The Stark effect in the 6snf Rydberg series of barium

The Stark effect has been studied in the odd-parity 6snf^1,3F₃ Rydberg series of barium with high-resolution laser-atomic-beam spectroscopy. Scalar and tensor polarizabilities have been measured of 6snf¹F₃ levels with n=11–30 and of 6snf³F₃ levels withn = 12 ? 40. The contributions of the adjacent even-parity Rydberg levels to these polarizabilities have been calculated as far as data are available. This results in important additional information on the only partly known 6sng^1,3G₄ series and confirms the perturbation of these series atn = 24 by a 5d7dJ= 4 level. A tentative three-channel quantum-defect-theory analysis of the^1,3G₄ series has been performed. It is shown that reported level energies of the 6snd^1,3D₂ series are systematically 0.14 cm^?1 too high.     

Tensor polarizabilities and lifetimes of levels of the configurations 4f 66s6p and 4f 55d6s2 in samarium I

Stark splittings of 7 levels of the configurations 4f ⁶6s6p and 4f ⁵5d6s² in Sm I were measured by quantum beat spectroscopy in pure electric fields, allowing the determination of tensor polarizabilities. Additionally, the lifetimes of 11 levels of these configurations were determined from time-resolved registration of the exponential decay. From these values the radial integrals I(6p,6s), I(6p,5d), and I(5d,4f) were derived by a parametric analysis. Theoretical values of tensor polarizabilities and lifetimes which were calculated using these radial integrals show good agreement with experimental data of various authors.     

Hyperpolarizabilities of alkaline-earth metal ions Be+, Mg+, and Ca+

The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 223001(2015)] proposed to establish all-optical trapped ion clocks using laser at the magic wavelength for clock transition. To evaluate the high-order frequency shifts in this new scheme of optical clocks, hyperpolarizabilities are needed, but absent. Using the finite field method based on the B-spline basis set and model potentials, we calculated the electric-field-dependent energy shifts of the ground and low-lying excited states in Be+, Mg+, and Ca+ in the field strength range of 0.0-6×10.5 a.u.. The scalar and tensor polarizabilities(α0, α2) and hyperpolarizabilities(γ0, γ2, γ4) were deduced. The results of the hyperpolarizabilities for Be+ showed good agreement with the values in literature, implying that the present method can be applied for the effective estimation of the atomic hyperpolarizabilities,which are rarely reported but needed in experiments. The feasibility of optical trapping of Ca+ is discussed, and the contributions of hyperpolarizabilities to the transition frequency shift for Ca+ in the optical dipole trap are estimated using quasi-electrostatic approximation.     

Observation of giant polarizabilities in atomic sodium Rydberg states

We have observed by quantum beat spectroscopy the Stark effect in a low electric field of highly excited Na nD states (n = 10, 11, 12). The polarizabilities are found to be 10⁶ to 10⁷ time larger than those of atoms in ground or low lying excited states and are in good agreement with theoretical values calculated from a hydrogenic model.     

Saturated absorption Stark spectroscopy of CH3OH with CO2 lasers

The vibration-torsion-rotation spectrum of CH₃OH has been studied by saturated absorption spectroscopy in applied electric fields up to 20 kV/cm, using ¹²C¹⁶O₂ and ¹²C¹⁶O₂ lasers. Frequency offsets for 129 absorption lines were measured relative to the frequency of a fluorescence stabilized reference laser with an accuracy of ±0.5 MHz for 75 lines inside the ±40 MHz tuning range and 2–5% for lines located up to 1.2 GHz outside the tuning range, but Stark tuned into resonance. For 36 lines we obtained fully-resolved Stark spectra, allowing determination of both lower and upper state K. Using this information in combination with information available from optically-pumped FIR laser emission, a total of 44 lines were completely assigned as transitions involving torsional n = 0, 1, 2 and 3 states of the CO stretch. Certain states belonging to n = 1 displayed an anomalous Stark effect which is at present not understood.     

