765.65 Two-Delta-Function Scattering (Princeton)
A freeparticle of mass traveling withmomentum parallel to the
scatters off the potentialCalculate the differential scatteringcross section, in theBorn ap-
proximation.Doesthis approximation provide areasonable description for
scatteringfromthis potential? Inotherwords, is it valid to useunperturbed
wave functions inthe scattering amplitude?5.66 Scattering of Two Electrons (Princeton)
Two electronsscatter in a screenedenvironment where theeffective poten-
tial iswhere is a constant. Consider bothelectrons inthe center-of-massframe,
where bothelectrons have energy Thisenergy ismuch largerthan a
Rydberg but muchlessthan so usenonrelativistic kinematics. Derive
an approximatedifferentialcrosssection forscatteringthrough anangle
when the two electrons are
a) in a total spin state of S = 0,
b) in a total spin state of S = 1.5.67 Spin-Dependent Potentials (Princeton)
Consider thenonrelativistic scattering of anelectron ofmass and mo-
mentum through anangle Calculate thedifferentialcrosssection in
the Born approximation for thespin-dependent potential
where are the Pauli spin matrices and arecon-
stants. Assume the initial spin is polarized along the incident direction, and
sum over allfinal spins.(Note:Ignorethat the potentialviolates parity.)
PROBLEMS