Test of advanced hyperfine structure theory by precision radio-frequency and laser spectroscopy in molybdenum

The hyperfine structure splittings of 32 even parity states and of 26 odd partity states of molybdenum have been measured by atomic beam magnetic resonance and by laser induced fluorescence. The analysis of the hyperfine structure data of the even parity configurations (4d+5s)⁶ yields experimental evidence for second order hyperfine interactions. In addition, theg _J factors of 19 fine structure levels have been determined in order to test the quality of intermediate coupling wave functions for the (4d+5s)⁶ configurations.     

Hyperfine structure in 5s 4d 3 D —5snf transitions of87Sr

The hyperfine spectra of the 5s4d ³ D ₁-5s20f, 5s4d ³ D ₂-5s23f, and 5s 4d ³ D ₃-5s32f transitions of⁸⁷Sr (I=9/2) have been measured by collinear fast beam laser spectroscopy. The structure in the upper configurations is highly perturbed by fine structure splitting that is of comparable size to the hyperfine interaction energy. These perturbations can be adequately treated with conventional matrix diagonalization methods, using the 5s-electron magnetic dipole interaction terma _5s and the unperturbed fine structure splittings as input parameters. Additionally, hyperfine constants for the lower 5s4d ³ D configurations, including theA- andB-factors and a separation of the individuals- andd-electron contributions to these factors, are derived.     

Hyperfine structure in the configurations 4f 13 6s6p and 4f 125d6s 2 of TmI

The laser-atomic-beam spectroscopy has been used to make precise measurements of the hyperfine structure in transitions starting from metastable states of the configuration 4f ¹²5d6s ² in¹⁶⁹TmI. With the resulting experimental magnetic dipole hyperfine constantsA _J andA _J values from former investigations a parametric analysis of the hyperfine structure in the configurations 4f ¹³6s6p and 4f ¹²5d6s ² has been performed using wavefunctions from fine structure calculations. A comparison of theoretical and experimental hyperfine constants allowed a test of the reliability of the wave-functions used. The hyperfine parameters respectively hyperfine radial integrals determined from the analysis were compared with corresponding data from ab initio calculations for the ground configuration in TmI.     

Hyperfine structure measurements in tantalum I using laser saturation spectroscopy in a sputtered vapour

Magnetic hyperfine interaction constants (A factors) and electric quadrupole interaction constants (B factors) have been determined for sixteen levels in tantalum I using the method of saturated absorption spectroscopy in a sputtered vapour. Five of these levels belong to the lowest configuration 5d ³ 6s ² which has been studied previously by other workers, and for one of these levels, thea ⁴ P _5/2 at 9253 cm^?1, our results are new. For the eleven levels belonging to the excited configurations 5d ³ 6s 6p and 5d ² 6s ² 6p our values are the first data reported in the literature.     

Hyperfine structure in the configuration 4f 115d6s 2 of Er I

Hyperfine constants of low lying levels of the configuration 4f ¹¹5d6s ² in Er I have been measured for the only stable odd isotope,¹⁶⁷Er, using high resolution laseratomic-beam spectroscopy. Hyperfine parameters were evaluated from the experimental data using the effective tensor operator formalism. For this purpose eigenfunctions have been determined from an analysis of the fine structure energies of Er I as well as from ab initio multiconfiguration Dirac-Fock calculations. With the latter method also ab initio hyperfine constants for the levels investigated were evaluated. A comparison of calculated fine structure energies, Landég _J -factors and hyperfine constants with the experimental data allowed a test of the reliability of the fine structure and multiconfiguration Dirac-Fock wavefunctions. Effective nuclear electric quadrupole moments for¹⁶⁷Er have been determined from the experimental hyperfine constants using both calculated relativistic electronic radial integrals and hyperfine parameters for the 4f and 5d electrons in the configuration 4f ¹¹5d6s ² in Er I. From a comparison with the nuclear quadrupole moment measured in the mesic atom Sternheimer shielding factors are calculated. Configuration-interaction contributions to the radial integrals 〈r ^?3〉 _nl ⁰¹ of the 4f and 5d electrons have been determined.     

