Atomic Hyperfine Structure Research Articles

Which Came First, Theory or Experiment?

As one who believes that the origins of fundamental scientific advances are sometimes experimental, other times theoretical, and often a combination of the two, I do not take sides in the debate between Lincoln Wolfenstein and Harry J. Lipkin in the January 2001 issue of Physics Today (page 13). However, I feel obliged to correct an important error.Wolfenstein states, “The most exciting results immediately following World War II were the precision atomic experiments verifying the renormalized quantum electrodynamics [QED] of Richard Feynman and Julian Schwinger.” This statement reverses the historical order, since the critical experiments preceded the theoretical explanations. Chronologically, the first critical experiment was the discovery by John Nafe, Edward Nelson, and I. I. Rabi that the hyperfine separation of atomic hydrogen was different from that predicted by the Dirac theory of the electron. 1 1. J. E. Nafe, E. B. Nelson, I. I. Rabi, Phys. Rev. 71, 914 (1947) https://doi.org/10.1103/PhysRev.71.914. This was independently confirmed a few months later. The other critical experiment was the discovery by Willis Lamb and Robert Retherford that the Dirac theory prediction of degeneracy for the 22S1/2 and 22P1/2 atomic hyperfine structure levels in atomic hydrogen was wrong by many times the experimental error of their new measurements. These experiments preceded their theoretical explanations, as I can show.The Nafe, Nelson, and Rabi letter 1 1. J. E. Nafe, E. B. Nelson, I. I. Rabi, Phys. Rev. 71, 914 (1947) https://doi.org/10.1103/PhysRev.71.914. was received by the Physical Review editor on 19 May 1947, and the first Lamb and Retherford experimental paper 2 2. W. Lamb, R. Retherford, Phys. Rev. 72, 241 (1947) https://doi.org/10.1103/PhysRev.72.241. was received on 18 June 1947. Those experiments were intensively discussed at the famous Shelter Island theoretical conference held in June 1947, with most attention being devoted to the Lamb-Retherford experiment, which gave a much bigger anomaly and was more easily explained. Hendrick Kramers and others argued that radiative corrections to the energy of an electron in a Coulomb field could produce a shift in the energy levels of hydrogen, and that it might be possible to calculate such an effect approximately, despite the infinities that plagued most radiative correction calculations. Hans Bethe, in an article received on 27 June 1947, 3 3. H. A. Bethe, Phys. Rev. 72, 339 (1947) https://doi.org/10.1103/PhysRev.72.339. published a nonrelativistic field theory calculation that accounted for most of the observed Lamb shift. The first theoretical publication to discuss the experimental hyperfine structure anomaly 4 4. G. Breit, Phys. Rev. 72, 984 (1947) https://doi.org/10.1103/PhysRev.72.984. was received from Gregory Breit on 29 September 1947. However, Breit merely suggested that the experiment was consistent with the electron’s having a magnetic moment different from the Dirac value; he made no effort to provide a QED explanation. Schwinger’s great renormalized field theory, 5 5. J. Schwinger, Phys. Rev. 73, 416 (1947) https://doi.org/10.1103/PhysRev.73.416. which accounted for both the hyperfine and fine structure anomalies, was received 30 December 1947, seven months after the experiments were reported.Surely the Nafe, Nelson, and Rabi hyperfine structure experiment was not invented to verify the renormalized electrodynamics, since it was invented by Rabi and me in late 1944. We gave it highest priority because we and others had measured the proton magnetic moment, the electron magnetic moment was given by the Dirac theory, and the electron wavefunction in hydrogen was known. Therefore, the hyperfine separation could be calculated, and the experiment would provide a fundamental test of the Dirac theory. We never mentioned QED, with or without renormalization. My second experience relating to the sequence of experiment and theory occurred in the summer of 1947 when I visited Cambridge, Massachusetts. Schwinger invited me to lunch and asked me searching questions about the reliability of the experimental hyperfine anomaly. He said he thought he could explain it, but would have to develop a relativistic QED; he was worried about doing all that work if the hyperfine anomaly wasn’t real. I told him I was convinced it was real. He then worked vigorously on this problem, and the following December submitted his paper that correctly accounted for both hyperfine and fine structure experimental anomalies as being due to radiative corrections that could be calculated in his theory, using both mass and charge renormalization. REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. J. E. Nafe, E. B. Nelson, I. I. Rabi, Phys. Rev. 71, 914 (1947) https://doi.org/10.1103/PhysRev.71.914. Google ScholarCrossref, ISI2. W. Lamb, R. Retherford, Phys. Rev. 72, 241 (1947) https://doi.org/10.1103/PhysRev.72.241. Google ScholarCrossref, ISI3. H. A. Bethe, Phys. Rev. 72, 339 (1947) https://doi.org/10.1103/PhysRev.72.339. Google ScholarCrossref, ISI4. G. Breit, Phys. Rev. 72, 984 (1947) https://doi.org/10.1103/PhysRev.72.984. Google ScholarCrossref, ISI5. J. Schwinger, Phys. Rev. 73, 416 (1947) https://doi.org/10.1103/PhysRev.73.416. Google ScholarCrossref, ISI© 2001 American Institute of Physics.

