Particle-hole configurations in reaction mechanisms for single-particle level densities for target nuclei in $(n,p)$ reactions at 14.8 MeV energy

Earlier, single-particle level densities were obtained for a large number of target nuclei from the analysis of experimental data on a $(n,p)$ reaction at 14.8 MeV neutron energy using the Kalbach model. Recently, we obtained theoretical values of excitation energy ${\varepsilon }_c$ for unbound states and Fermi energies (${\varepsilon }_f$) for bound states for these single-particle level densities for many target nuclei by using Shlomo's theory, which leads to a shell structure, when ${\varepsilon }_c$ was plotted as a function of the atomic weight $A$. This indicates support to the concept of multiple statistical direct (MSD) and multiple statistical compound preequilibrium processes that involves unbound and bound states. We have now calculated the particle-hole configurations which are dominantly involved in the reaction mechanism for creating the single-particle level densities for all target nuclei, including “spikes” and “dips” obtained in the data analysis earlier using the formulation given by Kalbach [Phys. Rev. C 23, 124 (1981)] and Shlomo [Nucl. Phys. A 539, 17 (1992)]. It seems that $h=2, p=0$ is the dominant configuration for most of the targets in the preequilibrium process, whereas spikes seem to correspond to the $h=1, p=1$ dominant configuration, corresponding to the direct reaction mechanism; and dips seem to belong to the $h=2, p=0$ configuration and $h=1, p=1$ and $h=0, p=2$ configurations somewhat equally giving compound nucleus formation due to quantum statistical fluctuations and MSD. The implication of these calculations and results is discussed.

Figure 1

The values of $a_1=\frac{{\pi }^2{g}_c}{6}$ and $a_2=\frac{{\pi }^2{g}_R}{6}$ as a function of atomic weight as derived from the comparison of the experimental data with the Kalbach model [2]. $A$ corresponds to the smooth part, $B$ corresponds to spikes, and $C$ corresponds to dips.

Figure 2

The values of $\frac{{\mathrm{\Delta }}_i}{R_{exp}}$ (a) for eight even-even nuclei, (b) for even-odd, odd-odd, and even some even-even nuclei for $i=1$, (c) for all targets for $i=2$, and (d) for all targets for $i=3$.

Figure 3

The values of $g_c\left(Th\right)$ of the spikes as a function of incident energy ε for ${}_{22}\mathrm{Ti}^{46}, {}_{23}\mathrm{V}^{51}, {}_{24}\mathrm{Cr}^{50}, {}_{24}\mathrm{Cr}^{52}, {}_{26}\mathrm{Fe}^{54}, {}_{28}\mathrm{Ni}^{60}$, and ${}_{29}\mathrm{Cu}^{63}$ along with $g_c(exp)$ and $g_R(exp)$.

Figure 4

The values of $\frac{{\mathrm{\Delta }}_i}{R_{exp}}$ for three cases of (a) for seven cases of spikes for $i=1$, (b) for seven cases of spikes for $i=2$, and (c) for seven cases of spikes for $i=3$.

Figure 5

The values of $g_c\left(Th\right)$ of dips as a function of incident energy for ${}_{40}\mathrm{Zr}^{90}, {}_{42}\mathrm{Mo}^{92}, {}_{41}\mathrm{Nb}^{93}, {}_{42}\mathrm{Mo}^{94}, {}_{42}\mathrm{Mo}^{95}$, and ${}_{42}\mathrm{Mo}^{96}$ along with $g_c(exp)$ and $g_R(exp)$.

Figure 6

The values of $\frac{{\mathrm{\Delta }}_i}{R_{exp}}$ for six cases of dips for (a) $i=1$, (b) $i=2$, and (c) $i=3$.