The Fock representation of the Coulomb interaction. II. Three-body bound states

Abstract

The Fock representation of the unscreened Coulomb interaction, a block of separable terms with analytic form factors and strengths, is included in the momentum-space Faddeev kernel of three-body bound states beside the separable nuclear terms. A bound-state kernel evaluates every pair interaction at negative pair energies, where the representation is exact and convergent, so the Coulomb force enters without a screening radius and without a limiting procedure. With this representation the ${}^3$H--${}^3$He splitting of the CD~Bonn potential is in very good agreement with the exact Faddeev result; in the $S$-wave model space the Coulomb-distorted form factors give about half the Fock value. The Feshbach--Schur projection of the Pauli-forbidden states acts on the forbidden eigenstates of the nuclear-plus-Coulomb pair Hamiltonian, the Coulomb-dressed states obtained inside the extended separable problem, as the eigenstate condition requires. The Coulomb displacements of the cluster-model states of ${}^6$Li, ${}^9$Be and ${}^{12}$C and of the ${}^9$Be--${}^9$B mirror pair are given. The eigenstate condition is tested in ${}^9$Be and ${}^{12}$C by replacing the Coulomb-dressed forbidden states with those of the Coulomb-subtracted interaction and with the oscillator functions of the orthogonality-condition model.

Comments: 20 pages