Neutrino Cross Section The nominal neutrino cross section for interaction with a nucleon increases with energy as indicated by the data at right cited by Rohlf. The data displayed at right is taken at energies far above the range of neutrinos from radioactive decay. The slope of the straight line at right, when extrapolated down to 1 MeV, gives a cross section more like 10-45 m2. This is still three orders of magnitude larger than the cross-section measured by Cowan & Reines in their pioneering experiment. Rohlf's comment was that this linear energy dependence of the cross-section was for neutrino energies large compared to the mass energies of the quarks, so an extrapolation to the energies of ordinary radioactive decay is asking too much. The original neutrino detection by Reines and Cowan was based on the reaction This interaction is related by crossing symmetry to the decay of the neutron, the simplest example of beta decay. It is in fact sometimes referred to as "inverse beta decay". So it would appear that the study of beta decay could give an approach to the cross-section for the neutrino interaction. The approach to calculating the cross-section for the interaction is based on Fermi's Golden Rule , and if a matrix element can be found for the weak interaction in one of these reactions it should be comparable in the other. Estimates of the weak interaction coupling strength come from applying the Fermi theory of beta decay in some special cases. Krane does this to arrive at an estimate of 10-43 cm2 = 10-47 m2 for the neutrino cross section in the beta decay range of energy. This is about 20 orders of magnitude less than the scattering cross-section for two nucleons at low energy! With this nominal cross section, some estimates of rates of interaction can be made. Multiplying the cross section times the nucleon density gives a number of interactions per meter, and the inverse of that is an estimate of the mean free path. For water with a density of 1000 kg/m3, the mean free path for a neutrino can be estimated from One perspective on these distances is to compare to a light year So this estimate of mean free path is more than a light year of lead! A fairly common qualitative statement in physics texts is that the mean free path of a neutrino is about a light-year of lead. Griffiths makes the statement "a neutrino of moderate energy could easily penetrate a thousand light-years(!) of lead." This cross section can also be used to estimate the number of events which can be expected in a given size of detector. The Bahcall calculation of the solar neutrino flux is about 5 x 106 /cm2s at the Earth's surface. In what is called the "solar neutrino problem", only about a third to one half this many were measured in early experiments. Current experiments at the Sudbury Neutrino Observatory suggest that neutrino oscillation transmutes some of the solar electron neutrinos into muon and tau neutrinos. When that is taken into account in the recent SNO experiments, the flux is in close agreement with the Bahcall estimate. Neutrinos as leptons Role in supernova Other neutrino types Neutrino cross-section in the Reines & Cowan experiment

Index



Reference

Rohlf

Sec 18.2



Griffiths

Sec. 1.5



Krane

Int. Nuclear Physics

Sec. 9.6