Question

5. The nucleus of 3He consists of two protons and a neutron. Ignore the spa tial degrees of freedom. Obtain the eigenstates of S2 and S, for the com bined system. How do you account for the appropriate antisymmetrization rules? (Hint: Couple the two protons first.)

Answer 1

Proton and neutron has spin - C oupling two protons first states can be s,m ) Now there is another neutron Eigen states are 3 3 3 13 1113 3 2 2/2 2/22/21 Out of these, due to pail exclusion principle 3 31 13 3 are not allowed states. AS, s, ls,m)-ms,m) Possible Eigen states of s &s. are When all the spins have both s & m. + that state is simply not allowed. This makes the total wave function anti symmetric an required