h[[Nu]_] := 2 BesselJ[1, [Nu]]/[Nu]

G[[Nu]_] :=
 Piecewise[{{(Abs[h[[Nu]]]^2)*(2*Pi*
        NIntegrate[(Abs[h[t]]^2)*t, {t, 0, a - [Nu]}] +
       2*NIntegrate[(Abs[h[t]]^2)*t*
          ArcCos[((t^2 + [Nu]^2 - a)/(2*t*[Nu]))]^2, {t,
          a - [Nu], [Nu] + a}]), [Nu] <
     a}, {(Abs[h[[Nu]]]^2)*(2*
       NIntegrate[(Abs[h[t]]^2)*t*
         ArcCos[((t^2 + [Nu]^2 - a)/(2*t*[Nu]))]^2, {t, [Nu] -
          a, [Nu] + a}]), [Nu] > a}}]