## How does the Sun shine? (Part 4: The Solar Neutrino Problem)

This post is based on my last two posts explaining the proton-proton chain and
the neutrino hypothesis and discovery.

As explained in the proton-proton chain post, solar neutrinos which are
also electron neutrinos, provide the only direct experimental evidence of the nuclear
fusion happening inside the core of the Sun. Because, unlike photons, neutrinos
produced by the ppI chain and other less probable branches are supposed
to go through the layers of the Sun almost undisturbed.

Solar neutrinos were studied in experiments undertaken by American physicist Raymond
Davis in 1968. He observed collisions between solar neutrinos and chlorine by
using underground tanks of chlorine.

$\large {\nu}_\textrm{e} + {}^{37}\textrm{Cl} \rightarrow {}^{37}\textrm{Ar} + \textrm{e}^{-}$

This pioneering experiment, called the Homestake experiment, on solar neutrinos started by Raymond Davis and collaborators (among them, John Bahcall, who made the predictions based on the Standard Solar Model) is based on the inverse beta decay process: Chlorine-37 absorbs the neutrino to yield Argon-37 and an electron. A tank containing 615 tons of a fluid rich in chlorine called tetrachloroethylene, a colorless liquid widely used for dry cleaning of fabrics, was placed in a gold mine in South Dakota (USA). The fluid was periodically purged with helium gas to remove the argon atoms which were then counted by means of their radioactivity. Due to the very weak interaction between neutrinos and the liquid, the experiment must have been like finding a particular grain of sand in the whole of the Sahara desert.

How many neutrinos were expected to show up during an experiment?

A simple calculation provides a good estimate of the expected flux of solar neutrinos produced by the PPI chain at the earth (and everywhere around the sun at a distance of 1 astronomical unit or AU). By first approximation, the PPI chain provides most of the
solar power we observe on earth, because it happens 85% of the time. As explained in a previous post, every iteration of this sequence results in 2 neutrinos for each 28 MeV of kinetic energy, which we observe eventually as Solar luminosity (Lsun).

$\large \phi = \frac{\textrm{n}_{\nu}}{S}$

$\large n_{reac} \times \frac{28MeV}{reac} = {\textrm{L}}_{sun}$

$\large n_{reac} = \frac{{n}_{\nu}}{2}$

$\large n_{\nu} = \frac{\textrm{L}_{sun} \times 2}{28 MeV}$

(*)$\large \phi = \frac{\textrm{L}_{sun} \times 2}{28 MeV} \times \frac{1}{4 \pi R^2}$

= units of particles per second per cm2
$\large \phi \approx 6.10^{10} / (cm^2 . s)$

At a radius R equal to 1 Astronomical Unit: R = 1 AU = 1.5*10^13cm,

Area = 4*pi*R^2 = 2.83*10^27cm^2

The problem with the Davis experiment was that the detection threshold in Davis’s experiment was 0.8 MeV. So, only neutrinos with energies above this threshold could be detected, and therefore only the less probable, and high-energy Boron-8 neutrinos (the ppIII chain) were detected. So they were not measuring the full spectrum of neutrinos from the Sun, they actually miss all of the most probable solar neutrinos and only measure the rarer types.

So, is there a solar neutrino problem?

The numbers that are being compared are the following: the theoretical neutrino flux in solar neutrino units (SNU) and the measured neutrino flux also in SNU. One SNU is equal to the neutrino flux producing 10^−36 captures per target atom per second. It is convenient given the very low event rates in radiochemical experiments. With typical neutrino flux of (*) 10^10 cm^−2 s^−1 and a typical interaction cross section of about 10^−45 cm^2, about 10^30 target atoms are required to produce one event per day.
Taking into account that 1 mole is equal to 6.022 10^23 atoms, this number corresponds to kilo tons of the target substances, whereas present neutrino detectors operate at much lower quantities.

So the expected neutrino flux of the 8B producing branch, is approximately 6 to 7.5 SNU (*), while Davis first experiment has observed only 2.5 SNU. Many similar experiments like Davis have been made at various locations, various neutrinos source have been used to calibrate these neutrino detectors but the results have been the same, only 1/3 of the expected neutrinos were observed. So, there seem to be a common problem of missing neutrinos everywhere the Solar neutrinos experiments took place.

In this picture, the estimated neutrino flux is given on the vertical axis in units cm^−2 s^−1. Different methods of detection, using Gallium and Chlorine, have various minimum neutrino’s energy threshold in order to be able to detect neutrinos. Note that the neutrinos with energies in the range 0.1-0.25 MeV does not have any associated detector. Also note that the 0 to 0.42 MeV range of the neutrinos from the PPI chain are only partly detected by Gallium-based detectors. The highest flux corresponds to the PPI chain neutrinos that we grossly estimated to be in the 10^10 cm−2 s−1 range, is the first curve with label “pp”. So, as explained previously, the Davis experiment detects neutrinos in the Chlorine detection range and misses the pp neutrinos.

The reason why only 1/3 of the expected neutrinos were detected in Davis experiment, remained a mystery until it was suggested that the electron-neutrinos produced in the sun may transform into other flavors of neutrino, which would not be detected, as they travel towards the Earth.

Sources:
Solar Neutrinos. John N. Bahcall. (http://arxiv.org/abs/hep-ph/0605186)

Solar Models: An Historical Overview. John N. Bahcall. (http://arxiv.org/abs/astro-ph/0209080)