Investigating the muon catalyzed fusion in muonic lithium hydride

TL;DR

This paper explores muonic lithium hydride as a potential stage in muon-catalyzed fusion, calculating bound states and sticking probabilities to evaluate its feasibility.

Contribution

It introduces a detailed three and four body quantum mechanical analysis of muonic LiH and LiH$^+$, providing new insights into their bound states and fusion dynamics.

Findings

Bound states in muonic LiH and LiH$^+$ are confirmed.

The dynamical behaviors are similar to those in dt$$ and dt$$ muonic molecules.

The alpha sticking probability in muonic LiH$^+$ is significantly lower than in dt$$ muonic fusion.

Abstract

In this work, we consider the muonic LiH as a new stage of the $\mu$ catalyzed fusion. We calculate the bound states of the muonic LiH and LiH$^+$ and their wave functions based on the three and four body approximation. In order to solve the Schr$\ddot{\rm o}$dinger equation, we apply the Gaussian expansion method which gives us both the eigen energies and the wave functions. The existences of the bound states in muonic LiH and LiH$^+$ are confirmed. We find the dynamical behaviors between the $^7$Li and proton in muonic LiH and LiH$^+$ are similar as the ones in dt$\mu_2$ and dt$\mu$, respectively. The $\alpha$ sticking probability in the muonic LiH$^+$ after the nuclear fusion is studied. The calculated $\alpha$ sticking probability of being captured to the ground state of He$\mu$ is 5 times smaller than the one in dt$\mu$.