Relativistic Correction to the Helium Dimer Interaction Energy

Cencek, Wojciech; Komasa, Jacek; Pachucki, Krzysztof; Szalewicz, Krzysztof

doi:10.1103/physrevlett.95.233004

Cited by 36 publications

(31 citation statements)

References 24 publications

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“…It has been computed for a range of R in Ref. [11], but only in the so-called Cowan-Griffin approximation which for R e is very inaccurate [14]. A part of the QED correction of the order 3 is accounted for using CP theory, but other 3 QED terms have been calculated thus far only for R e [15].…”

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Relativistic and Quantum Electrodynamics Effects in the Helium Pair Potential

et al. 2010

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The helium pair potential was computed including relativistic and quantum electrodynamics contributions as well as improved accuracy adiabatic ones. Accurate asymptotic expansions were used for large distances R. Error estimates show that the present potential is more accurate than any published to date. The computed dissociation energy and the average R for the (4)He(2) bound state are 1.62+/-0.03 mK and 47.1+/-0.5 A. These values can be compared with the measured ones: 1.1(-0.2)(+0.3) mK and 52+/-4 A [R. E. Grisenti, Phys. Rev. Lett. 85, 2284 (2000)].

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“…The relativistic correction of the order 2 , where ¼ 1=137:036 is the fine structure constant, has been computed accurately in Ref. [14] but only for R e . It has been computed for a range of R in Ref.…”

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Relativistic and Quantum Electrodynamics Effects in the Helium Pair Potential

et al. 2010

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“…Several improvements to the approach of Refs. [19,20] that have been made recently [21][22][23] enabled us to perform highly accurate ECG calculations for 46 values of the interatomic distance R.…”

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Pair Potential with Submillikelvin Uncertainties and Nonadiabatic Treatment of the Halo State of the Helium Dimer

et al. 2017

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The pair potential for helium has been computed with accuracy improved by an order of magnitude relative to the best previous determination. For the well region, its uncertainties are now below 1 millikelvin. The main improvement is due to the use of explicitly correlated wave functions at the nonrelativistic Born-Oppenheimer (BO) level of theory. The diagonal BO and the relativistic corrections were obtained from large full configuration interaction calculations. The nonadiabatic perturbation theory was used to predict the properties of the halo state of helium dimer. Its binding energy and the average value of interatomic distance are found to be 138.9(5) neV and 47.13(8)Å. The binding energy agrees with its first experimental determination of 151.9(13.3) neV [Zeller et al., PNAS 113, 14651 (2016)].Helium is expected to become an important medium in determining thermodynamic metrology standards and the future system of SI units [1,2]. Several elements of such standards will be established by ab initio quantum mechanical calculations [3][4][5][6][7]. An important theory input is the helium pair potential. Its knowledge is required to account for the imperfection of helium gas and the necessary extrapolations to zero pressure [2]. The more accurate this potential is, the smaller will be the uncertainties of the resulting standards.There are other reasons of interest in the helium pair potential. The dimer composed of 4 He atoms, 4 He 2 , has a single very weakly bound vibrational state-an example of a quantum halo state-where atoms move mainly in the classically forbidden tunneling region of the configuration space [8]. This state was the subject of several experimental investigations [9][10][11][12][13][14]. We present here the development of a new potential with uncertainties reduced by an order of magnitude compared to the previous most accurate determination [15]. This potential and the nonadiabatic perturbation theory [16], accounting for the coupling of the electronic and nuclear motion, are used to obtain an accurate theoretical prediction of the properties of the halo state.The potential of Ref.[15] contained the BornOppenheimer (BO) component from Ref. [17]. Its uncertainty, amounting to several millikelvin (mK) in the well region, was due to the slow convergence of a part of the wave function expanded in terms of orbital products. Since it is impossible to converge the orbital expansion sufficiently well [18], we now follow Refs. [19,20] and expand the BO wave function using the four-electron explicitly correlated Gaussian (ECG) basis. Several improvements to the approach of Refs. [19,20] In Ref.[15], the BO potential of Ref.[17] was combined with the adiabatic (diagonal BO), relativistic, and quantum electrodynamics (QED) contributions, as well as with an appropriate retardation correction [24]. Its uncertainties were almost entirely determined by the uncertainties of the BO component. With the much improved BO potential computed in the present work, the accuracy of the adiabatic and relativistic co...

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“…The differences between CCSDT and CCSD for X = 4, 5, 6 as well as the differences between Full CI and CCSDT for X = 4, 5 are given in Table 2. The SCF interaction energies and the extrapolated correlation contributions are listed in Table 3 The lowest-order relativistic correction to the interaction energy was calculated by Cencek et al [14] at R = 5.6 a 0 using the Breit-Pauli approximation [32]. It consists of four terms for a pair of Helium atoms: the mass-velocity term, the orbit-orbit term, and the 1-and 2-electron Darwin terms.…”

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Ab initiopotential energy curve for the helium atom pair and thermophysical properties of dilute helium gas. I. Helium–helium interatomic potential

2007

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To cite this version:Eckhard Vogel, Eckard Bich, Robert Hellmann. Ab initio potential energy curve for the helium atom pair and thermophysical properties of the dilute helium gas. I. Helium-helium interatomic potential. Molecular Physics, Taylor & Francis, 2007, 105 (23-24) A helium-helium interatomic potential energy curve was determined from quantummechanical ab initio calculations. Very large atom-centred basis sets including a newly developed d-aug-cc-pV8Z basis set supplemented with bond functions and ab initio methods up to Full CI were applied. The aug-cc-pV7Z basis set of Gdanitz (J. Chem. Phys., 113, 5145 (2000)) was modified to be more consistent with the aug-cc-pV5Z and aug-cc-pV6Z basis sets. The diagonal Born-Oppenheimer corrections as well as corrections for relativistic effects were also calculated. A new analytical representation of the interatomic potential energy was fitted to the ab initio calculated values. In a following paper this potential model will be used in the framework of the quantum-statistical mechanics and of the corresponding kinetic theory to calculate the most important thermophysical properties of helium governed by two-body and three-body interactions.

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Relativistic Correction to the Helium Dimer Interaction Energy

Cited by 36 publications

References 24 publications

Relativistic and Quantum Electrodynamics Effects in the Helium Pair Potential

Relativistic and Quantum Electrodynamics Effects in the Helium Pair Potential

Pair Potential with Submillikelvin Uncertainties and Nonadiabatic Treatment of the Halo State of the Helium Dimer

Ab initiopotential energy curve for the helium atom pair and thermophysical properties of dilute helium gas. I. Helium–helium interatomic potential

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