Pygmy and giant dipole resonances in the nitrogen isotopes

The configuration-interaction shell model with the WBP10 effective interaction has been used to investigate the pygmy and giant dipole resonances in the nitrogen isotopes. Large enhancement of low-lying dipole strength, i.e., pygmy dipole resonances (PDRs), is predicted in the neutron-rich $^{17,18,19,20}\mathrm{N}$. The nature of the PDRs is analyzed via the transition densities and transition matrix elements. It turns out these PDRs involve a larger amount of excitations between the $2s1d$ and loosely bound $1f2p$ shells. Combining with the transition densities, it is concluded that the PDRs in $^{17,18,19,20}\mathrm{N}$ are collective and due to the oscillation between the excess neutrons and the isospin saturated core. The isospin dependence of energy splitting and sum rule of isospin doublets is discussed. The theoretical energy splitting of isospin doublets can significantly deviate from the systematic values when nucleus is far away from the $\ensuremath{\beta}$-stability line. The ratios of ${T}_{l}$ and ${T}_{g}$ energy-weighted sum rule (EWSR) are consistently larger than the systematic values, and it is noticed that the calculated EWSR ratio over the systematic ratio increases with increasing isospin almost linearly. We also calculated the photoabsorption cross sections for the nitrogen isotopes. We proposed the normalization factors for $0--1\ensuremath{\hbar}\ensuremath{\omega}$ and $2--3\ensuremath{\hbar}\ensuremath{\omega}$ calculations. After the normalization, the shell model has well reproduced the experimental photoabsorption cross sections in $^{14,15}\mathrm{N}$, especially the detailed structure of resonances.