Subatomic Physics

11.11. Inverse Beta Decay: Reines and Cowan’s Detection of Neutrinos 361
are equal to each other within experimental errors, after radiative corrections have
been made. (20,25)
The hypothesis of the conservation of the vector current is based on the analogy
to the electromagnetic current, which is also a vector current. No electromagnetic
axial vector current exists, and it is thus not possible to refer to a well-known
theory for guidance. Indeed, G A F �= GF shows that the axial vector current is not
conserved. The fact, however, that G A F does not differ from GF by more than about
25% shows that the axial current is almost conserved. The detailed description
of this fact is called the PCAC hypothesis or the partially conserved axial vector
current hypothesis. (24)
11.11 Inverse Beta Decay: Reines and Cowan’s Detection of Neutrinos
We now turn to neutrinos: they had been hypothesized by Pauli to save the law of
conservation of energy in 1931, but Pauli thought that they were so weakly interacting
that they would never be detected, so he considered his hypothesis somewhat
sinful. In order to understand how neutrinos were detected, we consider the “elastic”
scattering of neutrinos or antineutrinos due to the charged weak currents, e.g.,
¯νp −→ l + n, (11.74)
where l + is a positive lepton. The transition rate for this semileptonic process is
given by the golden rule,
dw = 2π
� |〈nl+ |Hw|p¯ν〉| 2 ρ(E).
The transition rate gives the number of particles scattered per unit time by one
scattering center. Equation (2.14) then shows that cross section and transition
rates are connected by
dσ = dw
. (11.75)
F
Antineutrinos move close to the velocity of light; with the normalization of one
particle per unit volume, the flux F is equal to the velocity, F = c. Consequently,
the cross section becomes
dσ = 2π
�c |〈nl+ |Hw|p¯ν〉| 2 ρ(E). (11.76)
The density-of-states factor for two particles in the final state, in their c.m., is given
by Eq. (10.31). With V =1,ρ(E) isgivenby
EnElpl
ρ(E) =
(2π�) 3c2 (En + El) dΩl,
25P. DePommier et al., Nucl. Phys. B4, 189 (1968); D. Počanić et al., Phys. Rev. Lett. 93,
181803 (2004).