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 $
E ectofdtµquasi-nucleusstructureonenergylevelsofthe
(dtµ)Xeeexoticmolecule
arXiv:physics/0403116v2 [physics.atom-ph] 31 Mar 2004O.I.Kartavtsev,1A.V.Malykh,1,2andV.P.Permyakov31DzhelepovLaboratoryofNuclearProblems,JointInstituteforNuclearResearch,Dubna,141980,Russia2PhysicsDepartment,NovgorodStateUniversity,NovgorodtheGreat,173003,Russia3BogoliubovLaboratoryofTheoreticalPhysics,JointInstituteforNuclearResearch,Dubna,141980,Russia(Dated:February2,2008)AbstractPreciseenergiesofrovibrationalstatesoftheexotichydrogen-likemolecule(dtµ)Xeeareofimportancefordtµresonantformation,whichisakeyprocessinthemuon-catalyzedfusioncycle.Thee ectoftheinternalstructureandmotionofthedtµquasi-nucleusonenergylevelsisstudiedusingthethree-bodydescriptionofthe(dtµ)Xeemoleculebasedonthehierarchyofscalesandcorrespondingenergiesofitsconstituentsubsystems.Foranumberofrovibrationalstatesof(dtµ)deeand(dtµ)tee,theshiftsandsplittingsofenergylevelsarecalculatedinthesecondorderoftheperturbationtheory.PACSnumbers:36.10.-k,36.10.Dr,33.20.Wr