Long-range interactions of hydrogen atoms in excited states. II. Hyperfine-resolved (2S−2S) systems (original) (raw)
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Long-range interactions of hydrogen atoms in excited states. I.<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:mrowmml:mn2mml:miSmml:mo−mml:mn1mml:miSinteractions and Dirac-<mml:math xmlns:mml="http://www....
Physical review, 2017
The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C6(2S; 1S) describing the interaction of metastable atomic hydrogen (2S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a0 ≪ R ≪ a0/α, where a0 = /(αmc) is the Bohr radius and α is the fine structure constant, one finds the symmetry-dependent result E2S;1S(R) ≈ (−176.75 ± 27.98) E h (a0/R) 6 (E h denotes the Hartree energy). In the Casimir-Polder range a0/α ≪ R ≪ c/L, where L ≡ E 2S 1/2 − E 2P 1/2 is the Lamb shift energy, one finds E2S;1S(R) ≈ (−121.50 ± 46.61) E h (a0/R) 6. In the the Lamb shift range R ≫ c/L, we find an oscillatory tail with a negligible interaction energy below 10 −36 Hz. Dirac-δ perturbations to the interaction are also evaluated and results are given for all asymptotic distance ranges; these effects describe the hyperfine modification of the interaction, or, expressed differently, the shift of the hydrogen 2S hyperfine frequency due to interactions with neighboring 1S atoms. The 2S hyperfine frequency has recently been measured very accurately in atomic beam experiments.
Long-Range Interactions for Hydrogen Atoms in Excited D States
Atoms
Pressure shifts inside an atomic beam are among the more theoretically challenging effects in high-precision measurements of atomic transitions. A crucial element in their theoretical analysis is the understanding of long-range interatomic interactions inside the beam. For excited reference states, the presence of quasi-degenerate states leads to additional challenges, due to the necessity to diagonalize large matrices in the quasi-degenerate hyperfine manifolds. Here, we focus on the interactions of hydrogen atoms in reference states composed of an excited nD state (atom A), and in the metastable 2S state (atom B). We devote special attention to the cases n=3 and n=8. For n=3, the main effect is generated by quasi-degenerate virtual P states from both atoms A and B and leads to experimentally relevant second-order long-range (van-der-Waals) interactions proportional to the sixth inverse power of the interatomic distance. For n=8, in addition to virtual states with two states of P s...
Long-range interactions of hydrogen atoms in excited states. III. nS−1S interactions for n≥3
Physical review, 2017
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.
Long-Range Interactions for Hydrogen: 6P–1S and 6P–2S Systems
Atoms
The collisional shift of a transition constitutes an important systematic effect in highprecision spectroscopy. Accurate values for van der Waals interaction coefficients are required in order to evaluate the distance-dependent frequency shift. We here consider the interaction of excited hydrogen 6P atoms with metastable atoms (in the 2S state), in order to explore the influence of quasi-degenerate 2P and 6S states on the dipole-dipole interaction. The motivation for the calculation is given by planned high-precision measurements of the transition. Due to the presence of quasi-degenerate levels, one can use the non-retarded approximation for the interaction terms over wide distance ranges.
Interaction Between Two Closed Shell Atoms
Revista Brasileira de Física, 1987
We use the theory o f Boehm-Yaris and Jacobi-Csanak t o c a l c u l a t e the d i pele-d i pole, dipole-quadrupole, quadrupole-di pole and quadrupol e-quadrupole c o n t r i b u t i o n s t o the d i s p e r s i o n energy between two d i f f e r e n t closed s h e l l atoms. To t h i s energy we add one o f the Born-Meyer type wrresponding t o valence e f f e c t s. I n t h i s way we f i n d a f i n i t e t o t a l i nt e r a c t i o n energy f o r any interatomic distance, whose asymptotic behavior reproduces the usual d i s p e r s i o n energy.
International Frontier Science Letters
A new theoretical analytical investigation for the exact solvability of non-relativistic quantum spectrum systems at low energy for modified inverse power potential (m.i.p.) is discussed by means Boopp’s shift method instead to solving deformed Schrödinger equation with star product, in the framework of both noncommutativite two dimensional real space and phase (NC: 2D-RSP), the exact corrections for lowest excitations are found straightforwardly for interactions in one-electron atoms, muonic, hadronic and Rydberg atoms by means of the standard perturbation theory. Furthermore, the obtained corrections of energies are depended on the four infinitesimals parameters (θ,χ) and (θ,σ), which are induced by position-position and momentum-momentum noncommutativity, in addition to the discreet atomic quantum numbers (j=l±1/1,s=±1/2 andm) and we have also shown that, the old states are canceled and has been replaced by new degenerated 4(2l+1) sub-states.