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The independent particle model of Wilkinson had indicated that the most strongly absorbing dipole state formed was that involving nodeless wave functions in which the excited particle quantum numbers lp and jp are related to the hole quantum numbers lh and jh by For Zr90 , the dominant transition is 199/2 ---+ Ihll/ 2 ; in Pb 208 , it is li13/2 The stripping reaction studies give the energy separations as 9 MeV, respectively, while the respective giant resonance energies are 17 and 14 MeV. Brown and Bolsterli(67) recognized the fundamental difference between these types of experiment and accounted qualitatively for the increase in energy of the dipole state.

12 J The Giant Dipole Resonance 39 If it is assumed that isobaric spin is a good quantum number (evidence for this in a specific case will be discussed later), then the matrix elements of interest are those for which J = 1 and T = 1. In this case, (P4 h3! V! h1P2) = ::: X JdaCUl t 10 ! j2t)C(j3 t 10 ! j4t) [1+21J+HI - 21J)(k1 where k = I -1- 1 - k2)(ka - k4)]Gp2hlP4hs for j = 1- for j = (41) t 1+ t If isobaric spin is not treated as a good quantum number, then the transitions involving excitation of a proton or a neutron must be treated separately; in that case, one has twice as many transitions to consider, and the energy matrix is twice as large.

The results given by Barker and Mann(77) are used to relate the ratio of these cross sections to the isospin impurity in the states a(y,po) = Pp(Ep) Pn(En) a(y,n o) I 1+ a I 1- a 12 (46) where a is the amplitude of T = 0 isospin states in the assumed T = 1 states, and P(E) is the barrier penetration probability for a particle of energy E. The experimental comparison on this particular point will be considered later; here we give a description of the basis of the theory. , j,;nc I JM)( ,,;. )i,l+m,la,/a,\ 10) (47) where Af" are the superposition coefficients.

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