Abstract
Universal relationship of scaled size and scaled energy, which was previously established for two- and three-body systems in their ground state, is examined for four-body systems, using Quantum Monte Carlo simulations. We study in detail the halo region, in which systems are extremely weakly bound. Strengthening the interparticle interaction we extend the exploration all the way to classical systems. Universal size-energy law is found for homogeneous tetramers in the case of interaction potentials decaying predominantly as r−6. In the case of mixed tetramers, we also show under which conditions the universal line can approximately describe the size-energy ratio. The universal law can be used to extract ground-state energy from experimentally measurable structural characteristics, as well as for evaluation of theoretical interaction models.
Highlights
Universal relationship of scaled size and scaled energy, which was previously established for two- and three-body systems in their ground state, is examined for four-body systems, using Quantum Monte Carlo simulations
In few-body physics, universality is often observed in weakly-bound systems of particles with average interparticle distances larger than the range of their interactions
Naturally existing nuclei are not close to a resonance to clearly show the Efimov effect, their study encouraged the search of universality in atomic and molecular physics, and subsequently in condensed matter, all the way up to high-energy physics5,6
Summary
Universal relationship of scaled size and scaled energy, which was previously established for two- and three-body systems in their ground state, is examined for four-body systems, using Quantum Monte Carlo simulations. In few-body physics, universality is often observed in weakly-bound systems of particles with average interparticle distances larger than the range of their interactions. It is manifested as the independence of some system properties on the exact shape of the interaction potential and on the length scale. Atomic clusters, which are small aggregates of atoms whose interactions are well known, played a significant role in elucidating universal ground-state size-energy ratios in weakly-bound dimers and trimers. A thorough analysis for a large set of pure and mixed weakly-bound atomic dimers and trimers showed that universal size-energy scaling extends even below the halo area, in the so called quasi-halo region. Dimensionless scaling of two-body size follows straightforwardly from the halo definition using the mean square radius, and dividing it by the outer www.nature.com/scientificreports/
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