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Magic Numbers in Boson 4He Clusters: The Auger Evaporation Mechanism. Molecules 2021; 26:molecules26206244. [PMID: 34684825 PMCID: PMC8537914 DOI: 10.3390/molecules26206244] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2021] [Revised: 10/11/2021] [Accepted: 10/12/2021] [Indexed: 11/17/2022] Open
Abstract
The absence of magic numbers in bosonic 4He clusters predicted by all theories since 1984 has been challenged by high-resolution matter-wave diffraction experiments. The observed magic numbers were explained in terms of enhanced growth rates of specific cluster sizes for which an additional excitation level calculated by diffusion Monte Carlo is stabilized. The present theoretical study provides an alternative explanation based on a simple independent particle model of the He clusters. Collisions between cluster atoms in excited states within the cluster lead to selective evaporation via an Auger process. The calculated magic numbers as well as the shape of the number distributions are in quite reasonable agreement with the experiments.
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Rrapaj E, Roggero A. Exact representations of many-body interactions with restricted-Boltzmann-machine neural networks. Phys Rev E 2021; 103:013302. [PMID: 33601535 DOI: 10.1103/physreve.103.013302] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Accepted: 12/18/2020] [Indexed: 01/03/2023]
Abstract
Restricted Boltzmann machines (RBMs) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the representation power of RBMs to provide an exact decomposition of many-body contact interactions into one-body operators coupled to discrete auxiliary fields. This construction generalizes the well known Hirsch's transform used for the Hubbard model to more complicated theories such as pionless effective field theory in nuclear physics, which we analyze in detail. We also discuss possible applications of our mapping for quantum annealing applications and conclude with some implications for RBM parameter optimization through machine learning.
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Affiliation(s)
- Ermal Rrapaj
- Department of Physics, University of California, Berkeley, California 94720, USA.,School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Alessandro Roggero
- Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195, USA
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Dawkins WG, Carlson J, van Kolck U, Gezerlis A. Clustering of Four-Component Unitary Fermions. PHYSICAL REVIEW LETTERS 2020; 124:143402. [PMID: 32338952 DOI: 10.1103/physrevlett.124.143402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Accepted: 03/13/2020] [Indexed: 06/11/2023]
Abstract
Ab initio nuclear physics tackles the problem of strongly interacting four-component fermions. The same setting could foreseeably be probed experimentally in ultracold atomic systems, where two- and three-component experiments have led to major breakthroughs in recent years. Both due to the problem's inherent interest and as a pathway to nuclear physics, in this Letter we study four-component fermions at unitarity via the use of quantum Monte Carlo methods. We explore novel forms of the trial wave function and find one which leads to a ground state of the eight-particle system whose energy is almost equal to that of two four-particle systems. We investigate the clustering properties involved and also extrapolate to the zero-range limit. In addition to being experimentally testable, our results impact the prospects of developing nuclear physics as a perturbation around the unitary limit.
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Affiliation(s)
- William G Dawkins
- Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
| | - J Carlson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - U van Kolck
- Institut de Physique Nucléaire, CNRS-IN2P3, Université Paris-Sud, Université Paris-Saclay, 91406 Orsay, France
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
| | - Alexandros Gezerlis
- Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
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Bazak B, Kirscher J, König S, Valderrama MP, Barnea N, van Kolck U. Four-Body Scale in Universal Few-Boson Systems. PHYSICAL REVIEW LETTERS 2019; 122:143001. [PMID: 31050479 DOI: 10.1103/physrevlett.122.143001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2018] [Revised: 02/12/2019] [Indexed: 06/09/2023]
Abstract
The role of an intrinsic four-body scale in universal few-boson systems is the subject of active debate. We study these systems within the framework of effective field theory. For systems of up to six bosons we establish that no four-body scale appears at leading order (LO). However, we find that at next-to-leading order (NLO) a four-body force is needed to obtain renormalized results for binding energies. With the associated parameter fixed to the binding energy of the four-boson system, this force is shown to renormalize the five- and six-body systems as well. We present an original ansatz for the short-distance limit of the bosonic A-body wave function from which we conjecture that new A-body scales appear at N^{A-3} LO. As a specific example, calculations are presented for clusters of helium atoms. Our results apply more generally to other few-body systems governed by a large scattering length, such as light nuclei and halo states, the low-energy properties of which are independent of the detailed internal structure of the constituents.
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Affiliation(s)
- B Bazak
- The Racah Institute of Physics, The Hebrew University, 9190401, Jerusalem, Israel
| | - J Kirscher
- Department of Physics, The City College of New York, New York, New York 10031, USA
- Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, United Kingdom
| | - S König
- Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
- ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
| | - M Pavón Valderrama
- School of Physics and Nuclear Energy Engineering, International Research Center for Nuclei and Particles in the Cosmos and Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 100191, China
| | - N Barnea
- The Racah Institute of Physics, The Hebrew University, 9190401, Jerusalem, Israel
| | - U van Kolck
- Institut de Physique Nucléaire, CNRS-IN2P3, Université Paris-Sud, Université Paris-Saclay, 91406 Orsay, France
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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Kievsky A, Viviani M, Logoteta D, Bombaci I, Girlanda L. Correlations imposed by the unitary limit between few-nucleon systems, nuclear matter, and neutron stars. PHYSICAL REVIEW LETTERS 2018; 121:072701. [PMID: 30169068 DOI: 10.1103/physrevlett.121.072701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2018] [Revised: 07/04/2018] [Indexed: 06/08/2023]
Abstract
The large values of the singlet and triplet two-nucleon scattering lengths locate the nuclear system close to the unitary limit. This particular position strongly constrains the low-energy observables in the three-nucleon system as depending on one parameter, the triton binding energy, and introduces correlations in the low-energy sector of light nuclei. Here we analyze the propagation of these correlations to infinite nuclear matter showing that its saturation properties, the equation of state of β-stable nuclear matter, and several properties of neutron stars, as their maximum mass, are well determined solely by a few number of low-energy quantities of the two- and three-nucleon systems. In this way we make a direct link between the universal behavior observed in the low-energy region of few-nucleon systems and fundamental properties of nuclear matter and neutron stars.
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Affiliation(s)
- A Kievsky
- Istituto Nazionale di Fisica Nucleare, Largo Pontecorvo 3, 56127 Pisa, Italy
| | - M Viviani
- Istituto Nazionale di Fisica Nucleare, Largo Pontecorvo 3, 56127 Pisa, Italy
| | - D Logoteta
- Istituto Nazionale di Fisica Nucleare, Largo Pontecorvo 3, 56127 Pisa, Italy
| | - I Bombaci
- Istituto Nazionale di Fisica Nucleare, Largo Pontecorvo 3, 56127 Pisa, Italy
- Department of Physics, University of Pisa, 56127 Pisa, Italy
| | - L Girlanda
- Department of Mathematics and Physics, University of Salento, I-73100 Lecce, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Lecce, I-73100 Lecce, Italy
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