Tensor and Operator Forms of 3He and 3H Wave Functions for Parity-Violating Nuclear Forces

TL;DR

This paper develops tensor and operator representations for three-nucleon wave functions, incorporating parity-violating effects, and analyzes their properties under symmetry constraints.

Contribution

It introduces a tensor representation for 3N wave functions that includes parity-odd components and converts this into an operator form considering parity violation.

Findings

Wave functions have 16 complex components depending on relative momenta.

Parity-odd components are constructed alongside parity-even ones.

Operator form accounts for parity-violating contributions.

Abstract

Tensor representation (TR) for wave function (WF) of three-nucleon bound state with the total angular momentum I=1/2 is discussed. The WF in TR has 16 complex components depending on vectors of relative momenta. Constraints on the WF imposed by requirements of invariance with respect to space inversion and time reversal are studied. Both parity-even and parity-odd components of the 3N bound state are constructed using 16 scalar functions. The arguments of the functions are magnitudes of relative momenta and scalar product of the momenta. With nuclear forces being time-reversal invariant these functions are real. The WF in TR is converted into an operator form, accounting for parity violating contributions. Properties of operator representations for WFs of 2N and 3N nuclei are compared.