E1excitations inA=15nuclei

The ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}(p, \gamma ){}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ reaction was studied from $E_p=2.8\mathrm{} \mathrm{to} 30$ MeV corresponding to $E_x=13\mathrm{} \mathrm{to} 38$ MeV in ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ covering the region of the lowest $T=\frac{3}{2}$ states as well as the giant dipole resonance (GDR). The ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(p, \gamma ){}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ reaction measurements were extended for excitation regions from $E_x=24-33.5\mathrm{}$ MeV thus covering the analogous regions in ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$. Angular distributions obtained in the first reaction at the resonance energies of $E_p=4.83, 5.62, 6.65, 6.925, 10.0, 11.0, 12.35, 13.6, \mathrm{and} 16.4$ MeV indicated large negative $a_2$ coefficients in all cases. The new narrow (${\Gamma }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=90\mathrm{}$ keV) resonance at 6.925 MeV has $J^{\pi }={\frac{3}{2}}^{+}$ and $T=\frac{1}{2}$. A careful comparison of the ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(\gamma , p_0){}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}(\gamma , p_0){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ reactions is used to extract the $T=\frac{3}{2} \mathrm{and} \frac{1}{2}$ components of the GDR in $A=15\mathrm{}$. Most of the $T=\frac{3}{2}$ $E1\mathrm{}$ strength is located near $E_x=26\mathrm{}$ MeV. A microscopic calculation of $J^{\pi }\le {\frac{5}{2}}^{+}$ states with $T=\frac{1}{2} \mathrm{and} \frac{3}{2}$ in a 2h-1p and 1h basis of good isospin gives good agreement with the observed depleted $B\left(E1\mathrm{}\right)\mathrm{}$ values from the lowest $T=\frac{3}{2}$ states and reproduces the location of the collective $T=\frac{3}{2}$ $E1\mathrm{}$ states near 26 MeV. It also describes well the distribution of $T=\frac{1}{2}$ collective $E1\mathrm{}$ strength. Using this agreement with the theory which contains no adjusted parameters an effective symmetry potential of $U=28\mathrm{}$ MeV is extracted from the isospin energy splitting. This value is smaller than the typical 60 MeV found in heavier nuclei but agrees with a recent model-independent limit and with other cases of $\left|T_z\right|=\frac{1}{2}$nuclei.