Hyperfine structure of the ground state muonic <Superscript>3</Superscript>He atom

On the basis of the perturbation theory in the fine structure constant α and the ratio of the electron to muon masses we calculate one-loop vacuum polarisation and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of the muonic helium atom (μ e ³ ₂He). We obtain total results for the ground state hyperfine splitting Δ ν ^hfs = 4166.648 MHz which improves the previous calculation of Lakdawala and Mohr due to new corrections of orders α ⁵ and α ⁶. The remaining differences between our theoretical result and experimental value of the hyperfine splitting lie in the range of theoretical and experimental errors and require the subsequent investigation of higher order corrections.     

TDPAD measurements of magnetic hyperfine field for <Superscript>132</Superscript>Ba in ferromagnetic Ni

The magnetic hyperfine field of Ba in ferromagnetic Ni has been measured by time differential perturbed angular distribution technique using the 13 ns 10⁺ isomeric state in ¹³²Ba as probe which was populated in the reaction ¹²C(¹²⁴Sn, 4n) ¹³²Ba at beam energy of 60 MeV. The hyperfine field extracted from the observed Larmor precession frequency comes out to be ?84(5) kG. Our experimental results show good agreement with theoretical calculations performed within local density approximation of the density functional theory. The hyperfine field data presented here would be useful towards accurate determination of g-factor in other high spin states in Ba isotopes.     

Hyperfine-structure studies of the 1s<Superscript>2</Superscript>2snp (n=2, 3) <Superscript>3</Superscript>P states for the beryllium isoelectronic sequence

The hyperfine structure parameters of the 1s²2snp (n=2, 3) ³P states for the beryllium isoelectronic sequence from Z= 4 to 10 are calculated with the full-core plus correlation (FCPC) wave functions. For the 1s²2s2p ³P state of the beryllium atom, the calculated fine structure parameters are in good agreement with the latest theoretical and experimental data in the literature. It is shown that hyperfine constants of the low-lying excited states for the beryllium atom can be calculated accurately using this theoretical method. For 1s²2snp (n=2, 3) ³P states of the beryllium isoelectronic sequence, our predictions may provide valuable reference data for other theoretical calculations and experimental measurements in future.     

Hyperfine magnetic anomaly in isotopic pairs <Superscript>151, 152</Superscript>Eu and <Superscript>152, 153</Superscript>Eu

High-resolution laser spectroscopy measurements of optical hyperfine splitting on the ^{151, 152, 153}Eu isotopes were performed on the atomic transition 4f ⁷6s ^{2 8} S _7/2 → 4f ⁷6s6p ⁶ P _5/2 at λ ≈ 564.58 nm. Values of the nuclear magnetic dipole and electric quadrupole moments are obtained from the measured hyperfine splitting and the magnetic hyperfine anomalies in the isotope pairs ^{151, 152}Eu and ^{152, 153}Eu are deduced. The absolute values of the hyperfine anomaly in both cases are unusually large: 5 (1)%. The possible sources causing these anomalies are discussed.     

On the hyperfine structures of the ground state(s) in the <Superscript>6</Superscript>Li and <Superscript>7</Superscript>Li atoms

The hyperfine structure of the ground 2²S-states of the three-electron atoms and ions is investigated. By using our recent numerical values for the doublet electron density at the atomic nucleus, we determine the hyperfine structure of the ground (doublet) 2²S-state(s) in the ⁶Li and ⁷Li atoms. Our predicted values (228.2058 and 803.5581 MHz, respectively) agree well with the experimental values 228.20528(8) MHz (⁶Li) and 803.50404(48) MHz (⁷Li [R.G. Schlecht and D.W. McColm, Phys. Rev. 142, 11 (1966)]). The hyperfine structures of a number of lithium isotopes with short lifetimes, including ⁸Li, ⁹Li, and ¹¹Li atoms are also predicted. The same method is used to obtain the hyperfine structures of the three-electron ⁷Be⁺ and ⁹Be⁺ ions in their ground 2²S-states. Finally, we conclude that our approach can be generalized to describe the hyperfine structure in the triplet n³S-states of the four-electron atoms and ions.     

