Hyperfine Structure Interval Research Articles

Theoretical hyperfine structure of muonic helium

The study of the hyperfine structure of the muonic helium atom (${\ensuremath{\alpha}}^{++}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$) can provide a test of quantum electrodynamics and yield precise values for the magnetic moment and mass of the negative muon. In the lowest-order approximation the hyperfine structure interval $\ensuremath{\Delta}\ensuremath{\nu}$ is given by the Fermi formula. The principal corrections, which contribute about 10 MHz to the splitting, arise from the relativistic, radiative, and recoil effects. The theoretical hyperfine structure of the ground state of muonic helium is given as $\ensuremath{\Delta}\ensuremath{\nu}=4465.1\ifmmode\pm\else\textpm\fi{}1.0$ MHz.

Optical isotope shifts and hyperfine structure in Cd

The spectral lines λ226.5, λ441.6, λ806.7 and λ853.3 nm of Cd II and λ508.6 nm of Cd I have been studied under high resolution by means of digital recording interferometry. The relative positions of all the stable isotopes of cadmium in all the lines have been deduced from the measurements. The main object of this study was to provide precise data for the simple p–s transitions λ226.5, λ806.7 and λ853.3 nm. Such lines are the most favourable for theoretical interpretation, and the new results are intended to provide a basis for the separation of mass and field effects in measured isotope shifts in cadmium. The hyperfine structure intervals, which are important in the interpretation of isotope shifts, have also been measured for all the levels involved in the five transitions.

Effects of collisions on the magnetic quenching of positronium

A theory describing the behavior of positronium (Ps) in a magnetic field is presented including the effects of Ps collisions. Such effects are especially important if the Ps is formed in a medium containing unpaired electrons since Ps collisions with these electrons can provide an effective spin exchange mechanism. By integrating the equation of motion for the density matrix, it is shown that the dependence of any annihilation yield N on the static magnetic field x is of the form N (x) = (g + hx + kx2) / (l + mx2) for a wide class of quenching mechanisms with time independent reaction rates. The coefficients g, h, k, l, and m are evaluated explicitly for the 2γ and 3γ yields from Ps formed from polarized positrons assuming that the quenching mechanisms can be characterized by an effective spin exchange rate and an effective pickoff rate. The yields are also evaluated assuming zero positron polarization in formulas which include the interesting Ps chemical reaction rates directly. The formulas derived can be used to obtain information about such chemical reaction rates from magnetic quenching data. Diagrams which permit the quick estimation of magnetic quenching effects as a function of the quenching rates are presented. The formalism has also been extended to include an rf magnetic field and is used to compute the shift of the measured Ps hyperfine structure interval as a function of quenching and microwave power. The shifts are found to be extremely small as expected.

He-Ne Laser Stabilized by Saturated Absorption in I2

The mechanical construction of the stabilized lasers, and their electronic control equipment, are described. A free-running stability of 10-10 for 0.1 s and a servo-locked stability of better than 10-12 for 10 s counting time has been measured. Hyperfine structure intervals in both 127I2 and 129I2 with standard deviation of 12 kHz confirm earlier values.

Ground state hyperfine structures and nuclear quadrupole moments of95Mo and97Mo

Hyperfine structure interval in the 4d55s 7S3 atomic ground state of 95Mo and 97Mo have been measured by the methods of atomic beam magnetic resonance. A theory of quadrupole interactions in half filled atomic shells, known to be successful in several other cases, has been used to obtain the nuclear quadrupole moments from the B values with the results Q(95Mo)=-0.075(25) barns and Q(97Mo)=+0.15(4) barns. The atomic beam was produced by collimating atoms evaporating from a 2 mm diameter molten ball of molybdenum suspended on the end of a 0.3 mm diameter molybdenum wire.

