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arXiv:2310.17079 · Physical Review A

Four-boson first excited state near two-body unitarity

Feng Wu, T. Frederico, R. Higa, U. van Kolck

Published Apr 1, 2024• 3 citations
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Abstract

Near two-body unitarity, the three-boson system is characterized by an approximate discrete scale invariance manifest in a geometric tower of bound states (the Efimov effect). In the absence of a strong four-body force, the four-boson system has two states associated with each Efimov state, one very nearly unstable, the other several times deeper. We study correlations between the excited- and ground-state properties, such as binding energies and radii, up to next-to-leading order in an effective field theory for short-range forces. We obtain the parameters in these correlations from similar correlations arising from existing precise calculations based on short-range potentials. We also derive correlations among excited-state properties that emerge from the proximity of the state to the break-up threshold into a boson and a three-boson bound state, using an effective field theory for ``halo'' states.

DOI
10.1103/physreva.109.043301

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Abstract We investigate the two lowest-lying weakly bound states of N ≤ 8 bosons as functions of the strength of two-body Gaussian interactions. We observe the limit for validity of Efimov physics. We calculate energies and second radial moments as functions of scattering length. For identical bosons we find that two ( N − 1 ) -body states appear before the N -body ground states become bound. This pattern ceases to exist for N ≥ 7 where the size of the ground state becomes smaller than the range of the two-body potential. All mean-square-radii for N ≥ 4 remain finite at the threshold of zero binding, where they vary as ( N − 1 ) p with p = − 3 / 2 , − 3 for ground and excited states, respectively. Decreasing the mass of one particle we find stronger binding and smaller radii. The identical particles form a symmetric system, while the lighter particle is further away in the ground states. In the excited states we find the identical bosons either surrounded or surrounding the light particle for few or many bosons, respectively. We demonstrate that the first excited states for all strengths resemble two-body halos of one particle weakly bound to a dense N -body system for N = 3, 4. This structure ceases to exist for N ≥ 5 .
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