Operator form ofH3(He3)and its spin

Abstract

An operator form of the 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.

Nucleon Momentum Distributions in ³He and Three-Body Interactions

“…We used results of Ref. [13], where the calculations of the necessary scalar functions (appearing in the operator form representation of the bound 3N system) were performed with two potentials, which involve the effective 3N interactions, 2N interaction AV18 [14] with the interaction Urbana-IX [15] (AV18+U9), and 2N interaction CD-Bonn [16] with insertion of the 3N Tucson-Melbourne interaction [17] (CDBN+TM).…”

“…[13], that the ninth spin structure of the operator form of a 3N system is redundant and we, following to Ref. [13], omit this component.…”

“…The scalar functions φ i (p, q, x) have been calculated in Ref. [13] for two modern potentials: the 2N potential AV18 [14] with the 3N potential Urbana-IX [15] (AV18+U9) and the 2N potential CD-Bonn [16] with the 3N potential Tucson-Melbourne [17] (CDBN+TM). The functions φ i (p, q, x) are tabulated on a 3-dimensional grid (x, q, p) and can be downloaded from site [18].…”

“…[13,18], are represented on the 3-dimensional grid (p, q, x) which is not "dense" enough for needs of our calculations. (1 + 1 3…”

The Two-Nucleon and Three-Nucleon System in Three Dimensions

“…The general form of the 3N bound state is more complicated [3]. The wave function projected onto a 3N isospin state (t 1 2 )T | (where the isospins of two particles are coupled to t and then coupled with the isospin of the third particle to a total isospin T ) has the form(4) and a more detailed description of operators involved in (4) can be found in [3]. Also in this case the 3N wave function can be reconstructed from the set of scalar functions {φ (i) tT } of the magnitudes and the angle between the Jacobi momenta p, q.…”