Investigating the muon catalyzed fusion in muonic lithium hydride

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$\ddot{\mathrm{o}}$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$\mu$.

Comments: 5 pages, 3 figures