Muonium. II. Observation of the Muonium Hyperfine-Structure Interval

A full discussion is given of the microwave-spectroscopy resonance method of measuring the hyperfine-structure interval $\ensuremath{\Delta}\ensuremath{\nu}$ of the ground state of muonium, including the theoretical value for $\ensuremath{\Delta}v$, the transition frequencies, and the resonance line shape. A complete description is also given of our experimental method of measuring $\ensuremath{\Delta}\ensuremath{\nu}$ at strong magnetic field. The initial experimental results gave $\ensuremath{\Delta}\ensuremath{\nu}=4461.3\ifmmode\pm\else\textpm\fi{}2.0$ MHz, in good agreement with the theoretical value $\ensuremath{\Delta}\ensuremath{\nu}=4463.282\ifmmode\pm\else\textpm\fi{}0.062$ MHz. The first observations of muonium chemistry are described.

Hyperfine structure and nuclear moments of samarium

Experimental and theoretical work has been carried out on the hyperfine structure of the 4ƒ 6 7 F ground multiplet of samarium. Hyperfine structure intervals have been measured in the levels J = 1, 2, 3 and 4 for both odd isotopes 147 Sm and 149 Sm by the method of atomic beams. These intervals have been fitted to magnetic dipole and electric quadrupole interaction constants. Further measurements at high magnetic field by the method of triple resonance have led to the evaluation of the nuclear magnetic dipole moments of the two isotopes. It is shown that a calculation of the breakdown of L-S coupling and of second order corrections, off-diagonal in J , is necessary for an interpretation of the spectrum. The application of these corrections is facilitated by the formulation of an effective Hamiltonian, and the whole problem is treated step by step as a practical example of the use of tensor operator techniques. The spectrum is described in terms of a few overdetermined parameters, and in particular three radial parameters are evaluated. They are defined by the operator describing the magnetic field produced by the electrons at the nucleus: T ( e ) 1 = 2 β ∑ i ⁡ { < r l − 3 > 1 i − < r s C − 3 > √ 10 ( s C 2 ) i 1 + < r s − 3 > s i } . Their values are: < r i -3 > = 6.39 0 6 a 0 -3 , < r 5 C -3 > = 6.5 13 12 a 0 -3 , < r 5 -3 > = -0.20 8 6 a 0 -3 . The most important result is a precise determination of the nuclear magnetic moment of 147 Sm. It is μ I 147 = -0.807 4 7 n. m., uncorrected for diamagnetism. Also the ratio of the dipole interaction constants is A 1 147 / A 1 149 = 1.2130 5 2 for all J , and there is no observable Bohr-Weisskopf anomaly. It is shown that relativity is a plausible explanation for the non-vanishing of < r 5 -3 > in the contact term, but this explanation is not conclusive because the effect of relativity cannot be distinguished from that of configuration interaction in any part of the dipole interaction. The values of < r i -3 > and < r 5 C -3 >, which differ from each other, are compared with the value of an < r -3 > integral calculated by other workers. From the quadrupole interaction a value of –½ e 2 Q 147 < r Q -3 > = 149· 40 86 Mc/s is obtained and with less precision a value of Q 147 = -0.2 2 0 barn, uncorrected for shielding effects, is deduced. The ratio of the quadrupole moments is Q 147 / Q 149 = -3.460 3 1 , on the assumption that this ratio is the same as that of the quadrupole interaction constants.

The proton structure and hyperfine splitting of hydrogen energy levels

The quasipotential approach in quantum field theory is used to calculate the hyperfine structure interval in hydrogen. The quasipotential equation for the system of two fermions is obtained. The corrections of the relative order of α( m/ M) to the Fermi formula for the S levels are calculated with the account of the proton electromagnetic form factor. The theoretical and experimental values of the ground state hyperfine structure interval in hydrogen are compared.

Quadrupole Moment ofNe21

A hyperfine structure intervals in the metastable (2p)/sup 5/(3s),/sup 3/ P/sub 2/ state of Ne/sup 21/ were measured by the atomic-beam resonance method. The apparatus is the same as that used in the experimental determination of the spin of Ne/sup 21/, although extensive modifications were necessary to obtain an adequate signal-to-noise ratio. (W.D.M.)