Polarizability of the fine-structure components of low excited states of the F, Cl, and Br atoms

The dynamic scalar, tensor, and pseudovector polarizabilities of the low excited states (ns)⁴ P _J of the F, Cl, and Br atoms (n = 3, 4, and 5, respectively) are calculated for all the levels of the fine-structure multiplets with J = 5/2, 3/2, and 1/2 with the use of the quantum detect Green’s function, proposed earlier.     

Stark spectroscopy of high-lying odd parity levels in atomic samarium

We have performed a series of experiments to observe 11 Stark-induced E1 transitions from the 15650.55 cm^-1 level to higher levels with odd parity in samarium (Sm) with optical double-resonance technique. Five Stark-induced E1 transition to the 28233.08, 28613.22, 28913.97, 29041.31 and 29130.03 cm^-1 levels have been observed. In order to investigate the contributors to the Stark-induced E1 transition, we have measured scalar and tensor polarizabilities for the observed Stark-induced E1 transitions. Clear Stark splittings were observed for the levels 28233.08 and 28613.22 cm^-1, and their tensor polarizabilities were determined for each isotope. Scalar polarizabilities were determined for the 28233.08, 28613.22, 28913.97 and 29130.03 cm^-1 levels for the first time. Among them, scalar polarizability for the 28233.08 cm^-1 level was the largest in magnitude and was 3.60(10) x 10³ kHz/(kV/cm)² for Sm. We noticed that both scalar and tensor polarizabilities of the 28233.08 cm^-1 level depend on the isotope; the difference of magnitude of the scalar and tensor polarizabilities between Sm and Sm were remarkably large and were about 10 and 6 percent, respectively.Received: 10 February 2003, Published online: 30 July 2003PACS: 32.60.+i Zeeman and Stark effects - 32.10.Dk Electric and magnetic moments, polarizabilityD. Angom: Present address: Physical Research Laboratory, Navarangpura, Ahmedabad 380 009, India.     

Stark interaction in then s n p z 3 P 1 levels of zinc and cadmium

The tensor polarizabilities of then s n p z ³ P ₁ levels of Zn and Cd were measured using optical double resonance. From the rf-resonance signals in parallel electric and magnetic fields, the following tensor polarizabilities were deduced: Zn,α _ten(4s4pz ³ P ₁)=1.83(8) kHz/(kV/cm)²; Cd,α _ten(5s5pz ³ P ₁)=1.77(8) kHz/(kV/cm)². Theoretical values were calculated using Coulomb approximation. The results were then compared with previous theoretical and experimental values and, in addition, with values for Hg. Theoretical results obtained by a modified Sternheimer method (E.J. Robinson: J. Opt. Soc. Am.59, 782 (1969)) are in better agreement with the experimental values than the results of the Coulomb approximation calculations.     

Stark effect,hyperfine structure and isotope shifts in highly excited states of BaI and CaI

The electric dipole polarizabilities of 9 even-parity barium states (6s8s ¹ S ₀,³ S ₁; 6s7d ¹ D ₂,³ D _1,2; 5d7s ¹ D ₂ and 6p ^{2 3} P _0,1,2) in the interval 33,800–35,800 cm^?1 have been measured with high resolution laser-atomic-beam spectroscopy. Simultaneously, values of isotope shifts and hyperfine coupling constants for theJ=1 states have been obtained. Comparison of the experimental polarizabilities with calculated values as well as inspection of the data on isotope shifts and hyperfine structure from the present and earlier work strongly suggests erroneous assignments of theJ=2 states, with an exception for the 5d 7s ¹ D ₂ state. The influence of an electric field on the 3d ^{2 3} P _0,1,2 states of calcium has also been studied. A marked departure from a quadratic Stark effect has been observed at relatively small field strengths. This can be attributed to the large polarizabilities of neighbouring Rydberg states. The low field data allow the determination of admixtures of Rydberg states into the 3d ^{2 3} P-states as small as 0.02%.     

