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Manuscript Title: Monte Carlo integration program for the n-particle relativistic phase space integral in invariant variables.
Authors: R.A. Morrow
Program title: MCN
Catalogue identifier: AAWB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 13(1977)399
Programming language: Fortran.
Computer: IBM 370/148.
Operating system: CMS, DOS.
RAM: 31K words
Word size: 32
Keywords: Scattering, Particle physics, Elementary particle, Multiparticle, Monte carlo, Phase space, Lorentz invariant, Physical region, Exceptional region, Importance sampling, Cross section, Differential Distribution, Scatter plot.
Classification: 11.2.

Nature of problem:
In scattering and production reactions of relativistic elementary particles cross sections and differential distributions resulting from an assumed theoretical transition matrix element are often wanted. The n-particle relativistic momentum phase space integral must be numerically evaluated to yield such information. In the course of this evaluation not only are 3n-10 independent variables dealt with but, in general, several dependent variables are encountered as well.

Solution method:
A Monte Carlo integration method is used to numerically evaluate the phase space integral by randomly generating values of the independent variables. Subsequently several dependent invariants which depend on the independent ones in a nonlinear fashion are evaluated. The invariant variables used are squares of sums of adjacent 4-momenta. Facilities are also provided for the printing out of desired distributions in both tabular and histogram form.

Restrictions:
The program is dimensioned for up to 15 (incoming plus outgoing) particles, for up to 24 distributions and for up to 5 scatter (two dimensional) plots. Each of the 24 distributions can have up to 100 bins. Any or all of these limits can be easily increased by the user.

Unusual features:
MCN is unique in the manner in which the dependent invariants are calculated from randomly generated values of the independent ones. A rapid, direct, iterative method is used which is accurate even in the execptional regions of the physical region, e.g. those regions corresponding to forward-like scattering. Another unusual feature is that the first distribution printed out is actually a test distribution that serves to indicate how efficient the event generation has been. Details of the analytical work underlying this program can be found elsewhere.