Magnetic Dipole Constants Research Articles

Observation of magnetically-induced transition intensity redistribution in the onset of the hyperfine Paschen–Back regime

The Zeeman effect is an important topic in atomic spectroscopy. The induced change in transition frequencies and amplitudes finds applications in the Earth-field-range magnetometry. At intermediate magnetic field amplitude B∼B0=Ahfs/μB, where Ahfs is the magnetic dipole constant of the ground state, and μB is the Bohr magneton (B0≈1.7kG for Cs), the rigorous rule ΔF=0,±1 is affected by the coupling between magnetic sub-levels induced by the field. Transitions satisfying ΔF=±2, referred to as magnetically-induced transitions, can be observed. Here, we show that a significant redistribution of the Cs 6S1/2→6P3/2 magnetically-induced transition intensities occurs with increasing magnetic field. We observe that the strongest transition in the group Fg=3→Fe=5 (σ+ polarization) for B<B0 cease to be the strongest for B>3B0. On the other hand, the strongest transition in the group Fg=2→Fe=4 (σ− polarization) remains so for all our measurements with magnetic fields up to 9kG. These results are in agreement with a theoretical model. The model predicts that similar observations can be made for all alkali metals, including Na, K and Rb atoms. Our findings are important for magnetometers utilizing the Zeeman effect above Earth field, following the rapid development of micro-machined vapor-cell-based sensors.

Hyperfine structure measurements on a forbidden transition of Bi I using fourier transform spectroscopy

Hyperfine structure (hfs) investigations have been performed on a forbidden transition of the Bi I emission spectral line in the visible region at 15,437.49 cm−1, between the levels 6p3 4S3/2 and 6p3 2D5/2, by means of a Fourier Transform spectrometer. Electrodeless discharge lamps (EDL) containing BiI3 were utilized to generate the bismuth plasma. In these observations, all the 6 components of electric quadrupole (ΔF = ±2) transitions have been detected for the first time, in addition to the 12 components of magnetic dipole (ΔF = 0, ±1) transitions. Magnetic dipole constant (A) and electric quadrupole constant (B) have been derived for the combining levels.

Compact 459-nm Cs Cell Optical Frequency Standard with 2.1×10−13/τ Short-Term Stability

We achieve a compact optical frequency standard with an extended cavity diode laser locked to the 459-nm $6{S}_{1/2}$-$7{P}_{1/2}$ transition of thermal ${}^{133}\mathrm{Cs}$ atoms in a $\ensuremath{\phi}10\phantom{\rule{0.1em}{0ex}}\mathrm{mm}\ifmmode\times\else\texttimes\fi{}50\phantom{\rule{0.1em}{0ex}}\mathrm{mm}$ glass cell, using modulation transfer spectroscopy (MTS). The self-estimated frequency stability of this laser is $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}/\sqrt{\ensuremath{\tau}}$. With heterodyne measurement, we verify the linewidth-narrowing effect of MTS locking and measure the frequency stability of the locked laser. The linewidth of each laser is reduced from the free-running 69.6 to 10.3 kHz after MTS stabilization, by a factor of 6.75. The Allan deviation measured via beat detection is $2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/\sqrt{\ensuremath{\tau}}$ for each MTS-stabilized laser. In addition, we measure the hyperfine structure of the $7{P}_{1/2}$ energy level based on the heterodyne measurements, and calculate the magnetic dipole constant A of the Cs $7{P}_{1/2}$ level to be 94.38(6) MHz, which agrees well with previous measurements. This compact optical frequency standard can also be used in other applications that require high-stability lasers, such as laser interferometry, laser cooling, geodesy, and so on.

