def _R2deriv(self,R,z,phi=0.,t=0.):
        """
        NAME:
           _R2deriv
        PURPOSE:
           evaluate the second radial derivative for this potential
        INPUT:
           R - Galactocentric cylindrical radius
           z - vertical height
           phi - azimuth
           t - time
        OUTPUT:
           the second radial derivative
        HISTORY:
           2011-10-09 - Written - Bovy (IAS)
        """
        Rz= R**2.+z**2.
        sqrtRz= numpy.sqrt(Rz)
        return (3.*R**4.+2.*R**2.*(z**2.+self.a*sqrtRz)\
                    -z**2.*(z**2.+self.a*sqrtRz)\
                    -(2.*R**2.-z**2.)*(self.a**2.+R**2.+z**2.+2.*self.a*sqrtRz)\
                    *numpy.log(1.+sqrtRz/self.a))\
                    /Rz**2.5/(self.a+sqrtRz)**2.