direct reactions. optical model represent the target nucleus by a potential -- attenuation length
Post on 19-Dec-2015
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Direct Reactions
Optical modelRepresent the target nucleus by a potential --
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Veff = V + iU
€
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
€
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…