Astrophysical reaction rates with realistic nuclear level densities

Realistic nuclear level densities (NLDs) obtained within the spectral distribution method (SDM) are employed to study nuclear processes of astrophysical interest. The merit of SDM lies in the fact that the NLDs corresponding to many-body shell-model Hamiltonians consisting of residual interaction can be obtained for the full configurational space without recourse to the exact diagnolization of huge matrices. We calculate NLDs and $s$-wave neutron resonance spacings which agree reasonably well with the available experimental data. By employing these NLDs, we compute reaction cross sections and astrophysical reaction rates for radiative neutron capture in few Fe-group nuclei and compare them with experimental data as well as with those obtained with NLDs from phenomenological and microscopic mean-field models. The results obtained for the NLDs from SDM are able to explain the experimental data quite well. These results are of particular importance since the configuration mixing through the residual interaction naturally accounts for the collective excitations. In the mean-field models, the collective effects are included through the vibrational and rotational enhancement factors, and their NLDs are further normalized at low energies with neutron resonance data.

Figure 1

Shell-model ground-state energies for ${}^{51}\mathrm{V}, {}^{55}\mathrm{Fe}$, and ${}^{59}\mathrm{Ni}$ corresponding to different truncations with dimensions $N$ (red crosses). These energies are fitted to $a+b{e}^{-cN}$ as indicated by the solid line. The exponential converged ground-state energies for full $pf$-model space are obtained using this fitted expression with $N=N_{\mathrm{full}}$.

Figure 2

Nuclear level densities as a function of excitation energies ($E_{\mathrm{x}}$) for ${}^{51}\mathrm{V}, {}^{55}\mathrm{Fe}$, and ${}^{59}\mathrm{Ni}$ nuclei obtained from SDM in the $pf$-model space by considering the parity equilibration scheme [given by Eq. (6)] at $E_0=S_n$ and $0.8S_n$ labeled as SDM and SDM*, respectively. These results are compared with the experimental data [44, 45, 46] along with other microscopic mean-field models, HFB-u (un-normalized) and HFB as well as the phenomenological models, BSFG and GSM. Histograms represent the NLDs obtained from low-lying discrete levels [47].

Figure 3

Cross sections for $(n,\gamma )$ processes as a function of incident neutron energies in center-of-mass frame $(E_{\mathrm{c}}.\mathrm{m}.)$ calculated using NLDs from SDM and SDM* compared with those obtained from other models (as shown in Fig. 2), see the text for details. Evaluated data are adopted from evaluated nuclear data files (ENDF) [54]. The cross sections at low $E_{\mathrm{c}}.\mathrm{m}.$ are shown in the right panels together with the respective experimental data as Kapchigashev [55] for ${}^{50}\mathrm{V}(n,\gamma ){}^{51}\mathrm{V}$, Beer and Spencer [56], Allen et al. [57], Giubrone et al. [58], Wallner et al. [59] for ${}^{54}\mathrm{Fe}(n,\gamma ){}^{55}\mathrm{Fe}$, and Halban and Kowarski [60], Beer and Spencer [56], Wisshak et al. [61], Perey et al. [62], Popov et al. [63], Rugel et al. [64], Guber et al. [65], and Žugec et al. [66] for ${}^{58}\mathrm{Ni}(n,\gamma ){}^{59}\mathrm{Ni}$.

Figure 4

The astrophysical reaction rates as a function of temperature using NLDs from SDM and SDM* compared with those obtained for other models (as shown in Fig. 2). For comparison, the recommended values from endf [54] and “kadonis v0.3” [69] are shown. For the case of ${}^{50}\mathrm{V}(n,\gamma ){}^{51}\mathrm{V}$, kadonis estimates are purely theoretical.