Stars as Laboratories for Fundamental Physics - MPP Theory Group

Solar Neutrinos 355
Bahcall and Pinsonneault (1995) then find that the opacity-related
uncertainty of the 8 B neutrino flux is about 12%. For the 7 Be flux
the errors are thought to be roughly half as large, in agreement with
Eq. (10.5). However, as stressed by Bahcall and Pinsonneault (1995),
the interpretation as an effective 1σ error is misleading as the main
source of uncertainty is of a systematic and theoretical nature. Previously,
these authors had stated “theoretical 3σ errors;” in that sense
an opacity-related uncertainty of the 8 B flux of about 30% was found
in Bahcall and Pinsonneault (1992). Turck-Chièze and Lopes (1993)
adopted 15% without a commitment to a specific number of sigmas.
None of these errors can be interpreted in a strict statistical sense.
Rather, they give one an idea of what the workers in that field consider
a plausible range of possibilities.
b) Beryllium-Proton Reaction
A dominating uncertainty for the important flux of boron neutrinos
arises from the cross section 7 Be + p → 8 B + γ which plays no role
whatsoever for the energy generation in the Sun because the PPIII
termination of the pp chain is extremely rare. Therefore, a modification
of this cross section has no impact on the structure of the Sun and
thus no other observable consequence but to modify the high-energy
neutrino flux.
The cross section for this reaction is parametrized for low energies
in the usual form with an astrophysical S-factor
σ(E) = S(E) E −1 e −2πη(E) , (10.6)
with the Sommerfeld parameter
η = Z 1 Z 2 e 2 v −1 . (10.7)
Here, Z 1,2 e are the charges of the reaction partners, v their relative
velocity, and E their CM kinetic energy. The S-factor is expected to
be essentially constant at low energies unless there is a resonance near
threshold.
The six “classical” measurements of the 7 Be + p → 8 B + γ reaction
are referenced in Tab. 10.3. In the Sun, the most effective energy range
is around E = 20 keV, far in the tail of the thermal distributions of
the reaction partners, but still far below the lowest laboratory energies
of around 120 keV in the experiments of Kavanagh et al. (1969) and
Filippone et al. (1983). Therefore, one must extrapolate the factor