Experimental Hyperfine Structure Research Articles

Hyperfine Structure Constants of Sc i and Sc ii with Fourier Transform Spectroscopy

Abstract We report new experimental hyperfine structure (HFS) constants of neutral and singly ionized scandium (Sc i and Sc ii). We observed spectra of Sc–Ar and Sc–Ne hollow cathode discharges in the region 200–2500 nm (50,000–4000 cm−1) using Fourier transform spectrometers. The measurements show significant HFS patterns in 1431 spectral lines fitted in our 12 spectra given in Table 1. These were fitted using the computer package Xgremlin to determine the magnetic dipole hyperfine interaction constant (A) for 185 levels in Sc i and 6 levels in Sc ii, of which 80 Sc i levels had no previous measurements. The uncertainty in the HFS A constant is between 1 × 10−4 and 5 × 10−4 cm−1.

Hyperfine structure constants for neutral and singly ionized vanadium by Fourier transform spectroscopy data

The hyperfine structure (HFS) for V I and V II were investigated using the archival data recorded by the Fourier transform spectrometer (FTS) at the US National Solar Observatory (NSO) with a fitting program written by us. The magnetic dipole HFS constant A values for 53 levels of V I between 0 and 52,948 cm−1 and for 56 levels of V II between 36 and 72,952 cm−1 are obtained, of which 46 results for V I and 50 results for V II are reported for the first time, as far as we know. And to our knowledge, so far, the A constants of 370 levels of V I and 76 levels of V II have been measured in literature. The new results obtained in this work supplement more experimental HFS data very useful in astrophysics and atomic physics etc..

Hyperfine Anomalies in Gd and Nd

The hyperfine anomalies in Gd and Nd have been extracted from experimental hyperfine structure constants. In addition to the values of the hyperfine anomaly, new improved values of the nuclear magnetic dipole moment ratios are derived.

Parametric study of hyperfine structure of Zr II even-parity levels

Until now experimental hyperfine structure (hfs) data of 12 even-parity Zr II levels were given in the literature. Recently new hyperfine splitting measurements of 11 other Zr II levels, of the same parity are achieved, applying fast-ion-beam laser-fluorescence spectroscopy. The hfs of these 23 gathered levels has been analysed by simultaneous parametrisation of the one- and two-body interactions, first in model space (4d + 5s)3 and secondly in extended space. For the three lowest configurations, radial parameters of the magnetic dipole A and quadrupole electric B factors are deduced in their entirety for 91Zr II, compared and discussed with calculated values, available in the literature, and also with ours, computed by means of the ab initio method. For instance we give the main experimental values of the extracted single-electron hfs parameters of 4d25s: [Formula: see text] = –2701 MHz, [Formula: see text] = –122.4 MHz, and [Formula: see text] = –113.5 MHz.

Semi-empirical analysis of oscillator strengths for Nb II

Semi-empirical wave functions, proven via comparison of the expected and experimental hyperfine structure constants and gJ-factors in previous papers, were used for the parametrization of the oscillator strengths for electric-dipole transitions in Nb II, where reliable experimental data were available. The angular coefficients of the transition matrix in pure SL coupling were found from straightforward Racah algebra. The transition matrix was transformed into the actual intermediate coupling by the fine structure wave functions. The transition integrals were treated as free parameters in the least squares fit to experimental gf values. This procedure allowed us to obtain the values of transition integrals and predict the values of oscillator strengths for transitions from odd levels in a wide spectral range.

Semi-empirical calculations of oscillator strengths and hyperfine constants for Ti II

As the result of our studies on the atomic structure of complex atoms we produced high quality wave functions for both the even and odd systems of configurations. The quality of wave functions was proved via comparison of the expected and experimental hyperfine structure constants and gJ-factors. These wave functions were used for the parametrization of the oscillator strengths for electromagnetic transitions in Ti II, where reliable experimental data were available. The least squares fit to experimental values for some transitions, published in the NIST Atomic Spectra Database, allowed us to obtain the values of transition integrals and parametrize the oscillator strengths.

