Direct microscopic calculation of nuclear level densities in the shell model Monte Carlo approach

Nuclear level densities are required for estimating statistical nuclear reaction rates. The shell model Monte Carlo method is a powerful approach for microscopic calculation of state densities in very large model spaces. However, these state densities include the spin degeneracy of each energy level, whereas experiments often measure level densities, in which each level is counted only once. To enable the direct comparison of theory with experiments, we introduce a method to calculate directly the level density in the shell model Monte Carlo approach. The method employs a projection on the minimal absolute value of the magnetic quantum number. We apply the method to nuclei in the iron region and to the strongly deformed rare-earth nucleus ${}^{162}\mathrm{Dy}$. We find very good agreement with experimental data obtained by various methods, including level counting at low energies, charged particle spectra and Oslo method data at intermediate energies, neutron and proton resonance data, and Ericson's fluctuation analysis at higher excitation energies. We also extract a thermal moment of inertia from the ratio between the state density and the level density, and observe that in even-even nuclei it exhibits a signature of a phase transition to a superconducting phase below a certain excitation energy.

Figure 1

Level densities versus excitation energy $E_x$ for ${}^{56}\mathrm{Fe}$, ${}^{60}\mathrm{Ni}$, ${}^{62}\mathrm{Ni}$, and ${}^{60}\mathrm{Co}$. SMMC level densities $\tilde{\rho }\left(E_x\right)={\rho }_{M=0}\left(E_x\right)$ (solid circles) are compared with various experimental data sets [14]: level counting at low excitation energies (open diamonds), charged particle spectra [17] at intermediate energies (dashed lines), and Ericson's fluctuation analysis [18] at higher energies (open circles). For ${}^{60}\mathrm{Co}$ there is also the proton resonance data (open square) [19, 20].

Figure 2

Top panel: the SMMC state density (open squares) and level density (solid circles) versus excitation energy $E_x$ for ${}^{60}\mathrm{Co}$. The experimental level density data follow the same convention as in Fig. 1. Bottom panel: thermal moment of inertia for ${}^{60}\mathrm{Co}$ extracted from the ratio of the state density to the level density (solid circles). The dashed line is the rigid-body moment of inertia.

Figure 3

As in Fig. 2 but for ${}^{56}\mathrm{Fe}$.

Figure 4

Top panel: SMMC level density (solid circles) compared with the state density (open squares) in ${}^{162}\mathrm{Dy}$. Also shown are experimental data sets for the level density: level counting at low excitation energies (histograms) [24, 25], Oslo data at intermediate energies (open circles) [26, 27], and the neutron resonance data (triangle) [28]. Bottom panel: thermal moment of inertia $I$ of ${}^{162}\mathrm{Dy}$ (solid circles) as a function of excitation energy $E_x$. The dashed line is the rigid-body moment of inertia.