Angular momentum projected configuration interaction with realistic Hamiltonians

The projected configuration interaction method starts from a collection of mean-field wave functions and builds up correlated wave functions of good symmetry. It relies on the generator coordinator method techniques, but it improves the past approaches by a very efficient method of selecting the basis states. We use the same realistic Hamiltonians and model spaces as the configuration interaction (CI) method and compare the results with the full CI calculations in the $\mathit{sd}$ and $\mathit{pf}$ shell. Examples of ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, ${}^{48}\mathrm{Cr}$, ${}^{52}\mathrm{Fe}$, and ${}^{56}\mathrm{Ni}$ are discussed.

Figure 1

The Nilsson levels for $\mathit{sd}$ shell.

Figure 2

Energy surfaces of the USD Hamiltonian with respect to the unprojected SD$(s_0)$ (upper surface) and the projected SD$(s_0)$ with $I=0$ (lower surface), as functions of quadrupole ${\epsilon }_2$ and hexadecupole ${\epsilon }_4$ deformation.

Figure 3

The ground-state energies (upper panel) and the corresponding $\langle J^2\rangle$ values (lower panel) of ${}^{28}\mathrm{Si}$ from spherical and deformed CI as functions of different $n\mathrm{p}\text{−}n\mathrm{h}$ truncation

Figure 4

Calculations of the ground-state band in ${}^{28}\mathrm{Si}$ with different basis. Except for the GCM:D=41 case, the deformation for all the other cases is $({\epsilon }_2=-0.40,{\epsilon }_4=-0.20).$

Figure 5

Comparison of the calculated ground-state bands in ${}^{28}\mathrm{Si}$ with deformations $({\epsilon }_2,{\epsilon }_4){}_{\mathrm{pj}}=(-0.40,-0.20)$ [used in Fig. 4] and $({\epsilon }_2,{\epsilon }_4){}_{\mathrm{def}}=(-0.44,-0.10)$, as shown in Table .

Figure 6

$E_{\exp }(s,\epsilon )$ values in ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$, as functions of quadrupole deformation ${\epsilon }_2$. Each curve represents a Nilsson configuration $s$, while ${\epsilon }_4$ was chosen to minimize $E_{\exp }(s,\epsilon )$ for each ${\epsilon }_2$. The absolute minimum for each $s$ is indicated by a black dot.

Figure 7

Energies for ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ calculated using PCI (open circles) and full CI (filled circles). Twenty energies for each spin are presented.

Figure 8

The lowest five energies at each spin for ${}^{48}\mathrm{Cr}$ calculated using PCI (open circles) and full CI (filled circles).

Figure 9

Calculated yrast band energies using PCI (open circles) and full CI (filled circles) for ${}^{52}\mathrm{Fe}$ and ${}^{56}\mathrm{Ni}$. The deformed band in ${}^{56}\mathrm{Ni}$ starting around 5 MeV is also shown (see text for details).

Figure 10

Calculated quadrupole moments (upper panel) and $B(E2)$ (lower panel) from PCI (open circles) and full CI (filled circles) for ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, and ${}^{48}\mathrm{Cr}$.