Effect of dtmu quasi-nucleus structure on energy levels of t(14)

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 $

tions[9,10,18]wherethel-independentenergyshiftwasobtainedbyscalingtheresultfortheatom-likefour-bodysystem(dtµ)e.Aspointedoutinthispaper,themonopolecon-tributioncalculatedinRef.[8]dependsonthechoiceofthecoordinatesystemthatdoesnotallowacomparison.Forthisreason,onlythequadrupolecontributiontothe rst-orderPTenergyshiftsofRef.[8]willbecomparedwiththepresentresults.ThequadrupolecontributionofRef.[8]isgiveninTableIIofthatpaper,whileinthepresentapproach E(1)

Q=(10/3)v0AL2(l1l1),asfollowsfromEqs.(11),(22),and(27).Thebothresultsareinexcellentagreementwitheachother,asshowninTableI.Notethatinthepresentapproach

lLAL2(l1l1) E(1)(1)

Q EQ[8] v0

TABLEI:Quadrupolecontributions E(1)

Q(inmeV)tothe rst-orderPTenergyshiftsofthe

presentcalculationandthosefromRef.[8]fordi erentlandL.AlsopresentedaretheangularintegralsAL2(l1l1)andtheparameter v0correspondingtotheenergyshiftsofRef.[8].thedependenceonangularmomentaiscompletelydeterminedbythefactorAL2(l1l1)whichisalsopresentedinTableI.Toagoodaccuracy,theresultsofRef.[8]revealthesamedependenceonangularmomentawhichapprovesthedescriptionofenergyshiftsbyasingleparameterv0.Toemphasizethisfact,thequadrupolecorrectioncalculatedinRef.[8]isexpressedintheform E(1)

Q=(10/3) v0AL2(l1l1)withthevariable v0presentedinTableI.

Indeed,v 0ispracticallyindependentoflandLandagreeswithv0=1.81meV.Agreementbetweenthepresentone-parameterresultforthequadrupolecorrectionandtheelaboratesix-bodycalculation[8]isagoodargumentforthevalidityofthepresentapproach.Atlast,oneshouldobtainWlln

1(34),whichrequiresevaluationofJλ 1+Eν

E