Enhancing the Seasonal Variation Effect in the Case of the Vacuum Oscillation Solution of the Solar Neutrino Problem

We study in detail the threshold energy dependence of the seasonal variation effect in the energy integrated solar neutrino signal of the Super-Kamiokande detector in the case of the $\nu_{e}\leftrightarrow \nu_{\mu,\tau}$ vacuum oscillation (VO) solution of the solar neutrino problem. We show, in particular, that for the values of $\Delta m^2$ and $\sin^22\theta$ from the VO solution region, the predicted time and threshold e^- energy ($T_{e,Th}$) dependence of the event rate factorize to a high degree of accuracy. As a consequence, the VO generated seasonal variation asymmetry is given by the product of an time-independent function of $T_{e,Th}$ and the standard geometrical asymmetry. For any given $\Delta m^2$ and $\sin^22\theta$ from the VO solution region there exists at least one value of $T_{e,Th}$ from the interval (5 - 11) MeV, for which the seasonal variation effect in the solar neutrino sample of events, formed by recoil electrons with kinetic energy $T_{e} \geq T_{e,Th}$, is either maximal or very close to the maximal; it can vary dramatically with $T_{e,Th}$. Measuring the seasonal effect in each one of a large number of samples corresponding to different values of $T_{e,Th}$ from the indicated interval, say, to $T_{e,Th} = 5; 6; 7;...; 11 MeV$, provides a very effective test of the VO solution. Predictions for the magnitude of the seasonal effect in such samples are given for a large set of representative values of $\Delta m^2$ and $\sin^22\theta$ from the VO solution region.