  An efficient technique based on low-rank separated approximations is proposed
for computation of three-dimensional integrals arising in the energy deposition
model that describes ion-atomic collisions. Direct tensor-product quadrature
requires grids of size $4000^3$ which is unacceptable. Moreover, several of
such integrals have to be computed simultaneously for different values of
parameters. To reduce the complexity, we use the structure of the integrand and
apply numerical linear algebra techniques for the construction of low-rank
approximation. The resulting algorithm is $10^3$ faster than spectral
quadratures in spherical coordinates used in the original DEPOSIT code. The
approach can be generalized to other multidimensional problems in physics.
