Speaker
Prof.
Vladimir Kopeliovich
(Institute for nuclear research of RAS)
Description
The angular dependence of the cumulative particles production off nuclei near the kinematical boundary for multistep process is defined by characteristic polynomials in angular variables, describing spatial momenta of the particles in intermediate states [1, 2]. Physical argumentation, exploring the small phase space method, leads to the appearance of equations for these polynomials in $cos (\theta/N)$, where $\theta$ is the polar angle defining the momentum of final (cumulative) particle,
the integer $N$ being the multiplicity of the process (the number of interactions).
It is shown explicitly how these equations aappear, the recurrent relations between polynomials with different $N$ are obtained. Factorization properties of characteristic polynomials found in our previous work [3] are extended, and their connection with known in mathematics Chebyshev polynomials of 2-d kind [4, 5] is established.
As a result, differential cross section of the cumulative particle production has characteristic behaviour $d\sigma \sim 1/ \sqrt {\pi - \theta}$ near the strictly backward direction ($\theta = \pi$, the backward focusing effect). Such behaviour takes place for any multiplicity of the interaction, beginning with $n=3$, elastic or inelastic (with resonance excitations in intermediate states) and can be called
the nuclear glory phenomenon, or 'Buddha's light' of cumulative particles.
1. V.B. Kopeliovich. Sov.J.Nucl.Phys. 26 (1977) 87 [Yad.Fiz. 26 (1977) 168]
2. V.B. Kopeliovich. Phys. Rept. 139 (1986) 51
3. V.B.Kopeliovich, G.K.Matushko and I.K.Potashnikova J.Phys. G41 (2014) 125107;
Vladimir Kopeliovich and Galina Matushko. 'Buddha's light' of cumulative particles. Nuclear Glory Phenomenon. Scholars Press, Saarbruecken, Germany. 2015.
ISBN 978-3-639-76496-3.
4. Chebyshev polynomials. https://en.wikipedia.org/wiki/Chebyshevpolynomials
5. Mnogochleny Chebysheva. https://ru.wikipedia.org/wiki/Mnogochleny-Chebysheva
Primary author
Prof.
Vladimir Kopeliovich
(Institute for nuclear research of RAS)