Properties and hyperfine structure of helium-muonic atoms

Basic geometrical and dynamical properties of the ${}^{3}{\mathrm{He}}^{2+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ and ${}^{4}{\mathrm{He}}^{2+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ helium-muonic atoms are determined from high-precision, variational calculations. Only the bound ground states with $L=0$ are discussed. The estimated hyperfine splitting between ${}^{1/2}S$ and ${}^{3/2}S$ states in the ${}^{3}{\mathrm{He}}^{2+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ atom is $\ensuremath{\Delta}\ensuremath{\nu}=4166.389 \mathrm{MHz}.$ The analogous result for the hyperfine splitting between ${}^{0}S$ and ${}^{1}S$ states in the ${}^{4}{\mathrm{He}}^{2+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ atom is $\ensuremath{\Delta}\ensuremath{\nu}=4464.555 \mathrm{MHz}.$ Both obtained figures agree very well with the known experimental values. The evaluated hyperfine splitting for the ${}^{6}{\mathrm{Li}}^{3+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ ion is $\ensuremath{\approx}29311.4 \mathrm{MHz}$ and for the ${}^{7}{\mathrm{Li}}^{3+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ ion is $\ensuremath{\approx}36790.8 \mathrm{MHz}.$

Isomer separation and measurement of nuclear moments with the ISOLDE RILIS

Short-lived radioisotopes are element selectively ionized by the resonance ionization laser ion source (RILIS) of the on-line isotope separator ISOLDE (CERN). The relative production of low and high spin isomers can be significantly changed when a narrow-bandwidth laser is used to scan through the atomic hyperfine structure. This allows the assignment of gamma ray transitions to the decay of the individual isomers. Moreover, the measurement of the hyperfine splitting provides a very sensitive method for the determination of magnetic moments of exotic isotopes. The technical developments are discussed for the example of copper.

Recent progress in the theory of the complex atomic hyperfine structure

The revised analysis of the hyperfine structure of the complex atoms on several selected examples has been performed. The complete set of corrections up to the second order perturbation theory has been taken into account and the accuracy of the wave functions in the intermediate coupling scheme has been carefully checked. The still remaining discrepancies suggest that the commonly used approximate model of the hyperfine structure might require revision.

HYPERFINE STRUCTURE MEASUREMENT IN LaⅡ5d2 1Ｇ4 →4f5d 1F3

The knowledge of the hyperfine structure of 139LaⅡ has been very poo r until now.In our experiment,the atomic hyperfine structure spectra of 139 LaⅡ with 5d2 1Ｇ4 and 4f5d 1F 3 configurations have been measured using collinear fast-ion-beam las er spectroscopy,and the magnetic dipole and electric quadrupole coupling constan ts were determined.

Using effective operators in calculating the hyperfine structure of atoms

We propose a method for calculating the hyperfine structure (hfs) of multielectron atoms based on a combination of configuration superposition and many-body perturbation theory. The latter is used to construct an effective Hamiltonian and an effective hfs operator in configurational space. The method can be applied in calculations of the matrix elements of any one-electron operators. By way of an example we calculate the magnetic hfs constant A for several lowest levels of neutral thallium. We show that the method achieves a calculation accuracy of about 1%, which earlier was possible only for atoms with a single valence electron.

