Probing systematic model dependence of complete fusion for reactions with the weakly bound projectiles ${}^{6,7}\mathrm{Li}$

Background: Complete fusion cross section measurements involving weakly bound projectiles show suppression at above-barrier energies compared to coupled-channels (CC) calculations, but no definite conclusion could be drawn for sub-barrier energies. Different CC models often lead to contrasting results.

Purpose: We aim to investigate the differences in the fusion cross sections predicted by commonly used CC calculations, using codes such as fresco and ccfull, when compared to experimental data.

Methods: The fusion cross sections are normalized to a dimensionless form by isolating the effect of only dynamic channel couplings calculated by both fresco and ccfull, by the method of fusion functions, and compared to a universal fusion function. This acts as a probe for obtaining the model dependence of fusion.

Results: A difference is observed between the predictions of fresco and ccfull for all the reactions involving ${}^{6,7}\mathrm{Li}$ as projectiles, and it is noticeably more for systems involving ${}^7\mathrm{Li}$.

Conclusions: With the theoretical foundations of the two CC models being different, their calculation of fusion is different even for the same system. The conclusion about the enhancement or suppression of fusion cross sections is model dependent.

Figure 1

Experimental fusion functions using the results of fresco and ccfull calculations for several reactions involving weakly bound projectiles ${}^{6,7}\mathrm{Li}$. The solid lines represent universal fusion functions (UFFs) obtained from Eq. (6) and dashed lines represent renormalized UFFs to show the average suppression factors in experimental CF at above-barrier energies.

Figure 2

Same as Fig. 1 but plotted in logarithmic scale.

Figure 3

Comparison of the fusion cross sections ${\sigma }_F^{CC}$ for a few systems calculated using ccfull (solid lines) and its modified version ccfull_w that uses an imaginary potential as an input to simulate fusion (dotted lines), showing identical results.

Figure 4

Differences in the effect of inelastic couplings between ccfull and fresco for [(a) and (c)] ${}^6\mathrm{Li}+{}^{144}\mathrm{Sm}$ and [(b) and (d)] ${}^7\mathrm{Li}+{}^{144}\mathrm{Sm}$ reactions plotted in logarithmic and linear scales respectively. Calculated fusion cross sections are compared with experimental data taken from Rath et al. [7] and Rath et al. [4] respectively.

Figure 5

The quantity $F_{\mathrm{inelastic}}$ ($=1-{\sigma }_F^{\mathrm{uncoupl}}/{\sigma }_F^{\mathrm{coupl}}$ [38]) derived from the coupled and uncoupled fusion cross sections calculated using ccfull and fresco.

Figure 6

(a),(b) Experimental cross sections for elastic (circles) and inelastic scattering corresponding to the $2^{+}$ (0.55 MeV) state of ${}^{148}\mathrm{Sm}$ (diamonds) taken from Talon et al. [41] are compared with fresco results represented by solid and dashed lines respectively. (c) Experimental fusion cross sections taken from Leigh et al. [43] are represented by squares along with the theoretical results for fusion obtained from both fresco and ccfull represented by lines. (d) The quantity $F_{\mathrm{inelastic}}$ obtained from the results of ccfull and fresco with (without) projectile excitation are represented by dashed (long-short) and solid (dash-dot) lines respectively.