RSS feeds
РусскийEnglish
Issue 10, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2012

 / 

February

←  →

Methodological notes


Scattering phases for particles with nonzero orbital momenta and resonance regimes in the Pais approximation

,
Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation

The functional Pais equation for scattering phases with nonzero orbital momenta is solved in the case of low-energy particles. For short-range screened potentials, in particular, Yukawa or Thomas — Fermi potentials, the Pais equation is shown to reduce to transcendental equations. For the potentials varying $\sim r^{- n}$, $n > 0$, simple algebraic equations are obtained for determining the phases $\delta_l$, $l\ne 0$. Possible applications of the Pais approximation to the problem of finding resonance regimes in the scattering of low-energy particles with nonzero orbital momenta are discussed.

Fulltext pdf (203 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0182.201202e.0173
PACS: 03.65.Nk, 21.45.Bc, 34.50.Cx (all)
DOI: 10.3367/UFNe.0182.201202e.0173
URL: https://ufn.ru/en/articles/2012/2/d/
000304186400004
2-s2.0-84862082402
2012PhyU...55..161B
Citation: Bruk Yu M, Voloshchuk A N "Scattering phases for particles with nonzero orbital momenta and resonance regimes in the Pais approximation" Phys. Usp. 55 161–168 (2012)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 18th, March 2011, revised: 16th, May 2011, 8th, June 2011

Оригинал: Брук Ю М, Волощук А Н «Фазы рассеяния частиц с ненулевыми орбитальными моментами и резонансные ситуации в приближении Пайса» УФН 182 173–180 (2012); DOI: 10.3367/UFNr.0182.201202e.0173

References (15) Cited by (5) Similar articles (20) ↓

  1. A.I. Frank “On the properties of the "potential" neutron dispersion law in a refractive medium” Phys. Usp. 61 900–901 (2018)
  2. M.V. Lebedev, O.V. Misochko “On the question of a classical analog of the Fano problem” Phys. Usp. 65 627–640 (2022)
  3. Kraĭnov V L, L.P. Presnyakov “Phase functions for potential scattering in optics” Phys. Usp. 36 (7) 621–627 (1993)
  4. M.V. Kuzelev, A.A. Rukhadze “Nonrelativistic quantum theory of stimulated Cherenkov radiation and Compton scattering in a plasma” Phys. Usp. 54 375–380 (2011)
  5. S.V. Petrov “Was Sommerfeld wrong? (To the history of the appearance of spin in relativistic wave equations)” Phys. Usp. 63 721–724 (2020)
  6. A.V. Stepanov, Yu.M. Tsipenyuk “Semiclassical approach to nuclear gamma resonance in crystals” Phys. Usp. 43 79–87 (2000)
  7. R.Z. Muratov “Some useful correspondences in classical magnetostatics, and the multipole representations of the magnetic potential of an ellipsoid” Phys. Usp. 55 919–928 (2012)
  8. N.A. Vinokurov “Analytical mechanics and field theory: derivation of equations from energy conservation” Phys. Usp. 57 593–596 (2014)
  9. V.S. Olkhovsky “On the multiple internal reflections of particles and phonons tunneling in one, two, or three dimensions” Phys. Usp. 57 1136–1145 (2014)
  10. I.A. Sadovskyy “Reduction of the scattering matrix array” Phys. Usp. 58 872–876 (2015)
  11. V.I. Ritus “Lagrange equations of motion of particles and photons in the Schwarzschild field” Phys. Usp. 58 1118–1123 (2015)
  12. S.V. Goupalov “Classical problems with the theory of elasticity and the quantum theory of angular momentum” Phys. Usp. 63 57–65 (2020)
  13. L.I. Antonov “Macroscopic representation of the magnetization vector field in a magnetic substance” Phys. Usp. 46 1203–1207 (2003)
  14. S.P. Efimov “Coordinate space modification of Fock's theory. Harmonic tensors in the quantum Coulomb problem” Phys. Usp. 65 952–967 (2022)
  15. A.P. Vinogradov “On the form of constitutive equations in electrodynamics” Phys. Usp. 45 331–338 (2002)
  16. E.H. Lock, S.V. Gerus “Electromagnetic waves in a tangentially magnetized bi-gyrotropic layer (with an example of analysis of spin wave characteristics in a ferrite plate)” Phys. Usp. 67 1257–1270 (2024)
  17. A.V. Nefediev “On effective range expansion in a multichannel system and compositeness of near-threshold resonance” Phys. Usp. 67 71–79 (2024)
  18. G.S. Golitsyn “A N Kolmogorov's 1934 paper is the basis for explaining the statistics of natural phenomena of the macrocosm” Phys. Usp. 67 80–90 (2024)
  19. Yu.L. Klimontovich “What are stochastic filtering and stochastic resonance?” Phys. Usp. 42 37–44 (1999)
  20. B.I. Sturman, E.V. Podivilov “On characteristic times for kinetics of scattering” Phys. Usp. 69 195–198 (2026)

The list is formed automatically.
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions