# Physics Reports vol.361

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Iii) The total strength, resulting by summing over all partial transition matrix elements in the s–d shell, is much smaller than that found previously by using closure approximation. If this is true, the light neutrino contribution to muon–positron conversion is unobservable, in spite of the 25-fold enhancement due to the imaginary part. 7. Extraction of the lepton violating parameters The limits on the lepton-number violating parameters extracted depend on the values of nuclear matrix elements, the kinematical factors and the current experimental limit on the half-life for a given isotope [see Eq.

We should stress that this novel mechanism can lead to transitions J + , J = 0. So, contrary to conventional wisdom, from the observation of such transitions one cannot deÿnitely infer the existence of right-handed currents. 5. The e ective nucleon current As we have already mentioned, the relevant transition operators are deÿned at the quark level, but all computations are carried out at the nucleon level. One thus must have a rigorous and well-deÿned procedure on how to go from the quark to the nucleon level.

Note that i · j √ = − 3[ i ⊗ 0 j ]0 . The ÿrst spin antisymmetric operator is pe rij jL (pe Rij ) 2 i¡j √ √ √ [[ 4 Y (rˆij ) ⊗ 4 Y (Rˆ ij )]L ⊗ (− 2)[ i ⊗ j ]S ]J A1 = (116) − (i) − (j)f(rij )jl (117) ( = l; = L; S = 1). Note that i × j √ = (− 2)[ i ⊗ j] 1 (118) The second spin antisymmetric operator is A2 = √ − (i) − (j)f(rij )jl i¡j [[ 4 Y (rˆij ) ⊗ √ pe rij jL (pe Rij ) 2 4 Y (Rˆ ij )]L ⊗ ( i − J j )] : (119) ( = l; = L; S = 1). Note that each operator must be overall symmetric with respect to interchange of the particle indices.