Microscopic calculation of precompound excitation energies for heavy-ion collisions

We introduce a microscopic approach for calculating the excitation energies of systems formed during heavy-ion collisions. The method is based on time-dependent Hartree-Fock (TDHF) theory and allows the study of the excitation energy as a function of time or ion-ion separation distance. We discuss how this excitation energy is related to the estimate of the excitation energy using the reaction $Q$-value, as well as its implications for dinuclear precompound systems formed during heavy-ion collisions.

Figure 1

Internuclear potential $V(R)$ for the head-on collision of the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ system for various $E_{\mathrm{c}.\mathrm{m}.}$ values. The relative ground-state binding energy of the ${}^{32}\mathrm{S}$ nucleus is represented by the $-Q_{\mathit{gg}}$ value. The height of the barriers increase with $E_{\mathrm{c}.\mathrm{m}.}$.

Figure 2

Excitation energy for the head-on collision of the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ system for various $E_{\mathrm{c}.\mathrm{m}.}$ values (solid curves) as a function of the ion-ion distance $R$. Also shown are the corresponding collective kinetic energy $E_{\mathrm{kin}}$ values (dashed curves). As can be seen, both the excitation energy and the collective kinetic energy increase with $E_{\mathrm{c}.\mathrm{m}.}$.

Figure 3

Long-time evolution of the excitation energy, $E^{*}$, and the ion-ion potential, $V(R)$, for the head-on collision of the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ system at $E_{\mathrm{c}.\mathrm{m}.}=11$ MeV as a function of the ion-ion distance $R$.

Figure 4

Excitation energy for the head-on collision of the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ system for various $E_{\mathrm{c}.\mathrm{m}.}$ values at the point of capture (solid blue line) and the excitation energy calculated from Eq. (5) (solid red curve). Other curves are described in the text.

Figure 5

Internuclear potential for the head-on collision of the ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ system for various $E_{\mathrm{c}.\mathrm{m}.}$ values. The relative ground state binding energy of the ${}^{80}\mathrm{Zr}$ nucleus is represented by the $-Q_{\mathit{gg}}$ value. The height of the barriers increase with $E_{\mathrm{c}.\mathrm{m}.}$.

Figure 6

Excitation energy for the head-on collision of the ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ system for various $E_{\mathrm{c}.\mathrm{m}.}$ values (solid curves) as a function of the ion-ion distance $R$. Also, shown are the corresponding collective kinetic energy $E_{\mathrm{kin}}$ values (dashed curves). As can be seen, both the excitation energy and the collective kinetic energy increase with $E_{\mathrm{c}.\mathrm{m}.}$.

Figure 7

Excitation energy for the head-on collision of the ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ system for various $E_{\mathrm{c}.\mathrm{m}.}$ values at the point of capture (solid blue line) and the excitation energy calculated from Eq. (5) (solid red curve). Other curves are described in the manuscript.

Figure 8

Internuclear potential for the head-on collision of the ${}^{16}\mathrm{O}+{}^{34}\mathrm{Ne}$ system for various $E_{\mathrm{c}.\mathrm{m}.}$ values and two alignments of the ${}^{34}\mathrm{Ne}$ nucleus. The solid lines denote the potential for vertical alignment whereas the dashed curves are for the horizontal alignment of the ${}^{34}\mathrm{Ne}$ nucleus with respect to the collision axis. The height of the barriers increase with $E_{\mathrm{c}.\mathrm{m}.}$.

Figure 9

Excitation energy for the head-on collision of the ${}^{16}\mathrm{O}+{}^{34}\mathrm{Ne}$ system for various $E_{\mathrm{c}.\mathrm{m}.}$ values as a function of the ion-ion distance $R$. The solid lines denote the excitation energy for vertical alignment whereas the dashed curves are for the horizontal alignment of the ${}^{34}\mathrm{Ne}$ nucleus with respect to the collision axis. As can be seen, the excitation energy increase with $E_{\mathrm{c}.\mathrm{m}.}$.