Many-body effects in hyperfine interactions in <Superscript>205</Superscript>Pb<Superscript>+</Superscript>

Ab initio calculations have been carried out to study the magnetic dipole and electric quadrupole hyperfine structure constants of ²⁰⁵Pb⁺. Many-body effects have been considered to all orders using the relativistic coupled-cluster theory in the singles, doubles and partial triples approximation. The trends of these effects are found to be different from atomic systems that have been studied earlier.     

Effective regime of electromagnetically induced transparency in a Pr<Superscript>3+</Superscript>:LaF<Subscript>3</Subscript> crystal

The results of experimental and numerical investigations of electromagnetically induced transparency in a Pr³⁺:LaF₃ crystal have been presented. A spectrally isolated Λ system has been made of a specially prepared medium of an ensemble of particles with an inhomogeneous width less than the hyperfine splitting of both upper and lower operating levels. A considerable increase in the transmittance with respect to an unprepared medium has been demonstrated. It has been shown that, under the experimental conditions, the transmittance is limited by the apparatus (spread of the transmission peak by the instrumental linewidth specified by the probe pulse length).     

Qubits based on spectrally selected groups of Pr<Superscript>3+</Superscript> ions in a LaF<Subscript>3</Subscript> crystal

Spectral selection, i.e., the separation of a group of particles with a spread in resonance frequencies smaller than the hyperfine splitting of working levels has been implemented by the method of burning of long-lived spectral dips in the inhomogeneously broadened absorption line of Pr³⁺ in a LaF₃ crystal. The possibility of implementing qubits (basic elements of quantum computations) on ensembles of spectrally selected particles and the main operations with them, including the manipulation of the populations of hyperfine (qubit) levels and the controlled shift of the absorption line of one spectrally selected group of ions upon excitation of another group (two-qubit operations), has been demonstrated. The decay rates of the population of hyperfine sublevels of the ground state of the spectrally selected group of particles have been measured.     

Observation of sympathetically cooled <Superscript>43</Superscript>Ca<Superscript>+</Superscript> ions in a linear ion trap

We report the observation of sympathetically cooled ⁴³Ca⁺ (natural abundance 0.135%) in a linear ion trap utilizing simultaneously trapped isotope ions as coolant. We investigated different possibilities of realizing efficient sympathetic cooling and observed the peaks of the hyperfine transitions of ⁴³Ca⁺ under various experimental conditions.     

High-frequency EPR of Tb<Superscript>3+</Superscript>-doped KPb<Subscript>2</Subscript>Cl<Subscript>5</Subscript> crystal

High-frequency electron paramagnetic resonance (EPR) spectra of the KPb₂Cl₅:Tb³⁺ crystal have been investigated. Three types of spectra were observed in the frequency range of 74–200 GHz. The most intensive spectrum with the resolved hyperfine structure corresponded to transitions between sublevels of the¹⁵⁹Tb³⁺ ground quasi-doublet with the zero-field splitting (ZFS) close to 48 GHz. Experimental results were analyzed by the exchange charge model of the crystal field affecting terbium ions in low-symmetry Pb²⁺ positions with the chlorine sevenfold coordination and the charge compensating vacancy in the nearest potassium site. The calculated values ofg-factors and ZFS were in agreement with the experimental data. The nature of a broad EPR line with ZFS of about 180 GHz and of additional weak EPR lines observed as satellites of the main Tb³⁺ lines was discussed.     

Temperature Dependence of <Superscript>1</Superscript>H and <Superscript>17</Superscript>O NMR Shifts of Water: Entropy Effect

