PPT Slide

Plane Wave Born Approximation - Outline

Assume that the entrance yi = e iki•ri ?a ?A and exit yf = e ike•re ?b ?B states are plane waves

Golden Rule :

Transition rate =

dnf

? T i,f ?2

transition

M.E.

density

of states

T i,f = ?? f ? Vint ?? i ? ; Vint =

perturbative

interaction

causing

transition

Assume that Vint is zero range, i.e. that it acts only when a,b at origin, only at nuclear periphery R'

Vint = V0 ?(ri–re) ? (ri–R') … so T i,f = const ?

e iq•R' ?b ?B ?a ?A d?

; q = ki – ke = pt /?

R’ has length R’ and coordinates qint a nd f int = angle coordinates inside interaction region (integrated out)

But we can expand in ?(=?tran) : e iq•R' = S? i? ? [4p(2?+1)] ? j? (qR') ? Y(qint,f int)

Assume that only a single ? -value is allowed, by angular momenta of single particle states

… so T i,f = const ?

V0 ? ? ?b ?B ? ?a ?A ? ? j? (qR')

Bessel function with q(scattering angle)

dependence, entering through q?p? /?

? [ j? (qR') ]2

… first max at q ? (1.24 to 1.49) ? ? [?(?+1)] , as expected

In DWBA, (plane waves?distorted by optical potential) and often (interaction?finite range Woods-Saxon)