Precise energies of rovibrational states of the exotic hydrogen-like molecule $(dt\mu)Xee$ are of importance for $dt\mu$ resonant formation, which is a key process in the muon-catalyzed fusion cycle. The effect of the internal structure and motion of the $
=ρ/ρ,PK(x)istheLegendrewhereθistheanglebetweentwounitvectors r=r/randρ
polynomial,andthebisphericalharmonicsarede nedas
LM , Ylλ(ρr)= mµ )Yλµ( (lmλµ|LM)Ylm(ρr).(A2)
Evaluatingtheintegral(A1)onecomestotheexpressionintermsoftheClebsh-Gordoncoe cientsand6j-symbols
ALK(lλl1λ1)=( )l1+L
5δlLδl1L+
3(L+2)5(2L+1)δlL 1δl1L 1 L(L+1)
2
1 Lδl,L 1 √15(2l+1)(2l+3),l1=l+1(L l+2)(L l+3)(L+l 2)(L+l 1)