Contribution of hexadecapole alignment to the polarization of quadrupole emission under laser excitation conditions

The linear polarization of quadrupole emission by the J=2-J ₀=0 transition under conditions of laser excitation in a gas medium is studied. Cases of excitation through dipole and quadrupole absorption of monochromatic laser radiation are considered. Taking into account the anisotropy of collisional relaxation, the contributions of polarization moments of the second and fourth ranks, i.e., those with usual and hexadecapole alignments, to the signal of linear polarization of quadrupole emission are calculated. The dependence of this signal on the laser frequency, the density of the gas medium, and the angles determining the orientation of the system of axes of observation of light polarization relative to a laser ray is studied. The numerical calculations of contributions of usual and hexadecapole alignment to the signal of linear polarization are made for the magnetic quadrupole transition J=2-J ₀=0 between the states 2p ⁵(² P ₁ ^2/0 )3p′[3/2]₂ and 2p ⁵(² P ₁ ^2/0 )3s 3s′[1/2]⁰ of neon atoms in the xenon atmosphere.     

Hyperfine structure measurements in the4 I 9/2 ground state of141Pr

Using the atomic beam magnetic resonance method, the five hyperfine structure separations in the 4f ³ 6s ^{2 4}I_9/2 ground state of ₅₉ ¹⁴¹ Pr have been measured. The results are:F F′ E _FF′ ^* /h (MHz) 7 6 6477.913423(17) 6 5 5556.359848 (6) 5 4 4633.023306 (2) 4 3 3708.201146 (5) 3 2 2782.190601(15) From these quantities, the multipole interaction constantsA _k,k=1, 2, 3, 4 between the nucleus and the electron shell have been calculated.A ₄ especially then served to give the following limit for the intrinsic hexadecapole moment: ¦Q ₄₀¦<0.4eb ². Furthermore, theg _J -factors of the⁴ I multiplet have been measured at magnetic fields of 300 Oe. The results are:g _J(⁴ I _9/2)=0.7310371(15)g _J(⁴ I _11/2)=0.9651476(20)g _J(⁴ I _13/2)=1.1063197(40)g _J(⁴ I _15/2)=1.197963 (30) Small corrections due to perturbations by neighbouring fine structure levels are included.     

Spin-forbidden transitions between 2p 2 and 2s2p states in the beryllium isoelectronic sequence

Fine-structure splittings, wavelengths and transition probabilities are evaluated for transitions 2p ^{2 1} S ₀→2s2p ³ P ₁ ⁰, 2p ^{2 1} D ₂→2s2p ³ P _J ⁰ (J=1, 2) and 2p ^{2 3} P _J →2s2p ¹ P ₁ ⁰ (J =0, 1, 2) in beryllium-like ions using configuration interaction wavefunctions. Some significant differences with previous calculations are obtained. At present there are no experimental results. However, from calculations reported here it should clearly be worthwhile to search for these lines in laboratory and astrophysical spectra. The decay of the 2p ^{2 1} D ₂ level is discussed.     

High resolution Zeeman spectroscopy on the neon levels 2s 2 and 2p 4 by mode crossing at high magnetic fields

Mode crossing signals in laser intensity occur if the Zeeman splitting of one laser level equals the frequency separation between two laser modes. This kind of experiment using two optical frequencies for double resonance yields high resolution in Zeeman spectroscopy and allows very accurate determination ofg _J -values. Mode crossing dips of the 0.633μ, 1.152μ and 1.523μ transitions of the He-Ne-laser in an axial magnetic field were measured by tuning the field strength up to 0.17 Tesla. At this field strength the Zeeman splitting of the Dopplerbroadenedσ-lines corresponds to approximately 6 Gcps. The frequency separation between resonant modes was controlled by means of a scanning high resolution Fabry-Perot. The experimental results for theg _J -values areg _J =1.2211±0.002 for the Ne 2s ₂ level andg _J =1.3008±0.002 for the Ne 2p ₄ level. A pressure inducedg _J -shift of aboutΔg _J /(g _J ×p _He)=?1.6×10^?3/Torr for the 2p ₄ level has been observed. The influence of helium collisions disturbing the Zeeman splitting of the 2p ₄ state is discussed.     

