5.1.2. Neutrons in an External Field
For a neutron the Dirac Hamiltonian is somewhat simpler
with gn = -3.82. Again for pz = 0 the states of lowest energy, the ones we shall be interested in, have energies
Boosting to a finite pz we obtain
The wave functions corresponding to this energy are
where u(p, s = -1) is the standard spinor for a particle with momentum p, energy sqrt[p2 + Mn2] (not the energy of Eq. (5.12) and spin down.
In the non-relativistic limit
and the wave functions are