Nucleon-pair picture of low-lying states in semi-magic and open-shell nuclei

In this paper we demonstrate that a simple nucleon-pair picture, previously investigated for semi-magic even-even nuclei, survives in both odd-mass semi-magic nuclei and a few neutron-rich open-shell nuclei. This is exemplified by low-lying states of the semi-magic nuclei Ca43-48 and three open-shell nuclei Cd132, Ag131, and Pd130, calculated with effective interactions. Not only the generalized-seniority-zero, -one and -two states, but also states with larger seniority numbers are shown to be well represented by one-dimensional nucleon-pair wave functions. Very interestingly, such one-dimensional nucleon-pair wave functions are readily adopted to be those with the lowest expectation energies among all nucleon-pair basis states. This provides us with a simple approach to study yrast states of semi-magic nuclei as well as yrast states of open-shell nuclei with only a few valence nucleons.