Hartree-Fock and many body perturbation theory with correlated realistic NN interactions

We employ correlated realistic nucleon-nucleon interactions for the description of nuclear ground states throughout the nuclear chart within the Hartree-Fock approximation. The crucial short-range central and tensor correlations, which are induced by the realistic interaction and cannot be described by the Hartree-Fock many-body state itself, are included explicitly by a state-independent unitary transformation in the framework of the unitary correlation operator method (UCOM). Using the correlated realistic interaction $V_{\mathrm{UCOM}}$ resulting from the Argonne V18 potential, bound nuclei are already obtained on the Hartree-Fock level. However, the binding energies are smaller than the experimental values because long-range correlations have not been accounted for. Their inclusion by means of many-body perturbation theory leads to a remarkable agreement with experimental binding energies over the whole mass range from ${}^4\mathrm{He}$ to ${}^{208}\mathrm{Pb}$, even far off the valley of stability. The observed perturbative character of the residual long-range correlations and the apparently small net effect of three-body forces provides promising perspectives for a unified nuclear structure description.

Figure 1

Effect of the unitary transformation on energy expectation values of different nuclei with simple shell-model Slater determinants. The four levels for each nucleus indicate (from top to bottom) the expectation value of the bare Hamiltonian, the centrally correlated, the fully correlated Hamiltonian, and the experimental binding energy per particle, respectively. The AV18 potential with the optimal correlators for $I_{\vartheta }=0.09\mathrm{\hspace{1em}\hspace{1em}}{\mathrm{fm}}^3$ is used.

Figure 2

Ground-state energy of ${}^{16}\mathrm{O}$, ${}^{90}\mathrm{Zr}$, and ${}^{208}\mathrm{Pb}$ as a function of the oscillator length $a_{\mathrm{HO}}$ for different basis sizes $e_{max}$. The correlated AV18 potential with $I_{\vartheta }=0.09\hspace{1em}{\mathrm{fm}}^3$ is used.

Figure 3

Ground-state energies and charge radii of selected closed-shell nuclei resulting from a Hartree-Fock calculation with the correlated AV18 potential. Three different ranges for the triplet-even tensor correlator are used: $I_{\vartheta }=0.08\hspace{1em}{\mathrm{fm}}^3,0.09\hspace{1em}{\mathrm{fm}}^3$, and $0.10\hspace{1em}{\mathrm{fm}}^3$. The bars indicate experimental values [31, 32].

Figure 4

Single-particle energies for ${}^{40}\mathrm{Ca}$, obtained with the correlated AV18 potential by using three different values of $I_{\vartheta }$ as indicated by the labels. The experimental data is taken from Ref. 35.

Figure 5

Ground-state energies for selected closed-shell nuclei in HF approximation and with added second- and third-order MBPT corrections. The correlated AV18 potential with $I_{\vartheta }=0.09\hspace{1em}{\mathrm{fm}}^3$ was used. The bars indicate the experimental binding energies [31].

Figure 6

Ground-state energies for the O, Ca, Ni, and Sn isotope chains in HF approximation and with added second-order MBPT corrections (see Fig. 5). The correlated AV18 potential with $I_{\vartheta }=0.09\hspace{1em}{\mathrm{fm}}^3$ was used. The bars indicate the experimental binding energies [31].

Figure 7

Change of the mean occupation numbers of the HF single-particle states due to second-order perturbative corrections. Shown are the results for proton orbitals in ${}^{40}\mathrm{Ca}$ and ${}^{90}\mathrm{Zr}$ as functions of the corrected single-particle energy. The correlated AV18 potential with $I_{\vartheta }=0.09\hspace{1em}{\mathrm{fm}}^3$ was used.

Figure 8

Charge radii for selected closed-shell nuclei in the HF approximation and with added second-order MBPT corrections. The correlated AV18 potential with $I_{\vartheta }=0.09\hspace{1em}{\mathrm{fm}}^3$ was used. The bars indicate experimental charge radii [32].