Coherent Neutrino Scattering

Another possible window or telescope for observing the universe is in the detection of neutrinos. The Super Kamiokande neutrino facility in Japan and the Sudbury Neutrino Observatory (SNO) in Canada house two of the largest neutrino detectors, containing thousands of tons of water. Already they have determined that the flux of solar neutrinos from the Sun agrees with the standard solar model. In addition, research groups operating these neutrino detectors have verified neutrino oscillations in matter, the conversion of one type of neutrino to another.

The two neutrino detectors are enormous because neutrinos are notorious for their extremely small probability to interact with matter. Billions of neutrinos pass through our bodies each second and do no harm! A single electron neutrino would pass through solid lead (Pb), filling space from Earth to Jupiter with only a small chance of colliding with a Pb nucleus. However, in 1984 physicist J. Weber proposed that neutrinos of all energies could be coherently scattered by the nuclei in large defect-free single crystals of silicon, ruby, or diamond, thereby enhancing the neutrino scattering probability by a factor of 10²². Therefore, in the ideal case, practically all incident neutrinos would scatter at least once from the carbon nuclei in a perfect diamond crystal within the first centimeter or less!

Normally, one might expect only neutrinos of wavelengths much greater than the spacings between the nuclei in the crystal to have any chance at coherent scattering, analogous to light scattering coherently from a surface of atoms spaced much less than the wavelength of the incident light. Otherwise, when the nuclei are treated as scattering potentials, the phases contributed by the scattering nuclei to the QM amplitude are random, and the scattering probability will be proportional to N instead of N₂, like the result for X-rays discussed in a previous problem. What assumption have we made about the scatterers that Weber says leads to an incorrect conceptual argument against coherent scattering for the shorter-wavelength neutrinos?

Answer

In 1984, so the story goes, J. Weber proposed to build a detector for the coherent scattering of neutrinos in a proposal for research monies. The proposal review committee challenged him to write up the neutrino coherent scattering idea and publish the paper in a reputable physics journal. In December 1984 he submitted the paper, “Method for Observation of Neutrinos and Antineutrinos,” to Physical Review C, and the paper was accepted by a referee within eight days of the December 12 reception date!

The paper triggered an enormous response in parts of the physics community. Numerous rebuttals of his arguments appeared in the physics literature within months after this publication, but all of these rebuttals can be refuted. Every paper erroneously assumes that the nuclear scatterers act as potentials. Wrong! Weber shows in the first section of the paper that such an assumption cannot lead to coherent scattering for neutrino wavelengths less than the spacing between nuclei. However, everyone seems to ignore the details presented by Weber, who correctly explains why the nonrelativistic calculation does not predict coherent neutrino scattering for neutrino wavelengths less than the atomic spacing. The QM argument is essentially dependent on the fact that the scattering phases among the nuclei will be random, leading to a scattering probability proportional to N instead of N².

In later parts of the paper Weber does the relativistic QM scattering calculations to show that coherent scattering for all energies occurs that is, neutrinos of all energies will suffer coherent scattering. Included in these calculations are terms involving the stiffness of the defect-free crystal, and so on. The conceptual idea is that when the crystal as a whole recoils, like a Mossbauer Effect scattering, then one cannot determine (even in principle) where the nuclear scattering of the neutrino took place. Hence their responses are in phase and offer equivalent alternative scattering paths. One must sum the amplitudes over all possible paths that is, all nuclei to obtain the total amplitude for the neutrino scattering.

By QM rule 2, Ψ = ψ₁ + ψ₂ + ψ₃ + . . . , and Ψ = N ψ₁ with probability P = N² |ψ₁|², giving us coherent scattering proportional to N², where N is the total number of nuclei in the bar, about 10²³. One gains the enormous factor of 10²³ for neutrino scattering over the non-coherent cross section! The only remaining contention is whether all the phase relationships are properly accounted for in this relativistic calculation.

Weber (now deceased) actually conducted several experiments to check his relativistic calculations for a long defect-free single crystal detector. He claims to have verified the turning on and the turning off of a nuclear reactor in blind tests, the leaking of tritium from a highly radioactive tritium source, and the twice-daily passing of the Sun though the long axis of his crystal detector. In 1995 he determined that the total measured solar flux of neutrinos all three types, because the detector did not distinguish among them was equal to the total neutrino flux expected by the standard solar model. This predicted result agrees with the 2002 results reported by the heavy water detector at the Sudbury Neutrino Observatory (SNO).