  We consider a one-dimensional matter-wave bright soliton, corresponding to
the ground bound state of N particles of mass m having a binary attractive
delta potential interaction on the open line. For a full N-body quantum
treatment, we derive several results for the scattering of this quantum soliton
on a short-range, bounded from below, external potential, restricting to the
low energy, elastic regime where the centre-of-mass kinetic energy of the
incoming soliton is lower than the internal energy gap of the soliton, that is
the minimal energy required to extract particles from the soliton.
