Effect of dtmu quasi-nucleus structure on energy levels of t(9)

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 $

TheunharmonictermofthepotentialVu(ρ)leadsonlytomodi cationofthedipolematrixelement

DUnν=

η

3 2 √n+1δn+1,ν (n+1)(n+2)δn,ν 2+(2n+1)δn,ν (23)wheretheunharmoniccorrectionisproportionaltothedimensionlessparameterη=2µ2ω≈0.14.

Calculationofthequasi-nucleusmatrixelements(14,15)isbasedonthesmallnessofthetµsizeincomparisonwiththesizeofthelooselybounddtµstate(v=1,λ=1).Thus,almostinallthecon gurationspacetµanddmoveasfreeparticlesandthebound-statewavefunctionisapproximatedby

11(r)=Ca

whereκ=√1+κr κreκr2(24)

2

r

φk2(r)= ,(25)πk[cosδ2(k)j2(kr)+sinδ2(k)y2(kr)](26)

whereδλ(k)arethetµ+dscatteringphaseshiftsandj2(kr)andy2(kr)arethesphericalBesselfunctions.Thed-wavephaseshiftδ2(k)isactuallyverysmall,whichallowseithercoskrreplacingy2(kr)bytheleadingterm

kr

Q=5

µ1ε11(27)oneobtainsthequadrupolemomentum

andtheexpression

Iλ( )=24Ca