Imaginary part of the ${}^9\mathrm{C}\text{−}{}^9\mathrm{Be}$ single-folded optical potential

In a recent publication we have argued that using two very successful $n\text{−}{}^9\mathrm{Be}$ optical potentials [A. Bonaccorso and R. J. Charity, Phys. Rev. C 89, 024619 (2014)] and microscopic projectile densities, it is possible to build a single-folded (light-) nucleus-${}^9\mathrm{Be}$ imaginary optical potential which is more accurate than a double-folded optical potential. By comparing to experimental reaction cross sections, we showed for ${}^8\mathrm{B},{}^8\mathrm{Li}$, and ${}^8\mathrm{C}$ projectiles, that a very good agreement between theory and data could be obtained with such a “bare” potential, at all but the lowest energies where a small semimicroscopic surface term was added to the single-folded potential to take into account projectile breakup. In this paper we extend this study to the case of ${}^9\mathrm{C}$ projectiles and assess the sensitivity to the projectile density used. We then obtained the modulus of the nucleus-nucleus $S$ matrix and parametrize it in terms of a strong-absorption radius $R_s$ and finally extracted the phenomenological energy dependence of this radius. This approach could be the basis for a systematic study of optical potentials for light exotic nuclei scattering on light targets and/or parametrizations of the $S$ matrix. Furthermore our study will serve to make a quantitative assessment of the description of the core-target part of knockout reactions, in particular their localization in terms of impact parameters.

Figure 1

Potentials calculated at 20 (LHS) and 38 MeV/nucleon (RHS). These include the double-folded (d.f.) and the single-folded (s.f.) results. The surface contribution (surf), the sum of the single-folded and surface values (tot), and the JLM result. The double-folded potentials are calculated with the HF densities.

Figure 2

As for Fig. 1 but now the potentials are calculated at 66 (LHS) and 83 MeV/nucleon (RHS). At 66 MeV/nucleon the “bare” JLM (JLM bare) is also shown.

Figure 3

(LHS) Energy dependence of the reaction cross sections for ${}^9\mathrm{C}\text{−}{}^9\mathrm{Be}$ calculated according to Eq. (1). We compare results obtained using the the single-folding potential with $n\text{−}{}^9\mathrm{Be}$ from [3] and various projectile densities, in particular VMC [4], YK-E [28], PD [29] (see also text), and JLM. The two full lines are the results of calculations with the double-folded potentials. Thick maroon line is with HF densities, blue thin line with VMC densities. Data are from Ref. [32]. (RHS) We show here again the data from Ref. [32] and results of reaction cross section calculations which have been modified to fit the data. One is from the single-folding potential plus the additional surface term Eq. (9), the second is a renormalized JLM. For comparison results obtained for ${}^8\mathrm{Li}$ and ${}^8\mathrm{B}$ projectiles from Ref. [2] using the single-folded plus surface term potential. Data are from Refs. [33, 34].

Figure 4

${}^9\mathrm{C}$ densities used in the calculated cross sections shown in Fig. 2.

Figure 5

(LHS) $S$ matrices calculated at 66 MeV/nucleon with the potentials indicated in the legend. (RHS) Integrand in Eq. (1). See text for details.