Hyperfine structure measurements of the metastable (3d 6 4s 2)3 H 4, 5, 6 states of57Fe: Configuration interaction in the hyperfine structure of the iron atom

We report the hyperfine structure (hfs) measurement of the metastable (3d ⁶ 4s ²)a ³ H _{4, 5, 6} states of⁵⁷Fe. The kHz-precision of these experimental results together with the hyperfine structure values of (3d ⁶ 4s ²)a ⁵ D _{1, 2, 3, 4}, (3d ⁷ 4s)a ⁵ F _{2, 3, 4, 5}, and (3d ⁷ 4s)a ³ F _{2, 3, 4}, which were measured earlier, allowed to determine a very detailed set of effective radial parameters describing the hfs of these states, using a new parametrization method. This method treats one- and two-body contributions to the hfs separately. In this way configuration interaction effects in the hfs of the⁵⁷Fe atom can be studied in detail and compared with configuration interaction effects in the fine structure of the same atom.     

Laser and radio-frequency spectroscopy of the 5d 36s 2 4 P 3/2,5/2 states in Ta I

The hyperfine structure of the metastable atomic states 5d ³6s ^{2 4} P _3/2 and⁴ P _5/2 in¹⁸¹Ta has been studied using high resolution laser spectroscopy and laser radio-frequency double-resonance methods.     

Investigations of hyperfine structure and isotope shift predictions in Hf II

The fine structure of the even‐parity low configurations of singly ionized hafnium has been reanalyzed by simultaneous parameterization of the one‐ and two‐body interactions for the model space (5d + 6s)³. Using the calculated eigenfunctions, the magnetic‐dipole A hyperfine constants for the whole 37 existing levels of the model space were predicted and compared partially with those obtained using relativistic configuration‐interaction approach. Moreover, combined with experimental data, previously given in the literature, and pseudo‐relativistic Hartree–Fock estimates, the field shifts (FSs) and specific mass shifts (SMSs) of numerous configurations are deduced: FS(5d¹6s²) = 2265 MHz, FS(5d³) = ?1958 MHz, FS(5d¹6p²) = ?1696 MHz, FS(6s²6p¹) = 3135 MHz, and SMS(5d¹6s²) = ?78 MHz, SMS(5d³) = 64 MHz, SMS(6s²6p¹) = ?228 MHz, referred to 5d²6s for the pair ¹⁷⁸Hf–¹⁸⁰Hf. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Hyperfine structure and isotope shift of some even parity levels in the YbI spectrum

Using laser induced fluorescence spectroscopy the hyperfine structure of the even parity levels 4f ¹⁴6s6d ³ D ₁, 4f ¹⁴ 6s8s ³ S ₁ and 4f ¹³ 5d6s6p (7/2, 5/2)J=1,2,3 as well as of the odd parity level 4f ¹⁴ 6s6p ³ P ₂ in neutral ytterbium has been investigated. The isotope shift of the transitions 4f ¹⁴6s6p ³ P ₀ → 4f ¹⁴ 6s6p ³ D ₁ and 4f ¹⁴ 6s6p ³ P ₂ → 4f ¹⁴ 6s8s ³ S ₁, 4f ¹³ 5d6s6p (7/2, 5/2)J=1,2,3 could be measured with high accuracy. The results for the 4f ¹⁴ 6s6p ³ D ₁ level show a considerable influence of second order effects of the hyperfine interaction. The isotope shifts of the 4f ¹⁴ 6s8s ³ S ₁ and 4f ¹³ 5d6s6p (7/2, 5/2)J=1 levels indicate a possible configuration mixing for these levels.     