Ab initio calculations of the hyperfine structure of Ra+ and evaluations of the electric quadrupole moment Q of the 209,211,221,223Ra nuclei

The relativistic coupled-cluster method has been employed to calculate the energies, magnetic dipole, electric quadrupole and magnetic octupole hyperfine-structure constants of the low-lying states of Ra+. The validity of our calculations is substantiated by comparing the calculated binding energies and magnetic dipole hyperfine-structure constants with the corresponding available experimental results. The combination of our theoretical results with the available experimental values of the electric quadrupole hyperfine-structure constant, makes it possible to extract the electric quadrupole moments Q of the 209,211,221,223Ra nuclei. Our Q(221Ra) = 1.968(34) and Q(223Ra) = 1.248(22) are consistent with the referenced values 1.978(106) and 1.254(66) from a semi-empirical analysis (1988 Z. Phys. D 11 105), but Q(211Ra) = 0.33(2) is smaller than the referenced value 0.48(4) by about 30%. Furthermore, we also performed a procedure for assessing the contributions of magnetic octupole hyperfine interaction to the hyperfine splitting considering the preliminary value of magnetic octupole moment from the single-particle nuclear structure model. The sensitivity of hyperfine-structure interval measurements in 223Ra+ that can reveal the effect caused by the nuclear octupole moment are found to be on the order of kHz.

Theoretical analysis of the relativistic hyperfine interaction in 131Xe I

The relativistic hyperfine constants of the heavy inert gas element xenon-131 isotope have been calculated. The calculations, executed through the Multiconfiguration Dirac-Hartree-Fock method, yield the hyperfine constants of 128 levels belonging to the ns[K]J (n = 6, 7, 8, 9), nf [K]J (n = 4, 5, 6), nd[K]J (n = 5, 6, 7, 8), np[K]J (n = 6, 7, 8) and 5g[K]J intermediate Rydberg series. In order to draw further insights into the precision of our calculations and the accuracy of the obtained data, the resulting magnetic dipole and electric quadrupole hyperfine constants are analysed by comparing them with other experimental and theoretical results available in the atomic spectra database. Indeed, a satisfactory agreement is observed between our results and the other experimental and theoretical ones. Moreover, the absence of the hyperfine anomaly enables us to highlight the plausibility of our theoretical results through the calculation of the ratio A129A131 for a given state. The obtained values are found to be compatible with the ratio of nuclear moments of 129Xe and 131Xe isotopes. The consistency of these two different analyses confirms the accuracy of our data, on the one hand and classifies them as a reference in identifying the experimental spectrum in xenon, on the other hand. Based on this accuracy, the calculated values of the hyperfine constants for the levels under consideration, accompanied by the experimental values of the nuclear magnetic dipole and electric quadrupole moments, facilitated the calculation of the mean value of the magnetic as well as the electric field gradients produced by the electron at the tiny nucleus.

Absolute frequency measurement of rubidium 5S−6P transitions

We report on measurements on the 5S-6P rubidium transition frequencies for rubidium isotopes with an absolute uncertainty of better than \SI{450}{kHz} for the 5S $\rightarrow$ 6P$_{1/2}$ transition and \SI{20}{kHz} for the 5S $\rightarrow$ 6P$_{3/2}$ transition, achieved by saturation absorption spectroscopy. From the results we derive the hyperfine splitting with an accuracy of \SI{460}{kHz} and \SI{30}{kHz}, respectively. We also verify the literature values for the isotope shifts as well as magnetic dipole constant and the electric quadrupole constant.

Hyperfine constants and line separations for the S01−P13 intercombination line in neutral ytterbium with sub-Doppler resolution

Optical frequency measurements of the intercombination line $(6s^{2})\,^{1}S_{0} -(6s6p)\,^{3}P_{1}$ in the isotopes of ytterbium are carried out with the use of sub-Doppler fluorescence spectroscopy on an atomic beam. A dispersive signal is generated to which a master laser is locked, while frequency counting of an auxiliary beat signal is performed via a frequency comb referenced to a hydrogen maser. The relative separations between the lines are used to evaluate the $^{3}P_{1}$-level magnetic dipole and electric quadrupole constants for the fermionic isotopes. The center of gravity for the $^3P_1$ levels in $^{171}$Yb and $^{173}$Yb are also evaluated, where we find significant disagreement with previously reported values. These hyperfine constants provide a valuable litmus test for atomic many-body computations in ytterbium.

