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9 Gamma-Decay > 9.5 Selection Rules - Pg. 240

240 | Chapter 9 when we do the substitution of (9.110) and (9.111) in (9.104) and (9.105) ([Ja75, chap. 16]): Z Q lm (a, b) = e k=1 l r k Y l m ( k , k ) Z b a d , (9.112) M lm (a, b) = e 2mc(l + 1) l r k Y l m ( k , k ) · [r k × j k (a, b, r k )] d . k=1 (9.113) The expression (9.113) can be rewritten in another form, using the operator L = -ir × (9.114) and noticing, through an integration by parts, that the two portions of (9.111) are identical. In this way, (9.113) is rewritten as M lm (a, b) = - eh 2mc(l + 1) Z l r k Y l m ( k , k ) · [ k=1 b L k a ] d . (9.115) Expressions (9.112) and (9.115) only refer to the contribution of the motion of the protons. The spins of both protons and neutrons also give a contribution, but this will not be dis- cussed here. We saw that the values of the magnetic multipole moments are small in comparison to the electric moments of same order. We will show now that the transition probability