Calculation of the Thomas-Ehrman shift in ${}^{16}\mathrm{F}$ and ${}^{15}\mathrm{O}(p,p)$ cross sections within the Gamow shell model

The ${}^{16}\mathrm{F}$ nucleus is situated at the proton drip line and is unbound by proton emission by only about 500 keV. Continuum coupling is then prominent in this nucleus. Added to that, its low-lying spectrum consists of narrow proton resonances as well. It is therefore a very good candidate to study nuclear structure and reactions at the proton drip line. The low-lying spectrum and scattering proton-proton cross section of ${}^{16}\mathrm{F}$ were calculated with the coupled-channels Gamow shell model framework in this case using an effective Hamiltonian. Experimental data are very well reproduced, as were those of its mirror nucleus ${}^{16}\mathrm{N}$. Isospin-symmetry breaking generated by the Coulomb interaction and continuum coupling explicitly appears in our calculations. In particular, the different continuum couplings in ${}^{16}\mathrm{F}$ and ${}^{16}\mathrm{N}$ involving $s_{1/2}$ partial waves allow one to explain the different ordering of low-lying states in their spectra.

Figure 1

Low-lying energy spectra of the ${}^{16}\mathrm{F}$ and ${}^{16}\mathrm{N}$ nuclei obtained with GSM and GSM-CC and compared to experimental data (Exp). The proton-emission widths are indicated by filled squares and their numerical values are also indicated above. Excitation energies $E_x$ and proton-emission widths are given in keV. Experimental data are taken from Ref. [44].

Figure 2

Excitation function of the ${}^{15}\mathrm{O}(p,p)$ scattering reaction calculated with GSM-CC and compared to experimental data. Energies and cross section are defined in the laboratory frame. The cross section angle is defined in the center-of-mass frame and is equal to ${180}^{\circ }$. The low-lying resonance states of ${}^{16}\mathrm{F}$ are indicated on the figure next to their associated projectile excitation energy. Experimental data are taken from Ref. [9].