Hyperfine structure measurements of neutral atomic iodine (127I) in the infrared region (1800-6000 cm−1)

Experimental measurements of high resolution emission spectra of neutral atomic iodine (I I) have been extended to cover the mid-infrared spectral regions (1800–6000 cm−1) using Fourier transform spectroscopy. A total of 354 spectral lines are reported here in the above spectral range. While the region between 3000 and 6000 cm−1 were recorded using a conventional quartz Electrodeless Discharge lamps (EDL), spectra in the region 1800–3000 cm−1 were detected using specially prepared EDLs with a CaF2 window. Hyperfine structure analysis has been carried out on 224 spectral lines, of which 176 are reported for the first time. The magnetic dipole constant (A) and electric quadrupole constant (B) have been derived for 97 energy levels.

Ultraviolet laser spectroscopy of aluminum atoms in hollow-cathode lamp

We report on the precision measurement of aluminum atoms transition at 394 nm and transition at 396 nm in a hollow-cathode lamp. Both absorption and saturated absorption spectra are measured. From the absorption spectra, the Doppler linewidth is estimated to be 2.65 GHz. The saturated absorption spectra are analyzed based on a velocity-changing collisions model. With a frequency comb calibrated wavemeter, the frequencies of transition and transition are measured to be 759.905 204(1) THz and 756.547 133(3) THz, respectively. The hyperfine coupling constants of aluminum atoms are determined, and are compared with previously reported measurement results and theoretical calculation results. Reasonable agreement is found for the magnetic dipole constant (A constant), while the electric quadrupole constant (B constant) has a large deviation.

Hyperfine structure measurements on singly ionized atomic iodine (I II) using fourier transform spectroscopy

Hyperfine structure (hfs) investigations were performed on singly ionized atomic iodine (I II) in the spectral region 12,000 - 24,000 cm−1, utilizing microwave discharge method in combination with high resolution Fourier Transform Spectroscopy (FTS). Electrodeless discharge lamps (EDL) were used to generate the iodine plasma. In the present work, 141 hyperfine spectral transitions are reported. Hfs measurements were carried out on 73 well resolved spectral lines and derived the magnetic dipole constant (A) and electric quadrupole constant (B) for 61 energy levels (29 even parity and 32 odd parity). Further, a magnetic dipole transition (14,366 cm−1) and a blended line (20,611 cm−1) have been observed.

Hyperfine structure measurements of neutral atomic iodine (127I) in near infrared and visible regions

Hyperfine structure (hfs) investigations were performed on neutral atomic iodine (II) in the near-infrared and visible spectral regions. Fourier transform spectroscopy to investigate the emission spectrum of a microwave driven electrodeless discharge lamp operated in a mixture of iodine vapor and Ne gas. In the present investigations, the observation of 240 hyperfine resolved spectral lines were reported. Hfs analysis was carried out on 128 spectral lines for the first time and repeated on 49 spectral lines. The magnetic dipole constant (A) and electric quadrupole constant (B) were derived for 100 energy levels. Among the 100 energy levels, A and B constants for 18 levels were presented for the first time.

Spectroscopic study of the 7p1/2 and 7p3/2 states in cesium-133

Doppler free spectroscopy was performed on the 7p1/2 and 7p3/2 states in neutral cesium-133 using a frequency doubled titanium sapphire laser stabilized to a temperature-stabilized ultra-low expansion optical cavity. The absolute frequencies for the centers of gravity of the two states were determined to be cm−1 and cm−1, factors of 500 and 650 better than previously reported measurements, respectively. The magnetic dipole and electric quadrupole constants were measured to be MHz for the 7p1/2 state and MHz and MHz for the 7p3/2 state, which are consistent with previously published values.

