//-----------------------------------------
//   form factor |I(x)|^2
//-----------------------------------------
double I2(double x){
double pi = 3.141593;
double lambda= x*x;
double freal = -2.*pow(asin(0.5/sqrt(lambda)),2);
double fimag = 0.;
if(lambda < 0.25) {
   double etap = 0.5 + sqrt(0.25-lambda);
   double etam = 0.5 - sqrt(0.25-lambda);
   freal = 0.5*pow(log(etap/etam),2) - pi*pi/2;
   fimag = pi * log(etap/etam);
}
double Ireal = 3.*(2.*lambda + lambda*(4.*lambda-1) * freal);
double Iimag = 3.*lambda*(4.*lambda-1) * fimag;
return Ireal * Ireal + Iimag * Iimag;
}