A wealth of experimental data has been reported recently on the structure of neutron rich nuclei belonging to the sd shell in general and the phosphor chain in particular. In the obtained experimental spectra, there is coexistence, at relatively low excitation energy, of the normal 0ħω positive parity states and the intruder 1ħω negative parity states. It is the aim of our present work to describe both types of states in the shell model framework.
The properties of normal states in sd shell nuclei are well described using the shell model with USD (USDA or USDB) interactions. The intruder states result from the promotion of one nucleon from the p to sd shell or from the sd to pf shell. Up to now there has been no consistent description of these states. To study them, we must enlarge the model space from the 0ħω sd space (16O core) to the full p-sd-pf space allowing one nucleon jump (1ħω space, 4He core). This extension of the valence space requires the development of a new interaction compatible with the new space. The obtained interaction called PSDPF reproduces well both positive and negative parity states in nuclei through the sd shell. There are some discrepancies in the middle of sd due to the large number of valence nucleons. In this case, the wave functions of the intruders are strongly mixed and thus very sensitive to the nature of the 1ħω excitation.
The new PSDPF interaction was used to calculate the energy spectra and electromagnetic properties of the chain of phosphor isotopes with N = 15 to 20. Results of these calculations and their comparison with experimental data will be presented and discussed.