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Register a new userRelativistic corrections of malpha^6(m/M) order to the hyperfine structure of the H_2^+ molecular ion
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Added by
Vladimir I. Korobov
Publication date
2008
fields
Physics
and research's language is
English
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The malpha^6(m/M) order corrections to the hyperfine splitting in the H_2^+ ion are calculated. That allows to reduce uncertainty in the frequency intervals between hyperfine sublevels of a given rovibrational state to about 10 ppm. Results are in good agreement with the high precision experiment carried out by Jefferts in 1969.
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NRQED approach to the fine and hyperfine structure corrections of order m$alpha$ 6 and m$alpha$ 6 (m/M)-Application to the hydrogen atom The NRQED approach is applied to the calculation of relativistic corrections to the fine and hyperfine structure of hydrogenlike atoms at orders m$alpha$ 6 and m$alpha$ 6 (m/M). Results are found to be in agreement with those of the relativistic theory. This confirms that the derived NRQED effective potentials are correct, and may be used for studying more complex atoms or molecules. Furthermore, we verify the equivalence between different forms of the NRQED Lagrangian used in the literature.
A complete effective Hamiltonian for relativistic corrections at orders $malpha^6$ and $malpha^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are newly obtained. This allows improving the hyperfine structure theory in the hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calculated for a few transitions of current experimental interest.
Accurate predictions of hyperfine structure (HFS) constants are important in many areas of chemistry and physics, from the determination of nuclear electric and magnetic moments to benchmarking of new theoretical methods. We present a detailed investigation of the performance of the relativistic coupled cluster method for calculating HFS constants withing the finite-field scheme. The two selected test systems are $^{133}$Cs and $^{137}$BaF. Special attention has been paid to construct a theoretical uncertainty estimate based on investigations on basis set, electron correlation and relativistic effects. The largest contribution to the uncertainty estimate comes from higher order correlation contributions. Our conservative uncertainty estimate for the calculated HFS constants is $sim$ 5.5%, while the actual deviation of our results from experimental values was $<1$% in all cases.
We investigate finite-$N$ corrections to the superconformal indices of the theories realized on M2- and M5-branes. For three-dimensional theories realized on a stack of $N$ M2-branes we calculate the finite-$N$ corrections as the contribution of extended M5-branes in the dual geometry $AdS_4times boldsymbol{S}^7$. We take only M5-brane configurations with a single wrapping into account, and neglect multiple-wrapping configurations. We compare the results with the indices calculated from the ABJM theory, and find agreement up to expected errors due to the multiple wrapping. For six-dimensional theories on $N$ M5-branes we calculate the indices by analyzing extended M2-branes in $AdS_7times boldsymbol{S}^4$. Again, we include only configurations with single wrapping. We first compare the result for $N=1$ with the index of the free tensor multiplet to estimate the order of the error due to multiple wrapping. We calculate first few terms of the index of $A_{N-1}$ theories explicitly, and confirm that they can be expanded by superconformal representations. We also discuss multiple-wrapping contributions to the six-dimensional Schur-like index.
The hyperfine structure of the long-lived $5D_{3/2}$ and $5D_{5/2}$ levels of Ba$^+$ ion is analyzed. A procedure for extracting relatively unexplored nuclear magnetic moments $Omega$ is presented. The relevant electronic matrix elements are computed in the framework of the ab initio relativistic many-body perturbation theory. Both the first- and the second-order (in the hyperfine interaction) corrections to the energy levels are analyzed. It is shown that a simultaneous measurement of the hyperfine structure of the entire $5D_J$ fine-structure manifold allows one to extract $Omega$ without contamination from the second-order corrections. Measurements to the required accuracy should be possible with a single trapped barium ion using sensitive techniques already demonstrated in Ba$^+$ experiments.
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