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Exploring the leptonic sector in frontier experiments is more of importancenowadays, since the conservation of lepton flavor and total lepton number arenot guaranteed anymore in the Standard Model after the discovery of neutrinooscillations. $\mu^- + N(A,Z) \rightarrow e^+ + N(A,Z-2)$ conversion in amuonic atom is one of the most promising channels to investigate the leptonnumber violation process, and the measurement of this process is planned infuture $\mu^--e^-$ conversion experiments with a muonic atom in a muon-stoppingtarget. This paper discusses how to maximize the experimental sensitivity ofthe $\mu^--e^+$ conversion by introducing the new requirement of the massrelation of $M(A,Z-2)<M(A,Z-1)$, where $M(A,Z)$ is the mass of themuon-stopping target nucleus, to get rid of the background from radiative muoncapture. The sensitivity of the $\mu^--e^+$ conversion is anticipated to havefour orders of magnitude of improvement in forthcoming experiments using aproper target nucleus, which satisfies the mass relation. The most promisingisotopes found are $^{40}$Ca and $^{32}$S.

Future Experimental Improvement for the Search of LNV Process in $e\mu$ Sector