Integral equations in the Fock-Bargmann space and the generator-coordinate method

In the generator-coordinate method, the norm kernel built as a Slater determinant of the Brink-Bloch orbitals plays a role of unity for the complete set of orthonormalized states defined in the Fock-Bargmann space and satisfying the Pauli exclusion principle. The closure condition is then written as the Hilbert-Schmidt expansion of the norm kernel and can be derived by a simple algebraic procedure. A basis of eigenstates of the norm kernel is shown to be a powerful tool in resonating-group calculations.