Dissipation and tunneling in heavy-ion reactions near the Coulomb barrier

Influence of couplings to collective excitations on fusion process has been well established experimentally and theoretically. Much less is known about the influence of dissipation caused by transfer reactions, even less due to noncollective excitations. In this paper, we report the results of the comparison of experimental barrier distributions with the $\mathrm{CC}+\mathrm{RMT}$ model calculations taking into account noncollective excitations, in which the stationary coupled channels method is merged with a statistical approach based on the random matrix theory. In spite of many assumptions and approximations, we find that the model works well for medium systems without fitting parameters, describing the influence of dissipation on tunneling. On the other hand, for heavier systems this mechanism does not appear to be sufficient. This points to the importance of other dissipation mechanisms for these systems, such as nucleon transfer processes.

Figure 1

Theoretical single particle (s.p.) level densities of the relevant nuclei calculated with the Skyrme-Hartree-Fock-Bogoliubov (HFB) method, taken from Refs. [29, 30].

Figure 2

Excitation functions of quasielastic scattering for the ${}^{20}\mathrm{Ne}+{}^{90,92}\mathrm{Zr}$ systems calculated for ${\mathrm{\Theta }}_{\mathrm{c}.\mathrm{m}.}={148}^{\circ }$ (${\mathrm{\Theta }}_{\mathrm{lab}}={140}^{\circ }$). The experimental results (the dots), taken from Ref. [14], were measured at ${\mathrm{\Theta }}_{\mathrm{lab}}={130}^{\circ }, {140}^{\circ }$, and ${150}^{\circ }$. The dot-dot-dashed curves were calculated without taking into account any couplings, and the dashed curves were calculated by taking into account only the collective excitations of the projectile and target nuclei. The solid lines show the results with the additional including of 200 s.p. excitations.

Figure 3

Experimental (points) and theoretical quasielastic barrier distributions (BDs) for the ${}^{20}\mathrm{Ne}+{}^{90,92}\mathrm{Zr}$ systems. The dashed curves show results of the standard CC calculations taking into account the collective excitations only. The solid curves show the results of including in addition 200 s.p. excitations in the target nuclei. The experimental energy resolution of 1.2 MeV was taken into account by folding the calculated distributions with a Gaussian function of this FWHM. Since we are more interested in the shapes than the absolute positions of BD, the theoretical curves were normalized to the experimental data in the peaks, and also shifted to higher energy by 1.3 MeV – 1.6 MeV. The experimental data are taken from Ref. [14].

Figure 4

Experimental (points) and theoretical barrier distributions for the ${}^{20}\mathrm{Ne}+{}^{58,60,61}\mathrm{Ni}$. The dashed lines show results of the standard CC calculations taking into account couplings to the collective excitations only, and the solid lines were obtained after including also couplings to 200 noncollective ones. This corresponds to excitation energy up to 6.2 MeV in ${}^{58,60}\mathrm{Ni}$ and 4.2 MeV in ${}^{61}\mathrm{Ni}$. The experimental resolution of 1.0 MeV (FWHM) was taken into account. The ${\beta }_2$ value of 0.24 for the ${}^{61}\mathrm{Ni}$ target (see text) was critically important to achieving agreement between the experimental data and the calculations. To overlap the experimental and calculated peaks we shifted the latter ones to higher energy by 0.1–1.0 MeV. The experimental data originate from Ref. [12].

Figure 5

Experimental (points) and theoretical barrier distributions for the ${}^{20}\mathrm{Ne}+{}^{118}\mathrm{Sn}$ system. The dashed line show results of the standard CC calculations taking into account the couplings to the collective levels only, and the solid line was obtained after including also couplings to 150 s.p. ones, what corresponds to excitation energies up to 3.7 MeV. The experimental resolution of 1.5 MeV (FWHM) was taken into account. The calculated distributions were normalized and shifted (by $\sim 0.5$ MeV) to overlap the peaks. The experimental data (for ${\mathrm{\Theta }}_{\mathrm{c}.\mathrm{m}.}={135}^{\circ }, {145}^{\circ }$, and ${155}^{\circ }$) are taken from Refs. [32, 33].

Figure 6

The same as Fig. 5, but for the ${}^{20}\mathrm{Ne}+{}^{208}\mathrm{Pb}$ system. 150 s.p. levels corresponds to excitation energies up to 6.1 MeV. The experimental resolution of 0.7 MeV (FWHM) was taken into account. The experimental data taken from Ref. [15].The calculated distributions were normalized and shifted (by $\sim 1.3$ MeV) to overlap the peaks.

Figure 7

Fusion excitation functions for the ${}^{20}\mathrm{Ne}+{}^{90,92}\mathrm{Zr}$ systems calculated with several coupling schemes. The red dashed lines were obtained without any couplings. The red solid lines were obtained by taking into account couplings to the collective levels, while the blue dash-dot lines show the results with including dissipation: 200 s.p. levels.

Figure 8

Fusion barrier distributions $D_{\mathrm{fus}}$ of the ${}^{20}\mathrm{Ne}+{}^{90,92}\mathrm{Zr}$ systems. The black dotted lines show the distributions calculated without any couplings taken into account, the blue dashed lines were calculated with collective excitation included. The red dash-dot and solid lines show results of including 150 and 200 s.p. levels, correspondingly.

Figure 9

Comparison of $D_{\mathrm{fus}}$ and $D_{\mathrm{qe}}$ (calculated for 152 deg. in c.m. frame) for the ${}^{20}\mathrm{Ne}+{}^{90,92}\mathrm{Zr}$ systems calculated with couplings to collective (dashed lines) and collective $+$ 150 single-particle excitation levels (solid lines) in target nuclei taken into account. No energy shifts neither experimental resolution corrections were applied.

Figure 10

Barrier penetrability for the ${}^{20}\mathrm{Ne}+{}^{92}\mathrm{Zr}$ as a function of the projectile energy in the center-of-mass frame for the same conditions as in Fig. 7.