Bogoliubov Laboratory of Theoretical Physics

Seminar “Few-Body Systems”

Date and Time: Tuesday, 29 March 2022, at 2:30 PM

Venue: Blokhintsev Lecture Hall and online on Zoom, Bogoliubov Laboratory of Theoretical Physics

Link to join the seminar via Zoom

Seminar topic: “Regularisation of Zero-Range Two-Body Interactions in the Three-Body Problem”

Authors: A. V. Malykh (BLTP, JINR), O. I. Kartavtsev (DLNP, JINR)

Speaker: A. V. Malykh

Abstract:

Generally, taking the zero-range limit of two-body interactions, one meets difficulties in description of three-body problem, which manifests in Efimov (or Thomas) effect. To overcome this difficulties, Minlos and Faddeev suggested in [1] to regularize zero-range interaction in a specific way, which was further analyzed in [2, 3]. It was shown that the regularization parameter σ should exceed some critical value σ_c to avoid Efimov (or Thomas) effect and the exact value of σ_c was obtained for three identical bosons. Moreover, it was claimed in [2] that Hamiltonian is self-ajoint if σ > σ_c. At last, the detailed proof of this statement is given in [3].

The main goal of this work is to notice that the condition σ > σ_c merely forbids the Efimov (or Thomas) effect and the Hamiltonian is self-ajoint under the weaker condition σ> σ_r > σ_c. It turns out that in the interval σ_c ≤ σ < σ_r one needs to introduce the three-body parameter b, which describes the boundary condition at the triple-collision point and unambiguously determines the self-ajoint three-body Hamiltonian. To clarify the dependence on s and b, the bound-state energies are calculated and it is shown that there is one or no bound state in the interval σ_c ≤ σ < σ_r. Besides, similar analysis was carried out for the three-body problem containing two identical bosons interacting with distinct particle of the same mass and the critical values σ_c and σ_r are given.

One should note that the described scenario is quite general, in particular, it is similar to the case of three two-component fermions described in [4].

Sources:

[1] R.A. Minlos and L.D. Faddeev, Dokl. Akad. Nauk SSSR 141, 1335 (1961).
[2] S. Albeverio et.al., Phys. Lett. A 83, 105 (1981).
[3] G. Basti et.al., arXiv:2107.07188 (2021).
[4] O. I. Kartavtsev and A. V. Malykh, EPL, 115, 36005 (2016).