Neon 3p-excitation by proton impact (100 keV-1 MeV): Cross sections and line polarization

The excitation of all ten levels of the neon 2p ⁵3p configuration by proton impact (100 keV-1 MeV) has been investigated by the spectral analysis of photon emission. Absolute emission cross sections have been obtained by calibration with a standard light source. Cascade effects are shown to be very important especially in the case ofJ=1 levels. For the 3p(¹ S ₀) level, which we studied additionally for electron impact excitation (100 eV-1 keV), our experimental cross sections are compared with the first Born approximation. Furthermore the polarization of sixteen 3p—3s emission lines has been measured as a function of impact energy. The energy dependence of the line polarization is characterized by theJ quantum numbers of the atomic states involved in the respective transition. An anomalous polarization of all lines originating from the decay ofJ=1 levels has been found and is referred to dominant cascade effects.     

Manifestation of higher polarization moments in the dipole emission under conditions of stepwise excitation and anisotropic collisions

The induction of higher polarization moments-the octupole orientation and the hexadecapole alignment—in the case of two-step excitation of atoms through dipole transitions and their manifestation in the polarization of dipole emission under conditions of anisotropic collisions are studied. For all channels of the two-step excitation process J ₀→J ₁ J, the efficiencies of production of higher polarization moments with integer and half-integer angular momenta from J=2 to J=7 through the absorption of linearly or circularly polarized light are calculated. The rates of collisional relaxation and interconversion of higher polarization moments, for both orientation and alignment, as functions of frequency detuning of the laser line from the center of the Doppler profile are calculated. The theory is illustrated by an example of two channels of excitation of the atomic state J=2 by circularly polarized light: J ₀=0→J ₁=1J=2 and J ₀=3→J 1=2 (or 3)→J=2. In the first case, the octupole orientation enhances or attenuates the signal of circular polarization depending on the laser frequency detuning. In the second case, it represents the only source producing orientation and circular polarization of the emitted light.     

Nonlinear forward scattering of resonant laser light from excited neon systems

We investigate forward scattering induced by a powerful single mode dye laser interacting with excited neon systems. We present experimental data obtained with the three transitions: 1s ₄(J=1)-2p ₃(J=0), 1s ₂(J=1)-2p ₁(J=0), and 1s ₅(J=2)-2p ₄(J=2). The lineshape dependences on the gas pressure, the laser power and the laser field fluctuations are discussed in the context of published theories. Our data resemble the calculated lineshapes in which fluctuations in the interaction processes between atoms and laser fields are taken into account. In atomic systems having more complex level degeneracies [1s ₅(J=2)-2p ₄(J=2)] signal structures expected from higher order nonlinear coherences can occur. To theoretically reproduce these lineshapes a simple J=1J=0 model is fully appropriate provided that the level with J=1 has a narrow width.     

Observation of the electric hexadecapole moment of free Na atoms in a forward scattering experiment

We report the observation of an electric hexadecapole moment in the ground state of free sodium atoms. The Δm_F = 4 coherence, which corresponds to this moment, is created by the light field of a cw dye laser. The forward scattered light was used for detection, because of the higher sensitivity compared to lateral fluorescence.     

Order-order transitions in spin systems with double electron exchange

Spin systems in the presence of isotropic single and double electron exchange are investigated at nonzero temperature. We use a generalized mean field approximation that allows for a variable local axis of quantization. This leads to the introduction of an angular parameter Θ giving the angle between nearest neighbor quantization axes. It is shown that order-order transitions can occur between phases of partially aligned spins (general Θ) and pure ferro- (Θ = 0) or antiferromagnetic (Θ = π) spin structures for physically reasonable values of the exchange ratio J₂/J₁ of double to single exchange when J₂ > 0. The order-order critical temperature τ₀ is determined as a function of J₂/J₁ for the particular cases of atomic spin $\text{s = 1,}\text{3}\text{2}\text{, 2,}\text{5}\text{2}$, and the corresponding phase diagrams are presented. Biquadratic and three-atom double electron exchange effects are considered separately. Expressions for the paramagnetic transition temperature and for the spontaneous magnetization M_s for general atomic spin s are given, and the discontinuous change in M_s at τ₀ is also found as a function of J₂/J₁.     

A precision determination of the radial charge parameters and the quadrupole moment of 181Ta using muonic X-rays

We report the measurement of the energies of the 4f → 3d, 3d → 2p and 2p → 1s atomic transitions in muonic ¹⁸¹Ta. Using transitions to and from the 1s and 2p levels, as well as the hyperfine splittings of the 2p and 3d states, we obtained the radial charge parameters assuming deformed Fermi distributions. We found the intrinsic static quadrupole moment Q₀ = 6.82 ± 0.06 e · b, in excellent agreement with Coulomb excitation results. We verified that the dynamic (corresponding to transitions to the first excited state) and the static (ground state) E2 moments were equal to within 1.1 %. The intrinsic hexadecapole moment was determined to be Π₀ = ?0.12 ± 0.40 e · b².     

