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Manuscript Title: Approximation formula and ALGOL program of the Lorentz-invariant momentum-space integral for particles of equal masses.
Authors: A. Jabs
Program title: LIMS
Catalogue identifier: AAUE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 5(1973)217
Programming language: Algol.
Computer: UNIVAC 1108.
Operating system: EXEC 8.
RAM: 6K words
Word size: 36
Keywords: Elementary, Particle physics, Multi-particle Production, Phase space, Momentum space, Statistical model.
Classification: 11.2.

Nature of problem:
In high-energy particle reactions the transition probability can be written as the product of some squared transition-matrix element and the volume of momentum space of the outgoing particles. The statistical hypothesis means putting this matrix element independent of the individual particles' momenta, so that the transition probability is proportional to some momentum space integral. This idea, with due modifications, has proved rather useful in describing particle production spectra and in providing a well defined "kinematical" background from which can be distinguished "dynamical" effects such as resonances. The special case of equal masses gains interest from the fact that mostly pions are produced, and that the colliding nucleons are excluded from the statistical ensemble because they carry away a large fraction of their initial energy. Moreover, the special case can advantageously be used in comparisons between Lorentz-invariant and non-invariant momentum space as well as in studies of the high- particle-number limit.

Solution method:
The evaluation is based on the work of lurcat and Mazur. Restriction on the special case of equal masses has made it possible to approximate the formulae of Lurcat and Mazur by relatively simple expressions. In addition, a correction factor has been introduced which reduces the relative error to less than 0.5% for any values of the variables.