#### Title

Long-Range Interactions of Hydrogen Atoms in Excited States. III. nS−1S Interactions for n ≥ 3

#### Abstract

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 C_{6} coefficients. Furthermore, the energetically quasidegenerate 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 240000 (in atomic units) for states with n = 12. The nonretarded van der Waals result is relevant to the distance range R ≪ a_{0}/α, where a_{0} is the Bohr radius and α is the fine-structure constant. The Casimir-Polder range encompasses the interatomic distance range a_{0}/α R ≪ ≪ ħc/L, where L is the Lamb shift energy. In this range, the contribution of quasidegenerate 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 ≫ ħc/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.

#### Recommended Citation

C.
M.
Adhikari
et al.,
"Long-Range Interactions of Hydrogen Atoms in Excited States. III. nS−1S Interactions for n ≥ 3," *Physical Review A*, vol. 96, no. 3, American Physical Society (APS), Sep 2017.

The definitive version is available at https://doi.org/10.1103/PhysRevA.96.032702

#### Department(s)

Physics

#### Keywords and Phrases

Algebra; Atoms; Ground state; Poles; Quantum theory; Van der Waals forces, Computer algebra; Fine structure constants; Highly excited state; Inter-atomic distances; Long range interactions; Long-range oscillatory; Principal quantum numbers; Resonant emissions, Excited states

#### International Standard Serial Number (ISSN)

2469-9926; 2469-9934

#### Document Type

Article - Journal

#### Document Version

Final Version

#### File Type

text

#### Language(s)

English

#### Rights

© 2017 American Physical Society (APS), All rights reserved.

#### Publication Date

01 Sep 2017

## Comments

This projectwas supported by the National Science Foundation (Grants No. PHY-1403973 and No. PHY-1710856) and by theMissouri Research Board.