Spin Projection in the Shell Model Monte Carlo Method and the Spin Distribution of Nuclear Level Densities

We introduce spin projection methods in the shell model Monte Carlo approach and apply them to calculate the spin distribution of level densities for iron-region nuclei using the complete ($pf+g_{9/2}$) shell. We compare the calculated distributions with the spin-cutoff model and extract an energy-dependent moment of inertia. For even-even nuclei and at low excitation energies, we observe a significant suppression of the moment of inertia and odd-even staggering in the spin dependence of level densities.

Figure 1

SMMC spin distributions of the partition function $Z_J/Z$ for ${}^{55}\mathrm{Fe}$ (left panels), ${}^{56}\mathrm{Fe}$ (middle), and ${}^{60}\mathrm{Co}$ (right).

Figure 2

Spin distribution of level densities, ${\rho }_J/\rho$, at constant excitation energy $E_x$ for ${}^{55}\mathrm{Fe}$, ${}^{56}\mathrm{Fe}$, and ${}^{60}\mathrm{Co}$. The SMMC results (solid squares) are compared with the spin-cutoff model (11) with ${\sigma }^2$ fitted to the SMMC results (solid lines), and with ${\sigma }^2$ calculated from Eq. (12) using the rigid-body moment of inertia (dashed lines).

Figure 3

Shown from top to bottom are the spin-cutoff parameter ${\sigma }^2$ (extracted from the spin distributions), the moment of inertia $I$ in (12) and the $J=0$ pair correlation $⟨{\Delta }^{†}\Delta ⟩$ for ${}^{55}\mathrm{Fe}$ (left panels), ${}^{56}\mathrm{Fe}$ (middle), and ${}^{60}\mathrm{Co}$ (right). The SMMC results for ${\sigma }^2$ and $I$ are denoted by solid squares. The open circles with horizontal errors in the ${\sigma }^2$ panel of ${}^{55}\mathrm{Fe}$ are experimental data [9]. The dashed lines correspond to a rigid-body moment of inertia while the long dashed lines (for ${}^{56}\mathrm{Fe}$ only) correspond to half the rigid-body moment of inertia.

Figure 4

Total and $J=0$ level densities for ${}^{56}\mathrm{Fe}$. The total SMMC level density (solid squares) is well described by the BBF level density (dotted-dashed line). The $J=0$ SMMC level density (solid circles) is compared to the $J=0$ level density inferred from (11) with the fitted moment of inertia (solid line) and the rigid-body moment of inertia (dashed line). The suppression of the moment of inertia at low excitations enhances the $J=0$ level density $E_x\lesssim 8\mathrm{MeV}$.