# Forbidden Nuclear Reactions

## TL;DR

This paper investigates how small perturbations, such as impurities, can enable forbidden nuclear reactions at low energies by mixing states and producing finite cross sections, with numerical examples and astrophysical implications.

## Contribution

It introduces a quantum mechanical perturbation approach to show how forbidden nuclear reactions can occur at zero energy due to impurities and environmental effects.

## Key findings

- Impurities can induce finite cross sections in forbidden reactions.
- Numerical calculations of impurity-assisted nuclear reaction rates.
- Analysis of environmental effects on low-energy nuclear processes.

## Abstract

Exothermal nuclear reactions which become forbidden due to Coulomb repulsion in the\ $\varepsilon \rightarrow 0$ limit ($\lim_{\varepsilon \rightarrow 0}\sigma \left( \varepsilon \right) =0$) are investigated. ($\sigma \left( \varepsilon \right) $ is the cross section and $\varepsilon $ is the center of mass energy.) It is found that any perturbation may mix states with small but finite amplitude to the initial state resulting finite cross section (and rate) of the originally forbidden nuclear reaction in the $% \varepsilon \rightarrow 0$ limit. The statement is illustrated by modification of nuclear reactions due to impurities in a gas mix of atomic state. The change of the wavefunction of reacting particles in nuclear range due to their Coulomb interaction with impurity is determined using standard time independent perturbation calculation of quantum mechanics. As an example, cross section, rate and power densities of impurity assisted nuclear $pd$ reaction are numerically calculated. With the aid of astrophysical factors cross section and power densities of the impurity assisted $d(d,n)_{2}^{3}He$, $d(d,p)t$, $d(t,n)_{2}^{4}He$, $% _{2}^{3}He(d,p)_{2}^{4}He$, $_{3}^{6}Li(p,\alpha )_{2}^{3}He$, $% _{3}^{6}Li(d,\alpha )_{2}^{4}He$, $_{3}^{7}Li(p,\alpha )_{2}^{4}He$, $% _{4}^{9}Be(p,\alpha )_{3}^{6}Li$, $_{4}^{9}Be(p,d)_{4}^{8}Be$, $% _{4}^{9}Be(\alpha ,n)_{6}^{12}C$, $_{5}^{10}B(p,\alpha )_{4}^{7}Be$ and $% _{5}^{11}B(p,\alpha )_{4}^{8}Be$ reactions are also given. The affect of gas mix-wall interaction on the process is considered too.