introduction-weak-interaction-volume-one

traces of K-electron capture radiation, setting an upper limit on the
cross-section for the reaction (3 .2 .8) of
2 x 10-' 2 cm 2/atom . (3 .2 .10 )
3 .3 The:Neutron Decay Honiltonien .
In 1934,
Fermi suggested (21) that a Hamiltonian for the neutron
decay (3 .1 .1) might be constructed in direct analogy to that for th e
generation of electromagnetic radiation . The latter is proportional t o
the electric current four-vecto r
Jr = j e Yr , (3 .3 . 1 )
and Fermi postulated that the neutron should beta decay at a rat e
proportional to the 'current' ' " p
Y r Tf n associated with the protonneutron
transition . Since the complete Hamiltonian must be a Lorentz-invarian t
scalar, it must initially consist of the product of two four-vecto r
currents . Thus, anearcing that no derivatives of the basic fields ar e
involved, we write :
HI = (:G (- p Y r 'ti) ( "q' 'e yr`L'Iv) + Herm . conj., (3 .3 .2 )
where i is the beta decay coupling constant l , and we have transposed
all the particles in (3 .1 .1) on to the left hand side of the equation ,
since the Hamiltonian is slightly easier to handle in the more symmetri c
form (3 .3.2) . The latter is known as the 'four-fermion interaction' ,
since it involves four fermion fields interacting at a point in spacetime .
It is not, however, the most general neutron decay Hamiltonian, since
it assumes that only a vector Dirac interaction occurs . Generalizing fo r
all five bilinear covariants, and enforcing the condition that the
Hamiltonian be a Lorentz-invariant scalar, we obtain (22 )
HI
oi.( p Oi a ) ( ;lf e of '- v ) + Hem . conj . ,
(3 .3 .3 )
where the Oi are the five different types of Y -matrix product . The Ci
are the coupling constants for each kind of interaction . However, with
1 . Coupling constants are complex parneters which characterize th e
strength of a particular interaction . For an interesting discussion of
their underlying theory, see Heisenberg : Introduction to the Unified Field
Theory of Elementary Particles, Wiley 1966, pp . 79-89 .