Abstract
Quantum relativistic decay law of moving unstable particle is analytically calculated in the model case of the Breit–Wigner mass distribution. It turns out that Einstein time dilation of the moving particle decay holds approximately at times when the decay is exponential. The related correction is calculated analytically. Being very small at these times it is practically unobservable. It is shown that Einstein dilation fails for large times t when decay is not exponential. An unstable system of the kind of K 0-meson (which is the superposition of K s and K I) is also considered. In this case, the violation of Einstein dilation is shown to be appreciable at all times under some condition
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Alzetta, A. and d'Ambrogio, E. (1966). Evolution of a resonant state. Nuclear Physics 82, 683–689.
Bailey, J., et al. (1977). Measurement of relativistic time dilation for positive and negative muons in a circular orbit. Nature 268, 301–304.
Exner, P. (1983). Representations of the Poincaré group associated with unstable particles. Physical Review D 28(10), 2621–2627.
Farley, F. (1992). The CERN (g-2) measurements. Zeitschrift fur Physik C 56, S88, Sect. 5.
Fonda, L., Ghirardi, G., and Rimini, A. (1978). Decay theory of unstable quantum system. Reports on Progren in Physics 41, 587, Sect. 3.
Gi-Chol Cho, et al. (1993). The time evolution of unstable particles. Progress in Theoretical Physics 90(4), 803–816.
Goldberger, M. and Watson, K. (1964). Collision Theory, Wiley, New York, Chap. 8.
Gradshtein, I. and Ryzhik, I. (1962). Tables of Integrals, Sums, Series and Products, GIFML, Moscow.
Horwitz, L. (1995). The unstable system in relativistic quantum mechanics. Foundation of Physics 25(1), 39–65.
Levy, M. (1959). On the description of unstable particles in quantum field theory. Nuovo Cimento 13(1), 115.
Messiah, A. (1961). Quantum Mechanics, Vol. 2, North-Holland, Amsterdam, Chap. 21, 13.
Møller, C. (1972). The Theory of Relativity, Clarendon Press, Oxford, Chap. 2.6.
Norman, E. et al. (1988). Tests of the exponential decay law at short and long times. Physical Review Letters 60(22), 2246.
Perkins, D. (1987). Introduction to High Energy Physics, Addison-Wesley Reading, MA.
Prudnikov, A. P., et al. (2003). Integrals and Series, Vol. 1, 2nd edn., Fizmatlit, Moscow.
Stefanovich, E. (1996). Quantum effects in relativistic decays. International Journal of Theoretical Physics 35(12), 2539–2554.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shirokov, M. Decay Law of Moving Unstable Particle. International Journal of Theoretical Physics 43, 1541–1553 (2004). https://doi.org/10.1023/B:IJTP.0000048637.97460.87
Issue Date:
DOI: https://doi.org/10.1023/B:IJTP.0000048637.97460.87