Hydrogen hyperfine transition

Precise measurements on g factors of electrons bound in atomic Hydrogen and the Helium ion 4He+ were carried out by Robinson and coworkers. The accuracies of 3 x 10-8 for the Hydrogen atom [5] and of 6 x 10-7 for the Helium ion [6] were sensitive to relativistic effects. Other measurements of the magnetic moment of the electron in Hydrogen-like ions were performed at GSI by Seelig et al. for Lead (207Pb81+) [7] and by Winter et al. for Bismuth (209Bi82+) [8] with precisions of about 10-3 via lifetime measurements of hyperfine transitions. These measurements were also only sensitive to the relativistic contributions. 

NMR frequency of 7Li was measured relative to the hyperfine transition in the ground state of hydrogen to search for a diurnal variation of the ratio of these... 

This cosmic spectroscopy method has been extended to study variation of other fundamental parameters. The ratio of the hydrogen atom hyperfine transition frequency to a molecular (CO, CN, CS, HCO" ", HCN etc.) rotational frequency is proportional to y = a gp where Qp is the proton magnetic gr-factor [21]. A new prehminary result here is Ay/y = (—2.4 1.8) X 10 about 4 billion light years from us (the average z=0.47). Altogether, we now have 3 independent samples of data two optical samples (see [2,3]) and one radio sample. All 3 samples hint that Aa is negative. 

Originally it was thought that atomic hyperfine transition frequencies and atomic magnetic moments were too small for atomic hyperfine masers to be possible, but Ramsey and Kleppner pointed out that by storing atoms in a suitably coated bottle [15] coherency could be maintained for several seconds and the hyperfine resonance would be made so narrow that maser oscillations would take place. In 1961 Goldenberg, Kleppner and Ramsey [15] made an atomic hydrogen maser and found it had extremely high stability. 

Hyperfine transitions in ground state hydrogen-like and... 

Fig. 3. Energy levels for the hydrogen atom at constant magnetic field. The allowed transitions having energy = gftB (ha)j2, where a is the hydrogen hyperfine constant.

Isotope effects in atoms are on the order of p 10 and the magnetic hyperfine structure scales roughly as a pZgnuc 10 Zgnuc, where gnnc is the nuclear g-factor. One has to keep in mind that g uc also depends on p and the quark parameters Xq. This dependence has to be considered when comparing, for example, the frequency of the hyperfine transition in Cs (Cs frequency standard) [5] or the hydrogen 21 cm hyperfine line [30,31] with various optical transitions [5]. 

A comparison of the hyperfine transition in atomic hydrogen with optical transitions in ions on a cosmological timescale was described in Refs. [30] and [31]. This allows one to study the time variation of the parameter F = a gpp, where gp is the proton g-factor. The analysis of the absorbtion spectra of nine quasars with redshifts 0.23 < z < 2.35 yielded... 

Molecular lines observed in the microwave region are due to pure rotational or hyperfine transitions. Hydrogen is the most abundant element in the universe. The H2 molecule does not possess a dipole moment and thus no allowed electric dipole transitions are observed. This molecule can, therefore, not be observed. 

Fig. 9.64. Recording of the ls-2s transition in atomic hydrogen and deuterium using CW high resolution leisers [9.390, 9.391 first ref.]. As an insert a very recent, nan-ow-Iinewidth recording of one of the hyperfine transitions is shown [9.396]...

Figure Bl.4.9. Top rotation-tunnelling hyperfine structure in one of the flipping inodes of (020)3 near 3 THz. The small splittings seen in the Q-branch transitions are induced by the bound-free hydrogen atom tiiimelling by the water monomers. Bottom the low-frequency torsional mode structure of the water duner spectrum, includmg a detailed comparison of theoretical calculations of the dynamics with those observed experimentally [ ]. The symbols next to the arrows depict the parallel (A k= 0) versus perpendicular (A = 1) nature of the selection rules in the pseudorotation manifold.

We do not know exactly where the hydrogen binds at the active site. We would not expect it to be detectable by X-ray diffraction, even at 0.1 nm resolution. EPR (Van der Zwaan et al. 1985), ENDOR (Fan et al. 1991b) and electron spin-echo envelope modulation (ESEEM) (Chapman et al. 1988) spectroscopy have detected hyperfine interactions with exchangeable hydrous in the NiC state of the [NiFe] hydrogenase, but have not so far located the hydron. It could bind to one or both metal ions, either as a hydride or H2 complex. Transition-metal chemistry provides many examples of hydrides and H2 complexes (see, for example. Bender et al. 1997). These are mostly with higher-mass elements such as osmium or ruthenium, but iron can form them too. In order to stabilize the compounds, carbonyl and phosphine ligands are commonly used (Section 6). 

In the transition from Pair B to Pair C, the overall symmetry of the site is restored by an analogous 180° rotational translation of the second radical. In Pair C there is rapid internal rotation about the Ca—Cf bond, and the anisotropy of hyperfine splitting by the alpha hydrogens establishes the direction of the first C—C bonds in the radicals. This direction confirms the supposed screw motion. The breaking of symmetry in the first step, its subsequent restoration in the third, and the overall similarity in the motions of the two radicals give support to the hypothesis that the radicals move one by one. Infrared evidence discussed in Sections IX and VII-B.4.a confirms this inference. 

Here is yet another bizarre result of quantum mechanics for you to ponder. The lx wavefunction for a hydrogen atom is unequal to zero at the origin. This means that there is a small, but nonzero probability that the electron is inside the proton. Calculation of this probability leads to the so-called hyperfine splitting —the magnetic dipoles on the proton and electron interact. This splitting is experimentally measurable. Transitions between the hyperfine levels in the lx state of hydrogen are induced by radiation at 1420.406 MHz. Since this frequency is determined by... 

It is now recognized that cold collision frequency shifts [32] is a crucial issue for every high precision atomic frequency standard, microwave or optical. For hydrogen at a density of 109 cm-3 the shift of the 1S-2S transition is about 0.4 Hz, [8], or a fractional shift of 1.7 x 10-16. For a rubidium hyperfine standard operating at the same density, the shift is about 6 xlO-14 [45,46]. 

---