Atomic hyperfine structure studies using temperature/current tuning of diode lasers: An undergraduate experiment

We present a simple and inexpensive experimental arrangement for hyperfine structure studies in atoms using commercially available laser diodes and hollow cathode lamps. The experiment is highly suitable for the undergraduate laboratory. This technique can be employed to investigate the hyperfine structure of rare earth and other elements such as Ta and Nb which have large nuclear magnetic and or quadrupole moments. In this paper, we report well-resolved hyperfine structure spectra recorded for holmium employing optogalvanic spectroscopy. We also report Doppler limited hyperfine structure measurements on the ground state of rubidium using injection current/temperature tuning of the diode laser. This involves a simple experimental arrangement suitable for undergraduate laboratories. The hyperfine coupling constants for the level at 31 443.26 cm−1 in Ho I are reported for the first time. Details of the data analysis to obtain accurate hyperfine structure coupling constants from the observed spectra are presented. A number of commercially available diode lasers in the visible and the near infrared regions and simple in-house developed or commercially available low cost current and temperature controllers can be employed for the present studies. We employ simple cooling/heating or current modulation for tuning the output wavelength of the diode laser. The presently proposed experimental arrangement can be assembled easily and requires no machine/glass shop facilities.

Atomic Beam Diode-Laser Spectroscopy

Combined with a collimated atomic beam source, diode laser without external cavity has been used as a spectroscopic light source to study atomic hyperfine structures and isotope shifts of Ba i. Spectroscopic measurements of the 6s21S0 – 6s6p3P1 transition of Ba i have been carried out. All hyperfine peaks of 135,137Ba have been clearly seen and resolution of 50 MHz has been attained. Hyperfine constants A and B of the 3P1 state of 135,137Ba have been determined. Isotope shifts of stable Ba isotopes have also been measured. From the measured isotope shifts, the 6s electron density at the nucleus has been deduced to be 76.4(53) a.u. and discussed in terms of the Hartree-Fock approximation.

Coherent repopulation of the components of a three-level quantum system in the field of a pulsed bichromatic radio frequency wave

The coherent repopulation of a quantum system consisting of three nonequidistant levels in the field of a resonant bichromatic rf wave is studied. The atoms are assumed to have an impulsive interaction with the rf wave in which the pulse duration is less than any of the relaxation times. The hyperfine structure of gas atoms and a system of atomic oscillator levels in a magnetic trap are considered as examples of such a quantum system. It is shown that in the second case, the coherent repopulation effect can be used to cool neutral atoms in magnetic traps.

Some analytic results on the Uehling correction to hyperfine splitting in a muonic atom

We analyze the Uehling correction to the hyperfine structure of the ground state in hydrogenlike electronic and muonic atoms with a pointlike nucleus. The results are obtained analytically without any expansion over ~k. PACS No.: 31.20D Resume : Nous analysons la correction d’Uehling a la structure hyperfine du fondamental d’atomes hydrogenoides, electroniques ou muoniques, avec un noyau ponctuel, les resultats sont analytiques, sans recours a une expansion en puissances de ~k. [Traduit par la redaction] This work is a direct continuation of a previous paper [1] devoted to the Uehling correction to the Lamb shift (Fig. 1a) in a hydrogenlike atom with a pointlike nucleus. Here we calculate the spin-dependent part of the correction (Figs. 1b and 1c). In ref. 1, we examined the kind of integral for the complete Dirac wave function and the Uehling potential as a perturbation. More details will be found in a later paper1 where the method will be developed for any single-photon potential diagram including the one in Fig. 1b. The hyperfine structure (hfs) is more sensitive to the nuclear structure than the Lamb shift. As is well known, the theoretical uncertainty of the hyperfine splitting value for a hydrogenlike atom comes mainly from estimates of the nuclear magnetization distribution correction (the Bohr–Weisskopf effect). That is correct both for muonic and electronic atoms, but in the first case this correction is significantly larger and investigations of the hyperfine structure of muonic atoms can be used as a way to measure that effect and to apply the result to an electronic atom with the same nucleus. The hyperfine structure in a muonic atom being of the order +] ,p @ps is more important 1 S.G. Karshenboim. Manuscript in preparation. Received June 8, 1998. Accepted July 2, 1998. S.G. Karshenboim. D.I. Mendeleev Institute for Metrology, 198005 St. Petersburg, Russia. Telephone: 7-812-2591051; FAX: 7-812-1130114; e-mail: sgk@onti.vniim.spb.su V.G. Ivanov. Pulkovo Observatory, 196140, St. Petersburg, Russia. e-mail: ivanovv@gao.pnpi.spb.ru V.M. Shabaev. St. Petersburg State University, 198904, St. Petersburg, Russia. e-mail: shabaev@pobox.spbu.ru Can. J. Phys. 76: 503–506 (1998) © 1998 NRC Canada 504 Can. J. Phys. Vol. 76, 1998 Fig. 1. The Uehling corrections to the energy. The orbiting particle with mass 6 is either a muon or an electron and a particle in vacuum polarization loop is an electron.

