Ground-state correlations within a nonperturbative approach

The contribution of the two-phonon configurations to the ground state of ${}^4\mathrm{He}$ and ${}^{16}\mathrm{O}$ is evaluated nonperturbatively using a Hartree-Fock basis within an equation-of-motion phonon method using a nucleon-nucleon optimized chiral potential. Convergence properties of energies and root-mean-square radii versus the harmonic oscillator frequency and space dimensions are investigated. The comparison with the second-order perturbation theory calculations shows that the higher-order terms have an appreciable repulsive effect and yield too-small binding energies and nuclear radii. It is argued that four-phonon configurations, through their strong coupling to two phonons, may provide most of the attractive contribution necessary for filling the gap between theoretical and experimental quantities. Possible strategies for accomplishing such a challenging task are discussed.

Figure 1

HF ground-state energy of ${}^4\mathrm{He}$ (a), ${}^{16}\mathrm{O}$ (b), and ${}^{40}\mathrm{Ca}$ (c) versus the HO frequencies $\omega$ for different HO space dimensions $N_{\text{max}}$.

Figure 2

Ground-state energy of ${}^4\mathrm{He}$ (a), ${}^{16}\mathrm{O}$ (b), and ${}^{40}\mathrm{Ca}$ (c) versus the HO frequency $\omega$ for different $N_{\text{max}}$ computed in HF plus second-order perturbation theory.

Figure 3

Systematic of ground-state energy computed in HF and second-order perturbation theory. The calculations are performed for $N_{\text{max}}=14$ and different HO frequencies $\omega$.

Figure 4

The EMPM ground-state energy of ${}^4\mathrm{He}$ (a) and ${}^{16}\mathrm{O}$ (b) versus the HO frequency $\omega$ for different $N_{\text{max}}$.

Figure 5

HF point proton radius versus the HO frequency $\omega$ for different $N_{\text{max}}$ in ${}^4\mathrm{He}$ (a) and ${}^{16}\mathrm{O}$ (b).

Figure 6

Systematic of root-mean-square point proton radii computed in HF. The calculations are performed for $N_{\text{max}}=14$ and different HO frequencies $\omega$. The experimental data are from Ref. [49].

Figure 7

HF and EMPM point proton radii of ${}^4\mathrm{He}$ (a) and ${}^{16}\mathrm{O}$ (b) versus $N_{\text{max}}$ for fixed frequency ($\hslash \omega =26$ MeV).

Figure 8

Squared amplitudes (multiplied by 100) of the two-phonon components (a) of the ground state in ${}^{16}\mathrm{O}$ and their running sum (b).