  The scattering of massless fermions on a one-dimensional Q-ball is studied
both analytically and numerically in the background field approximation. The
wave functions of the fermionic scattering states are found in analytical form.
General expressions are derived for the transmission and reflection
coefficients and the corresponding $S$-matrix elements. General formulae
describing the evaporation of the Noether charge of the one-dimensional Q-ball
are given. A numerical study of the transmission and reflection coefficients
along with the corresponding S-matrix elements is performed for a range of
values of the model parameters. A study of the dependence of the evaporation
rate of the Q-ball on the Yukawa coupling constant is carried out for several
values of the Noether charge.
