Large-magnitude high-spin nuclear parameters in a Ti3+ center from X-band EPR measurements at 10 K

Precise 10 K X-band EPR measurements and subsequent spin-Hamiltonian analysis by direct matrix diagonalization methods are reported for a Ti3+ (S = 1/2) center in tetragonal zircon (zirconium silicate, ZrSiO4). A special, and previously unobserved, feature of the supposedly uniaxial spectrum is the marked angular dependence of the titanium hyperfine lines in the perpendicular, ab crystal plane. As discussed, this can only arise from the presence of high-spin nuclear terms of dimension BIk, SIk (k = 3, 5) in the spin Hamiltonian. Parameters arising from these terms were determined to have magnitudes very much larger than observed previously in first-row transition ions. The consequences of precise determination of these high-spin parameters are significant and several: a precise determination of the nuclear quadrupole tensor leading to a ratio 47P/49P in excellent agreement with the ratio derived from the corresponding nuclear quadrupole moments; an apparent anisotropy in the nuclear Zeeman interaction which can be identified with anisotropy in the chemical shielding "tensor"; a marked hyperfine anomaly. The origin and significance of these observations are discussed.     

Elektronen-Kern-Doppelresonanz-Untersuchung vonU 2-Zentren in Kaliumchlorid

U ₂-centers in alkali halides are neutral hydrogen atoms in interstitial lattice sites, as has been shown by EPR measurements. The hyperfine interactions with the proton and with the four nearest halogen nuclei are resolved in the EPR spectrum. In order to resolve hyperfine interactions with further nuclei of the surrounding lattice ENDOR measurements have been performed onU ₂-centers in KCl at 77 °K. The analysis of the ENDOR spectra gave precise values for the hyperfine and quadrupole interaction constants of the nearest neighbour chlorine and potassium nuclei. The isotropic hyperfine constant of the chlorine neighbours is 24 times larger than that of the potassium neighbours although both nuclei are on equivalent first shell lattice positions. The hyperfine interactions of second shell potassium nuclei [(1/2, 1/2, 3/2)-position] show an unexpectedly large isotropic hyperfine constant. One expects a pure magnetic dipole-dipole interaction for the outer shell nuclei because of the concentrated hydrogen wave function. Two further chlorine shells could be approximately analysed. A theoretical estimate of the hyperfine and quadrupole interaction constants was made by orthogonalizing the 1s hydrogen wave function to the cores of the surrounding ions. If one takes into account the mutual overlap of neighbouring potassium and chlorine ions, one gets the right order of magnitude of the measured constants and a value of 10.4∶1 for the ratio of the isotropic hyperfine constants of the first shell chlorine and potassium nuclei. The relatively large isotropic constant of the second shell potassium nuclei can also be explained on this basis.     

Precise measurement of hyperfine structure in the 52P1/2 state of Rb

We have measured hyperfine structure in the 5 ²P_1/2 state of Rb using a frequency-stabilized diode laser, which is locked to one hyperfine transition, and an acousto-optic modulator, whose frequency is locked to the interval of interest. We check for optical-pumping errors by repeating the measurement at different values of pump power in the saturated-absorption spectrometer. We obtain precise values of the hyperfine constant: A=120.645(5) MHz for ⁸⁵Rb and A=406.119(7) MHz for ⁸⁷Rb. The values resolve a large discrepancy between two earlier high-accuracy measurements on this state.     

Beta-decay energy and nuclear mass of100Nb

Radiofrequency measurements of the zero-field hyperfine intervals in low levels of¹⁶⁷Er and^161,163Dy have been made as part of a systematic study of the second half of the 4f^N6s² configuration of the neutral rare-earth atoms. Almost no precise hfs data exist for this region, and a preliminary analysis indicates systematic differences between ab initio theory and experiment.     

