Intruder states of the odd-massN=27isotones

Energy levels and electromagnetic properties of the N=27 and 28 nuclei are studied systematically in terms of the shell model within the $f_{7/2}^n$+$f_{7/2}^{n\mathrm{-}1}$($p_{3/2}$,$p_{1/2}$,$f_{5/2}$ ${)}^1$ configurations. The effective interactons are made up of empirical matrix elements and phenomenological potentials superposed with two and three central interactions. Least-squares fitting calculations of selected energy levels are performed to fix some of the matrix elements and the strength parameters of the potentials. It is shown that some states with a collective nature appear in ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ and ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}$ which are connected to each other by the enhanced E2 transitions, whereas no such states appear in ${}_{}{}^{47}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{49}{}_{}{}^{}\mathrm{Ti}$. The anomalously large B(E2) values observed in the transitions between the intruder states can be reproduced very well. The hindrance of the E2 transitions between the intruder state and the normal $f_{7/2}^n$ state is obtained in the present model, being in qualitative agreement with the experiments. Both of the proton-neutron (p-n) interactions (1) among the $f_{7/2}$ nucleons and (2) between the $f_{7/2}$ and the other fp nucleons are very important in order to obtain proper understanding of the nuclei in this mass region.