Many-body approximations in the $\mathit{sd}$-shell “sandbox”

A new theoretical approach is presented that combines the Hartree-Fock variational scheme with the exact solution of the pairing problem in the finite orbital space. Using this formulation in the $\mathit{sd}$-space as an example, we show that the exact pairing significantly improves the results for the ground state energy.

Figure 1

Pairing correlation energy Eq. (18) for all $\mathit{sd}$-shell nuclei.

Figure 2

Four selected cuts on the correlation energies displayed in Fig. 1.

Figure 3

Energy difference between the exact results and our HFP model for all $\mathit{sd}$-shell nuclei.

Figure 4

Four selected cuts on the energy difference between the exact results and our HFP model displayed in Fig. 3.

Figure 5

Intrinsic quadrupole moment $Q$, in units $b^2$ ($b$ is the oscillator parameter), for the lowest energy configuration for all $\mathit{sd}$-shell nuclei.

Figure 6

Energy gain from PN $T=1$ correlations.

Figure 7

Energy gain from PN $T=1$ correlations for $N+Z=28$.