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. Received: 17 February 1998     

Doppler-free spectroscopy of the 8s state of Cs

Doppler-free two-photon spectroscopy and ion detection in a thermionic diode were used to measure the hyperfine splitting and absolute term energy of the 8S state of Cs. The results, a=219.3(2) MHz for the magnetic dipole coupling constant, and E(8S)=24317.1499(4) cm^-1 for the term value of the c.g. of the 8S state relative to the c.g. of the ground state, agree well with earlier, less precise measurements. The hyperfine coupling also agrees well with a recent relativistic Hartree-Fock calculation.     

A rubidium-stabilized ring-cavity resonator for optical frequency metrology: precise measurement of the D1 line in 133Cs

We have developed a ring-cavity resonator that can be used to measure the absolute frequencies of optical transitions with an uncertainty below 40 kHz. The length of the resonator is calibrated against a reference laser locked to the D₂ line of ⁸⁷Rb, the frequency of which is known with 6 kHz accuracy. We demonstrate the power of this technique by measuring the absolute frequencies of various hyperfine transitions in the D₁ line of ¹³³Cs. Our results agree with earlier measurements using the frequency-comb technique, and have similar accuracy. Measurement of the D₁-line frequency could lead to a more precise determination of the fine-structure constant. We also report a precise value of A=291.918(8) MHz for the hyperfine constant in the 6P_1/2 state.     

Applications of the two-photon doppler-free method: Hyperfine interactions and isotope shift measurements

The hyperfine structures are generally of the same order of magnitude as the Doppler broadening of optical transitions and so are the isotopic shifts in the case of heavy elements. When these structures are too small, one must use Doppler-free methods. Among these methods, the two-photon spectroscopy has obtained good results in highly excited levels. In our laboratory in Paris, we did measurements on neon and helium by two-photon excitation from metastable levels. The precision of the measurements is of the order of one MHz, which permits a precise comparison with theory. We compare the measurements on neon with the theory by Liberman and we obtain a good fit in the first approximation, but must introduce mixing of wave functions for an exact explanation. In the case of helium, we obtain a good fit with the theoretical values obtained from the wave functions by Accad, Pekeris and Schiff. We also give an example where another technique by polarization measurements permits us to obtain experimentally a hyperfine structuresmaller than the natural width. We also present a short review of the measurements done by the two-photon method in other laboratories on other elements, Pb, Tl, In and alkaline earths Ca, Sr. Ba.     

Precise frequency measurements of atomic transitions by use of a Rb-stabilized resonator

We demonstrate a technique for frequency measurements of atomic transitions with a precision of 30 kHz. The frequency is measured with a ring-cavity resonator whose length is calibrated against a reference laser locked to the D2 line of 87Rb, the frequency of which is known with 10-kHz accuracy. We have used this method to measure the hyperfine structure in the 5P(3/2) state of 85Rb. We obtain precise values for the hyperfine constants, A = 25.041(6) MHz and B = 26.013(25) MHz, and a value of 77.992(20) MHz for the isotope shift in the D2 line.     

Determination of signs of hyperfine coupling constants for an S = ½ system through E.P.R., ENDOR and double ENDOR

A systematic method of obtaining relative signs of hyperfine coupling constants is described. It applies to systems consisting of (a) a set of one or more nuclei coupled fairly strongly to the electron spin, and possessing a two-fold (or higher) axis of symmetry, together with (b) a set of weakly coupled nuclei defining superhyperfine transitions. ENDOR measurements for several E.P.R. hyperfine transitions, with the field oriented along the symmetry axis, give relative signs of hyperfine components for this direction. Signs for the other directions can then be obtained through ENDOR measurements on a single hyperfine transition at various field orientations. Additional double ENDOR measurements may be necessary for very weakly coupled nuclei. This method can complement double ENDOR studies in favourable cases. It is illustrated by the determination of signs of coupling constants of protons and of ⁷⁵As in the AsO₄ ^4- radical in KH₂AsO₄.     

