Three-body collapse for Tabakin potentials and the Thomas effect

Abstract

A system constituted of three bosons interacting via two-body separable potentials with fixed twoboson binding is known to lead to bound-state collapse in the case where the potential parameters allow two-boson S-matrix poles close to (resonance) and on (continuum bound state) the real momentum axis. The collapse is shown to be accompanied by an increase in the average kinetic energy of the two-body bound state, which signals a decrease in the range of the two-body interaction for fixed two-body binding. The collapse is claimed to be a manifestation of the well-known Thomas effect which leads to a collapse of the three-body system when the range of the two-body interaction goes to zero for a fixed two-body binding. PACS number(s): 21.45.+v, 03.65.Nk

Breakdown of universality in few-boson systems

“…Effect seen in that work may be well related with the one we discuss, since the potential of Ref. [20] may be rewritten as a rank 2 potential with only two independent λ ij parameters and therefore has the structure comparable to ours with several attractive and repulsive regions. However, in Ref.…”

“…6. Furthermore, we would like to mention that Delfino et al [20] have found a strong collapse of the trimer for a rank 1 separable potential with two-term form factors. Effect seen in that work may be well related with the one we discuss, since the potential of Ref.…”

Unusually strong attraction in the presence of continuum bound state

“…The use of these potentials in (three-nucleon) 3N and four-nucleon bound-state calculations [7] leads to ground states of unusually large binding of several hundred MeV's in addition to a weakly bound excited state. [7,9,10] One …”

Universality and Halo Nuclei

“…[22]). The collapse of the three-body ground-state for zero-range two-body interactions, sometimes also referred as Thomas's collapse, has been discussed in many other subsequent works: in the context of three-nucleon systems [23][24][25][26][27][28], as well as when discussing more general low-energy few-body properties and correlations [5,6,[29][30][31][32][33][34]. It was pointed out by Gibson and Stephenson [26] that such collapsing effect can be understood by a qualitative simplified argument given by Wigner [35], relating the kinetic and potential energies in the deuteron and triton, when ignoring short-range repulsion and problem of saturation.…”

“…[29] the BSC was investigated for the case of two-terms form-factor Tabakin potential [28]. In this case, after recognizing that such BSC is a manifestation of the Thomas collapse, the effect was shown to be accompanied by an increase in the average kinetic energy of the two-body bound state, which signals a decrease in the range of the twobody interaction for fixed two-body binding.…”