New approach to numerical computation of the eigenfunctions of the continuous spectrum of three-particle Schrödinger operator: I. One-dimensional particles, short-range pair potentials

V. S. Buslaev, S. B. Levin, Pekka Neittaanmäki +1 more

Basing on analogy between the three-body scattering problem and the diffraction problem of the plane wave (for the case of the short range pair potentials) by the system of six half transparent screens, we presented a new approach to the few-body scattering problem. The numerical results have been obtained for the case of the short range nonnegative pair potentials. The presented method allows a natural generalization to the case of the long range pair potentials.

arXiv:0909.4529Journal of Physics A Mathematical and TheoreticalJun 16, 201014 citations

Lecture notes in mathematics

Quantum scattering theory for two- and three-body systems with potentials of short and long range

Volker Enß

Published Jan 1, 1985• 40 citations

Publisher

DOI: 10.1007/bfb0080332

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New approach to numerical computation of the eigenfunctions of the continuous spectrum of three-particle Schrödinger operator: I. One-dimensional particles, short-range pair potentials

V. S. Buslaev, S. B. Levin, Pekka Neittaanmäki +1 more

arXiv:0909.4529Journal of Physics A Mathematical and TheoreticalJun 16, 201014 citations

A+(BC)\rightarrow A+B+C

, and

(ABC)\rightarrow A+(BC)

, respectively. Recently, the author proposed a general particle

{transfer}

(GPT) potential which appears, not only at the 3BT, but also at the Q2T between A and (BC). The new potential indicates a Yukawa-type potential for short range, but a

1/r^n

-type potential for long range. The long range part of the GPT potential for

n=1

indicates an attractive Coulomb-like or a gravitation-like potential. While,

n=2

indicates the Efimov-like potential between A and (BC). The three-body binding energy:

E_n=\epsilon +\zeta _n

with the two-body binding energy

\epsilon

, and the separation energy

\zeta _n

for

(ABC)\rightarrow A+(BC)

satisfies

E_n/E_{n+1}=\zeta _n/\zeta _{n+1}

=const for

\epsilon =0

or the two-body scattering length:

a\rightarrow \infty

(i.e. the two-body unitary limit). At the Q2T, the condensation of the three-body binding energy is given by the GPT-potential in the form of

E_n/E_{n+1}=(\zeta _n+\epsilon )/(\zeta _{n+1}+\epsilon )\rightarrow 1

(const) for

n\rightarrow \infty

(with

\zeta _n\rightarrow 0

) which implies the existence of Efimov-like states at the Q2T in the hadron systems, thereby the possibility of “ultra low energy nuclear transformation”, where the three-body binding energies degenerate at zero energy. Finally, the origin of such a long range potential will be clarified.

N

charged particles. To deal with thermodynamic properties of finite systems we develop and discuss a recent Green function methodology designed for the non-perturbative regime. In addition, we give a brief account on how thermodynamic properties and critical phenomena can be exposed in finite interacting systems.