Problems

Consider the center of mass system of two interacting identical fermions with spin (such as neutron-like particles without isospin.)

(a) What is the consequence of the Pauli exclusion principle on the two-particle wavefunction?

(b)  Let S1 and S2 be the spin operators of the two individual neutrons.  Show that the operators P=(1/2)(1/4) S1S2/ are the projection operators of the triplet states and the singlet states of the spin wavefunctions.

(c)  Using the Pauli exclusion principle and the symmetry properties of the spin and relative orbital angular momentum L , find the allowed values of L for any bound triplet state of the two-particle system.

(d)  Again using the Pauli exclusion principle and the symmetry properties of the space coordinate, show that the particles in a triplet state can never scatter through an angle of 90 degrees in their center of mass system.


The Coulomb scattering amplitude for two non-relativistic particles in the center of mass system is

 Image778.gif (1598 bytes)

where Image779.gif (1092 bytes)and m is the reduced mass, and k is the wave number.  Find the differential cross section in the center of mass if the two particles

(a)  are distinguishable,
(b)  are distinguishable, but the identity of the particles is not observed in either bin,
(c)  are identical spin-zero particles,
(d)  are identical spin particles in a spin-triplet state,
(e)  are identical spin particles in a spin-singlet state,
(f)  are identical unpolarized spin particles.

You may ignore any relativistic spin effects for fc(q).

Image780.gif (997 bytes)