The structure of the spherical tensor forces in the USD and GXPF1A shell model Hamiltonians

The realistic shell model Hamiltonians, USD and GXPF1A, have been transformed from the particle-particle (normal) representation to the particle-hole representation (multipole-multipole) by using the known formulation in Ref. [1]. The obtained multipole-multipole terms were compared with the known spherical tensor forces, including the coupled ones. It is the first time the contributions of the coupled tensor forces to the shell model Hamiltonian have been investigated. It has been shown that some coupled-tensor forces, such as [r2Y2 ⊗σ ]1, also give important contributions to the shell model Hamiltonian. (authors)