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Second excited state of ${}^4\mathrm{He}$ tetramer

A. Deltuva

TL;DR

This work investigates the existence of the second excited ${}^4\mathrm{He}$ tetramer as an unstable bound state in the continuum by analyzing atom-trimer scattering with the momentum-space Alt-Grassberger-Sandhas (AGS) formalism. Using two realistic He–He potentials, LM2M2 and PCJS, the authors extract a resonant structure in the J=0 channel near the excited-trimer threshold and determine the resonance position and width, including finite-range corrections that shift the width upward relative to zero-range universal predictions. They find a pronounced resonance with a relatively sharp width and show that nonresonant contributions from higher-J partial waves increase the total cross section, making the resonance potentially observable. The results illuminate finite-range corrections to Efimov-type tetramer states and provide guidance for experimental searches in ultracold helium systems.

Abstract

The four-boson universality suggests the existence of the second excited tetramer state in a system of cold ${}^4\mathrm{He}$ atoms. It is not bound but could be seen as a resonance in the atom-trimer scattering. This process is rigorously calculated using the momentum-space transition operator framework with two realistic interatomic potentials. The $S$-wave phase shift and cross section show a resonant behavior below the excited trimer threshold, but there are sizable nonresonant contributions from $P$ and $D$ waves as well. The position and width of the resonant state is determined, and for the latter significant finite-range effects are found.

Second excited state of ${}^4\mathrm{He}$ tetramer

TL;DR

This work investigates the existence of the second excited tetramer as an unstable bound state in the continuum by analyzing atom-trimer scattering with the momentum-space Alt-Grassberger-Sandhas (AGS) formalism. Using two realistic He–He potentials, LM2M2 and PCJS, the authors extract a resonant structure in the J=0 channel near the excited-trimer threshold and determine the resonance position and width, including finite-range corrections that shift the width upward relative to zero-range universal predictions. They find a pronounced resonance with a relatively sharp width and show that nonresonant contributions from higher-J partial waves increase the total cross section, making the resonance potentially observable. The results illuminate finite-range corrections to Efimov-type tetramer states and provide guidance for experimental searches in ultracold helium systems.

Abstract

The four-boson universality suggests the existence of the second excited tetramer state in a system of cold atoms. It is not bound but could be seen as a resonance in the atom-trimer scattering. This process is rigorously calculated using the momentum-space transition operator framework with two realistic interatomic potentials. The -wave phase shift and cross section show a resonant behavior below the excited trimer threshold, but there are sizable nonresonant contributions from and waves as well. The position and width of the resonant state is determined, and for the latter significant finite-range effects are found.
Paper Structure (4 sections, 8 equations, 3 figures, 3 tables)

This paper contains 4 sections, 8 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Atom-trimer scattering equations
  3. Results
  4. Discussion and conclusions

Figures (3)

  • Figure 1: (Color online) Schematic Efimov plot for the system of four ${}^4\mathrm{He}$ atoms, i.e., the energy levels and thresholds as functions of the inverse two-atom scattering length. Only two families of states are shown. The energies of tetramers are displayed by thick curves; those labeled 4, 4* and 4** correspond to the ground, first and second excited states, respectively. The thin curves correspond to few-cluster thresholds. The vertical dashed line labels the physical ${}^4\mathrm{He}$ point.
  • Figure 2: (Color online) Energy dependence of the $J=0$ phase shift for the LM2M2 interaction model in the vicinity of the second excited tetramer state.
  • Figure 3: (Color online) The total cross section and its $J=0$ contribution as functions of energy calculated using the LM2M2 interaction model in the vicinity of the second excited tetramer state.