5.1.2. Neutrons in an External Field

For a neutron the Dirac Hamiltonian is somewhat simpler

(5.10)

with g_n = -3.82. Again for p_z = 0 the states of lowest energy, the ones we shall be interested in, have energies

(5.11)

Boosting to a finite p_z we obtain

(5.12)

The wave functions corresponding to this energy are

(5.13)

where u(p, s = -1) is the standard spinor for a particle with momentum p, energy sqrt[p² + M_n²] (not the energy of Eq. (5.12) and spin down.

In the non-relativistic limit

(5.14)

and the wave functions are

(5.15)