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Manuscript Title: Relativistic kinematics for two-body final states.
Authors: W.J. Braithwaite
Program title: TWOBDY
Catalogue identifier: ABOS_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 4(1972)227
Programming language: Fortran.
Computer: IBM 360/91.
Operating system: OS 360.
RAM: 2K words
Word size: 64
Keywords: Nuclear physics, Kinematics, Final-states, Collision, Two-body, Conservation, Relativistic, Symmetry, Nuclear reaction.
Classification: 17.8.

Nature of problem:
Although two-body reactions occur within a plane, it is convenient to specify all momentum vectors using three-dimensional rectangular coordinates. Such a formulation permits different orientations of the beam or that of the detected outgoing particles to be more easily described. Use of rectangular coordinates to describe both position and momentum is convenient for finite-geometry kinematic calculations and results in greater speed of calculation since trancendental functions, (other than square root) are avoided.

Solution method:
All particle types are assumed known (this specifies each rest mass). Since the reaction Q-value is deemed convenient for input, it has been used to calculate the rest mass of the second outgoing particle. The direction of emission (P1) of outgoing particle 1 is taken as input, leaving four unknowns: P1 and P2. Conservation of 4-momentum (Po,Eo) yields a set of 4 equations which are solved by FORTRAN IV subroutine TWOBDY, providing the needed information. This subroutine additionally provides the jacobian of the transformation from laboratory to centre- of-mass frame (i.e. delta Omega L/delta Omega C). TWOBDY is lengthened by this inclusion, so users not needing centre-of-mass information are referred to subroutine TWOBOD in program BODY3 which is considerably shorter. This jacobian is used in the "test program" to provide a value for kinematic broadening (i.e., delta E1/delta theta 1). The "test program" generates a table of kinematic values for both the laboratory and centre-of-mass by enumerating, in equal step sizes, the in-plane laboratory-angle-of-emission of one outgoing particle (called PART3.). The program enumerates its laboratory energy, its corresponding centre- of-mass angle, its transformation jacobian (delta Omega L/delta Omega C), its kinematic boardening (delta E/delta theta), as well as the laboratory energy and angle of the second (recoil) particle. The output format is nearly the same as that of HEEWEE. Both kinematic branches are treated when appropriate.