Extended Brueckner–Hartree–Fock theory with pionic correlation in finite nuclei

Abstract

We formulate a nuclear many-body theory with explicit treatment of the strong tensor correlation caused by the pion-exchange interaction. To do this, we have to extend the Hartree–Fock variational model space to include 2-particle 2-hole (2p–2h) states, which are able to handle the tensor correlation and to contain high momentum components originating from its pseudo-scalar nature of the pion. We take the variational principle of the total energy, and obtain equations of motion for the variational parameters as the Hartree–Fock single particle states and 2p–2h states. As for the short range repulsion, we use the unitary correlation operator method (UCOM) to express the short range correlation in the ground state wave function. We then arrive at an extended Hartree–Fock equation with the inclusion of the effect of the pion exchange and short range repulsive interactions. We find this extended Hartree–Fock equation has a structure of the Brueckner theory. Thus, we name the present theoretical framework as an extended Brueckner–Hartree–Fock (EBHF) theory. We compare the EBHF theory with the Feshbach projection method and the Brueckner–Hartree–Fock theory.