Operator form ofH3(He3)and its spin structure

Abstract

An operator form of the three-nucleon $(3N)$ bound state is proposed. It consists of eight operators formed out of scalar products in relative momentum and spin vectors, which are applied on a pure $3N$ spin $1∕2$ state. Each of the operators is associated with a scalar function depending only on the magnitudes of the two relative momenta and the angle between them. The connection between the standard partial wave decomposition of the $3N$ bound state and the operator form is established, and the decomposition of these scalar function in terms of partial wave components and analytically known auxiliary functions is given. That newly established operator form of the $3N$ bound state exhibits the dominant angular and spin dependence analytically. The scalar functions are tabulated and can be downloaded. As an application the spin dependent nucleon momentum distribution in a polarized $3N$ bound state is calculated to illustrate the use of the new form of the $3N$ bound state.