Fine Structure Analysis of the Configuration System of V II. Part I: Even-Parity Levels

Using a linked-parameter technique of level-fitting calculations in a multi configuration basis, a parametric analysis of fine structure (fs) for even-parity levels of V II, involving six configurations, has been performed. This led us to exchange the assignments of two triplets, 3d3(2F)4s c 3F and 3d4 d 3F, reported in earlier analyses as being located at 30,300 cm-1 and 30,600 cm-1, respectively. This is confirmed by experimental hyperfine structure (hfs) A constants, used as fingerprints. Moreover, the current singlet 3d24s2 1D2 position is likely too high. The fs parameters, magnetic Lande g-factors, and the percentage of leading eigenvectors of levels are calculated. We present also predicted singlet, triplet and quintet positions for missing experimental levels up to 100,000 cm-1. The single-electron hfs parameters are determined in their entirety for 51V II for the model space (3d + 4s)4 with good accuracy. For the model space (3d + 4s)4 of 51V II the single-electron hfs parameters are computed; furthermore, our achieved theoretical evaluations of the single-electron hfs parameters, thanks to the use of ab initio calculations, reinforce the validity of these hfs parameter values, deduced from experimental data.

Reexamination of nuclear quadrupole moments in39−41K isotopes

Nuclear quadrupole moments ($Q$'s) in three isotopes of the potassium atom (K) with mass numbers 39, 40, and 41 are evaluated more precisely in this work. The $Q$ value of ${}^{39}$K is determined to be 0.0614(6) $b$ by combining the available experimental result of the electric quadrupole hyperfine structure constant ($B$) with our calculated $B/Q$ result of its $4{P}_{3/2}$ state. Furthermore, combining this $Q$ value with the measured ratios $Q$(${}^{40}$K)$/Q$(${}^{39}$K) and $Q$(${}^{41}$K)$/Q$(${}^{39}$K), we obtain $Q$(${}^{40}$K)$=\ensuremath{-}0.0764(8)\phantom{\rule{4pt}{0ex}}b$ and $Q$(${}^{41}$K)$=0.0747(7)\phantom{\rule{4pt}{0ex}}b$, respectively. These results disagree with the sub-1$%$ accuracy standard values recently quoted by Pyykk\"o [Mol. Phys. 106, 1965 (2008)]. The calculations were carried out by employing the relativistic coupled-cluster theory at the single, double, and involving important valence triple approximation. The accuracies of the calculated $B/Q$ results can be viewed on the basis of comparison between our calculated magnetic dipole hyperfine structure constants ($A$'s) with their corresponding measurements for many low-lying states. Both $A$ and $B$ results in a few more excited states are presented. Also, we find that the latest reported experimental hyperfine structure constant results for the $4P$ states in ${}^{39}$K are inconsistent with our calculations.

Defect model and spin-Hamiltonian parameters for the tetragonal Nd 3+ center in the tetragonal phase of SrTiO 3 crystal

The spin-Hamiltonian parameters ( g factors g ∥, g ⊥ and hyperfine structure constants 143A ∥, 143A ⊥, 145A ∥ and 145A ⊥) of the tetragonal Nd 3+ center in the low-temperature ( T≈4.2 K) tetragonal phase of SrTiO 3 are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are attached to the conventional Hamiltonian and a 52×52 energy matrix concerning the ground term 4 H J ( J=9/2, 11/2, 13/2, 15/2) is constructed. The Nd 3+ center is attributed to Nd 3+ occupying the 12-fold coordinated Sr 2+ site in SrTiO 3. Differing from the defect model assumed in the previous paper that the tetragonal distortion of this Nd 3+ center is due to the association of one interstitial oxygen ion at a nearest neighborhood of Nd 3+ and the Nd 3+ displacement Δ z along C 4 axis, we suggest that it is due to the distortion of SrTiO 3 lattice in the tetragonal phase. The calculated g factors g ∥ and g ⊥ show good agreement with the experimental values, suggesting that our defect model of Nd 3+ center in SrTiO 3 is reasonable. The experimental hyperfine structure constants were not reported and so our calculated results remain to be checked by EPR experiment.

Hyperfine structure investigation of Sc I, part II: theoretical studies of the odd configurations

Based on the experimental hyperfine structure data given in our previous study, the multi-configuration method has been used to calculate the fine structure of the odd parity configurations 3d4s4p, 4s2 4p and 3d2 4p of neutral Scandium taking into account configuration interaction effects. Magnetic dipole hyperfine structure constants are analysed in the effective-operator formalism for the isotope 45Sc. Relativistic one-electron parameters of the magnetic dipole hyperfine structure anlkskl(kskl= 01, 10, 12) were fitted to the experimental data by a least-squares fit procedure. Theoretical predictions for the magnetic dipole hyperfine structure constants A for all levels of the three configurations are given.

