Microscopic calculation of symmetry projected nuclear level densities

We present a quantum Monte Carlo method with exact projection on parity and angular momentum that is free of a sign problem for seniority-conserving nuclear interactions. This technique allows the microscopic calculation of angular momentum and parity-projected nuclear level densities. We present results for the ${}^{55}\mathrm{Fe}$, ${}^{56}\mathrm{Fe}$, and ${}^{57}\mathrm{Fe}$ isotopes. Signatures of the pairing phase transition are observed in the angular momentum distribution of the nuclear level density.

Figure 1

The angular momentum distribution of the level density at a given excitation energy $E_x$ for the iron isotopes ${}^{55}\mathrm{Fe}$, ${}^{56}\mathrm{Fe}$, and ${}^{57}\mathrm{Fe}$. Solid squares are the Monte Carlo results in the $\mathit{pf}+g_{9/2}$ valence space. The solid lines are fits to the spin-cutoff model Eq. (1). Also shown are distributions given by the spin-cutoff model with ${\sigma }^2$ calculated from Eq. (7) using the rigid body moment of inertia (dotted-dashed lines) and from Eq. (6) (dotted lines).

Figure 2

(Top panels) The moment of inertia $I$ (in units $\hslash {}^2$) for ${}^{55}\mathrm{Fe}$ (left), ${}^{56}\mathrm{Fe}$ (middle), and ${}^{57}\mathrm{Fe}$ (right) versus excitation energy $E_x$. The solid lines are moments of inertia calculated from Eqs. (7) and (6), and the solid circles are from Eq. (7) with ${\sigma }^2$ determined by ${\rho }_0/\rho$ (in the even-even case) and ${\rho }_{1/2}/\rho$ (in the odd-even case). The horizontal dashed lines describe the rigid-body moments of inertia. (Bottom panels) The pair correlation energy $\langle S^{†}S\rangle$.

Figure 3

The angular momentum and parity-projected level densities of ${}^{56}\mathrm{Fe}$ for the four lowest angular momentum values. A strong parity dependence is found for excitation energies up to $~20$ MeV. The valence model space is $\mathit{sd}+\mathit{pf}+g_{9/2}+\mathit{sd}$. For $J=2$, we also show results for the smaller $\mathit{pf}+g_{9/2}$ valence space (dashed lines).

Figure 4

The total QMC level density for ${}^{56}\mathrm{Fe}$, well described by the backshifted Bethe formula (dotted-dashed line), together with the projected densities $J=0,J=2$ (left panel) and $J=1,J=3$ (right panel). The solid lines connect the $J$-projected Monte Carlo results, while the dashed lines show the projected level density from the spin-cutoff model Eq. (1) using rigid-body values of ${\sigma }^2$.