Hyperfine Separation Research Articles

Electric Field Dependence of the Atomic-Hydrogen Hyperfine Separation

The Stark shift of the atomic-hydrogen hyperfine separation has been measured in a hydrogen maser, designed to study in particular the dependence of the shift on the angle $\ensuremath{\theta}$ between the external electric and magnetic fields. A method of designing shielded solenoids to produce arbitrary magnetic fields is presented. The result of the experiment is $\ensuremath{\delta}{\ensuremath{\nu}}_{\mathrm{stark}}=(\ensuremath{-}7.1\ifmmode\pm\else\textpm\fi{}1.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{E}^{2} (\ensuremath{\theta}=0)$ using electrostatic units for the electric field $E$, and $\frac{\ensuremath{\delta}{\ensuremath{\nu}}_{\mathrm{stark}}(\ensuremath{\theta}=0)\ensuremath{-}\ensuremath{\delta}{\ensuremath{\nu}}_{\mathrm{stark}}(\ensuremath{\theta}=\frac{\ensuremath{\pi}}{2})}{\ensuremath{\delta}{\ensuremath{\nu}}_{\mathrm{stark}}(\ensuremath{\theta}=0)}=\ensuremath{-}1%\ifmmode\pm\else\textpm\fi{}10%.$

Pairwise Trapping of Radicals in Irradiated High Polymers as Studied by Electron Spin Resonance

We have observed the ΔMs = 2 spectra due to radical pairs in a number of typical polymers irradiated at 77°K. The formation of radical pairs is not a particular phenomenon in some particular crystalline solids. The crystallinity of the polymers does not affect the formation of radical pairs in an apreciable amount. The buildup curve of the radical pairs suggests that the pairwise trapping is not due to the occasional overlapping of the spurs and that there is an intrinsic value of formation. The hyperfine separation of the ΔMs = 2 spectra of polyethylene and polypropylene have the values which are half of those of the isolated radicals. This means that the paired radicals are probably two alkyl radicals trapped in pair. The urea addition compounds of some polymers did not give any signal due to the ΔMs = 2 spectra.

Theory of Polarization of Molecular Line Radiation Excited by Electron Impact

The Percival-Seaton theory for the polarization of atomic impact radiation is extended to the case of diatomic molecules. Similar to the atomic case, it is shown that for excitation by electron impact involving a change of electronic angular momentum along the molecular internuclear axis, the threshold polarization can be determined from the symmetry of the total molecular wave function without a detailed knowledge of the inelastic cross sections. General expressions are developed for the cases of fine and hyperfine splitting, and explicit relations are given for the first two rotational levels of a $^{3}\ensuremath{\Pi}_{u}$ state undergoing a radiative transition to a $^{3}\ensuremath{\Sigma}_{g}$ state in the limit of fine and hyperfine separations being much larger than the natural linewidth. This theory is valid when the radiative state is populated by a direct interaction, and the radiative transition between rotational states is resolved.

Measurements ofgJRatios forRb85,Rb87, Hydrogen, and Deuterium, and of the Hyperfine Separation of Deuterium

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Hyperfine Separation of Tritium

The hyperfine separation of tritium has been measured with respect to the hyperfine separation of hydrogen by comparing the frequency of the tritium maser with that of a hydrogen maser. The result is $\ensuremath{\Delta}\ensuremath{\nu}(\mathrm{T})=1516701470.8087\ifmmode\pm\else\textpm\fi{}0.0071$ Hz, where it is assumed that $\ensuremath{\Delta}\ensuremath{\nu}(\mathrm{H})=1420405751.8$ Hz. Wall shifts were measured for tritium and hydrogen for FEP Teflon at 35\ifmmode^\circ\else\textdegree\fi{}C. For a spherical bulb, $d$ cm in diameter, the fractional wall shift for hydrogen is $\ensuremath{-}(3.61\ifmmode\pm\else\textpm\fi{}0.54)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}10}}{d}$, and for tritium it is $\ensuremath{-}(3.14\ifmmode\pm\else\textpm\fi{}0.47)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}10}}{d}$.

