Discrete and Continuum Spectra in the Unified Shell Model Approach

A new version of the nuclear shell model unifies the consideration of the discrete spectrum, where the results reproduce the standard shell model, and continuum. The ingredients of the method are the non-Hermitian effective Hamiltonian, energy-dependent one-body and two-body decay amplitudes, and self-consistent treatment of thresholds. The results for helium and oxygen isotope chains reproduce the data well.

Figure 1

CSM results for He isotopes, on the left for each isotope; experimental data, on the right. Experimentally observed states are linked to theoretical counterparts. The decay width is shown on the right in MeV. Energies (or centroids of decaying states) are not shown, but the energy scale is given on the vertical axis.

Figure 2

CSM calculations for oxygen isotopes with the HBUSD interaction. States from yellow (long lifetime) to red (short lifetime) are resonance states. In black and white print these resonances are differentiated by shades of gray, from lighter to darker, respectively. States shown in black are stable in our model; they are either below decay thresholds or with decays forbidden due to the angular momentum restrictions in the selected valence space. The inset in the upper right shows a more detailed picture for the lightest ${}^{16}\mathrm{O}$ to ${}^{19}\mathrm{O}$ isotopes. Decays from all states that are experimentally measured are shown with arrows. A full comparison between available data and the calculation is given for ${}^{19}\mathrm{O}$. Energies are expressed in units of keV. A comparison of widths with available data is given in the table in the left lower corner. For both insets the interaction USD was used that works better for lighter isotopes.