Spectroscopy with diode-laser noise

Conversion of laser frequency noise to amplitude noise via interaction with a resonant medium is described. Both experiment and theory show an asymmetric M-shaped noise intensity as a function of laser frequency. We also observe features corresponding to ground state atomic hyperfine structure in the rf spectrum of the noise for the case of K vapor. A calculation of the intensity correlation function of the transmitted light yields an rf spectrum which has the qualitative features observed in the experiment.

Nuclear laser spectroscopy with on-line ion traps

The hyperfine structure of atoms informs us various static characteristics of nuclei, particularly for electro-magnetic moments and their distributions. We have been developing an experimental method to perform laser-microwave double-resonance spectroscopy for the hyperfine structure of Be and Ca isotopes, including unstable nuclei. The purpose and the status of the experiments are described.

Theory of slow-atom collisions.

A general theory of slow-atom collisions is presented with special emphasis on the effects of nuclear statistics and atomic fine and/or hyperfine structures. Symmetry properties of the collision complex and correlations between the molecular states and the separated-atom states are carefully examined. The frame transformations between various angular momentum coupling schemes are derived, which, in combination with the multichannel quantum defect theory, provides a solid foundation for the computation and the physical interpretation of slow-atom collision processes. The theory reduces to those of Stoof {ital et} {ital al}. [Phys. Rev. B {bold 38}, 4688 (1988)] and Zygelman {ital et} {ital al}. [Phys. Rev. A {bold 49}, 2587 (1994); {bold 50}, 3920 (1994)] in their respective ranges of validity. {copyright} {ital 1996 The American Physical Society.}

HFS92: A program for relativistic atomic hyperfine structure calculations

We describe a program for the computation of magnetic dipole and electric quadrupole diagonal ( A J , B J ) and off-diagonal ( A J, J−1 , B J, J−1 , B J, J−2 ) hyperfine interaction constants. Approximate atomic wavefunctions are assumed to be linear combinations of configuration state functions, which are, in turn, constructed from four-component spin-orbitals to be many-particle eigenfunctions of the parity and angular momentum operators.

Remarks on the interpretation of very high-precision measurements of hyperfine-structure splittings in neutral and singly ionized complex atoms

The studies of hyperfine structure (HFS) of free atoms is shortly summarized. A hyperfine structure many-body parametrization method is described. The utility of this method as a source of information on atomic structure and for prediction of hfs of the fine structure levels, still undetermined experimentally, has been demonstrated on the examples of Co, Ti and Ta atoms.

Hyperfine structure of hydrogenlike and lithiumlike atoms.

