Charge-exchange quasi-elastic process $nd\to p(nn)$ under $0^\circ$ in the frame of elastic $np\to np$ scattering to $180^\circ$

TL;DR

This paper analyzes the charge-exchange quasi-elastic process in neutron-deuteron scattering, comparing different representations of neutron-proton interactions and deriving formulas within the impulse approximation framework.

Contribution

It introduces an alternative formula for the $nd o p(nn)$ process based on neutron elastic scattering at angle $ heta$ and $ heta$'s complement, expanding the theoretical understanding of spin physics in these reactions.

Findings

Derived the Dean formula for $nd o p(nn)$ scattering.

Presented an alternative formula using neutron elastic scattering at $ heta$ and $ heta$'s complement.

Compared different representations of neutron-proton interactions in charge-exchange processes.

Abstract

It is considered the problem of spin physics related with the difference of representation of the elastic interaction between the neutron and proton. In the first case the charge-exchange reaction $np\to pn$ under the angle $\theta$ is supposed, in the second --- the simple elastic scattering of $np\to np$, when the neutron is going in opposite direction $\pi-\theta$. The transition from one representation to another is provided by the Majorana operator. In the framework of impulse approximation it is twice calculated the quasi-elastic charge-exchange reaction of a neutron on a deuteron. In the frame of $nd\to p(nn)$ scattering of proton to the angle $\theta$ it gives the well-known Dean formula. Using other representation $nd\to (nn)p$ as a neutron elastic scattering under the angle $\pi-\theta$ (together with neutron-spectator in $nn$-pair) the alternative formula is presented.