PPT Slide

known as radial form factor

for the transferred nucleon

often simple,

e.g. if a = d

Distorted Wave Born Approximation - Outline

e.g. (d,p) with a deuteron beam (following H.A.Enge Chap.13 with ref. also to N.Austern)

H tot = S T + S V ... in either entrance/exit ch

Entrance: H tot = TaA + Txb + Vxb + VxA + VbA

Exit: H tot = TbB + TxA + Vxb + VxA + VbA

Same in each case

But the final scattering state can be written

approximately as an outgoing DW using

the optical potential for the exit channel:

? ?f ? ? ? ?B ? ? ?B ? ? –bB

Internal

wave functions

outgoing

distorted wave

In the optical model picture, Vxb + VbA ? UbB ( = VoptbB + i WoptbB, the optical potential)

And the final state, we have said, can be approximated by an eigenstate of UbB

Thus, the transition is induced by the interaction Vint = Hentrance - Hexit = Vxb + VbA - UbB

Remnant term

? 0 if x < < A

i.e. Vint ? Vxb which we can estimate reasonably well

Ti,f DWBA = ? ?b ?B ?bB– ? Vxb ??aA+ ?a ?A ?

so Ti,f DWBA = ? ?rel,Ax ?bB– ? Vxb ??aA+ ?rel,bx ?

= ? x ? A ?rel,Ax

= ? x ? b ?rel,bx