Forbidden nuclear reactions

Exothermal nuclear reactions that become forbidden due to Coulomb repulsion in the $\varepsilon \to 0$ limit $[{lim}_{\varepsilon \to 0}\sigma \left(\varepsilon \right)=0]$ 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 in finite cross section (and rate) of the originally forbidden nuclear reaction in the $\varepsilon \to 0$ limit. The statement is illustrated by modification of nuclear reactions due to impurities in a gas mix of atomic state. The change of the wave function 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 $d(d,n){}_2{}^3\text{He}$, $d(d,p)t,d(t,n){}_2{}^4\text{He}$, ${}_2{}^3\text{He}(d,p){}_2{}^4\text{He}$, ${}_3{}^6\text{Li}(p,\alpha ){}_2{}^3\text{He}$, ${}_3{}^6\text{Li}(d,\alpha ){}_2{}^4\text{He}$, ${}_3{}^7\text{Li}(p,\alpha ){}_2{}^4\text{He}$, ${}_4{}^9\text{Be}(p,\alpha ){}_3{}^6\text{Li},{}_4{}^9\text{Be}(p,d){}_4{}^8\text{Be},{}_4{}^9\text{Be}(\alpha ,n){}_6{}^{12}\text{C},{}_5{}^{10}\text{B}(p,\alpha ){}_4{}^7\text{Be}$, and ${}_5{}^{11}\text{B}(p,\alpha ){}_4{}^8\text{Be}$ reactions are also given. The affect of gas mix-wall interaction on the process is considered too.

Figure 1

The energy $\left(E\right)$ dependence of the differential cross section $d{\sigma }_{23}^{\left(2\right)}/\left(dEd\mathrm{\Omega }\right)=F\left(E\right)$ of $d(d,t)p$ reaction in the case of deuterized Pd. $F$ is given in 10 pb/keV units. $E$ is the energy of the assisting particle 1 (in this case Pd) in keV units. The accelerator potential $U=1$ keV. The possible maximum value of $E_{\text{.}}$ is 146.65 keV.