The Hyperfine Structure of the3pP122State ofAl27

The hyperfine structure interval of the $3p^{2}P_{\frac{1}{2}}$ state of ${\mathrm{Al}}^{27}$ has been measured and found to be 1506.14\ifmmode\pm\else\textpm\fi{}0.05 Mc/sec. From this datum and the known hyperfine structure of the $3p^{2}P_{\frac{3}{2}}$ state a recalculation of the nuclear electric quadrupole moment, taking into consideration configuration interactiion, yields the value $Q=+0.149\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$.

Configuration Interaction in the Pb III Spectrum

The Slater and the configuration perturbation parameters were evaluated for configurations of Pb III by fitting the calculated to the observed term values. The wave functions of 52 levels were determined in terms of the ($\mathrm{LS}$) functions, and for many of the levels were found to be linear combinations of the ($\mathrm{LS}$) functions of two or more configurations. The $g$-values, hyperfine structure interval factors, and isotope shifts evaluated from the precise wave functions are in excellent agreement with the observed values. Thus the theory gives an internally consistent explanation of the spectroscopic properties. Since the isotope shifts were calculated as a field effect the agreement shows that the specific mass effect is relatively unimportant for heavy elements. The values of the shift and hyperfine structure interaction constant for the $6s$ electron obtained from this analysis are 0.50 ${\mathrm{cm}}^{\ensuremath{-}1}$ and 2.60 ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively.

XXV. Hyperfine structure in the arc spectrum of tin

Abstract Hyperfine structure measurements are made on lines of the tin arc spectrum, most of which lie in the ultra-violet region. It is confirmed that the two odd isotopes 117, 119, have nuclear spins of 1/2 and identical nuclear magnetic moments. No even isotope displacements are observed, and from observations upon reversals it is shown that any existing even isotope displacements must be very small. The classified lines amongst those observed are analysed, and hyperfine structure interval factors are derived for seven terms. Amongst these are the complete group belonging to the deep 5p 2 electron configuration. The nuclear coupling of the 5p 2 electron group is shown to be large, in agreement with deductions about the nuclear coupling of the 5p 4 electron group in iodine. A J-value has deen allocated to one term on the basis of hyperfine structure evidence.

Evidence for a Nuclear Electric Quadrupole Moment forSb123

Measurements of the hyperfine structure of the line λ5895 of Sb II by the use of a Fabry-Perot interferometer have shown that there are deviations from the interval rule in the case of the isotope with mass number 123. The hyperfine structure intervals of the ^3D_1 level of Sb^(121) (I=5/2) are found to be 0.6801 and 0.4832 cm^(−1). The corresponding intervals in Sb^(123) (I=7/2) are 0.4814 and 0.3603 cm^(−1). The error in these measurements is of the order of 0.001 cm. The observed ratio of the two separations gives 1.407 and 1.336 for the light and heavy isotope, respectively, whereas the corresponding ratios on the basis of the interval rule are 1.400 and 1.286. The deviation in the case of the light isotope is within the experimental error. The deviation for the heavy isotope, however, is a real effect which cannot be accounted for on the basis of perturbing effects of neighboring levels and must therefore be ascribed to the presence of an electric quadrupole moment of the nucleus of Sb^(123).

