Method for Calculating Matrix Elements of a Three-Body Hamiltonian in a Gaussian Basis

A method for determining the matrix elements of a three-body Hamiltonian in a multidimensional Gaussian basis for use in nuclear and atomic physics, as well as nuclear astrophysics, is discussed in detail. Both central and noncentral (spin–orbit and tensor) interactions between particles are considered. It is shown that the proposed method makes it possible to reduce the matrix elements to relatively simple analytical expressions capable of providing high accuracy in determining the Hamiltonian eigenvalues.