Hyperfine Separation of Deuterium

The hyperfine separation of deuterium has been measured by a spin-exchange technique in which deuterium interacts with radiating hydrogen in a hydrogen maser. Resonance of the deuterium is detected by its effect on the hydrogen oscillation power level. The result is $\ensuremath{\Delta}\ensuremath{\nu}(\mathrm{D})=327 384 352.3\ifmmode\pm\else\textpm\fi{}0.25$ cps in the $A1$ time scale [$\ensuremath{\Delta}\ensuremath{\nu}(\mathrm{Cs})=9 192 631 770$ cps]. A theoretical analysis of the technique and experimental details are presented.

Radiative corrections to hyperfine structure in hydrogen

Because of a reported discrepancy of (34±21) parts per million between measured and calculated values of the hyperfine separation of the ground state of atomic hydrogen, the next higher-order radiative corrections beyond the previously calculated order of α2Sh.f. were investigated. Besides the expected presence of corrections of order α3 ln αSh.f., a larger correction of order α3ln2Sh.f. was found. The calculation of the level shift of both of these logarithmic orders has been completed yielding results which agree with those of Layzer. In the case of hydrogen the numerical contribution is − 9.28 ppm. When this is combined with previous results, the discrepancy between measured and calculated values is increased to (43±21) ppm. The uncertainty is due largely to the uncertainty in the value of α, which is obtained from finestructure measurements, and which appears in the theoretical formula for the hyperfine separation. Possible explanations of the discrepancy are either an inaccuracy in the accepted value of the fine-structure constant or an inadequate evaluation of the contribution from intermediate states in which mesons are excited.

Stark Shift of the Hydrogen Hyperfine Separation

Stark Shift of the Hydrogen Hyperfine Separation

Hyperfine Separation of Ground-State Atomic Hydrogen

The hyperfine separation of hydrogen in its ground state was determined by means of the hydrogen maser. Two masers were operated simultaneously for purposes of tuning, checking internal consistency, and measuring the wall shift. A secondary frequency standard was also used. Corrections were made for the magnetic field offset, secondorder Doppler shift, and the wall shift. (C.E.S.)

Properties of the Hydrogen Maser

Properties of the hydrogen maser and details of the apparatus are discussed. Experimental work is described which yields a new value for the hyperfine separation of hydrogen in its ground state. The result is Δν=1,420,405,762±4cps.This result is based on a value of the hyperfine separation in Cs133 which is taken to be Δν(Cs133)=9,192,631,840cps.

Hyperfine Structure, Zeeman Effects, and Separation of Lines in Terbium Spectra.

Hyperfine Structure, Zeeman Effects, and Separation of Lines in Terbium Spectra.

Nuclear Spin and Hyperfine Interaction ofIn113m

The hyperfine structure of the 1.7-hr, 393-kev metastable state of ${\mathrm{In}}^{113}$ has been studied by use of the atomic-beam magnetic-resonance technique. The nuclear spin is found to be \textonehalf{} and the magnetic dipole moment to be -0.21050\ifmmode\pm\else\textpm\fi{}0.00002 nm, subject to a possible hyperfine anomaly. The hyperfine separation in the atomic ${P}_{\frac{1}{2}}$ state is measured to be 781.084\ifmmode\pm\else\textpm\fi{}0.010 Mc/sec.

Theory of the Effects of Exchange on the Nuclear Fine Structure in the Paramagnetic Resonance Spectra of Liquids

A theory of the influence of exchange forces in liquids upon the nuclear hyperfine structure in paramagnetic ``spin resonance'' spectra is presented. Formulas are derived for two limiting cases: for the exchange J much larger than the hyperfine separation A, and for A≪J. It is found that as J increases the hyperfine lines broaden (exchange broadening) and start to shift towards the ``unsplit'' Zeeman frequency. For J≈A, the hyperfine lines have coalesced into a single broad line and for J&amp;gt;A the line narrows (exchange narrowing) about the ``unsplit'' Zeeman frequency. These calculations are discussed in considerable detail. The effect upon the spectrum of electronic-electronic and electronic-nuclear dipolar interactions and the effect of the rapid molecular motions in liquids have also been considered, as well as their interactions with the exchange forces.

