${}^{57}\mathrm{Fe}$($\alpha$,$p$) reaction.

Figure 9

Comparison between the experimental angular distributions for the ${}^{57}\mathrm{Fe}$($\alpha$,$\mathit{xp}$) reaction and the curves obtained by fitting using Eq. (1). The results are displayed as a function of $\cos \theta$ in order to show the exponential fall off of the cross section at forward angles at 16 and 20 MeV.