Effect of dtmu quasi-nucleus structure on energy levels of t(10)

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 $

viathedimensionlessintegrals

J0(z)=∞ 0[sinδ0(k) (k2+3)(k/2)cosδ0(k)]dk2

(k2+1)4(k2+z)

B.Shiftandsplittingofenergylevels.(30)

Energyshiftsareobtainedbysolvingthesecularequation(6)whichisreduced,dueto

theselectionrulesforangularmomentalandl1,toa2×2matrixequationforl,l1=L±1(L=0)andascalarequationforl=l1=L=0.TheenergyshiftswithrespecttotheunperturbedrovibrationalenergiesEnl+ε11aredenotedas 0(n)and ±(nl)forl=Landl=L±1,respectively.NotethatthestatewithL=0andl=l1=1isuncoupled;however,itsenergyshift +(n1)willbedeterminedinthesamemannerasfortheotherL=0states.

nThe rst-orderPTmatrixelementsVllinEq.(6)arecalculatedbysubstitutingthe1

M,QradialintegralsUnn(22),thequadrupolemomentumQ(27),andtheangularintegrals

nAL2(l1l11)(A4)inEq.(11).NotethatVll1appearstobeindependentofthevibrational

quantumnumbernandthisindexwillbeomittedinwhatfollows.Thematrixelementsarescaledbyasingledimensionalparameter

v0=2m1m3ω2Ca

2L+1 1

L(L+1)2 1 inwhichthe rstrowandcolumncorrespondtol,l1=L 1andthesecondonesto

l,l1=L+1.

(33)