Hyperfine structure in the arc spectrum of bromine

In an earlier work Tolansky (1932) reported measurements for the hyperfine structures of 18 lines of the arc spectrum of bromine. Although resolution was incomplete in every line, it was possible to prove that both the bromine isotopes 79 and 81 have the same nuclear spin, 3/2, and have practically identical nuclear magnetic moments. In carrying out the hyperfine structure term analysis at that time, use was made of the interesting graphical method proposed by Fisher and Goudsmit (1931) and thus approximate hyperfine structure interval factors could be derived. At the time this work was done the existence of deviations from the interval rule was not suspected. Any such deviations destroy the validity of the Fisher-Goudsmit method of analysis. The frequent occurrence of nuclear electrical quadrupole moment leads one to suspect that there may be deviations from the interval rule in many spectra; hence we have undertaken a new and more complete examination of the hyperfine structures of the lines of Br I. The measurements reported here are more extensive and more accurate than those previously given. We have measured the structures of 76 lines extending from the infra-red at 8700 A down to 4390 A. All the principal lines in this region have been measured and, with very few exceptions, the structures have been completely accounted for. The results obtained here are much more accurate than those given earlier for the following reasons: (1) The modified source is much more intense. (2) It is cooled, giving sharper lines. (3) In place of the single Fabry-Perot previously available (with one thickness of silvering) we have used various silvered Fabry-Perot interferometers, similar interferometers coated with aluminium, and a high-quality quartz Lummer plate. (4) The camera focal length used now is 125 cm., that of the earlier instrument being only 50 cm. (5) Much more rapid plates are now available, particularly in the infra-red region.

The Radiofrequency Spectra of Atoms Hyperfine Structure and Zeeman Effect in the Ground State ofLi6,Li7,K39andK41

The molecular beam magnetic resonance method previously used for the study of molecules has been extended to the study of atoms. Transitions between the members of hyperfine structure multiplets of the ground state of atoms have been observed directly. In this way the hyperfine structure intervals of the normal states of ${\mathrm{Li}}^{6}$, ${\mathrm{Li}}^{7}$, ${\mathrm{K}}^{39}$ and ${\mathrm{K}}^{41}$ have been measured. Since the measurement of frequency alone is involved, the results are of very high precision. These spectra have been observed in external magnetic fields varying from 0.05 to 4000 gauss, i.e., from the ordinary Zeeman to the complete Paschen-Back region. The lines in the pattern are completely resolved even at the low fields. The h.f.s. separations derived from measurements at different fields are in excellent agreement. Comparison is made between the ratio of the nuclear moments of ${\mathrm{Li}}^{7}$ and ${\mathrm{Li}}^{6}$ as derived from the h.f.s. measurements with the directly measured ratio. The two ratios are 3.9610 and 3.9601, respectively. They agree within the experimental error of 0.04 percent. The h.f.s. separations are given both in absolute frequency units and in wave numbers. ${{\mathrm{sec}.}^{\ensuremath{-}1}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6},{\mathrm{cm}}^{\ensuremath{-}1}}{{\mathrm{Li}}^{6},228.220.007613}{{\mathrm{Li}}^{7},803.540.026805}{{\mathrm{K}}^{39},461.750.015403}{{\mathrm{K}}^{41},254.020.008474}$

On the Hyperfine Structure Interval Rule in Indium

Interferometric measurements on $\ensuremath{\lambda}7182(5s6p^{3}P_{1}\ensuremath{\rightarrow}5s6s^{3}S_{1})$ and $\ensuremath{\lambda}7276(5s6p^{3}P_{0}\ensuremath{\rightarrow}5s6s^{3}S_{1})$ of In II indicate that the separations of the state $5s6s^{3}S_{1}$ follow the interval rule to within the experimental error (approximately 0.05 percent). Perturbations by neighboring states are negligible and there are no effects for this state due to the known electric quadrupole moment of the nucleus. The results indicate that the assumption of a nuclear magnetic moment is very successful in accounting for the observed relative separations.

The nuclear magnetic moment of copper

The doublet hyperfine structures of the resonance lines of the copper arc spectrum, λ3247 and λ3274, have been measured with a quartz Lummer plate. The lines are produced free from reversal effects, the doublet separations being respectively 379 and 405 × 10-3 cm-1. The following hyperfine structure interval factors are calculated: 3d104s2S½ = 197.5, 3d104p2P½ = 14 and 3d104p2P1½ = 4.8 (all in cm-1 × 10-3). The mean nuclear magnetic moment for the two copper isotopes, 63 and 65, is derived from the ground state, 3d104s2S½. The value found is μ = 2.47 nuclear magnetons, this being probably a better estimate than that given by other terms, since the ground state is spherically symmetrical and thus not affected by quadrupole moment of the nucleus. By adopting Schüler and Schmidt's value for the ratio of the magnetic moments of the two isotopes, it is found that μ (63Cu) = 2.43 and μ (65Cu) = 2.54 nuclear magnetons.

