Microscopic multiphonon approach to spectroscopy in the neutron-rich oxygen region

Background: A fairly rich amount of experimental spectroscopic data have disclosed intriguing properties of the nuclei in the region of neutron rich oxygen isotopes up to the neutron dripline. They, therefore, represent a unique laboratory for studying the evolution of nuclear structure away from the stability line.

Purpose: We intend to give an exhaustive microscopic description of low and high energy spectra, dipole response, weak, and electromagnetic properties of the even ${}^{22}\mathrm{O}$ and the odd ${}^{23}\mathrm{O}$ and ${}^{23}\mathrm{F}$.

Method: An equation of motion phonon method generates an orthonormal basis of correlated $n$-phonon states ($n=0,1,2,\cdots$) built of constituent Tamm-Dancoff phonons. This basis is adopted to solve the full eigenvalue equations in even nuclei and to construct an orthonormal particle-core basis for the eigenvalue problem in odd nuclei. No approximations are involved and the Pauli principle is taken into full account. The method is adopted to perform self-consistent, parameter free, calculations using an optimized chiral nucleon-nucleon interaction in a space encompassing up to two-phonon basis states.

Results: The computed spectra in ${}^{22}\mathrm{O}$ and ${}^{23}\mathrm{O}$ and the dipole cross section in ${}^{22}\mathrm{O}$ are in overall agreement with the experimental data. The calculation describes poorly the spectrum of ${}^{23}\mathrm{F}$.

Conclusions: The two-phonon configurations play a crucial role in the description of spectra and transitions. The large discrepancies concerning the spectra of ${}^{23}\mathrm{F}$ are ultimately traced back to the large separation between the Hartree-Fock levels belonging to different major shells. We suggest that a more compact single particle spectrum is needed and can be generated by a new chiral potential which includes explicitly the contribution of the three-body forces.

Figure 1

Theoretical versus experimental [15] spectra of ${}^{22}\mathrm{O}$. The dashed line denotes a level of unknown spin and parity. The dotted line indicates the neutron decay threshold.

Figure 2

TDA (a) and EMPM (b) $E1$ reduced strength distributions in ${}^{22}\mathrm{O}$.

Figure 3

Theoretical versus experimental [16] $E1$ cross section in ${}^{22}\mathrm{O}$. A Lorentzian of width $\mathrm{\Delta }=2$ MeV is used.

Figure 4

Isoscalar (a) versus isovector (b) $E1$ transitions.

Figure 5

Transition densities for the low-lying $1_1^{-}$ state (a) and one falling in the region of the GDR (b).

Figure 6

Level schemes of ${}^{23}\mathrm{O}$ computed in HF and in spaces including up to $N_{\mathrm{ph}}=1$ and $N_{\mathrm{ph}}=2$ phonons. The experimental data are from [13].

Figure 7

Level schemes of ${}^{23}\mathrm{F}$ computed in HF and in spaces including up to $N_{\mathrm{ph}}=1$ and $N_{\mathrm{ph}}=2$ phonons. The experimental data are from [5, 6].