Approximation of an exponential sum

Question

Consider the flowing exponential sum with $x,\,y \ge 0$ and $c_i,\, d_i$ is a real number for $i=1,..,N$ $$ E=\sum\limits_{i = 1}^N \exp \left(- \left( x - c_i \right)^2 - \left( y - d_i \right)^2 \right) $$ Are there any method to approxiate $E$ by an exponential function? For example, it maybe happen that $E \approx E_{apx} = \exp(-\alpha(x^2+y^2)-(1-\alpha)(c_i^2+d_i^2))$, for $0 \le \alpha \le 1.$ I don't know. I stried to find $\alpha$ to fit $E_{apx}$ to $E$ but no hope.