On the vacuum oscillation solutions of the solar neutrino problem

We study the stability of the two-neutrino vacuum oscillation solution of the solar neutrino problem with respect to changes of the total fluxes of ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ neutrinos, ${\mathrm{\Phi }}_{\mathrm{B}}$ and ${\mathrm{\Phi }}_{\mathrm{Be}}$. For any value of ${\mathrm{\Phi }}_{\mathrm{Be}}$ from the interval 0.7${\mathrm{\Phi }}_{\mathrm{Be}}^{\mathrm{BP}}$≤${\mathrm{\Phi }}_{\mathrm{Be}}$≤1.3${\mathrm{\Phi }}_{\mathrm{Be}}^{\mathrm{BP}}$ the solar ${\nu }_{\mathit{e}}$ oscillations into an active neutrino, ${\nu }_{\mathit{e}}$⇆${\nu }_{\mathrm{\mu }\left(\mathrm{\tau }\right)}$, provide at 95% C.L. a description of the existing solar neutrino data for ${\mathrm{\Phi }}_{\mathrm{B}}$≃(0.35–3.4)${\mathrm{\Phi }}_{\mathrm{B}}^{\mathrm{BP}}$, ${\mathrm{\Phi }}_{\mathrm{B}}^{\mathrm{BP}}$ and ${\mathrm{\Phi }}_{\mathrm{Be}}^{\mathrm{BP}}$ being the fluxes in the solar model of Bahcall and Pinsonneault from 1992. For ${\mathrm{\Phi }}_{\mathrm{Be}}$≃(0.7–1.3)${\mathrm{\Phi }}_{\mathrm{Be}}^{\mathrm{BP}}$ we find also at 95% C.L. two new [one new] ${\nu }_{\mathit{e}}$⇆${\nu }_{\mathrm{\mu }\left(\mathrm{\tau }\right)}$ [${\nu }_{\mathit{e}}$⇆${\nu }_{\mathit{s}}$] oscillation solutions: (i) for ${\mathrm{\Phi }}_{\mathrm{B}}$≃(0.35–0.43)${\mathrm{\Phi }}_{\mathrm{B}}^{\mathrm{BP}}$ at Δ${\mathit{m}}^2$≃(4.7–6.5)×${10}^{\mathrm{-}12}$ ${\mathrm{eV}}^2$ [(4.8–6.4)×${10}^{\mathrm{-}12}$ ${\mathrm{eV}}^2$] and ${\sin }^2$2θ≳0.71[0.74], and (ii) for ${\mathrm{\Phi }}_{\mathrm{B}}$≃(0.45–0.65)${\mathrm{\Phi }}_{\mathrm{B}}^{\mathrm{BP}}$ at Δ${\mathit{m}}^2$≃(3.2–4.0)×${10}^{\mathrm{-}11}$ ${\mathrm{eV}}^2$ and ${\sin }^2$2θ≳0.59.