Stars as Laboratories for Fundamental Physics - MPP Theory Group

348 Chapter 10
nuclei, the usual weak decay by e + ν e emission is not possible and so the
conversion proceeds by electron capture, leading to the emission of an
almost monochromatic neutrino. In about 10% of all cases the capture
reaction goes to the first excited state (478 keV) of 7 Li so that there are
two neutrino lines.
Instead of an electron, 7 Li very rarely captures a proton and forms
8 B which subsequently decays into 8 Be, a nucleus unstable against spontaneous
fission into 4 He + 4 He. This PPIII termination occurs in about
0.02% of all cases, too rare to be of importance for nuclear energy generation.
Its importance arises entirely from the high energy of the 8 B
neutrinos which are the ones least difficult to measure.
The neutrino-producing reactions are summarized in Tab. 10.1 with
their maximum energies, and with the resulting neutrino flux at Earth
found in the solar model of Bahcall and Pinsonneault (1995).
Apart from small screening and thermal broadening effects, the
spectral shape for each individual source is independent of details of
the solar model. The pp, 13 N, 15 O, and 17 F reactions are allowed or
superallowed weak transitions so that their spectra are
dN/dE ν = A (Q + m e − E ν ) [ (Q + m e − E ν ) 2 − m 2 e] 1/2
E
2
ν F ,
(10.2)
where Q is the maximum e + kinetic energy and also the maximum
ν e energy, A is a normalization constant, and F is a function of E e +
which takes the e + final-state interactions into account. For the low-Z
nuclei under consideration this correction is small for most of the neutrino
spectrum. With F = 1 the normalization constants are given in
Tab. 10.2. In Fig. 10.3 the normalized spectra from the pp and the 15 O
processes are shown where the pp spectrum was taken from the tabulation
of Bahcall and Ulrich (1988). Using Eq. (10.2) instead would cause
a change so small that it would be nearly hidden by the line width of
the curve in Fig. 10.3.
Table 10.2. Normalization of the spectrum Eq. (10.2) with F = 1.
Source Q [MeV] A [MeV −5 ]
pp 0.420 193.9
13 N 1.199 3.144
15 O 1.732 0.668