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SUMMARY:Mathematical aspects of the nuclear glory phenomenon: from backwar
 d focusing to Chebyshev polynomials
DTSTART;VALUE=DATE-TIME:20161014T101500Z
DTEND;VALUE=DATE-TIME:20161014T103500Z
DTSTAMP;VALUE=DATE-TIME:20260720T013409Z
UID:indico-contribution-749@cern.ch
DESCRIPTION:Speakers: Vladimir Kopeliovich (Institute for nuclear research
  of RAS)\nThe angular dependence of the cumulative particles production of
 f nuclei near the kinematical boundary for multistep process is defined by
  characteristic polynomials in angular variables\, describing spatial mome
 nta of the particles in intermediate states [1\, 2]. Physical argumentatio
 n\, exploring the small phase space method\, leads to the appearance of eq
 uations for these polynomials in $cos (\\theta/N)$\, where $\\theta$ is th
 e polar angle defining the momentum of final (cumulative) particle\, \nthe
  integer $N$ being the multiplicity of the process (the number of interact
 ions).\nIt is shown explicitly how these equations aappear\, the recurrent
  relations between polynomials with different $N$ are obtained. Factorizat
 ion 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. \nAs a result\, differenti
 al cross section of the cumulative particle production has characteristic 
 behaviour $d\\sigma \\sim 1/ \\sqrt {\\pi - \\theta}$ near the strictly ba
 ckward direction ($\\theta = \\pi$\, the backward focusing effect). Such b
 ehaviour takes place for any multiplicity of the interaction\, beginning w
 ith $n=3$\, elastic or inelastic (with resonance excitations in intermedia
 te states) and can be called \nthe nuclear glory phenomenon\, or 'Buddha's
  light' of cumulative particles.\n\n1. V.B. Kopeliovich.  Sov.J.Nucl.Phys.
  26 (1977) 87 [Yad.Fiz. 26 (1977) 168] \n\n2. V.B. Kopeliovich.  Phys. Rep
 t. 139  (1986) 51\n\n3. V.B.Kopeliovich\, G.K.Matushko and I.K.Potashnikov
 a J.Phys. G41 (2014) 125107\; \nVladimir Kopeliovich and Galina Matushko. 
 'Buddha's light' of cumulative particles. Nuclear Glory Phenomenon. Schola
 rs Press\, Saarbruecken\, Germany. 2015. \nISBN 978-3-639-76496-3. \n\n4. 
 Chebyshev polynomials. https://en.wikipedia.org/wiki/Chebyshevpolynomials\
 n5. Mnogochleny Chebysheva. https://ru.wikipedia.org/wiki/Mnogochleny-Cheb
 ysheva\n\nhttps://indico.particle.mephi.ru/event/4/contributions/749/
LOCATION:Milan Hotel Verdi
URL:https://indico.particle.mephi.ru/event/4/contributions/749/
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