Hyperfine Structure of the Metastable Deuterium Atom

The hyperfine separation $\ensuremath{\Delta}\ensuremath{\nu}(2S; \mathrm{D})$ of the metastable $2^{2}S_{\frac{1}{2}}$ state of the deuterium atom has been measured by an atomic-beam magnetic-resonance method that has been described previously. We found that $\ensuremath{\Delta}\ensuremath{\nu}(2S; \mathrm{D})=40924.439\ifmmode\pm\else\textpm\fi{}0.020$ kc/sec. From this result and the ground-state separation $\ensuremath{\Delta}\ensuremath{\nu}(1S; \mathrm{D})$ we obtain $R(\mathrm{D})\ensuremath{\equiv}\frac{\ensuremath{\Delta}\ensuremath{\nu}(2S; \mathrm{D})}{\ensuremath{\Delta}\ensuremath{\nu}(1S; \mathrm{D})}=\frac{1}{8}(1.0000342\ifmmode\pm\else\textpm\fi{}0.0000006)$. Comparison of this value with the corresponding quantity for hydrogen, $R(\mathrm{H})=\frac{1}{8}(1.0000346\ifmmode\pm\else\textpm\fi{}0.0000003)$, confirms within experimental error the theoretical prediction that $R(\mathrm{D})=R(\mathrm{H})$.

Hyperfine Structure of the Metastable Hydrogen Atom

The hyperfine separation $\ensuremath{\Delta}\ensuremath{\nu}(2S)$ of the metastable $2^{2}S_{\frac{1}{2}}$ state has been measured by a new atomic-beam magnetic-resonance method. Rf transitions were detected by utilizing a property peculiar to metastable hydrogen atoms, namely, that atoms with ${m}_{J}=\ensuremath{-}\frac{1}{2}$ decay much more rapidly in passing through a magnetic field of about 575 gauss than do atoms with ${m}_{J}=+\frac{1}{2}$. We found that $\ensuremath{\Delta}\ensuremath{\nu}(2S)=177556.86\ifmmode\pm\else\textpm\fi{}0.05$ kc/sec. From this result and the very accurately known hyperfine separation $\ensuremath{\Delta}\ensuremath{\nu}(1S)$ of the ground state, we obtain $R\ensuremath{\equiv}\frac{\ensuremath{\Delta}\ensuremath{\nu}(2S)}{\ensuremath{\Delta}\ensuremath{\nu}(1S)}=\frac{1}{8}(1.0000346\ifmmode\pm\else\textpm\fi{}0.0000003)$. The deviation of $R$ from the presently available theoretical value suggests the existence of a higher-order quantum-electrodynamic term.A method of velocity selection by electron impact is described.

Radiofrequency Spectrum of Indium. Nuclear Spin ofIn113

The atomic beam methods of studying the radiofrequency spectra of atoms in the ground state has been applied to indium. Lines characterized by the transitions $\ensuremath{\Delta}F=0$, $\ensuremath{\Delta}m=\ifmmode\pm\else\textpm\fi{}1$, were observed, in magnetic fields ranging from 3000 to 7000 gauss, for ${\mathrm{In}}^{113}$ as well as for ${\mathrm{In}}^{115}$. The experiments give conclusive evidence that the nuclear spin of ${\mathrm{In}}^{113}$ is 9/2 and that its moment is positive, the same as that of ${\mathrm{In}}^{115}$. The ratio of the hyperfine separation of the ground state of ${\mathrm{In}}^{115}$ to that of ${\mathrm{In}}^{113}$ was found to be 1.00224\ifmmode\pm\else\textpm\fi{}0.00010. This is also the ratio of the magnetic moments of the two isotopes. A h.f.s. value of (11413\ifmmode\pm\else\textpm\fi{}3) ${10}^{6}$ cycles/sec. and a nuclear moment of 5.49\ifmmode\pm\else\textpm\fi{}0.04 nuclear magnetons were found for ${\mathrm{In}}^{115}$

A note on the hyperfine structure in the arc spectrum of xenon

The hyperfine structures of the Xe-I lines ??9045, 9799 and 9923 are described and analysed, and the hyperfine separations of the terms 2p9 and 2p10 are derived. It is also found that the lines 1s5-2p are readily self-reversed. Previous nuclear spin data are confirmed.

