Linear correlations between 4He trimer and tetramer energies calculated with various realistic 4He potentials

Emiko Hiyama, M. Kamimura

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27 Citations (Scopus)

Abstract

In a previous work we calculated, with the use of the Gaussian expansion method for few-body systems, the energy levels and spatial structures of the 4He trimer and tetramer ground and excited states using the LM2M2 potential, which has a very strong short-range repulsion. In this work, we calculate the same quantities using the currently most accurate 4He-4He potential that includes the adiabatic, relativistic, QED, and residual retardation corrections. Contributions of the corrections to the tetramer ground-(excited-) state energy -573.90(-132.70) mK are respectively -4.13(-1.52) mK, +9.37(+3.48) mK, -1.20(-0.46) mK, and +0.16(+0.07) mK. Further including other realistic 4He potentials, we calculated the binding energies of the trimer and tetramer ground and excited states, B3(0),B3(1),B4(0), and B4(1), respectively. We found that the four kinds of the binding energies for the different potentials exhibit perfect linear correlations between any two of them over the range of binding energies relevant for 4He atoms (namely, six types of the generalized Tjon lines are observed). The dimerlike-pair model for 4He clusters, proposed in the previous work, predicts a simple interaction-independent relation B4(1)B 2=B3(0)B 2+23, which precisely explains the correlation between the tetramer excited-state energy and the trimer ground-state energy, with B 2 being the dimer binding energy.

Original languageEnglish
Article number062505
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume85
Issue number6
DOIs
Publication statusPublished - Jun 6 2012
Externally publishedYes

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trimers
binding energy
excitation
ground state
energy
energy levels
dimers
expansion
atoms
interactions

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

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title = "Linear correlations between 4He trimer and tetramer energies calculated with various realistic 4He potentials",
abstract = "In a previous work we calculated, with the use of the Gaussian expansion method for few-body systems, the energy levels and spatial structures of the 4He trimer and tetramer ground and excited states using the LM2M2 potential, which has a very strong short-range repulsion. In this work, we calculate the same quantities using the currently most accurate 4He-4He potential that includes the adiabatic, relativistic, QED, and residual retardation corrections. Contributions of the corrections to the tetramer ground-(excited-) state energy -573.90(-132.70) mK are respectively -4.13(-1.52) mK, +9.37(+3.48) mK, -1.20(-0.46) mK, and +0.16(+0.07) mK. Further including other realistic 4He potentials, we calculated the binding energies of the trimer and tetramer ground and excited states, B3(0),B3(1),B4(0), and B4(1), respectively. We found that the four kinds of the binding energies for the different potentials exhibit perfect linear correlations between any two of them over the range of binding energies relevant for 4He atoms (namely, six types of the generalized Tjon lines are observed). The dimerlike-pair model for 4He clusters, proposed in the previous work, predicts a simple interaction-independent relation B4(1)B 2=B3(0)B 2+23, which precisely explains the correlation between the tetramer excited-state energy and the trimer ground-state energy, with B 2 being the dimer binding energy.",
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