The stark effect in the 6snf Rydberg series of barium

The polarizabilities of the barium 6snf ³ F ₂ levels with principal quantum numbern ranging from 11 to 40 have been measured in a high resolution laser-atomic-beam experiment. In Coulomb approximation the contributions to the polarizabilities of all known even-parity levels connected with the³ F ₂ levels via the electric dipole operator have been calculated. In this way information on the to a large extent unknown 6sng ³ G ₃ Rydberg series is extracted. The results support earlier observations of a perturbation of this series in betweenn = 18 and 19, but no evidence has been found for a perturbation nearn = 14.     

(n*)6-Dependence of tensor polarizabilities of 6snd 1 D 2 Ba Rydberg states

Tensor polarizabilities of levels of the 6snd¹D₂ Rydberg series between n=15 and n=22 were measured by quantum beat spectroscopy. The tensor polarizabilities depend on the sixth power of the effective principal quantum number, which can be explained by a simple theoretical consideration.     

Stark effect investigations of the 4f 14 6s 6p 3 P 1 and1 P 1 levels of ytterbium

The tensor polarizabilities of the 4f ¹⁴ 6s 6p ³ P ₁ level were investigated for all stable Ytterbium isotopes by the method of optical double resonance. The tensor polarizabilities were deduced from the rf-resonance signals in parallel electric and magnetic fields. The value obtained for the even Yb isotopes is in good agreement with the results derived from the measurements on the odd isotopes. The mean value isα _ten(³ P ₁)0=5.99(34)kHz/(kV/cm)². The tensor polarizability of the 4f ¹⁴ 6s 6p ¹ P ₁ level of¹⁷¹Yb was measured by means of the level crossing technique with parallel electric and magnetic fields. The experimental result isα _ten(¹ P ₁)=?14.3(1.4)kHz/(kV/cm)². This is compared with the prediction of the LS coupling approximation using the experimental data of the³ P ₁ level. Only poor agreement is obtained which is due to the configuration mixing in the¹P₁ level.     

A comparison of density-functional-theory and coupled-cluster frequency-dependent polarizabilities and hyperpolarizabilities

The frequency-dependent polarizabilities and hyperpolarizabilities of HF, CO, H₂O and para-nitroaniline calculated by density-functional theory are compared with accurate coupled-cluster results. Whereas the local-density approximation and the generalized gradient approximation (BLYP) perform very similarly and overestimate polarizabilities and, in particular, the hyperpolarizabilities, hybrid density-functional theory (B3LYP) performs better and produces results similar to those obtained by coupled-cluster singles-and-doubles theory. Comparisons are also made for singlet excitation energies, calculated using linear response theory.     

Electronegativity and tetragonal distortions in AIIBIVCV2 semiconductors

Empirical correlations are established between the tetragonal distortions 2-c/a and dielectrically defined electronegativities based on polarizabilities of AⁿB^8-n compounds. Optical data, including the birefringence parameter δn = n_e - n_o, are summarized. No simple relation is found to exist between δn and the principal optical gaps and tetragonal distortions of seven chalcopyrite compounds.     

Probabilities of radiative dipole transitions of parahelium in an electric field

Quadratic Stark corrections to the wave functions, matrix elements, and probabilities of transitions between the singlet states ¹ S ₀ and ¹ P ₁ of helium atoms are calculated. The coefficients of the polynomials that depend on the effective principal quantum number of the upper level v _f and that approximate the numerical values of the polarizabilities, the quadratic corrections to the wave functions, and the probabilities of transitions to highly excited Rydberg states with large v _f are determined. The results of calculations testify that the probabilities of all σ transitions n _i ¹ S ₀ → n _f ¹ P ₁ and π transitions to the states with n _f > n _i /2 are decreased with increasing electric field strength, except for the transition 2¹ S ₀ → 2¹ P ₁, whose probability increases both for σ and for π transitions.     

