We calculate the influence of resonant neutrino scattering [the Mikheyev-Smirnov-Wolfenstein (MSW) effect] in the Sun and in the Earth on measurable quantities in solar-neutrino-electron scattering experiments. The MSW effect reduces the expected rate for X~-neutrino-electron scattering by a factor that ranges from -0.8 to -0.2 if resonant scattering is the correct explanation for the discrepancy between observation and calculation in the ' '~1 experiment. The Earth can produce a significant diurnal effect for certain values of the neutrino mixing angle and mass difference. I. I N T R O D U C T I O NHow do neutrino oscillations that are amplified by interactions with matter, the Mikheyev-SmirnovWolfenstein (MSW) effect,"' influence the observable quantities in v-e solar-neutrino scattering experiments? The general effect of oscillations is to reduce the cross section for solar-neutrino-electron scattering: electron neutrinos have a larger cross section (by a factor3 that is e 6 to 7 for the most likely experimental conditions) than do neutrinos of other flavors by virtue of the same charged-current diagram as is responsible for the MSW effect itself. Thus the total cross section decreases whenever electron neutrinos are converted to other types of neutrinos. For the experimentally most accessible neutrinos that are produced by the decay of 'B and by the 3~e + p reaction, we calculate the different observable quantities that are implied by a wide range of possible MSW parameters. The results will be useful in planning and interpreting a number of experiments which are presently underway or being d e v e~o~e d .~-'~ Many have contributed recently to the basic understanding of the MSW effect and have determined the range of parameters appropriate to an explanation of the solar-neutrino problem by means of resonantly amplified neutrino oscillations. We adopt here the parameters determined in previous studies and apply the results to neutrino-electron scattering experiments. For the commonly discussed case in which two neutrino flavors are related to the mass eigenstates by a mixing angle 0, solutions compatible with both standard solar models and the 3 7~1 experiment25 requirewhere Am '=rnz2-rn ' and 1,2 are the two mass eigenstates. I n uacuo, the mass eigenstates are related to the flavor eigenstates by the transformation vl=cosOv, -sinOvp, v2=sin0v, +cosOvp. The MSW effect can explain the solar-neutrino problem provided that Am ' lies in the above range. For each value of Am 2, specific values of sin220 are reauired in order to match the observed counting rate in the "CI experiment. For mass differences larger than the range shown in Eq. (la), there is no resonance conversion in the Sun and for smaller mass differences the conversion effect is insufficient to exwlain the difference between calculation and observation (conventional assumptions) in the 3 7~1 experiment.We have purposely refrained from showing explicitly the coupled nature of the constraints in Eqs. ( l a ) and (lb), since the numerical expression of...

The phenomenon of double beta decay is discussed rather fully both from the experimental and from the theoretical point of view, the relation between double beta decay and the possible kinds of inverse beta decay being also briefly treated. A summary of the available experimental data is given, all methods of detection of the various double beta decay processes being considered. The theory of double beta decay, both in the no-neutrino and in the two-neutrino cases, is worked out, ab initio, on the basis of a nucleon-lepton interaction without conservation of parity. It is particularly emphasized that, with a ' twocomponent neutrino ' type nucleon-lepton interaction without conservation of parity, absence of no-neutrino /3p decay does not by itself uniquely imply that neutrino and anti-neutrino are distinguishable and that the total lepton charge is conserved.Comparison of the experimental limits on the double beta decay half-lives with the corresponding theoretical values indicates that two neutrinos are emitted together w-ith two electrons in each double beta decay process-this conclusion is, however, not yet certain and must be confirmed by further experimental work. A treatment is given of the implications of the actual occurrence of two-neutrino rather than no-neutrino double beta decay for the problems of neutrino-anti-neutrino identity and conservation of total lepton charge.It is concluded, on the basis of (i) the available double beta decay, inverse beta decay and muon decay experimental data and (ii) the provisional assumption of the universal applicability of ' two-component neutrino ' type coupling, that a verdict may be tentatively reached in favour of a ' Dirac ' neutrino, operationally distinguishable from a ' Dirac ' anti-neutrino, and with conservation of total lepton charge valid in all neutrino interactions. 9 1 , I N T R O D U C T I O N N the process of double beta decay, the (very long-lived) nucleus ( A , Z ) disintegrates spontaneously to the isobaric nucleus ( A , Z i: 2) with the simultaneous I emission of two electrons-negatrons or positrons-accompanied by either ( U ) two anti-neutrinos or neutrinos, or ( b ) no anti-neutrinos or neutrinos. Alternative to the emission of two positrons, emission of one positron and absorption of one orbital negatron, or absorption of two orbital negatrons, is always possible energetically. T h e existence of double beta decay is expected on general theoretical

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Recent years have witnessed a remarkable change of attitude among physicists toward baryon-number and lepton-number conservation. With the advent of the grand unified theories of strong, electromagnetic, and weak interactions (Langacker 1980, Ellis 1980, the old belief that baryon number and lepton number were exactly conserved has given way to a new belief that, because of the intrinsic structure of most grand unified theories, baryon-number and lepton-number conservation is only approxi mate. In part motivated by this new belief, active searches are now under way for baryon-number and lepton-number nonconserving processes such 145