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Proton-neutron random phase approximation studied by the Lipkin-Meshkov-Glick model in the Su(2)$$times$$Su(2) Group

Minato, Futoshi

The random phase approximation (RPA) is one of the useful approaches to describe a collective motion of nuclei. However, RPA intrinsically considers only 1 particle-1 hole (1p1h) excitations, as a result it fails to describe the width of the excited states, for example the Gamow-Teller (GT) state. To include higher-order particle-hole excitations, one can extend RPA to Second RPA (SRPA) which includes 2p2h excitations in a similar way to RPA with the quasi-boson-approximation (QBA). However, it fails to describe the GT distribution even with those model. A part of the problem may arise from the use of QBA. In past studies, SRPA was compared with exact solution using the Lipkin Model and the validity of application of QBA to them was examined. In this work, we examine proton-neutron SRPA (pnSRPA) in SU(4) basis. SU(4) is naturally required in this case to take into account two different particles having two levels each. The first and second excited states are calculated by the diagonalization of Hamiltonian and pnSRPA.

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