The forbidden (J → J + 1) spectrum of CH4 in the ground vibronic state

The pure rotational R-branch spectrum of CH₄ arising from the centrifugal distortion moment has been studied using a simple 12.10-m light-pipe cell and a conventional interferometer. Ten forbidden (J → J + 1) transitions for J = 7 to J = 16 have been observed in the spectral region 80–200 cm^?1 with a theoretical resolution of 0.5 cm^?1. The integrated intensity of the six strongest lines has been measured and was found to be of the order of twice that calculated from the distortion moment obtained earlier from a molecular beam study of the (J = 2) rotational level. In the approximation that frequency shifts due to this excess intensity are neglible, it has been determined that the rotational constant B₀ = (5.245 ± 0.004) cm^?1 and the scalar distortion constant D_S = (1.19 ± 0.09) × 10^?4 cm^?1. It is argued that the excess intensity is due to higher-order terms in the dipole moment operator and the validity of the frequency analysis is considered in this context.     

Quadrupole and higher-order pairing forces

Recent work suggests that the quadrupole pair field may be important in describing certain properties of the crossings of high-spin rotational bands (e.g. crossing frequencies) in quantitative detail. We investigate its relative importance by performing an exact diagonalisation of a cranked deformed hamiltonian containing short-range residual interactions in a single j-shell. The major diflerence between odd and even particle-number crossing frequencies is seen to be described by blocking plus quadrupole pairing (J = 2) along with a significant hexadecapole pairing effect (J = 4). Absolute crossing frequencies are also sensitive to higher J-values. The interactions between the crossing levels are also discussed.     

Hyperfine structure measurements in metastable states of165Ho

The hyperfine structure constants and the electronic g _J factor of the state 4f ¹¹ 6s ^{2 4} I _11/2 belonging to the holmium ground multiplet have been measured using the atomic beam magnetic resonance technique combined with a state-selective laser-induced detection of the resonant atoms. By the same method the g _J factor of the level 4f ¹¹6s ²⁴ I _9/2 was determined, while the hyperfine structures of this metastable state and of two high-lying even parity states have been investigated by high resolution laser spectroscopy. The results for the experimentalA andB factors of all four members of the ground multiplet allow a least-squares evaluation of the three magnetic dipole and the three electric quadrupole effective radial parameters for the configuration 4f ¹¹ 6s ² of holmium, yielding an accurate value for the spectroscopic nuclear electric quadrupole moment:Q _hfs(¹⁶⁵Ho)=2.716(9)b (uncorrected for quadrupole shielding). From a comparison to the quadrupole moments measured in mesic holmium atoms the shielding factor could be estimated.     

Inversion-rotation spectrum and spectroscopic parameters of 14ND3 in the ground state

The far-infrared spectrum of ¹⁴ND₃ has been recorded in the region between 30 and 220 cm^?1 at a resolution, before deconvolution, of approximately 0.004 cm^?1. ΔJ = +1, ΔK = 0, a ← s and s ← a inversion-rotation transitions have been measured and assigned up to J″ = 19. These transitions, the pure inversion-microwave transitions and ground-state combination differences from the analysis of the ν₂ and ν₄ bands have been fitted simultaneously to an inversion-rotational Hamiltonian which includes Δk = ±3 and Δk = ±6 interaction terms. The ground-state spectroscopic parameters obtained in this way reproduce the transition frequencies within the accuracy of the measurements.     

Laser-rf double-resonance hyperfine structure measurements of the metastable 3d 4s 1 D 2 state of43Ca

The hyperfine structure of the (3(d 4s)¹ D ₂metastable state of⁴³Ca has been measured using theABMR-LIRF method (atomic beam magnetic resonance, detected by laser induced resonance fluorescence). The measurements yielded for the magnetic dipole and electric quadrupole constantsA=?17.650(2) MHz andB=?4.642(12) MHz, respectively. From the measuredB factor the spectroscopic electric quadrupole moment (uncorrected for shielding effects) has been calculated to beQ(⁴³Ca)=?0.062(12) barn. In addition, isotope shifts in the lines (3d 4s)¹ D ₂(3d 4p)¹ F ₃ ⁰ and (3d 4s)¹ D ₂(4s 5p)¹ p ₁ ⁰ for the stable calcium isotopes have been obtained by high resolution laser spectroscopy.     

