Excitation of giant resonances via direct reactions Page: 5 of 66
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5
one shell-model level to another, the latter tell us how much total tran-
sition strength we can expect for a mode having particular (L,T,S)
values. Throughout this talk giant resonance strength will be described
in terms of the energy weighted sum rule (LWSR) which is a particularly
useful sum rule because it is nearly model independent. Generally, the
criterion for a transition to be considered collective is that its tran-
sition rate be many ( 10) times the single particle value, in which case
the transition would exhaust an appreciable fraction of the EWSR for the
mode in question. As we shall see giant resonances exhaust 20%-90% of
their sum rules.
For direct reactions the transition rate and the angular momentum
transfer are generally deduced by comparison of measured angular distri-
butions with those calculated by use of the Distorted Wave Born
Approximation (DWBA). The analysis procedure for giant resonance states
is the same as has been established for direct excitation of low-lying
states. In the case of electron scattering the transition rate, B(EL),
for the state in question can be directly obtained. In inelastic hadron
scattering however, the situation is not nearly so direct. Comparison of
the calculated cross sections with those measured, yields a quantity
called the deformation parameter, L' as:
2 = do(L) measured / da L) calculated (1)
If aL is assumed to be proportional to the mass multipole moment for a
uniform distribution then
= B(EL)( 41 \2 (2)
3ZRL)
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Bertrand, F.E. Excitation of giant resonances via direct reactions, article, January 1, 1982; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1055749/m1/5/: accessed July 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.