Extensive and accurate relativistic calculations of atomic data on the 83Kr I spectrum

We provide an extensive, accurate and complete new spectroscopic data set for many levels belonging to the intermediate perturbing Rydberg series ns[K]J (5 ≤ n ≤ 8), nd[K]J (4 ≤ n ≤ 7) and the autoionizing Rydberg series np[K]J (5 ≤ n ≤ 7) and nf[K]J (4 ≤ n ≤ 5) relative to the ground state 4p6 1S0 for neutral krypton-83 isotope. The data set is composed of the energy levels, the oscillator strengths the radiative transition rates the Landé g-factors, the magnetic dipole and electric quadrupole hyperfine constants. The values of these spectroscopic parameters are calculated in the multiconfiguration Dirac-Hartree–Fock (MCDHF) framework. The calculations are carried out in the active space where the electron correlation effects, contributions from relativistic configuration interaction (RCI), the quantum electrodynamics (QED) effects with transverse photon Breit interaction and vacuum photon polarization, specific mass shift and self-energy corrections are included. In addition, we provide the oscillator strengths and transition rates in Coulomb and Babushkin gauges for the 4p5(2P)4d–4p5(2P)5p, 4p5(2P)5s–4p5(2P)5p, 4p5(2P)6s–4p5(2P)5p, 4p5(2P)4d–4p5(2P)44f, 4p5(2P)5d–4p5(2P)4f, 4p5(2P)5d–4p5(2P)6p, 4p5(2P)7s–4p5(2P)6p, 4p5(2P)4d–4p5(2P)5f, 4p5(2P)5d–4p5(2P)5f, 4p5(2P)6d–4p5(2P)5f, 4p5(2P)7p–4p5(2P)6d and 4p5(2P)8s–4p5(2P)7p transition arrays. Extensive comparisons with other experimental and theoretical data from the reference databases are carried out in order to judge the reliability of our data. These comparisons indicate that our results are accurate. The present spectroscopic data may be useful for line identification in observed spectra as well as modelling and diagnostics of astrophysical and fusion plasmas.

Selective Reflection of Potassium Vapor Nanolayers in a Magnetic Field

The selective reflection of laser radiation from the interface between a dielectric window and the atomic vapors confined in a nanocell of thickness L ≈ 350 nm is used to develop effective Doppler-broadening- free spectroscopy of potassium atoms. A small atomic line width and a relation between the signal intensity and the transition probability allowed us to resolve four lines of atomic transitions responsible for the D1 lines of the 39K and 41K isotopes. Two groups containing four atomic transitions form in an applied magnetic field upon pumping by radiation with circular polarization σ+ or σ–. Different intensities (probabilities) of transitions for the σ+ and σ– excitations are detected in magnetic field B0 ≈ A hfs /μB ≈ 165 G (A hfs is the magnetic dipole constant for the ground state and μB is the Bohr magneton). A substantially different situation is observed at B ≫ B0, since high symmetry appears for the two groups formed by radiation with circular polarization σ+ or σ–. Each group is the mirror image of the other group with respect to the frequency of the 42S1/2–42P1/2 transition, which additionally proves the occurrence of the complete Paschen–Back regime of the hyperfine structure at B ≈ 2.5 kG. A developed theoretical model well reproduces the experimental results. Possible practical applications are described. The results obtained can also be applied to the D1 lines of 87Rb and 23Na.

Second spectrum of Manganese (Mn II), Part I: Fine and hyperfine structure analysis of even-parity levels

We have taken advantage of the existence of some experimental Mn II hyperfine magnetic dipole constant (A) values given in literature with low uncertainties to achieve for a first time an accurate hyperfine structure (hfs) parametric study. The monoelectronic hfs parameter values were extracted in their entirety for the alone stable 55Mn II. For example for 3d44s configuration we obtain: a4s10=198.08 mk and a3d01=17.14 mk. These semi-empirically extracted single-electron parameters were analyzed and compared with ab-initio calculations. In this first part of a global work, devoted particularly to even-parity levels we have at beginning studied a fine structure of two hundred levels, giving their leading eigenvector percentages and their calculated Landé-factor gJ. We present also predicted singlet, triplet and quintet positions of missing experimental levels up to 120000 cm−1, not far from Mn II ionization energy of 126000 cm−1. We close this work by giving predicted values of magnetic dipole hfs constants of all known levels of the most relevant Mn II even-parity configuration: 3d44s, whose splitting is not yet measured.

