Pseudo algebraically closed fields over rings

We prove that for almost all σ ∈G ℚ the field {Mathematical expression} has the following property: For each absolutely irreducible affine variety V of dimension r and each dominating separable rational map φ{symbol}:V→ {Mathematical expression} there exists a point a ∈ {Mathematical expression} such that φ{symbol}(a) ∈ ℤ^r. We then say that {Mathematical expression} is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields {Mathematical expression} other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ.