Scattering and fusion of identical heavy ions with arbitrary spin

The cross sections of elastic scattering and fusion of identical heavy ions with arbitrary spin, $s$ are derived. Applications to several light heavy ions at near-barrier energies are made. It is found that the transverse isotropy; namely, the flat angular distribution which sets in at a critical value of the energy, becomes less pronounced with higher values of the spin. The oscillations in energy in the fusion cross section was found to go as $1/(2s+1)$. A similar factor is found in the angle-oscillating term in the elastic-scattering cross section.

Figure 1

Second derivatives of the differential cross sections for ${}^6\mathrm{Li}+{}^6\mathrm{Li}$ elastic scattering, at $\theta =\pi /2$. The results for the three potentials considered in the text are shown as functions of collision energy. The solid circles indicate the TI energies.

Figure 2

Angular distributions of ${}^6\mathrm{Li}+{}^6\mathrm{Li}$ scattering at 1.25 and 2.05 MeV calculated with the AW potential (blue solid lines) and with the phenomenological WS potentials with set 1 (green dashed lines) and set 2 (red dot-dashed lines).

Figure 3

Angular distributions of ${}^6\mathrm{Li}+{}^6\mathrm{Li}$ scattering at the TI energies below 10 MeV. The curves correspond to calculations with the Akyüz–Winther potential, normalized with respect to their values at $\theta =90$ degrees.

Figure 4

Second derivatives of the angular distribution of ${}^{10}\mathrm{B}+{}^{10}\mathrm{B}$ scattering with respect to $\theta$, taken at $\theta =\pi /2$. The curves correspond to results for the three nuclear potentials discussed in the text, and for the Mott-scattering case. The solid circles indicate the TI energies.

Figure 5

Angular distributions in ${}^{10}\mathrm{B}+{}^{10}\mathrm{B}$ at three energies, calculated for the three potentials of Table 3. For details see text.

Figure 6

Fusion cross sections for the identical projectile-target systems (a) ${}^6\mathrm{Li}+{}^6\mathrm{Li}$ and (b) ${}^7\mathrm{Li}+{}^7\mathrm{Li}$. For details see the text.

Figure 7

The oscillatory terms, $\mathrm{\Delta }{\sigma }_0\left(E\right)$ and ${\sigma }_{\mathrm{osc}}\left(E\right)$ of Eqs. ((72) and (73)) vs the center-of-mass energy for the systems ${}^6\mathrm{Li}+{}^6\mathrm{Li}$ and ${}^7\mathrm{Li}+{}^7\mathrm{Li}$. See text for details.

Figure 8

Damping of ${\sigma }_{\mathrm{osc}}\left(E\right)$ in the ${}^6\mathrm{Li}+{}^6\mathrm{Li}$ and ${}^7\mathrm{Li}+{}^7\mathrm{Li}$ collisions: panel (a) shows the damping parameter, $\xi$, in the two cases; panel (b) shows the ratio of the two attenuation factors ($A_{\mathrm{tt}}=exp(-\pi \xi )$) for the two Li systems. See text for details.

Figure 9

Influence of the spin and the mass of the identical nuclei on the exchange effects. The figure shows the ratio ${\sigma }_{\mathrm{osc}}/{\sigma }_0$ for several systems as functions of the dimensionless energy variable, $x=(E-V_{\mathrm{B}})/\hslash \omega$. Clearly, the importance of exchange effects (measured by the amplitude of the oscillations) decreases with the mass and the spin.

Figure 10

The contour $\mathrm{\Gamma }$ used in evaluation of the integral of Eq. (B1). The three poles of the integrand closest to the real axis are represented by circles. Only the contribution from the pole with smallest imaginary part (green solid circle) is taken into account. Contributions for other poles (open circles) are neglected.