Hyperfine structure constants for singly-ionized manganese (Mn II) using Fourier Transform Spectroscopy.

We expand on the comprehensive study of hyperfine structure (HFS) in Mn II conducted by Holt et al. (1999) by verifying hyperfine magnetic dipole constants (A) for 20 levels previously measured by Holt et al. (1999) and deriving A constants for 47 previously unstudied levels. The HFS patterns were measured in archival spectra from Fourier transform (FT) spectrometers at Imperial College London and the National Institute of Standards and Technology. Analysis of the FT spectra was carried out in XGREMLIN. Our A constant for the ground level has a lower uncertainty by a factor of six than that of Blackwell-Whitehead et al. (2005b).

Photoionization spectroscopy for laser extraction of the radioactive isotope 177Lu

The hyperfine structure of the 5d6s22D3/2 → 5d6s6p4F5/2 transition of the radioactive isotope 177Lu has been investigated by laser photoionization spectroscopy. Measured spectra permitted the determination of hyperfine magnetic dipole constants and electric quadrupole constants for ground and excited state as well as the isotope shift of the 177Lu isotope. The data obtained were used to confirm the selective photoionization of 177Lu from a neutron-irradiated sample that initially had a natural isotope composition. A concentration for 177Lu of 50 % was achieved, and the photoionization efficiency was estimated as suitable for technological application.

Magnetic dipole and electric quadrupole hyperfine constants for V II 3d4, 3d3 4s and 3d2 4s2J = 1–5 states

Relativistic configuration interaction (RCI) calculations have been done for hyperfine constants and Lande g-values for 69 even parity V II states. Our results are in good agreement with the few recent experimental magnetic dipole results. We suggest that several Lande g-values need to be re-measured. Our electric quadrupole constants seem to be the first ones available. Analysis and methodology improvements include the introduction of an approximate sum rule for hyperfine constants, and a way of producing a more diagonal reference basis function set. The importance of mixing of 3dn−1 4s basis members with near degenerate 3dn or 3dn−2 4s2 is emphasized.

Parametric study of the fine and hyperfine structure for the even parity configurations of atomic niobium

In this work a parametric study of the fine and hyperfine structure (hfs) for the even parity configurations of atomic niobium (Nb I) is presented. A large amount of new experimental data, published during the last decade, have been considered for the fine and hfs analysis. A multi-configuration fit of 14 configurations have been performed by taking into account second-order of perturbation theory including the effects of closed shell-open shell excitations. Predicted values of level energies as well as magnetic dipole and electric quadrupole hfs constants of A and B are listed, if no experimental values are available.

Determining the hyperfine structure constants of caesium 8S1/2 state aided by atomic coherence

High-sensitivity spectroscopy of caesium's higher excited 8S1/2 state is obtained by a coherent two-photon transition via an intermediate resonance state. The ladder-type atomic system is driven by two counter-propagating low-power diode lasers, the probe laser being tuned to the transition from the ground state to the intermediate state (6S1/2–6P1/2), and the coupling laser to that between the intermediate and the final state (6P1/2–8S1/2). By locking the probe laser and scanning the coupling laser, the electromagnetically induced transparency (EIT) peaks appear in the probe transmission when the coupling laser resonates with each of the hyperfine levels. Compared with conventional EIT, where the signal-to-noise ratio is limited by the absorptive Doppler background, here these narrow-linewidth peaks have no Doppler background. The peak centres are well determined from theoretical fits to the experimental data. To accurately measure the 8S1/2 hyperfine structure splitting, we developed a simple method to eliminate error arising from the nonlinear frequency scanning by employing an optical waveguide phase modulator and a confocal Fabry–Perot cavity. The hyperfine structure constants of the caesium 8S1/2 state are obtained from hyperfine structure splitting measurements. Systematic effects from the ac-Stark and Zeeman shifts are studied. The measured hyperfine magnetic dipole constant A = (219.08 ± 0.12) MHz is consistent with previous results.