Stars as Laboratories for Fundamental Physics - MPP Theory Group

350 Chapter 10
In principle, any of the neutrino-producing reactions in the Sun
with a final-state positron can also occur with an initial-state electron
such as pe − p → d ν e instead of pp → de + ν e . In most cases, however,
the electron-capture process is strongly suppressed relative to positron
emission because of an unfavorable phase-space factor, or equivalently
because of the relatively small electron density. (For a general comparison
between these two reaction channels see Bahcall 1990.) The
only exception is pep which yields a nonnegligible contribution because
the Q value of the pp reaction and thus the available positron phase
space are rather small. Another exception are the beryllium neutrinos
because positron emission is inhibited entirely by the small energy
difference between the ground states of 7 Be and 7 Li.
The shapes of the neutrino spectra from the individual source reactions
are determined entirely by the matrix element and phase space
of the microscopic reactions apart from small broadening effects by the
thermal motion of the reaction participants. As typical thermal energies
in the Sun are 1 keV the spectral modification by such effects
is entirely negligible. (For a detailed discussion of this point see Bahcall
1991.) The high-energy part of the solar neutrino spectrum between
about 2−15 MeV is dominated by the boron neutrinos (Fig. 10.1), i.e.
by a single source reaction. Therefore, this energy range is a clean
example to test the spectral shape. The confirmation of the expected
spectral shape above 7 MeV by the Kamiokande II detector excludes
Fig. 10.4. Normalized spectra of the thermally and Doppler broadened beryllium
neutrino lines where E 0 is the corresponding laboratory energy (Bahcall
1994). The line shapes involve an integral over a solar model.