Experimental hyperfine structure investigation of atomic La

Optogalvanic laser spectroscopy has been applied to measure the hyperfine structure of 19 spectral lines of La I in the wavelength regions from 570 to 590 nm and 700 to 825 nm. Experimental hyperfine structure constants A and B of the isotope139La have been measured for 16 levels of odd parity. From those values six magnetic dipole and ten electric quadrupole constants have been determined for the first time. Some disagreements with previously obtained values are discussed.

Hyperfine structure parametrisation in Maple

In hyperfine structure examinations, routine high resolution spectroscopy methods have to be combined with exact fine structure calculations. The so-called magnetic A and electric B factor of the fine structure levels allow to check for a correct fine structure analysis, to find errors in the level designation, to find new levels and to probe the electron wavefunctions and its mixing coefficients. This is done by parametrisation of these factors into different contributions of the subshell electrons, which are split further into their radial and spin–angular part. Due to the routine with which hyperfine structure measurements are done, a tool for keeping the necessary information together, performing checks online with the experiment and deriving standard quantities is of great help. Maple [Maple is a registered trademark of Waterloo Maple Inc.] is a highly-developed symbolic programming language, often referred to as the pocket calculator of the future. Packages for theoretical atomic calculation exist ( Racah and Jucys) and the language meets all the requirements to keep and present information accessible for the user in a fast and practical way. We slightly extended the Racah package [S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51] and set up an environment for experimental hyperfine structure calculations, the Hfs package. Supplying the fine structure and nuclear data, one is in the position to obtain information about the hyperfine spectrum, the different contributions to the splitting and to perform a least square fit of the radial parameters based on the semiempirical method. Experimentalist as well as theoretical physicist can do a complete hyperfine structure analysis using Maple. Program summary Title of program: H fs Catalogue number: ADXD Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADXD Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computers for which the program is designed: All computers with a license of the computer algebra package Maple Installations: University of Kassel (Germany) Operating systems under which the program has been tested: Linux 9.0 Program language used: Maple, Release 7, 8 and 9 Memory required to execute with typical data: 5 MB No. of lines in distributed program, including test data, etc.: 34 300 No. of bytes in distributed program, including test data, etc.: 954 196 Distribution format: tar.gz Nature of the physical problem: Atomic state functions of an many configuration many electron atom with several open shells are defined by a number of quantum numbers, by their coupling and selection rules such as the Pauli exclusion principal or parity conservation. The matrix elements of any one-particle operator acting on these wavefunctions can be analytically integrated up to the radial part [G. Gaigalas, O. Scharf, S. Fritzsche, Central European J. Phys. 2 (2004) 720]. The decoupling of the interacting electrons is general, the obtained submatrix element holds all the peculiarities of the operator in question. These so-called submatrix elements are the key to do hyperfine structure calculations. The interaction between the electrons and the atomic nucleus leads to an additional splitting of the fine structure lines, the hyperfine structure. The leading components are the magnetic dipole interaction defining the so-called A factor and the electric quadrupole interaction, defining the so-called B factor. They express the energetic splitting of the spectral lines. Moreover, they are obtained directly by experiments and can be calculated theoretically in an ab initio approach. A semiempirical approach allows the fitting of the radial parts of the wavefunction to the experimentally obtained A and B factors. Method of solution: Extending the existing csf_LS() and asf_LS() to several open shells and implementing a data structure level_LS() for the fine structure level, the atomic environment is defined in Maple. It is used in a general approach to decouple the interacting shells for any one-particle operator. Further submatrix elements for the magnetic dipole and electric quadrupole interaction are implemented, allowing to calculate the A and B factors up to the radial part. Several procedures for standard quantities of the hyperfine structure are defined, too. The calculations are accelerated by using a hyper-geometric approach for three, six and nine symbols. Restrictions onto the complexity of the problem: Only atomic state functions in nonrelativistic LS-coupling with states having l ⩽ 3 are supported. Typical running time: The program replies promptly on most requests. The least square fit depends heavily on the number of levels and can take a few minutes.

