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Manuscript Title: Rapidity generator for Monte-Carlo calculations of cylindrical phase space.
Authors: S. Jadach
Program title: GENRAP
Catalogue identifier: AAUO_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 9(1975)297
Programming language: Fortran.
Computer: CDC 7600.
Operating system: SCOPE 2.0.
RAM: 6K words
Word size: 60
Keywords: Elementary, Particle physics, Hadrons, Phase space, Monte carlo, Rapidity, Integration, Importance sampling.
Classification: 11.2.

Nature of problem:
Analysis of high energy collisions of hadrons in the framework of many theoretical models needs numerical evaluation of multidimensional integrals over Lorentz invariant phase space. In practice, the only method of evaluating them exactly is the Monte-Carlo method. However, if we use methods of random generation of points in the phase space known up to now, the time of evaluation of these integrals increases not only with the number of particles, but also very rapidly with energy and the Monte-Carlocalculation of phase space integrals for laboratory momentum over a thousand GeV/c are practically impossible.

Solution method:
The time of Monte-Carlo evaluation of integrals can be shortened by the importance sampling method. The first step in solving the problem of importance sampling for calculating of the Lorentz invariant, cylindrical phase space was done by proposing the method of generation of the transverse momenta in a limited region. However, even when this method is applied, the calculation time increases appreciably with increasing energy. We present here a new method of solving this problem. We propose to generate rapidity variable instead of longitudinal momenta, or some kind of intermediate masses. When this method is applied the calculation time for a fixed number of outgoing particles remains nearly constant when the energy increases.

This program has a very good importance sampling for purely cylindrical phase space, i.e. for phase space with transverse momentum cut-off only. Derivations of the model from purely cylindrical phase space may decrease the efficiency of the program. The efficiency also decreases with increasing number of particles.

Running time:
The generation time of one event is approximatley proportional to the number of particles. However, at low energies there is a number of zero-weight events. The time generation of one zero-weight event is shorter than that of non-zero-weight event. For example, the generation time of one event for 10 particles, for CDC 7600 computer at CERN is 2.3 X 10**-4 s, and is nearly the same as in the case of a typical phase space Monte-Carlo program like FOWL.