Effect of dtmu quasi-nucleus structure on energy levels of t(16)

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 $

toanincreasinginthesecond-orderPTcontribution.Thecancellatione ectwaswidelydiscussed,e.g.,in[9,10,18];nevertheless,thedependenceonthemolecularquantumstatewasbeyondthescopeofthosepaperswhereonlytheatom-likesystem(dtµ)ewascalculated.Ontheotherhand,thecalculation[8]determinedthel-dependenceonlyinthe rst-orderPT.

ThedependenceoftheenergyshiftsonquantumnumbersisillustratedinFigure1forthe(dtµ)deestateswithn=2,3andl=0 4.Inadditiontoadecreasingintheenergy

2

1.6

1.2

0.8

0.401234

l

FIG.1:Energyshifts(meV)of(dtµ)dee.Crosses,squares,andcirclesdenote,respectively, +, ,and 0.Theresultsobtainedbysimpli edformulas(39),(41)aredenotedbythesolid,dashed,anddottedlines,respectively.Threeuppercurvescorrespondtothevibrationalquantumnumbern=2andtheloweroneston=3.

shiftsforhighern,noticetheinverseorderingoflevels,i.e.,thehighestlevelwithL=l 1forn=2becomesthelowestforn=3.Exceptfor +,whosevaluesatsmalll=1,2arequitedi erent,theresultsrevealweakdependenceonlwithsplittingoflevelsoftheorderof0.2meV.

AsdiscussedattheendofSectionIIIB,thedependenceofenergyshiftsandlevelsplittingonquantumnumbersareexpressedtoagoodaccuracybysimpleformulas(39),(41)viafewparameters.Numericalvaluesof16ω