The hyperfine splitting values of the ground state of the hydrogenlike atoms $^{13}\mathrm{C}^{5+}$, $^{14}\mathrm{N}^{6+}$, $^{17}\mathrm{O}^{7+}$ and the lithiumlike atoms $^{7}\mathrm{Li}^{0}$, $^{14}\mathrm{N}^{4+}$, $^{19}\mathrm{F}^{6+}$, $^{23}\mathrm{Na}^{8+}$, $^{25}\mathrm{Mg}^{9+}$, $^{27}\mathrm{Al}^{10+}$, $^{29}\mathrm{Si}^{11+}$, $^{35}\mathrm{Cl}^{14+}$, $^{57}\mathrm{Fe}^{23+}$ are calculated. The calculations of the lithiumlike ions (Z\ensuremath{\ge}7) are based on a combination of the 1/Z perturbation theory and the configuration interaction Hartree-Fock method. The relativistic corrections are calculated in the zeroth and first orders in 1/Z. The nuclear charge and magnetization distribution corrections and the radiative corrections are taken into account. The uncertainty of the calculations is estimated to be \ensuremath{\sim}0.02% for the hydrogenlike ions and \ensuremath{\sim}0.06% for the lithiumlike ions, except $^{57}\mathrm{Fe}^{23+}$, for which the uncertainty is about 0.15%. The hyperfine structure constant of the ground state of Li is calculated to be A=401.5(4) MHz. The results of the calculations are compared with the theoretical values obtained with other methods and with experiment.

Hyperfine structure calculations for inner atomic levels

The results of Hartree-Fock-Dirac numerical calculations are given for the magnetic dipole and electric quadrupole hyperfine constants for the K and LI-III shells for all Z from Z=10-100. A comparison is made with results obtained with simple analytic formulae for the case of hydrogen-like ions with a simple screening and nuclear finite-size corrections taken into account. Formulae are given for the atomic inner-shell hyperfine structure in the form suitable to calculate the hyperfine shifts of atomic states, excited in different processes, such as electron capture or an internal conversion.

The interactions between alkali metals and C 2H 2. Density functional theory as an analytic tool

The interactions between an alkali metal atom (Li, Na, K) and acetylene/vinylidene are investigated by means of gradient corrected (‘PWP’) density functional theory. Particular emphasis is made on the determination of equilibrium geometries, energetics and atomic hyperfine structures of the MHCCH van der Waals addition complexes, and the MHCCH and MCCH 2 charge-transfer complexes. The PWP optimized geometries are found to be similar to previous ab initio data, and the generated hyperfine structures are in excellent accord with experimental matrix isolation ESR data recorded at 4 K. In the charge transfer complex formation, the metal atoms are found to donate 0.6–0.8 electron from an excited p orbital to the antibonding CC π ∗ orbital of the hydrocarbon fragment. The calculated trend in charge donation matches the order of increasing atomic s → p excitation energies, K < Li < Na. This is the first application of the present method to metal atom hyperfine structures, and the results are promising for future studies.

Inclusion of Hartree–Fock exchange in density functional methods. Hyperfine structure of second row atoms and hydrides

Isotropic and anisotropic hyperfine coupling constants of second row atoms have been studied using extended basis sets with a number of different density functionals. Local functionals give even the wrong sign for some atoms, and the same occurs when the Perdew’s correlation functional is coupled to the Becke exchange one. Much better results are obtained using the Lee–Yang–Parr correlation functional. Introduction of some Hartree–Fock exchange in the functional delivers a further significant improvement, approaching the accuracy of the most refined post-Hartree–Fock computations. Purposely tailored basis sets are also introduced which are small enough to be used in molecular computations, but still give high quality geometries and hyperfine coupling constants.

Multi-configuration Hartree- and Dirac-Fock calculations of atomic hyperfine structures

Recent multi-configuration Hartree-Fock (MCHF) calculations of atomic hyperfine structures are reviewed. In particular, spin-polarization and relativistic effects are considered. Using a systematic active space MCHF approach, combined with large multi-reference configuration interaction (MR-CI) calculations, it is shown that hyperfine structures in many cases can be calculated very accurately. For few-electron systems, like lithium and beryllium, the remaining discrepancies between theory and experiments largely come from neglected relativistic effects, showing the necessity of fully relativistic calculations even for these systems. The physical effects of relativity on the hyperfine structure are discussed and fully relativistic multi-configuration Dirac-Fock (MCDF) calculations using the systematic active space approach are performed for lithium-like fluorine.