Hydrogen atom hyperfine splitting

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.

It can be noticed there are two types of hydrogen atoms atoms 1-5 lying in the molecular plane and atoms 6 and 7 lying out of the plane. Thus, the hyperfine splitting constants (an) cannot be interpreted by means of one relationship, but the expressions... 

The lines in the spectrum of Fig. 1 are, even under optimum experimental conditions, quite broad. This is due to small unresolved hyperfine interaction with the eighteen equivalent hydrogen atoms. Either the width of the lines, or nmr measurements (La Mar et al., 1973) can reveal the magnitude of this y-hydrogen splitting (ca. 0.15 G—dependent on temperature and solvent). 

For instance, nitration of naphthalene, azulene, biphenylene, and triphenylene proceeds preferentially in positions with the greatest constant of hyperfine splitting at the hydrogen atom in ESR spectra of corresponding cation-radicals. The constant is known to be proportional to the spin density on the carbon atom bearing the mentioned hydrogen. It is important, however, that the same orientation is also observed at classical mechanism of nitration in cases of naphthalene, azulene, and biphenylene, but not triphenylene (see Todres 1985). 

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... 

Free radicals originating from starch, amylose, and amylopectin form well-distinguished 1 3 1 or 1 4 1 triplets showing hyperfine splitting of 30 gauss. These triplets are attributed to the derivatives of alkyl radicals produced by abstraction of hydrogen atoms from the 2-, 3-, and/or 4-positions of glucose residues.269... 

Later, after experiments performed by Rabi, Lamb and Kusch and their colleagues, it was discovered that the actual hydrogen spectrum was in part in contradiction to Dirac theory (see Fig. 1). In particular, the theory predicted a value of hyperfine structure interval in the ground state of the hydrogen atom, different from the actual one by one part in 103, and no splitting between 2si/2 and... 

Abstract. The usefulness of study of hyperfine splitting in the hydrogen atom is limited on a level of 10 ppm by our knowledge of the proton structure. One way to go beyond 10 ppm is to study a specific difference of the hyperfine structure intervals 8Au2 — Avi. Nuclear effects for axe not important this difference and it is of use to study higher-order QED corrections. 

The hyperfine splitting of the ground state of the hydrogen atom has been for a while one of the most precisely known physical quantities, however, its use for tests of QED theory is limited by a lack of our knowledge of the proton structure. The theoretical uncertainty due to that is on a level of 10 ppm. To go farther with theory we need to eliminate the influence of the nucleus. A few ways have been used (see e. g. [1]) ... 

Recently there has been considerable progress in measurement and calculation of the hyperfine splitting of the ground state and the 2si/2 state in the hydrogen atom. The 2.s-, /2 hyperfine splitting in hydrogen was determined to be [6]... 

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