Hyperfine Structure Measurements of Neutral Manganese with Fourier Transform Spectroscopy

We report experimental hyperfine structure constants of levels in the neutral manganese atom, measured using Fourier transform spectroscopy of hollow cathode discharges. In total, 208 spectral lines of astrophysical interest have been analyzed to obtain hyperfine structure constants for 106 levels in Mn i, of which 67 have no previous hyperfine structure measurements. The uncertainties in the magnetic dipole constants, A ,a re between 1; 10 � 4 and 5 ;10 � 4 cm � 1 . Hyperfine structure constants for an additional 18 levels compiled from the literature are also given. Subject headingg atomic data — line: profiles — methods: laboratory

Hyperfine Structure Investigation of Mn I Part II: Theoretical Studies of The Odd Configurations

The parametric method has been used to calculate the fine structure of the odd configurations 3d54s4p, 3d54s5p and 3d64p of Mn I taking into account configuration interaction effects. Based on the results of the fine structure calculations and recent experimental hyperfine structure data, the magnetic dipole hyperfine structure is analysed using the effective-operator formalism. One-electron parameters anlkskl (kskl = 01, 10, 12) were determined for the three configurations and theoretical predictions for the magnetic dipole hyperfine structure constants A for all levels of these configurations up to 52 000 cm-1 are given.

Hyperfine Structure Investigations of Mn I. Part I: Experimental and Theoretical Studies of the Hyperfine Structure in the Even Configurations

Optogalvanic laser spectroscopy has been applied to measure the hyperfine structure of 12 spectral lines of Mn I in the wavelength regions of 660–645 nm and 933–911 nm. Experimental hyperfine structure constants A and B of the isotope 55Mn have been determined for seven levels of even and seven levels of odd parity. Additionally, a parametric analysis of the fine structure and the magnetic dipole hyperfine structure has been performed for the three even configurations 3d54s2, 3d64s and 3d7. Very large values for the ratio a3d10/a3d01 are found. Theoretical predictions for the magnetic dipole hyperfine structure constants A for all levels of the configurations 3d54s2, 3d64s and 3d7 are given.

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.

Extraction of hyperfine anomalies without precise values of the nuclear magnetic dipole moment

A new method for extracting the hyperfine anomaly from experimental hyperfine structure constants is suggested. Instead of independent high-precision measurements of the nuclear magnetic dipole moment, precise measurements of magnetic dipole hyperfine interaction constants for two atomic states and a theoretical analysis can be used. This can lead to determination of hyperfine anomaly for radioactive isotopes where the nuclear magnetic dipole moment is not known with high accuracy.

Laser spectroscopic hyperfine structure measurements of 51V as a test of a new parametrization of the hyperfine structure

The hyperfine structure (HFS) of the four high lying and metastable fine structure levels of vanadium-51 have been calculated. The calculations are based on the parametrization of one- and two-body interactions to the second order perturbation theory for a model space of the three configurations 3d 3+ M 4s M ( M = 0, 1, 2). The experimental HFS data were measured using the laser spectroscopic double-resonance technique (ABMR-LIRF) with high-frequency precision.

Further computer simulation studies of experimental Zeeman-effect patterns of mixed second-order radiation of Bi i

In continuation of a study of so-called forbidden lines (second-order radiation) in general and of the application of computer simulation techniques in particular, two more lines of the Bi i 6p3 ground configuration were investigated. A visual selection of calculated Zeeman profiles best matching the experimental patterns leads to the following estimates of the electric quadrupole admixture: 30% ± 8% for the 5640-A line and 2.25% ± 0.5% for the 8755-A line. In the case of the 5640-A line, a better value of the electric quadrupole admixture was obtained, and the limits of uncertainty were reduced by the use of photographic photometry for the conversion of plate density into relative intensities. This was done for the zero-field case. A comparison of the converted experimental hyperfine structure pattern with the calculated profiles gave a final result of 28% ± 3%. Both investigated lines exhibit a reversed interference phase (reversal of π–L views) relative to the 7330-A line of Pb i. A general and simple rule governing the phase sign is formulated that relates the phase sign to the signs of hyperfine structure splitting constants of the levels involved in the transition. No traces of the 8691-A line were found, even for extended exposures (estimated intensity I8691 < 00001I8755). The 3014-A line was observed but not analyzed.

Electronic and hyperfine structures of hydrocarbon radical cations

Ab initio calculations on alkane and alkene radical cations with 2 to 6 carbon atoms are reported. Geometry optimizations were performed on both the unrestricted Hartree-Fock (UHF) and second-order perturbation theory (MP2) levels, with subsequent hyperfine structure (HFS) calculations on the optimized geometries, by means of relatively large (30000–60000) configuration-interaction calculations including single and double excitations (SDCI). By comparison with experimental HFS data, it was deduced that the MP2 optimizations are able to provide accurate geometries in most cases, but that the basis-set requirements are very stringent, at least for smaller radicals. For the alkene cations, it is found that the HFS is dominated by the region immediately surrounding the double bond, with virtually no influence from protons which are not bonded to the α or β carbon atoms.