cross section for scattering particle (mass,m; charge, z 1 e) by a screened coulomb potential...
Post on 22-Dec-2015
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Cross section for scattering particle (mass,m; charge, Z1e)by a screened Coulomb potential (source,Z2e of infinite mass)
22
14
)(q
a
qF
In the limit a (no screening) this reducesto Rutherford’s scattering formula
2
42
2
)(1
4qF
m
d
d
Fermi’s Golden Rule
(see Gasiorowicz)
2222
22
2142
2
)cos1)(/2()/1(
161
4
paeZZ
m
d
d
using (1-cos)=sin2(/2)12
2
2222
221
)2/(sin4)/(
2
pa
eZmZ
d
d
2
222
221
)2/(sin4)2/(
Ema
eZZ
d
d
Using E=p2/2m (the classical expression) for the incoming particle
Breakdown of RutherfordScattering formula
When an incident particlegets close enough to the targetPb nucleus so that they interact
through the nuclear force (inaddition to the Coulomb forcethat acts when they are furtherapart) the Rutherford formula
no longer holds.
The point at which this breakdown occurs gives a
measure of the size of the nucleus.
R.M.Eisberg and C.E.PorterRev. Mod. Phys, 33, 190 (1961)
Radial probability distributions for a particle in a Coulomb potential(hydrogenic atom). Note the probability vanishes at r=0.