Transition rates in phonon-particle coupled nuclei

The low-lying non-normal parity states of ⁴¹Ca and ³⁹K (positive-parity and negative-parity spectra respectively) are treated as a particle (hole) coupled to the low-lying negative-parity states of ⁴⁰Ca (often called vibrational states). These spectra are calculated by the technique of Sherwood and Goswami¹), in which the RPA is extended from a closed shell to a closed shell plus a particle or hole. The calculated spectra are compared with experimental results. It is observed that the diagonalization of the energy matrix leads to roughly twice the number of physical states. It is shown that the doubling of the number of physical states does not lead to a breakdown of the theory, and a way to distinguish the physical states from the non-physical states is indicated. A method for calculating transition rates in the phonon-particle coupling is developed and is applied to the known electromagnetic transitions in ³⁹K. In the calculated spectra, it is found that two vibrations are usually important, namely, the lowest J = 3^- and 5^- states of ⁴⁰Ca. It is noted that the concept of a particle coupled to a vibration is ambiguous. The non-orthogonality is handled correctly in this microscopic theory and is quite important in calculating transition rates. The phonon-particle coupling model predicts that the non-normal parity states in ⁴¹Ca and ³⁹K lie much lower in energy and are in much better agreement with experiment than according to conventional p-h calculation (TDA). The experimental levels (in MeV) and their calculated transition rates (in Weisskopf units) are 2.82 (2.5, 9), 3.02 (15 × 10^-4, 13 × 10^-4), 3.60 (16, 23), 3.94 (17, 16). The 4p-3h states were not included. Free charges rather than effective charges were used in the calculation of the transition rates.