Laser and radiofrequency spectroscopy of the 5d 4 6s 6 D multiplet in Ta I

The hyperfine structure (hfs) of¹⁸¹Ta has been investigated using laser radio-frequency double resonance and high resolution laser spectroscopy on collimated atomic beams. The magnetic dipole and electric quadrupole hyperfine structure coupling constants of the 5d ^{4 6} s 6D _{3/2, 5/2, 7/2, 9/2} metastable states have been determined using radio-frequency spectroscopy. In the 5d ⁴ 6s ⁶ D _1/2 metastable state and the excited 5d ³ 6s 6p ⁴ D _3/2,⁶ D _{5/2, 9/2} as well as the unidentified 28 182.6 cm^–1 and 30 021.2 cm^–1 states, hfs constants have been obtained from high resolution laser spectroscopy. A radio-frequency converter has been developed in order to reach the frequency region 2.7–10 GHz.     

New levels and calculations in the Nd I spectrum

The energies of all the levels of Nd I 4f ⁴ 6s ^{2 5} F and of⁵ S ₂ as well as of 4f ⁴ 5d 6s ⁷ H ₂ have been determined by means of laser-induced fluorescence in a hollow cathode. Their interpretation was carried out with the use of hyperfine structure data and a new parametric calculation of (4f ⁴ 6s ² + 4f ⁴ 5d 6s). Furthermore, the energies andJ values of 5 new odd levels were found.     

Experimental and theoretical study of the hyperfine structure in the (5d+6s)96p configurations of Pt I

The hyperfine structure of the odd configurations 5d ⁹6p and 5d ⁸6s6p was studied with laser optogalvanic spectroscopy and high resolution interferometry in a platinum hollow cathode. A parametric hyperfine structure analysis for the configurations (5d+6s)⁹6p with 10 excited odd-parity levels was performed for¹⁹⁵Pt. We obtained one-electron hfs parameters,a _5d ⁰¹ =1160(320) MHz,a _6s ¹⁰ =35600(5300) MHz anda _6p ⁰¹ =1300(780) MHz for the configuration 5d ⁸6s6p. The corresponding $\left\langle {r^{ - 3} } \right\rangle _{nl}^{k_s k_l } $ values are compared with those known for other 5d-elements.     

Isotope shift in hafnium I: Parametric analysis,ab initio calculation,and changes in nuclear charge radii

The isotope shift in the arc spectrum of hafnium was studied in 10 lines for the isotopes¹⁷⁶Hf,¹⁷⁸Hf, and¹⁸⁰Hf by means of a photoelectric recording Fabry-Perot spectrometer with digital data processing. The observed shifts together with results from an earlier study were analyzed by means of the parametric method. The field shift difference between the terms 5d ³(⁴ F) 6s ⁵ F and³ F resulted in 17(2) mK for the isotope pair^178,180Hf. This reflects the influence of a second-order effect which is described by the parameterg ₂=?4.4(6) mK. The parameterz _5d , displaying the magnitude of spin-dependent effects in the isotope shift of 5d ³6s, was found to be 0.8(2) mK for the same isotope pair. The experimental data are compared with results obtained from the non-relativistic Hartree-Fock method. The calculated electron densities describe the experimental field shifts with good accuracy. Hartree-Fock screening ratios for various types of transitions were used to evaluate changes in mean-square nuclear charge radii. The mean value ofλ ^178,180≈δ〈r ²〉^178,180 equals 0.069(10) fm².     

Hyperfine structure in the configurations4f 4 6s 2 and4f 4 5d 6s of Nd I

The high resolution laser-atomic-beam technique was used to investigate the hyperfine structure in Nd I 4f ⁴6s ^{2 5} I,⁵ F,⁵ S and 4f ⁴5d6s ⁷ L,⁷ K,⁷ I,⁷ H. The metastable states were populated by an arc discharge burning in the atomic beam. The measured hyperfine constantsA andB of the levels of 4f ⁴6s ² and 4f ⁴5d6s allow a parametric analysis to be performed using the effective tensor operator formalism. The experimental radial integrals of the 4f and 5d electrons fit with those of the other lanthanides. The 4f radial integrals are in agreement with values of optimized Hartree-Fock-Slater calculations. The spectroscopic quadrupole moments of¹⁴³Nd and¹⁴⁵Nd are deduced from the 4f parameters:Q _I =?0.610(21) b and ?0.314(12) b, respectively. TheQ _I resulting from the 5d parameter are in satisfactory agreement with these values. The hyperfine anomaly due to thes electron in 4f ⁴5d 6s amounts to about 1%.     