Determination of hyperfine parameters using quantum beats

We have observed the delayed time spectra of the coherently scattered radiation following nuclear Bragg diffraction of incident synchrotron radiation pulses. The measurements were carried out using single crystals of⁵⁷Fe-YIG and⁵⁷FeBO₃ by conventional coincidence techniques. Although the intention of these measurements was only to show effects like speed-up and quantum beats, the spectra also provide the possibility of a sensitive direct measure of the hyperfine interaction parameters. It is demonstrated that even with a counting rate of only 1 Hz it was possible to obtain within 1–2 hours (in the case of⁵⁷FeBO₃) spectra of sufficient statistics to derive precise hyperfine parameters.     

Hyperfine structure of highly charged 23892U ions with rotationally excited nuclei

The hyperfine structure (hfs) of electron levels of 23892U ions with the nucleus excited in the low-lying rotational 2(+) state with an energy E(2(+)) = 44.91 keV is investigated. In hydrogenlike uranium, the hfs splitting for the 1s(1/2) ground state of the electron constitutes 1.8 eV. The hyperfine-quenched (hfq) lifetime of the 1s2p 3P0 state has been calculated for heliumlike 23892U and was found to be 2 orders of magnitude smaller than for the ion with the nucleus in the ground state. The possibility of a precise determination of the nuclear g(r) factor for the rotational 2(+) state by measurements of the hfq lifetime is discussed.     

Muonium spectroscopy

The electromagnetic interactions of electrons and muons can be described to very high accuracy within the framework of standard theory, in particular within the hydrogen like muonium atom. Therefore, precision measurements are able to test basic interactions in physics and to search for yet unknown forces. Accurate values for fundamental constants can be obtained. Results from experiments on the ground state hyperfine structure and the 1s–2s intervals in muonium are described together with their relations to a new measurement of the muon magnetic anomaly. This revised version was published online in August 2006 with corrections to the Cover Date.     

Constraints on proton structure from precision atomic-physics measurements

Ground-state hyperfine splittings in hydrogen and muonium are very well measured. Their difference, after correcting for magnetic moment and reduced mass effects, is due solely to proton structure-the large QED contributions for a pointlike nucleus essentially cancel. The rescaled hyperfine difference depends on the Zemach radius, a fundamental measure of the proton, computed as an integral over a product of electric and magnetic proton form factors. The determination of the Zemach radius, (1.019+/-0.016) fm, from atomic physics tightly constrains fits to accelerator measurements of proton form factors. Conversely, we can use muonium data to extract an experimental value for QED corrections to hydrogenic hyperfine data. There is a significant discrepancy between measurement and theory, in the same direction as a corresponding discrepancy in positronium.     

High-precision optical measurement of the 2S hyperfine interval in atomic hydrogen

We have applied an optical method to the measurement of the 2S hyperfine interval in atomic hydrogen. The interval has been measured by means of two-photon spectroscopy of the 1S-2S transition on a hydrogen atomic beam shielded from external magnetic fields. The measured value of the 2S hyperfine interval is equal to 177 556 860(16) Hz and represents the most precise measurement of this interval to date. The theoretical evaluation of the specific combination of 1S and 2S hyperfine intervals D21 is in fair agreement (within 1.4 sigma) with the value for D21 deduced from our measurement.     

Hyperfine anomaly measurements in francium isotopes and the radial distribution of neutrons

We have performed precision measurements in a magneto-optical trap of the 7P_1/2 hyperfine structure of the isotopes ^209-210Fr. The ratio of these hyperfine constants to the previously measured 7S_1/2 ground state values reveals a significant hyperfine anomaly. This anomaly results from the different radial dependence of the electron density in the two atomic levels. The measurements are sensitive to changes in the radial distribution of the neutron magnetism. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nuclear Quadrupole Tensors for (35)Cl and (37)Cl in cis-1-chloro-2-fluoroethylene Obtained by Detection of Perturbation-Allowed DeltaJ = 2 and DeltaJ = 3 Transitions

