Statistical theory of multiple meson production with angular momentum conservation
The conventional statistical theory (with energy momentum but without angular momentum conservation) gives the same results (multiplicities and spectra) as obtained iron a model assuming the existence of an intermediate'-hot spot'' in the collision of two high-energy particles. if the''hot-spot-' formation is statistically independent of its decay into many particles. The model is suggested by the formulas used in statistical theory, which in effect put the probability to produce n particles proportional to the probability of finding a particles together in a volume OMEGA . Angular momentum conservation (together with energy and momentum conservation) can be satisfied by considering only states of n particles with prescribed values of total J, energy and momentum. By using the formalism of the density matrix and an explicit expression for the projection operators on states of given angular momentum, a modified form of the phase-space integral is obtained, which is simply related to the probability to produce n particles. The theory with angular momentum but without momentum conservation, as given by Koba, is shown to be a special case easily derivable from the present formalism. The classical'' theory of angular momentum conservation by Ericson is shown to be a limiting ease of wide applicability, however. The conventional theory is valid only if all end particles are in s- states. The formulas were derived for a spherical Gaussian shape-for OMEGA . Allowance for contracted shapes can be made. A MonteCarlo program is proposed to evaluate this phase-space integral. The method will allow computation of spectra of the longitudinal and the transverse momenta of the final particles. The effect on multiplicity of J-conservation is evaluated. Compared to the conventional theory, multiplicity' is increased by 10% in p-p annihilation and decreased by 10% in 6-Bev p-p collisions.
- Research Organization:
- European Organization for Nuclear Research (CERN), Geneva (Switzerland); and Institut Interuniversitaire des Sciences Nucleaires, Brussels
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-16-010850
- OSTI ID:
- 4801864
- Journal Information:
- Nuovo Cimento, Vol. 22, Issue 5; Other Information: Orig. Receipt Date: 31-DEC-62; ISSN 0029-6341
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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Related Subjects
ANGULAR MOMENTUM
ANNIHILATION
ANTIPROTONS
COLLISIONS
DENSITY
DIFFERENTIAL EQUATIONS
ENERGY
ENERGY RANGE
ERICSON THEORY
FIELD THEORY
GEV RANGE
HOT SPOT
INTEGRALS
MATHEMATICS
MATRICES
MESONS
MOMENTUM
MONTE CARLO METHOD
MULTIPLICITY
NUMERICALS
PARTICLE MODELS
PHASE SPACE
PROBABILITY THEORY
PRODUCTION
PROGRAMMING
PROTONS
QUANTUM MECHANICS
SPECTRA
STATISTICS