Density functional theory together with statistical thermodynamics based on the equilibrium constants method and concept of orientational entropy were applied to reproduce the temperature dependences of ¹H and ¹⁷O nuclear magnetic resonance (NMR) chemical shifts in liquid water. Despite a rather simple theoretical model, a satisfactory agreement between calculated NMR quantities and corresponding experimental data was found. By using only a single adjustable parameter of arbitrary directionality, we succeeded to imitate the first-order temperature effect for both (¹H and ¹⁷O) NMR signals in the neat water. ¹H and ¹⁷O magnetic shielding tensors of water molecules in various water clusters have been calculated using the density functional theory. The full geometry optimization was performed using Becke's three-parameter hybrid method and the Lee–Yang–Parr correlation functional (B3LYP) combined with 6-311++G^** basis set. Magnetic shielding tensors have been calculated using the modified hybrid functional of Perdew, Burke and Ernzerhof, and the gauge-including atomic orbital approach was applied to ensure gauge invariance of the results. Solvent effects were taken into account by the polarized continuum model. Authors' address: Vytautas Balevicius, Faculty of Physics, Vilnius University, Sauletekio 9, Vilnius 10222, Lithuania     

Photonuclear Reactions on Bypassed Nuclei <Superscript>84</Superscript>Sr and <Superscript>92</Superscript>Mo

The yields of photonuclear reactions on mixtures of natural isotopes of strontium and molybdenum that result in the formation and decay of bypassed nuclei ⁸⁴Sr and ⁹²Mo are measured and compared to theoretical results obtained using the TALYS code and calculations in the combined model of photonucleon reaction (CMPR). The need is demonstrated to consider isospin splitting in cases of photoproton reactions. The yields of the ⁹²Mo(γ,p)⁹¹mNb, ⁸⁴Sr(γ,p)⁸³Rb reactions that make the main contribution to the formation and decay of ⁸⁴Sr and ⁹²Mo in the p-process of nucleosynthesis differ from the TALYS and CMPR results by several hundred percent.     

Experimental search for laser-induced effects in <Superscript>151</Superscript>Eu and <Superscript>57</Superscript>Fe doped crystals

We studied the Mössbauer effect in ¹⁵¹Eu and ⁵⁷Fe doped crystals in the search for laser-induced effects caused by changes in the hyperfine interaction due to electronic excitation. The Mössbauer spectra observed in the presence of laser radiation demonstrated a notable change of the shape of the ¹⁵¹Eu spectrum and the appearance of an additional hyperfine pattern in the case of the ⁵⁷Fe Mössbauer resonance.     

Hyperfine structure and absolute frequency measurements of <Superscript>127</Superscript><Emphasis Type="Italic">I</Emphasis><Subscript>2</Subscript> transitions with monolithic Nd:YAG 561-nm lasers

The precision hyperfine structures of the ¹²⁷ I ₂ transitions at 561.4 nm are measured by the heterodyne beat between two home-made ¹²⁷ I ₂-stabilized Nd:YAG lasers. The theoretical distributions of the observed transitions’ hyperfine sublevels are used to identify the two transitions. High-accuracy hyperfine constants are obtained by fitting the measured hyperfine splittings to the four-term Hamiltonian, which includes the electric quadruple, spin-rotation, tensor spin–spin and scalar spin–spin interactions. The absolute frequencies of the observed four transitions are measured by an optical frequency comb based on a mode-locked erbium-fiber laser.     

Radiative and interelectronic-interaction corrections to the hyperfine splitting in highly charged B-like ions

The ground-state hyperfine splitting values of high-Z boronlike ions are calculated. Calculation of the interelectronic-interaction contribution is based on a combination of the 1/Z perturbation theory and the large-scale configuration-interaction Dirac-Fock-Sturm method. The screened QED corrections are evaluated utilizing an effective screening potential approach. Total hyperfine splitting energies are presented for several B-like ions of particular interest: ⁴⁵Sc¹⁶⁺, ⁵⁷Fe²¹⁺, ²⁰⁷Pb⁷⁷⁺, and ²⁰⁹Bi⁷⁸⁺. For lead and bismuth the experimental values of the 1s hyperfine splitting are employed to improve significantly the theoretical results by reducing the uncertainty due to the nuclear effects.     

