We represent in fig.3 .12 ) ] . Hence the existing shift between each adjacent dashed and full line represents the small change in the sterile neutrino component , proportional to cos 2 α , resulting from introducing in the scheme aν X component up to its 95 % CL upper bound . This shows that the possible sterile neutrino flux is hardly sensitive to the presence of antineutrinos , a fact whose origin becomes clear on examination of the denominator in eq.(2.13 ): the multiplier of sin 2 α is very close to unity for any value of ψ owing to the fact thatr d ≃ 1 . From fig.3 it is also seen that in the absence ofν x ( x = e , sin 2 ψ = 1 ) the fraction of solar neutrinos oscillating to active ones is greater than 0.59 ( SNO II ) and 0.63 ( SNO I ) at 2σ of the non - ν e flux . Allowing for non - electron antineutrinos up to their 2σ upper bound this fraction becomes respectively 0.62 and 0.66 . This result is consistent with the result of ref . [ 15 ] where the authors also included KamLAND data in their analysis but were restricted to the case sin 2 ψ = 1 .