Attempts to account for the observations by astrophysical and nuclear
physics explanations have to be divided into two categories. First let us
consider the standard solar models [26,27]. I will
use as an example the Bahcall-Pinnsonneault model [26], which
includes helium diffusion and an improved estimate of 
, which is an
energy dependent factor
[2]Similarly 
,
, and 
are proportional to 
, and 
, respectively.
[3]This cross section is especially uncertain because two
measurements are not in agreement [7].
proportional to 
. The BP model is
in agreement with most other calculations when the same inputs are used,
and is in agreement with helioseismology data and information about main
sequence stars. Within the model there are uncertainties due to the input
parameters. In particular, uncertainties in the metallicity, Z, and
other contributions to uncertainties in the opacities are important. They
mainly manifest themselves for the neutrinos by modifying the predicted
core temperature, 
, to which the predicted rates of higher energy
neutrinos are extremely sensitive. There are also nuclear cross section
uncertainties, both for the production reactions within the sun and for the
detectors. The production cross sections
are problematic because the energies involved are lower
than can easily be measured in the laboratory. The experimental cross
sections must therefore be extrapolated to low energy, and, since they involve
barrier penetration, there is considerable energy dependence.
Nevertheless, given the
canonical estimates of the uncertainties the standard solar model is certainly
excluded by the data.
What is still possible, however, are nonstandard solar models (NSSM).
These involve new ingredients compared to the SSM,
e.g., there could be new physics inputs such as core rotation, magnetic
fields, WIMP's, or gravitational settlings. Most of these
effects manifest themselves by leading to a cooler sun. The high
energy neutrinos are very sensitive to this; one estimate
[46] is that the fluxes vary as 
and 
, so that small reductions in the core temperature could
suppress the number of high energy neutrinos significantly. It should be
cautioned that such nonstandard models may conflict with helioseismology
data, main sequence stairs, etc. I will not worry about that, but
will simply concentrate on whether they can, in fact, describe the neutrino
data.
Another type of nonstandard model is one in which there are large
differences in the cross sections from what is usually assumed. In
particular, it is possible that 
is lower than the usual estimates,
and one preliminary experiment suggests that that may be the case
[47]. This would certainly lower the predicted flux of 
\
neutrinos, and could easily account for the Kamiokande results. However,
it does not explain the larger suppression of Homestake compared to
Kamiokande, and, in fact, it aggravates that difficulty since most of the
expected Homestake rate is also from 
neutrinos.