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The Journal of Chemical Physics

Field shifts and lowest order QED corrections for the ground 1S1 and 2S3 states of the helium atoms

Alexei M. Frolov

Published Mar 13, 2007• 28 citations
Publisher

Abstract

The bound state properties of the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe helium atoms are determined to very high accuracy from the results of direct numerical computations. To compute the bound state properties of these atoms the author applied his exponential variational expansion in relative/perimetric three-body coordinates. For the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe atoms the author also determined the lowest order QED corrections and the field component of isotopic shift (=field shift). For the 2 3S(L=0) state of the 3He atom the hyperfine structure splitting is evaluated. The considered properties of the ground 1 1S state and the lowest 2 3S state in the 3He and 4He atoms are of great interest in a number of applications.

DOI
10.1063/1.2709880

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The bound state properties of the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe helium atoms are determined to very high accuracy from the results of direct numerical computations. To compute the bound state properties of these atoms the author applied his exponential variational expansion in relative/perimetric three-body coordinates. For the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe atoms the author also determined the lowest order QED corrections and the field component of isotopic shift (=field shift). For the 2 3S(L=0) state of the 3He atom the hyperfine structure splitting is evaluated. The considered properties of the ground 1 1S state and the lowest 2 3S state in the 3He and 4He atoms are of great interest in a number of applications.
Variational calculations of the ground state energy of 4He trimers are reported and are compared with the Hall-Post-Stenschke lower bound on the ground state energy. The variational result for the ground state energy for a range of model pair potentials is in the range −0.05 to −0.2 K; the effect of the triplet nonadditive term is estimated to be less than 1% of the contribution of the pair potentials. A study of the variation of the ground state energy of 3 bosons with pair potential coupling constant is also reported for a Lennard-Jones and a Morse potential model. There is no bound spin 3/2 3He trimer; a lower bound is given for the ground state energy of the spin 1/2 trimer and analogy with the boson results is used to argue that the spin 1/2 trimer is probably not bound. This paper contains computational applications of formal results derived elsewhere.
The bound state spectrum of the low-lying triplet states in the Be atom is investigated. In particular, we perform accurate computations of the bound triplet SSS, PPP, DDD, FFF and GGG states in the four-electron Be atom. The results of these calculations are employed to draw the spectral diagram which contains the energy levels of the triplet states of Be atom. Based on our computational results we can observe transitions from the low-lying bound states to the weakly-bound, Rydberg states. For the 23S2^3S23S and 33S3^3S33S states in the Be atom we also determine a number of bound states properties and discuss the hyperfine structure by using our results of highly accurate computations.
New variational techniques are described which yield a factor of 1000 improvement in accuracy for the energies of the 1snd 1D^{1}\mathrm{D}1D and 3D^{3}\mathrm{D}3D states of helium up to n=8. Convergence to better than \ifmmode\pm\else\textpm\fi{}10 kHz is obtained, making possible high-precision comparisons with experiment for fine structure and singlet-triplet splittings. The comparisons are sensitive to QED, relativistic recoil, and second-order mass-polarization corrections.
The three-body Schrdinger equation is approximately solved in the hyperspherical coordinates and the binding energies of the three-body weakly bound systems are calculated with the purpose to find if He-He-Ba trimers could exist. Using the special feature of the B-spline function like the flexible and highly localized properties, hypersphercial potentials are obtained by modifying the knots distribution of the B-spline basis of different weakly bound three-atom systems. Employing the best empirical interaction potentials between each pair of particles, we obtain that in the ground state binding energies of the weakly bound typical three-atom systems, the bindings of the molecules, 4He-4He-138Ba, 4He-3He-138Ba and 3He-3He-138Ba are possible. The binding energies of these systems are shown in the order of 1 Kelvin, each system could support only one bound state. These weakly bound molecules can exist only in a very cold environment. To get insight into the geometry of the molecules, the features of the channel functions associated with the hyperspherical potential curves of each system are investigated.
Hyperfine structure of the 23S−2^3S-23S−state in the 9{}^99Be atom
A number of bound states properties and the hyperfine structure of the 23S(L=0)-state in the Be atom are determined from the results of highly accurate computations. The energies of the hyperfine structure levels for this state are ε(F=12) = -13725.635(7) MHz, ε(F=32) = -5490.254(7) MHz and ε(F=52) = 8235.381(7) MHz, respectively. The hyperfine structure splittings are Δ12 = 8235.381(7) MHz and Δ23 = 13725.635(7) MHz, respectively. The spectrum of low-lying (bound) triplet states in the Be atom is briefly investigated.