The nuclear quadrupole hyperfine structure in rotational transitions of cis-1-chloro-2-fluoroethylene was measured for both (35)Cl and (37)Cl containing isotopomers in the millimeter-wave region. Near degeneracies of the 9(3,7) and 10(2,9) levels of (35)ClHC&dbond;CFH and of the 19(9,10/11) and 17(10,7/8) levels of (37)ClHC&dbond;CFH cause strong perturbations of the hyperfine patterns and give rise to perturbation-allowed DeltaJ = 2 and DeltaJ = 3 transitions. Lamb-dip measurements of such perturbed hyperfine patterns and of forbidden DeltaJ = +2 and perturbation-enhanced DeltaJ = 0 transitions of (35)ClHC&dbond;CFH provided an accurate determination of chi(ab), the off-diagonal element of the inertial nuclear quadrupole tensor. For (37)ClHC&dbond;CFH, chi(ab) was determined for the first time thanks to the observation of perturbed hyperfine patterns and of forbidden DeltaJ = +3 and DeltaJ = -2 transitions. Additional measurements of hyperfine structures led to improved values for the diagonal elements of the chi tensor of both (35)Cl and (37)Cl. Moreover, the complete inertial nuclear quadrupole tensor was evaluated from the field gradient at the chlorine nucleus computed by using the Multi-Configuration Self-Consistent Field (MCSCF) approach and employing basis sets of triple-zeta quality: very good agreement with the experiment was obtained. Copyright 2000 Academic Press.     

由基样条构造有限基集计算的超精细结构常数(英文)

多体微扰论有效算符方法应用于超精细结构的计算 .由HF波函数计算零阶超精细常数 .使用基样条构造了薛定谔方程的有限基集 .使用这些有限基集计算了原子实极化和关联 ,以及 7Li,2 3 Na ,3 9K和4 3 Ca离子的s1/ 2 ,p1/ 2 和p3 / 2 态的超精细结构常数和4 3 Ca离子的d3 / 2和d5/ 2 态的超精细常数 . The effective-operator form of many-body theory is applied to the calculation of hyperfine structure. The zeroth order hyperfine constants are evaluated with Hartree-Fock wavefunction. Τhe finite basis sets of Schrdinger s equation are constructed by using B-splines. With the finite basis sets, we have calculated the core polarization, and the correlation diagrams. The hyperfine constants of the s 1/2, p 1/2and p 3/2 states of 7Li, 23Na, 39K, 43Ca + as well as the d 3/2...     

NMR study of hyperfine interactions in R1−xLuxFe2 (R = Gd, Tb)

Spin-echo NMR measurements on ¹⁵⁵Gd, ¹⁵⁹Tb and ¹⁷⁵Lu have been done for the cubic Laves phase compounds Gd_1−xLu_xFe₂ and Tb_1−xLu_xFe_x. The observed hyperfine fields of Gd and Lu in those compounds increase with increasing Lu concentration. The concentration dependence of the Lu hyperfine field is qualitatively discussed.     

Confirmation of the giant hyperfine anomaly of the system184W2+-183W g by new spin-echo experiments with183WFe and remarks on possible explanations

Spin-echo measurements on¹⁸³W were performed with dilute alloys of W (0.1, 0.25, 0.5 and 1 at %) in Fe. The result for the hyperfine field:B _4.2K ^hf =(?)62 · 54 (3) T agrees with the old data of Kontani and Itoh, but the accuracy is much better. The giant hyperfine anomaly of¹⁸³W with respect to¹⁸⁴W₂₊ observed by Alzner et al. is thus confirmed and the errors are reduced to:¹⁸⁴W₂₊Δ¹⁸³W_g=+0.150(31). This is the first case of a very large hyperfine anomaly in electronic hyperfine fields which is not caused by the pathological cancellation of orbital and spin magnetism in jackknifep _1/2 ord _3/2 single proton configurations. A detailed discussion shows that the large hyperfine anomaly may be related to the anomalously small magnetic dipole moment of¹⁸³W. Our result should stimulate further theoretical work with the aim to understand this magnetic moment as well as the giant hyperfine anomaly.