  A quantum theory is developed for the scattering of a nonrelativistic
particle in the field of a cosmic string regarded as a combination of a
magnetic and gravitational strings. Allowance is made for the effects due to
the finite transverse dimensions of the string under fairly general assumptions
about the distribution of the magnetic field and spatial curvature in the
string. It is shown that in a definite range of angles the differential cross
section at all absolute values of the wave vector of the incident particle
depends strongly on the magnetic flux of the string.
