An analysis of neutrino electron scattering as applied to the SuperKamiokande solar neutrino experiment with the data from the Homestake experiment leads to an upper bound on the neutrino magnetic moment in the range . This range is determined by the spread in the flux predictions from six different standard solar models. We assume equal magnetic moments for all neutrino flavours. This limit is obtained when neutrinos do not undergo any “disappearance” mechanism other than the magnetic moment conversion due to the solar magnetic field and for a total or nearly total suppression of the intermediate energy neutrinos. We also point out that the limit may be further reduced if the threshold energy of the SuperKamiokande detector is decreased.

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