### 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 C6 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?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/αRc/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/R2 and 1/R4 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 Rc/L. The familiar 1/R7 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.

Original language | English |
---|---|

Article number | 032702 |

Journal | Physical Review A |

Volume | 96 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 5 2017 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*96*(3), [032702]. https://doi.org/10.1103/PhysRevA.96.032702

**Long-range interactions of hydrogen atoms in excited states. III. nS-1S interactions for n≥3 LONG-RANGE INTERACTIONS .. III. nS-1S .. C. M. ADHIKARI, V. DEBIERRE, and U. D. JENTSCHURA.** / Adhikari, C. M.; Debierre, V.; Jentschura, U.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 96, no. 3, 032702. https://doi.org/10.1103/PhysRevA.96.032702

}

TY - JOUR

T1 - Long-range interactions of hydrogen atoms in excited states. III. nS-1S interactions for n≥3 LONG-RANGE INTERACTIONS .. III. nS-1S .. C. M. ADHIKARI, V. DEBIERRE, and U. D. JENTSCHURA

AU - Adhikari, C. M.

AU - Debierre, V.

AU - Jentschura, U.

PY - 2017/9/5

Y1 - 2017/9/5

N2 - 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 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?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/αRc/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/R2 and 1/R4 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 Rc/L. The familiar 1/R7 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.

AB - 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 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?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/αRc/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/R2 and 1/R4 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 Rc/L. The familiar 1/R7 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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U2 - 10.1103/PhysRevA.96.032702

DO - 10.1103/PhysRevA.96.032702

M3 - Article

AN - SCOPUS:85029584648

VL - 96

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 032702

ER -