Tensor polarizabilities of levels of the configurations 4f 13 6s6p and 4f 12 5d6s 2 in thulium I

The level-crossing technique with parallel electric and magnetic fields was used to measure the tensor polarizabilities of six levels of the configuration 4f ¹³ 6s6p + 4f ¹² 5d6s ² in the Tm I-spectrum. Using intermediate coupling wave functions given by Camus and the experimental values of the tensor polarizabilities, the radial integrals for electric dipole transitions from levels of the configuration 4f ¹³6s6p + 4f ¹²5d6s ² to levels of the configuration 4f ¹³ 5d6s + 4f ¹² 6s ²6p have been determined. The results areI(4f ¹³6s6p,4f ¹³5d6s)=1.98(45)ea ₀ andI(4f ¹²5d6s ²,4f ¹²6s ²6p) = 0.88(25)ea ₀. A comparison between the experimental and the calculated values of the tensor polarizabilities shows an excellent agreement, provided that these radial integrals and the radial integrals for the electric dipole transitions to the ground state configuration 4f ¹³6s ² as determined by Wallenstein from lifetime measurements are used in the calculation, instead of radial integrals computed by Camus with Hartree-Fock wave functions.     

MO analysis of the high statistics Belle results on γ γ→π + π −, π 0 π 0 with chiral constraints

We reconsider Muskhelishvili–Omnès (MO) dispersive representations of photon–photon scattering to two pions, motivated by the very high statistics results recently released by the Belle collaboration for charged as well as neutral pion pairs and also by recent progress in the determination of the low-energy π π scattering amplitude. Applicability of this formalism is extended beyond 1 GeV by taking into account inelasticity due to  $K\bar{K}$ . A modified MO representation is derived which has the advantage that all polynomial ambiguities are collected into the subtraction constants and have simple relations to pion polarizabilities. It is obtained by treating differently the exactly known QED Born term and the other components of the left-hand cut. These components are approximated by a sum over resonances. All resonances up to spin two and masses up to ?1.3 GeV are included. The tensor contributions to the left-hand cut are found to be numerically important. We perform fits to the data imposing chiral constraints, in particular, using a model independent sum-rule result on the p ⁶ chiral coupling c ₃₄. Such theoretical constraints are necessary because the experimental errors are dominantly systematic. Results on further p ⁶ couplings and pion dipole and quadrupole polarizabilities are then derived from the fit. The relevance of the new data for distinguishing between two possible scenarios of isospin breaking in the f ₀(980) region is discussed.     

Detection and study of Rb I Rydberg states

We describe the details of an experiment using an atomic beam of rubidium which allowed us to detect by field ionization techniques the np Rydberg states from n = 28 up to n = 78, to detect also ns and nd states using a Stark mixing, and for all of these detected states to check the classical law E_c = [16n^*4]^?1 concerning the critical ionizing electric field E_c. It turns out that for n as high as 65 this law is quite well verified.     

Tensor hyperpolarizability of the 6 s 19 d1D2 barium rydberg state

Tensor polarizability and tensor hyperpolarizability of the 6s19d¹D₂ Rydberg state of Barium were derived from Stark splittings measured by quantum beat spectroscopy. The hyperpolarizability appearing in the fourth order contribution of the perturbation expansion was expressed in spherical tensor form. Using Coulomb approximation numerical values were calculated which are in fair agreement with experimental results.     

Spectra of direct excitation of phosphorescence in an isotopic mixed naphthalene crystal

Distributed polarizabilities of a series of n-alkanes C _n H_2n+2 (n = 2-7) in various conformations have been determined using Bader's topological theory of atoms in molecules. Using an appropriate localization scheme, a simple distributed model is constructed, where the methyl and methylene groups are characterized by their dipole polarizability tensors in local frames, and all charge flow polarizabilities between them are retained. A set of average polarizability parameters is proposed that takes into account the local environment of the methyl and methylene groups, and that not only reproduces the polarizability tensor for any member of the n-alkane series in an arbitrary conformation, but also is suitable for the calculation of induction energies.