Direct Reactions

Optical modelRepresent the target nucleus by a potential --

€

Veff = V + iU

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ψout = Aeikx k =2meff E

h

ψ in = Beiκx κ =2meff E −Veff( )

h

κ = κ r + κ i = κ r +i

L

ψ in = Beiκx = Beiκ r xex L

L =h2κ r

Umeff

κ r ≈2meff E + Vo( )

h

Attenuation length

Optical modelRepresent the target nucleus by a potential --

€

Veff = Vo + iU

Attenuation length

T V0 U0 K LMeV MeV MeV 1/fm fm

0 - 4 50 3 1.6 2210 50 7 1.7 1017 50 8.5 1.8 940 35 15 1.9 5

€

L =h2κ r

Umeff

κ r ≈2meff E + Vo( )

h

Optical model

completely elastic scattering completely

absorbing nucleus

partially absorbing nucleus

transmitted waves

incident waves

scattered waves diffracted waves

interference

Forward peaking in elastic scattering cross section (with absorption)

(interference between transmitted wave and diffracted + scattered waves)

Optical model predictions in agreement with experiment

Surface interaction modelT V0 U0 K L

MeV MeV MeV 1/fm fm

0 - 4 50 3 1.6 2210 50 7 1.7 1017 50 8.5 1.8 940 35 15 1.9 5

~Rnucleus

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CB + BD = nλ

2 ⋅2Rsinθ

2= nλ

constructive interference

interference maxima peaks in cross section

plane wave

At higher energies, no penetration

nuclear elastic (surface) scattering producing diffraction

Surface interaction model

Estimates of nuclear radius

Abrupt changes are significant

Stripping reactions

d (Z,A)

initial state

(Z,A+1)

p

final state

Especially useful in this case -- neutron beams are much harder to make and control.

32S + d p + 33S

proton (spectator particles) typically goes forward

Stripping reactions

The fission process

(thermal)

initial state

compound nucleus

fission

fission fragments

~2.5 n/fission

6 delayed neutron groups- different lifetimes-

Fission fragment mass distributions

decays

Fast neutron induced fission

gone…