NUCLEAR MOMENTS OF ANTIMONY ISOTOPES—DISCUSSION OF LANDÉ'S THEORY

Hyperfine structures in the Sb IV spectrum have been investigated. Analysis of the hyperfine patterns shows that the I-values of Sb121 and Sb123 are [Formula: see text] and [Formula: see text] respectively, in agreement with those deduced by Badami from Sb II. The magnetic moments of Sb121 and Sb123, calculated from the hyperfine separations in Sb IV, are 4.0 and 3.2 proton magnetons respectively. For antimony the ratio of the g(I) factors is g(I)121/g(I)123 = 1.82 ±.02. The application of the Landé g(I) formula to this accurate ratio leads to a value gs = 3 for the magnetic factor of the proton spin, instead of gs = 4 as found by Landé. The value gs = 3 gives slightly better general agreement between the observed and the calculated g(I) factors than is obtained for gs = 4. However, since no specific value of gs will satisfy the accurate ratio criterion for all the Zodd, Modd isotopes to which the test can be applied, it is concluded that the theory is incomplete.

Societies and Academies

LONDON Physical Society, June 1. G. F. HULL, S. E. GREEN and MARY BELL: The pressure of radiation. A historical statement. A brief account of some early experiments on radiation pressure, dealing in particular with the investigations of Lebedew and of Nichols and Hull. A. H. JAY: The estimation of small differences in X-ray wave-lengths by the powder method. It has been found possible by the use of a microphotometer to determine accurately the positions of lines at high angles of reflection on a powder photograph. With a powder photograph of clear colourless quartz taken with copper Ka radiation, the distance apart of the two component lines of a well-resolved doublet was measured to within 0-0002 cm. The measurements were then corrected for systematic errors-eccentricity of specimen, absorption of the radiation in the specimen, and divergence of the X-ray beam. The wave-length difference (Xa) was finally calculated in terms of the given wave-length V The value of (X-Xx) for copper Ka radiation is given as 3′833X. H. STAFFORD HATFIELD: The action of alternating and moving magnetic fields upon particles of magnetic substances. An explanation of the translatory movement observed by Mr. W. M. Mordey in magnetic particles subjected to a multi-phase alternating field. A. MOBBIS CASSIE: Time scale and electron relay used with a cathode ray oscillograph for the investigation of switch-gear and circuit phenomena. EGWYNNE-JONES: Note on the hyperfine structure in the arc spectrum of xenon. The hyperfine structures of the Xe I lines XX 9045, 9799 and 9923 are described and analysed, and the hyperfine separations of the terms 2p, and 2plfl are derived. It is also found that the lines 1st - 2p are readily self-reversed. Previous nuclear spin data are confirmed.

Interpretation of hyperfine structure.—Discussion of H. F. S. in Tl II. Relative g (I) factors of Tl, Bi and Pb (207), and nuclear structure

As the theory of hyperfine structure separations is employed in section II in discussing the hyperfine structure of Tl lI, and again in section III in comparing the Landé g (I) factors of Tl, Pb and Bi, its status is briefly considered in this introduction. The theory of the interaction of a single valence electron of the s type with a magnetic nucleus is somewhat indefinite, insomuch as it can not be directly verified. The expression for the interaction W = a ns I. s cos (Is) (1) is undoubtedly correctly formulated, as it has been experimentally verified. The relative hyperfine separations of states of the 6 snd and the 6 snf configurations of Tl II, treated in this paper, and of certain configurations in other spectra. in which the interactions with the magnetic nucleus of all the valence electrons except the deeply penetrating s electron are negligible, are in good agreement with the predictions based on this equation. The theoretical expression for the interaction constant, a ns , which governs the magnitude of the separations, can only be determined by a quantum mechanical treatment of the state of the atom under consideration; and always involves the factor g (I), which as yet has never been determined by other independent methods. Consequently, the validity of the expression for a ns cannot be checked directly. There is, however, the possibility of checking somewhat inexactly the expression for a ns by comparing the value of g (I) calculated from the experimental data by the use of the theoretical expression with that expected from our conception of the nucleus. Such comparisons show that g (I) is of the order expected for a spinning proton; but beyond this are, as yet, of little value in checking the formula for a ns since our theory of the nucleus is very uncertain, especially in view of the conclusion expressed in section III.