Abstract:
We study the wave function of a system of three particles in a continuum. The Faddeev equations are used to explicitly identify the singularities of the wave function in the momentum space. We obtain the asymptotic behavior of the wave function in the configuration space by calculating the asymptotic behavior of the Fourier transform of the wave function in the momentum space. Our attention is focused on configurations in which two particles are at a relatively small distance from each other while the third particle is significantly remote from the center of mass of the pair. We show that the coordinate asymptotic form of the wave function for such a configuration contains scattered waves of a new type in addition to the standard terms. We use the obtained exact data concerning the coordinate asymptotic form of the wave function to critically analyze the multiplicative ansatz used in several works to describe systems of three particles in a continuum.
Keywords:
three-particle scattering, single rescattering, double rescattering,
asymptotic behavior of the three-particle wave function in the two-particle sector.
Citation:
S. L. Yakovlev, “Asymptotic behavior of the wave function of three particles in a continuum”, TMF, 186:1 (2016), 152–163; Theoret. and Math. Phys., 186:1 (2016), 126–135
\Bibitem{Yak16}
\by S.~L.~Yakovlev
\paper Asymptotic behavior of the~wave function of three particles in a~continuum
\jour TMF
\yr 2016
\vol 186
\issue 1
\pages 152--163
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\transl
\jour Theoret. and Math. Phys.
\yr 2016
\vol 186
\issue 1
\pages 126--135
\crossref{https://doi.org/10.1134/S0040577916010116}
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Linking options:
https://www.mathnet.ru/eng/tmf8972
https://doi.org/10.4213/tmf8972
https://www.mathnet.ru/eng/tmf/v186/i1/p152
This publication is cited in the following 3 articles:
S. L. Yakovlev, “Asymptotic behavior of the wavefunction for the scattering of three particles with the Coulomb interaction”, JETP Letters, 116:4 (2022), 268–274
Dhevan Gangadharan, “Numerical calculation of 3-pion Coulomb scattering using scalar QED”, Physics Letters B, 832 (2022), 137280
S. L. Yakovlev, “Weak asymptotics of the wave function for an N-particle system and asymptotic filtration”, Theoret. and Math. Phys., 206:1 (2021), 68–83
Citation in format AMSBIB
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