  A detailed analysis of transverse momentum spectra of several identified
hadrons in high energy collisions within the canonical framework of the
statistical model of hadronisation is performed. The study of particle momentum
spectra requires an extension of the statistical model formalism used to handle
particle multiplicities, which is described in detail starting from a
microcanonical treatment of single hadronising clusters. Also, a new treatment
of extra strangeness suppression is presented which is based on the enforcement
of fixed numbers of ssbar pairs in the primary hadrons. The considered
centre-of-mass energies range from ~ 10 to 30 GeV in hadronic collisions
(pion-p, pp and Kp) and from ~ 15 to 35 GeV in e+e- collisions. The effect of
the decay chain following hadron generation is accurately and exhaustively
taken into account by a newly proposed numerical method. The exact p_T
conservation at low energy and the increasing hard parton emission at high
energy bound the validity of the presently taken approach within a limited
centre-of-mass energy range. However, within this region, a clear consistency
is found between the temperature parameter extracted from the present analysis
and that obtained from fits to average hadron multiplicities in the same
collision systems. This finding indicates that in the hadronisation process the
production of different particle species and their momentum spectra are two
closely related phenomena governed by one parameter.
