Collective enhancement in nuclear level density of $^{72}$Ga and its effect on $^{71}$Ga(n, $\gamma$)$^{72}$Ga capture cross-section

The $\gamma$-gated proton spectra measured in the reactions $^{64}$Ni($^{9}$Be, p2n)$^{70}$Ga and $^{64}$Ni($^{9}$Be, pn)$^{71}$Ga, have been utilized to obtain the nuclear level density (NLD) of $^{71}$Ga and $^{72}$Ga nuclei by using the statistical model (SM) calculations. It is seen that the $\gamma$-gated proton spectrum are reasonably explained by using the large value of the inverse level density parameter ($k$ = 11.2 MeV) in the NLD prescription of the Fermi gas (FG) model. The large value of $k$ is indicative of the rotational enhancement, which is consistent with the earlier results in other mass regions. Furthermore, a rotational enhancement factor has been included in the NLD and used in the SM calculation keeping the systematic value of $k$=8.6 MeV and it explains the $\gamma$-gated proton spectrum nicely. The result clearly indicates the presence of collective enhancement in NLD. Subsequently, the NLD with collective enhancement has been utilized in the TALYS calculation, for the first time, to calculate the $^{71}$Ga(n, $\gamma$)$^{72}$Ga capture cross-section. It is observed that, while the FG model without the collective enhancement in the NLD for $^{72}$Ga under predicts the capture data, with the rotational enhancement correction the FG model over predicts the data by similar amount at higher energies. However, in the energy range of 0.01 MeV to 0.1 MeV, the FG model corrected for rotational enhancement describes the data quite well. Thus, the present work indicates that collective enhancement, whenever required, should be taken into account fro proper description of low energy capture cross section data.