Long-range interactions of hydrogen atoms in excited states. I.<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:mi>S</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mi>S</mml:mi></mml:mrow></mml:math>interactions and Dirac-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>δ</mml:mi></mml:math>perturbations

Adhikari, Chandra Mani; Debierre, Vincent; Matveev, A.; Kolachevsky, Nikolai N.

doi:10.1103/physreva.95.022703

Cited by 22 publications

(44 citation statements)

References 53 publications

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“…We have recently analyzed [1] the interaction of metastable 2S hydrogen atoms with ground-state atoms. A long-standing discrepancy regarding the numerical value of the van der Waals C 6 coefficient could be resolved, and the mixing term was treated for 2S-1S interactions [1,[5][6][7]. In [8], we have analyzed 2S-2S interactions, and we have determined the hyperfine-resolved eigenstates of the van der Waals interaction, both among the S-S, P -P as well as the S-P submanifolds of the n = 2 hydrogen states.…”

Section: Introductionmentioning

confidence: 99%

Long-range interactions of hydrogen atoms in excited states. III. nS−1S interactions for n≥3

Adhikari

Debierre

2017

Phys. Rev. A

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The long-range interaction of excited neutral atoms has a number of interesting and surprising properties, such as the prevalence of long-range, oscillatory tails, and the emergence of numerically large van der Waals C6 coefficients. Furthermore, the energetically quasi-degenerate nP states require special attention and lead to mathematical subtleties. Here, we analyze the interaction of excited hydrogen atoms in nS states (3 ≤ n ≤ 12) with ground-state hydrogen atoms, and find that the C6 coefficients roughly grow with the fourth power of the principal quantum number, and can reach values in excess of 240 000 (in atomic units) for states with n = 12. The nonretarded van der Waals result is relevant to the distance range R ≪ a0/α, where a0 is the Bohr radius and α is the fine-structure constant. The Casimir-Polder range encompasses the interatomic distance range a0/α ≪ R ≪ c/L, where L is the Lamb shift energy. In this range, the contribution of quasi-degenerate excited nP states remains nonretarded and competes with the 1/R 2 and 1/R 4 tails of the pole terms which are generated by lower-lying mP states with 2 ≤ m ≤ n − 1, due to virtual resonant emission. The dominant pole terms are also analyzed in the Lamb shift range R ≫ c/L. The familiar 1/R 7 asymptotics from the usual Casimir-Polder theory is found to be completely irrelevant for the analysis of excited-state interactions. The calculations are carried out to high precision using computer algebra in order to handle a large number of terms in intermediate steps of the calculation, for highly excited states.

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Section: Introductionmentioning

confidence: 99%

Long-range interactions of hydrogen atoms in excited states. III. nS−1S interactions for n≥3

Adhikari

Debierre

2017

Phys. Rev. A

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“…Short Range.-For interatomic separations in the range a 0 ≪ R ≪ a 0 /α (where a 0 is the Bohr radius), the interaction energy (2) is well approximated as ∆E ≈ ∆E vdW where A; B)) . Here, D 6 is the direct, and M 6 is the mixing van der Waals coefficient [2][3][4][5][6][7]. For energetically lower states in atom A (with E v,A = E m,A < 0), the representation (8) is obtained by carefully considering the contributions from the Wick-rotated term W and the pole term P.…”

mentioning

confidence: 99%

Virtual Resonant Emission and Oscillatory Long-Range Tails in van der Waals Interactions of Excited States: QED Treatment and Applications

Adhikari¹,

Debierre²

2017

Phys. Rev. Lett.

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We report on a quantum electrodynamic (QED) investigation of the interaction between a ground state atom with another atom in an excited state. General expressions, applicable to any atom, are indicated for the long-range tails that are due to virtual resonant emission and absorption into and from vacuum modes whose frequency equals the transition frequency to available lower-lying atomic states. For identical atoms, one of which is in an excited state, we also discuss the mixing term that depends on the symmetry of the two-atom wave function (these evolve into either the gerade or the ungerade state for close approach), and we include all nonresonant states in our rigorous QED treatment. In order to illustrate the findings, we analyze the fine-structure resolved van der Waals interaction for nD-1S hydrogen interactions with n=8, 10, 12 and find surprisingly large numerical coefficients.

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“…3.3). The data in Table 2, with appropriate modifications of the hyperfine averages [12][13][14], could be used for the description of pressure shifts in 1S-nS (n = 2, 3, 4) and 2S-nP experiments (n = 4, 6). An application of the developed formalism to recent and planned 2S-4P and 2S-6P experiments is discussed in Sec.…”

Section: Discussionmentioning

confidence: 99%

“…For example, the coefficients C 6 (2S; 1S) (see Ref. [12]) and C 6 (3S; 1S) (see Ref. [17]) are given as…”

Section: Peculiarities Of Van Der Waals Coefficients For S Statesmentioning

confidence: 99%

Pressure shifts in high-precision hydrogen spectroscopy: II. Impact approximation and Monte-Carlo simulations

Matveev

Kolachevsky

Adhikari

2019

J. Phys. B: At. Mol. Opt. Phys.

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We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on the recent hydrogen 2S-4P experiment (and an ongoing 2S-6P experiment) in Garching, but numerical input data are provided for other transitions (e.g., involving S states), as well. We show that the frequency shifts can be described, to sufficient accuracy, in the impact approximation. The pressure related effects were separated into two parts, (i) related to collisions of atoms inside of the beam, and (ii) related to collisions of the atoms in the atomic beam with the residual background gas. The latter contains both atomic as well as molecular hydrogen. The dominant effect of intra-beam collisions is evaluated by a Monte-Carlo simulation, taking the geometry of the experimental apparatus into account. While, in the Garching experiment, the collisional shift is on the order of 10 Hz, and thus negligible, it can decisively depend on the experimental conditions. We present input data which can be used in order to describe the effect for other transitions of current and planned experimental interest.

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Long-range interactions of hydrogen atoms in excited states. I.2S−1Sinteractions and Dirac-δperturbations

Cited by 22 publications

References 53 publications

Long-range interactions of hydrogen atoms in excited states. III. nS−1S interactions for n≥3

Long-range interactions of hydrogen atoms in excited states. III. nS−1S interactions for n≥3

Virtual Resonant Emission and Oscillatory Long-Range Tails in van der Waals Interactions of Excited States: QED Treatment and Applications

Pressure shifts in high-precision hydrogen spectroscopy: II. Impact approximation and Monte-Carlo simulations

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