Hyperfine structure investigation on the (3d 4)3 G 4,5 levels of47Ti

Using two-step laser spectroscopy with the sideband technique the hyperfine structure (hfs) splittings of the levels (3d ⁴)³ G _4,5 in⁴⁷Ti have been measured. These are the first hfs measurements of the levels belonging to the 3d ^N+2 configuration of the system (3d+4s) ^N+2. The experimental results indicate a strong increase of the core polarization effect due to excitation of both 4s-electrons to the open 3d-shell.     

High resolution spectroscopy of iridium in a hollow cathode discharge

We demonstrate the possibility of performing high resolution laser spectroscopy of iridium atoms produced by sputtering in a hollow cathode discharge. By resolving the hyperfine structure of ultraviolet transitions from the ground state, we measure the magnetic dipole and electric quadrupole constants of the 5d ⁷ 6s 6p ⁶ G _11/2 and 5d ⁷ 6s 6p ⁶ F _7/2 excited levels and we obtain accurate values for the isotope shifts. Iridium is also discussed as possibly providing reference spectra in the 243 nm region, close to the wavelength of the 1s–2s two-photon transition of hydrogen.     

Isotope shifts and hyperfine structures investigation of doubly excited levels in SrI

We measured isotope shifts and hyperfine structure of visible transitions of stable strontium isotopes by means of Doppler-free saturated absorption spectroscopy. In particular, we investigated transitions between excited states where the upper level involves two excited electrons. We report hyperfine coupling constants for the levels 5p4d¹D₂, 5p4d³F₂, 5s4d³D₁, 5s6s³S₁, 5s5p³P₁ and, for some of the studied transitions, we separate the specific mass and volume contribution to the isotope shifts.     

On the hyperfine structure in the configurations 4f n 6s 2, 4f n 5d6s, 4f n 6s6p,and 4f n−15d6s 2 of the lanthanides

A survey of hyperfine analyses in the low-lying configurations 4f ⁿ 6s ², 4f ⁿ 5d6s, 4f ⁿ 6s6p, and 4f ^n?1 5d6s ² of the lanthanides is given. Experimental hf radial integrals 〈r ^?3〉 _nl ^kj are indicated for the configurations under investigation. From a comparison of experimental and theoretical hf radial integrals configuration-interaction contributions Δ _nl ^kj to the hfs have been evaluated for the configurations for which corresponding integrals were available. With nuclear electric quadrupole moments from muonic x-ray investigations and radial integrals 〈r ^?3〉 _nl ⁰¹ and 〈r ^?3〉 _nl ⁰² from experimental hfs quadrupole shielding correctionsR _nl ⁰¹ have been obtained. The variation of hyperfine radial integrals, configuration-interaction contributions and quadrupole shielding corrections over the 4f shell in the configurations under study is discussed. Trends of these quantities in different configurations are compared.     

Hyperfine structure investigations of the tantalumI blend λ=6356.14 Å

The TaI line 6356.14 Å, up to now classified as the transition 5d ³6s ² a ⁴ P _5/2?5d ³6s(a ⁵ F)6p z ⁴ F ₇ ^2/0 , is a blend with a second transition, which is related to the additional levels 5d ⁴(b ³ G)6s a ⁴ G _9/2?39641.24 cm^?1 J=7/2°. Using laser excitation with optogalvanic and laser-induced fluorescence detection, the hyperfine constants of the four levels involved and the distance of the center wavelengths of the two fine structure transitions could be determined.