**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[**p**^{2} +
*M*_{n}^{2}] (not the energy
of Eq. (5.12) and spin down.

In the non-relativistic limit

(5.14) |

and the wave functions are

(5.15) |