Pre-equilibrium mechanisms in the ${}^{93}\mathrm{Nb}(\vec{p},\alpha )$ inclusive reaction at incident energies from 65 to 160 MeV

The reaction mechanism of pre-equilibrium proton-induced $\alpha$-particle emission from ${}^{93}\mathrm{Nb}$ at an incident energy of 100 MeV was investigated with polarized projectiles. A formalism based on the statistical multistep direct emission model of Feshbach, Kerman, and Koonin was found to give a reasonably good reproduction of cross section and analyzing power angular distributions at various emission energies. Existing experimental distributions for the same reaction at an incident energy of 65 MeV were also analyzed with the same model. The incident-energy variation from 65 MeV up to 160 MeV was found to be consistent with the predictions of the basic model. However, whereas knockout of an $\alpha$ cluster is the dominant reaction mechanism in the final stage at the lowest and highest incident energies, at 100 MeV a pickup process competes with comparable intensity in yield.

Figure 1

Double-differential cross section (a) and analyzing power (b) as a function of scattering angle $\theta$ for the ${}^{93}\mathrm{Nb}(p,\alpha )$ reaction at an incident energy of 100 MeV and an $\alpha$-particle emission energy of 86 MeV. Results for only the pickup component of the reaction mechanism are used to display contributions of various steps. Theoretical cross-section calculations for one step $\left(---\right)$, two steps $\left(·····\right)$, and three steps ($-·-·-$) are shown, with the sums of the contributions plotted as continuous curves. The experimental analyzing power distribution is compared with theoretical calculations for a one-step reaction $\left(---\right)$, a one-step plus a two-step reaction $\left(·····\right)$, and a one plus two plus three-step reaction (solid lines).

Figure 2

Double-differential cross section (a) and analyzing power (b) as a function of scattering angle $\theta$ for the ${}^{93}\mathrm{Nb}(p,\alpha )$ reaction at an incident energy of 100 MeV and an $\alpha$-particle emission energy of 86 MeV. Theoretical cross section and analyzing power calculations for $N^I=1$ (dashed line) and $N^I=2$ (solid line) in Eq. (9) are compared with the experimental data. Results for only the pickup component of the reaction mechanism are used to display the trends.

Figure 3

Double-differential cross sections (a)–(e) and analyzing power (f)–(j) as a function of scattering angle $\theta$ for the ${}^{93}\mathrm{Nb}(p,\alpha )$ reaction at an incident energy of 100 MeV and various $\alpha$-particle emission energies $E_{\mathrm{out}}$ as indicated. Theoretical cross-section calculations for pickup (dashed lines) and knockout (dashed-dotted lines) are shown, with the sums of both reaction mechanisms plotted as continuous curves. The experimental analyzing power distributions are compared with theoretical calculations for pickup (dashed lines), knockout (dashed-dotted lines), and the sum of both reaction mechanisms (solid lines).

Figure 4

Double-differential cross sections (a)–(c) and analyzing power (d)–(f) as a function of scattering angle $\theta$ for the ${}^{93}\mathrm{Nb}(p,\alpha )$ reaction at an incident energy of 65 MeV and various $\alpha$-particle emission energies $E_{\mathrm{out}}$ as indicated. Theoretical calculations for a knockout reaction mechanism (solid line) are compared with the experimental data by Sakai et al. [16].

Figure 5

Ratio of cross sections for pickup and knockout as a function of $\alpha$-particle emission energy $E_{\mathrm{out}}$. Solid circles represent results for an incident energy of 100 MeV, and open circles are for 160 MeV from previous work [15]. Error bars are only rough estimates, and the curve is an exponential fit to the data.