Consider a beta transition between two nuclear states of well defined
angular momentum with the emission of, say, an electron and an
antineutrino. In this transition, the total angular momentum and the
parity of the angular momentum states must be conserved.
The total angular momentum is the sum of orbital and intrinsic
contributions. Thus the change in angular momentum between initial and
final states is 
where
and 
are the orbital angular momentum and spin
carried off by the outgoing leptons.
Transitions with 
are known as allowed transitions;
the parity change is 
and so allowed transitions must have the
same parity in initial and final states. Transitions with
are known as forbidden (although they can occur, as we
shall see, via higher order terms in the matrix element).
Thus, for allowed transitions,
.
Since the leptons have spin half, there are two cases to consider, S=0
or S=1. The S=0 transitions are known as Fermi transitions;
the electron and antineutrino have ``antiparallel'' spins and
.
The S=1 transitions are known as Gamow-Teller transitions;
the electron and antineutrino have ``parallel'' spins and
or 1. (However, since there must be a change of one unit in
angular momentum, 
requires a change of `magnetic' substate,
. Thus the spin is reoriented; because of this 
to
GT transitions are forbidden -- there is only an
M=0 substate. This spin substate transition can be viewed as a
``spin-flip''. Thus GT transitions are referred to as ``spin-flip
transitions''.)