Transition probabilities of OI spectral lines

Dipole transition probabilities connecting the 1s²2s²2p³(⁴S⁰)nl^3,5L_J levels are presented for (nl) up to (15,5). The calculations are based on the single-configuration Hartree-Fock wave functions with the 1s and 2s orbitals treated as a frozen core. The results generally agree well with earlier works (theoretical and experimental) on transitions involving low quantum numbers.     

Superparamagnetic-like behaviour of magnetic alloys

The effect of antiferromagnetic interaction on a binary Ising ferromagnetic alloy A_pB_1?p is studied based on cluster-variational method and assuming either J_AB or J_BB or both exchange interactions to be of antiferromagnetic type. In a ferromagnetic state the moment saturates to a value much lower than its full value. Within the temperature interval where moment saturates, the system exhibits superparamagnetic-like behaviour. The induced moment becomes a function of $\text{h}\text{T}$ only, and the zero-field susceptibility follows Curie law. The incomplete saturation of moment persists up to a large value of $\text{h}\text{T}$. The short-range order parameter at T = 0 is much less than that of homogeneous ferromagnet.     

Polarisierte Anregung der metastabilen 6s 5d-Terme im Ba I-Spektrum und Messung derg J-Faktoren

In an atomic beam experiment Ba-atoms were excited in the metastable levels of the 6s 5d-configuration by optical pumping and electron impact. The three states 6s 5d ¹ D ₂ and³ D _1,2 were populated by optical excitation of the 6s 6p ¹ P ₁- and³ P ₁-level resp., which decay partly into the metastable states. The¹ D ₂- and³ D ₃-level could be excited and aligned by impact of 50 eV-electrons. Radiofrequency transitions between Zeemansublevels were detected by resonance scattering of light and theg _J-values of the four 6s 5d-levels were measured:g _J(^1D ₂)=1.0032 (2),g _J(^3D ₁)=0.4986 (2),g _J(^3D ₂)=1.1638 (2) andg _J(^3D ₃)=1.3341 (2).     

Effective magnetic moments of the europium-monochalcogenides

We have measured the paramagnetic susceptibility and the saturation magnetic moment of a number of polycrystalline samples of all four europium monochalcogenides. Many of them exhibit a negative susceptibility at 2 K and magnetic fields of 70 kOe, rather than the expected saturation behaviour. These anomalies are believed to be due to lattice defects. Reproducible saturation moments have been obtained after subtraction of this linear high field magnetization. Since all materials were nonstoichiometric to within a few percent, the ratio between the Curie-Weiss constantC and the saturation momentM ₀ has been evaluated in order to eliminate the unreliably known numberN of the Eu^{+ +} ions. The quantityR = g _J (J+1) extracted in this way should have the valueR ₀ = 9.00 forg = 2 andJ ≡S = 7/2. The measured values, 9.72, 9.33, 9.32 and 9.50 for EuO, EuS, EuSe and EuTe, respectively, can be correlated directly with the magnetic hyperfine fields, which are ? 305, ? 330, ? 328 and ? 315 kOe in the ferromagnetic aligned states. Both results together lead to the assumption that the magnetic moment per Eu-ion is enhanced over the⁸ S _7/2-value by spin contributions of outer 5d or 6s electrons.     

Ab-initio interpretation of 〈r−3〉 electronic quantities in the hfs of Mg I 3s 3p 3 P and1 P

It has been known for a long time that, in a two-electron arc spectrum, the properties of the³ P and¹ P terms of the lowests p configuration cannot be interpreted correctly in a pure-configuration model. Following the experimental determination of the hyperfine constantA(3s 3p ¹ P ₁) in Mg I by Kluge and Otten, this paper presents the ab-initio interpretation of the 〈r ^?3〉_3p hyperfine electronic quantities in 3s 3p through the use of the multiconfigurational Hartree-Fock method. It appears that taking into account the effects of the monoelectronic excitations 3s→nd, 2p→np and 3p→np leads to ab-initio evaluations in very good agreement with experiment. The case of the 3p→np excitation, to which Brillouin's theorem should apply in principle, is discussed. Using the same method, a refined evaluation is proposed for the nuclear electric-quadrupole moment of Mg²⁵ (Q=0.200 ± 0.01 barn).