Ja n 19 94 The 7 Be Solar Neutrino Line : A Reflection of the Central Temperature Distribution of

A precise test of the theory of stellar evolution can be performed by measuring the average difference in energy between the neutrino line produced by 7Be electron capture in the solar interior and the corresponding neutrino line produced in a terrestrial laboratory. This energy shift is calculated to be 1.29 keV (to an accuracy of a few percent) for the dominant ground-state to ground-state transition. The energy shift is approximately equal to the average temperature of the solar core, computed by integrating the temperature over the solar interior with a weighting factor equal to the locally-produced 7Be neutrino emission. Therefore, a measurement of the energy shift is a measurement of the central temperature distribution of the sun. The energy profile of the 7Be line is derived analytically and is evaluated numerically. The line shape is asymmetric: on the low-energy side, the line shape is Gaussian with a half-width at half-maximum of 0.6 keV and on the high-energy side, the line shape is exponential with a half-width at halfmaximum of 1.1 keV. The effective temperature of the high-energy exponential tail is 15 × 106 K. The energy profile of the 7Be neutrino line should be taken into account in calculations of vacuum neutrino oscillations and of the absorption cross section for 7Be solar neutrinos incident on 7Li nuclei.