Multiplet and Hyperfine Structure Analyses of Bi IV. Discussion of Perturbation Effects

Three hundred and sixty lines of Bi IV, excited in an electrodeless discharge, have been classified. Twenty-seven terms of $6snx$ configurations, four terms of $6{p}^{2}$ and six terms of $5{d}^{9}6{s}^{2}6p$ have been identified. Evidence of perturbation of $6s5f$ and $6s7p$ by $5{d}^{9}6{s}^{2}6p$ and of $6s6d$ by $6{p}^{2}$ is presented. The perturbation of $6s6d$ by $6{p}^{2}$ in Bi IV and other members of the Hg I sequence is shown to agree qualitatively with Bacher's theory of $sd\ensuremath{-}{p}^{2}$ interactions. The hyperfine structure intervals of many of the terms of Bi IV have been evaluated. They are compared with the theoretical formulae for hyperfine structure separations and shown to be consistent with our multiplet analysis. Anomalous hyperfine structure has been observed in $6s7{p}_{\frac{1}{2}}$. This is interpreted as a coupling effect due to the approximate equality of the multiplet and hyperfine structure separations of $6s7{p}_{\frac{1}{2}}$. Goudsmit and Bacher's theory of hyperfine structure perturbations due to a change in coupling is applied to the four hyperfine levels of $6s7{p}_{\frac{1}{2}}$. Their theory accounts for the observed distribution of these levels and for the appearance of forbidden transitions.

Hyperfine Structure in Neutral Manganese, Mn I.

Observations. The hyperfine structure patterns of some 30 or 40 lines in the spectrum of Mn I have been photographed by means of a prism spectrograph and silvered Fabry-Perot etalons. A tube, designed by Sch\uler, and operated at liquid air temperatures, has been used as a light source for most of the lines and a king vacuum furnace for the others. Patterns of from 2 to 6 components are found, some degrading in intensity and intervals toward low frequencies and others toward higher frequencies.Interpretation. The strictly $\mathrm{LS}$ coupling in the well-known multiplet structure of Mn I, and $\mathrm{Ji}$ coupling in the hyperfine structure enable vector diagrams to be drawn for the space quantization of each valence electron with respect to the nucleus. Some of the hyperfine structure terms are computed directly from observed term differences while others are computed from the observed diagonal components. The normal state $^{6}S_{2\frac{1}{2}}(3{d}^{5}4{s}^{2})$ is found to be quite narrow, whereas the metastable $^{6}D(3{d}^{5}4s)$ terms show the widest separations. While the hyperfine structure intervals for any given term are proportional to $cos (\mathrm{Ji})$ the total separations are approximately determined by $cos (\mathrm{Si})$ the $l$ values of the electrons contributing but very little.Theoretical computations. A study of the vector diagrams for the different multiplet terms shows quite definitely that while the hyperfine structure is determined primarily by the coupling between the $4s$ electron and the nucleus, the remaining valence electrons must also be taken into account. The hyperfine structure formula given by Goudsmit and Bacher for the interaction between an $s$ electron spin and the nuclear spin is extended so as to include not only the spins of all of the valence electrons but their $l$ values as well. From the derived general formula and the observed hyperfine structure term separations, coupling constants to be associated with each electron have been computed. While the energy of interaction between electron spin $s$ and nuclear spin $i$ is given by $\mathrm{ais} cos(\mathrm{is})$ the energy of interaction between electron $l$ value and nuclear spin $i$ is given by $\mathrm{ail} cos(\mathrm{il})$.