Charge dependent calculations of single particle energies in nuclei around O-16 with modern nucleon nucleon interactions

The binding energies of the ground states and several excited states related to single-particle and -hole states in nuclei around $^{16}\mathrm{O}$ are calculated taking charge dependence into account. Effective interactions on the particle basis are constructed from modern charge-dependent nucleon-nucleon interactions and the Coulomb force within the framework of the unitary-model-operator approach. Single-particle (-hole) energies are obtained from the energy differences of the binding energies between a particle (hole) state in $^{17}\mathrm{O}$ or $^{17}\mathrm{F}$ ($^{15}\mathrm{N}$ or $^{15}\mathrm{O}$) and the ground state of $^{16}\mathrm{O}$. The resultant spin-orbit splittings are small for the hole state and large for the particle state in comparison with the experimental values though the differences between the experimental and calculated values are not very large. The charge dependence of the calculated single-particle energies for the ground states are in good agreement with the experimental values. Furthermore, the Thomas-Ehrman shift due to the Coulomb force for the $1{s}_{1∕2}$ states in $^{17}\mathrm{O}$ and $^{17}\mathrm{F}$ can be observed.

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