<Superscript>55</Superscript>Mn spin relaxation with the participation of mobile carriers in doped perovskites

Analytical expressions are derived for the rates of longitudinal and transverse nuclear spin relaxation under conditions of fast modulation of the magnitude and direction of a hyperfine field induced by unpaired electrons of an ion. The results obtained are used to explain the data available in the literature on the ⁵⁵Mn spin relaxation in the ferromagnetic metallic phase of doped perovskites, in which the modulation of the hyperfine field is caused by the hopping of e _g electrons between Mn³⁺ and Mn⁴⁺ ions. It is demonstrated that, within this model, the rates of longitudinal and transverse relaxation are characterized by the same temperature dependence and their ratio is independent of temperature, which is in agreement with the experimental data.     

Tailored Nitroxide Radicals and Biradical Containing <Superscript>13</Superscript>C Enriched Acetylene Groups: ENDOR and DFT Investigation

A specially synthesized nitroxide biradical R₅-C≡¹³C-(p-C₆H₄)₂-¹³C≡C-R₅ (B4) and two radicals, R₅-C≡¹³CH (RCC) and R₅-C≡¹³C-C₆H₅ (RCCPh), where R₅ is 1-oxyl-2,2,5,5-tetramethyl-pyrroline group, have been studied by X- and W-band electron paramagnetic resonance (EPR) spectroscopy, and by W-band electron-nuclear double resonance (ENDOR). Spin density distribution and hyperfine splitting (hfs) constants on ¹³C atoms were experimentally determined and also calculated using ORCA 3.0.3 program package. The biradical and radicals geometries were optimized on UKS/B3LYP/cc-pVDZ level. Hfs constants were calculated using density functional theory (DFT) with PBE0 functional and N07D, and were compared with the experimental value of the hfs constant on ¹³C atoms, measured from ENDOR spectra. It is concluded that at small values of the exchange integral as J ≤ a/2 ≈ 7–8 G, the current quantum chemical approaches do not allow determining precise values of the hfs constants on the ¹³C atoms in the bridge connecting two paramagnetic nitroxide rings of the biradical.     

Diffractive scattering of <Superscript>7</Superscript>Be and <Superscript>8</Superscript>B nuclei by <Superscript>12</Superscript>C nuclei

A theory of the diffractive scattering of loosely bound three-cluster nuclei by nuclei was developed with allowance for Coulomb interaction. The differential cross sections for the scattering of projectile exotic nuclei ⁷Be and ⁸B by ¹²C nuclei at an energy of 40 MeV per nucleon were calculated within the proposed formalism. The results describe satisfactorily relevant experimental data.     

Data on photoneutron reactions from various experiments for <Superscript>133</Superscript>Cs, <Superscript>138</Superscript>Ba and <Superscript>209</Superscript>Bi nuclei

Basic methods for determining cross sections for photoneutron partial reactions are examined. They are obtained directly in experiments with quasimonoeneregetic annihilation photons or from the cross section for the (γ, xn) = (γ, 1n) + 2(γ, 2n) + 3(γ, 3n) +... neutron-yield reaction in experiments with bremsstrahlung photons by introducing corrections based on statistical nuclear-reaction theory. The difference in the conditions of these experiments, which leads to discrepancies between their results because of sizable systematic errors, is analyzed. Physical criteria are used to study the reliability of data on the photodisintegration of ¹³³Cs, ¹³⁸Ba, and ²⁰⁹Bi nuclei. The cross sections for partial and total reactions satisfying the reliability criteria are evaluated within the experimental–theoretical method (σ^eval(γ, in) = F_i^theor × σ^expt(γ, xn)) on the basis of the experimental cross sections σ^expt(γ, xn) and the results of the calculations within the combined model of photonuclear reactions.     

Phase shift analysis of the <Superscript>6</Superscript>He+<Superscript>208</Superscript>Pb and the <Superscript>6</Superscript>He+<Superscript>197</Superscript>Au systems

We present the elastic scattering of the ⁶He+²⁰⁸Pb and the ⁶He+¹⁹⁷Au systems at the laboratory energy of E _lab=27 MeV within the framework of the McIntyre parametrization, and systematically investigate χ ²/N analysis of both systems to obtain an excellent agreement between the theoretical results and the experimental data. We find large diffusivity parameters indicating long range absorption mechanisms. We also show that both systems lack both the nuclear and the Coulomb rainbow scattering for obtained S-matrix parameters.