Magnetic circular dichroism of transition metal ions in solids—II K2NaGaF6: Cr3+

The absorption and MCD spectra of the ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{a}}$ and ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{b}}$ spin-allowed transitions of Cr³⁺ in K₂NaGaF₆ are reported. It is shown that transitions to the ${}^4\text{T}{}_{\mathrm{1g}}$. states are induced by T_1u vibratio the other spin-allowed transition, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, there are three competing intensity mechanisms: electric dipole induced by T_1u vibrations, electric dipole induced by T_2u vibrations and magnetic dipole, and an estimate is made of the relative importance of these. The magnetic dipole ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^2\text{E}{}_{\mathrm{g}}$ zero-phonon line is observed to be accompanied by a vibrational sideband for which the coupling is predominantly with T_2u vibrations. Other weak transitions are observed in MCD spectra and their origin briefly discussed.     

Laser excitation spectra of He2

Metastable $\text{a(2sσ)}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ He₂ molecules are produced by a dc discharge in a flowing He stream. Laser excitation downstream of the discharge produces excitation spectra for a number of He₂ states. LIF spectra are observed for the $\text{(npπ)}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ series for n = 4–9, excepting 5 and the $\text{(npπ)}{}^3\text{Π}{}_{\mathrm{g}}$ series for n = 5–15.     

Model calculation of the electronic structure and spectroscopy of Hg2

Energy curves and transition moments of the excited valence states of Hg₂ were obtained in a model calculation based on calculated Mg₂ energy levels and the assumption that the asymptotic spin-orbit matrix elements for the Hg atom are applicable to the molecular states. The spin-orbit and orbital-rotational interaction of the excited states of Hg₂ is analyzed in both a Hund's case (c) and (a) representation. The intermediate (a) → (c) transition moments are obtained as a function of the internuclear distance. The effect of the orbital-rotational interaction which introduces Hund's case (b) and (e) couplings is found to be small for transitions among excited states under the conditions normally encountered for populating excimer states.Using the energy level positions and transition moments, the observed spectra and predicted spectra are compared for both radiative transitions including the ground state and among the excited states. The lifetime of the $\text{1}{}_{\mathrm{u}}\text{(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{)}$ excimer state is calculated to be 1.4 μsec with the 335 nm band assigned to the $\text{1}{}_{\mathrm{u}}\text{→ X}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ transition. The 485 nm bands cannot be assigned to any Hg₂ transitions. Strong bound-continuum absorptions are predicted for the 485 nm bands. On the other hand, the 335 nm emission is predicted to be absorbed by bound-bound transitions only.     

Electron-vibration splitting of the vibronic levels of the 1T2g state of MgO:Ni2+

Magnetic circular dichroism (MCD) and magnetic linear dichroism (MLD) measurements of the ${}^3\text{A}{}_{\mathrm{2g}}\text{→}{}^1\text{T}{}_{\mathrm{2g}}$ absorption band in MgO:Ni²⁺ are reported. It is shown that for the lowest energy vibrational peak there is considerable evidence of splitting of the T_2g × T_1u vibronic levels by the electron-vibration interaction.     

Analysis of the B′3Σu− → B3Πg (0,0) emission band of molecular nitrogen

The (0,0) band of the $\text{B′}\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{→ B}{}^3\text{Π}{}_{\mathrm{g}}$ emission (Infrared Afterglow) system of molecular nitrogen has been recorded with a resolution of 0.046 cm^?1 and a line position accuracy of 0.007 cm^?1. Six hundred and seventy-two lines are tabulated into a line list for the 1.53 μm (low-resolution) emission feature. Of these, 482 are assigned as members of the 27 branches of the B′ → B transition, while 150 are identified with the 1PG (3,6) band. Molecular constants for the v = 0 levels of the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ and B³Π_g states have been computed and tabulated.     

Absorption spectra of Ni2+ in (NH4)2Mg(SO4)2·6H2O and Co2+ in Na2Zn(SO4)2·4H2O

Optical absorption spectra of Ni²⁺ in (NH₄)₂Mg(SO₄)₂·6H₂O and Co²⁺ in Na₂Zn(SO₄)₂·4H₂O single crystals have been studied at room and liquid nitrogen temperatures. From the nature and position of the observed bands, a successful interpretation could be made assuming octahedral symmetry for both the ions in the crystals. The splitting observed for ${}^3\text{T}{}_{\mathrm{1g}}\text{(F)}$ band in Ni²⁺ and ${}^4\text{T}{}_{\mathrm{2g}}\text{(F)}$ band in Co²⁺ at liquid nitrogen temperature have been explained as due to spin-orbit interaction. The extra band observed at 16,325 cm^-1 in the case of Ni²⁺ at low temperature has been interpreted to be the superposition of vibrational mode of SO^2-₄ radical on ${}^3\text{T}{}_{\mathrm{1g}}\text{(F)}$ band. The observed band positions in both the crystals have been fitted with four parameters B, C, Dq and ζ.     

The g-factor difference for the 61+ and 88+ states in 210Po

The difference in g-factors for the 6₁⁺ and 8₁⁺$\text{(πh}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}{}^2\text{)}$ states in ²¹⁰Po has been measured as $\text{(g}{}_6\text{? g}{}_8\text{)}\text{g}{}_8\text{= 2.0 ± 0.7\%}$. This result represents a small violation of additivity. A value of g₈ = 0.909 ± 0.011, independent of g₆, was also obtained.     

Energy levels of low lying triplet states of N2 from infrared emission studies

A theoretical model used to describe the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ and B³Π_g states of N₂ is presented. Using recently acquired high resolution spectra of the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{→ B}{}^3\text{Π}{}_{\mathrm{g}}$ (0-0) band, rotational energy levels of the v = 0 vibrational levels of these two states are generated with this model. These levels are in excellent agreement with those obtained using a combination differences technique. The precision of the model generated levels is 0.01 cm^?1. The previously unpublished rotational levels of Dieke and Heath for the $\text{A}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, B³Π_g and C³Π_u states are referenced to the $\text{N}{}_2\text{X}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ (v = 0, J = 0) ground level and tabulated here. Estimates of the precision of their work are made.     

Resolution of the discrepancies concerning the optical and microwave values for B0 and D0 of the X 3Σg− state of O2

The discrepancies concerning the optical and microwave values of B₀ and D₀ for the X${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state of O₂ have been removed by a nonlinear least-squares fit to all of the lines of the O₂, $\text{b}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{-X}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Red Atmospheric bands recorded by Babcock and Herzberg (Astrophys. J., 108, 167, 1948). The resulting values for B₀″ and D₀″ are in excellent agreement with the Raman and microwave values. Improved values are determined for B₁″, D₁″, γ₁″ (spin-rotation), and ?₁″ (spin-spin). Both γ_v″ and ?_v″ increase in magnitude from v″ = 0 to v″ = 1. Improved Dunham Y_i0 and Y_i1 expansion coefficients are determined for the $\text{b}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, from which the Rydberg-Klein-Rees potential is constructed.     

Ni2+ emission in MgO,KMgF3, KZnF3 and MgF2

The emission of Ni²⁺ ions in MgO, KMgF₃, KZnF₃ and MgF₂ crystals has been investigated. The fine structure on the bands at about 20 000 cm^-1 and 13 000 cm^-1 has been studied in detail and from this and the excitation spectra these bands are assigned to ${}^1\text{T}{}_{\mathrm{2g}}\text{→}{}^3\text{A}{}_{\mathrm{2g}}$ and ${}^1\text{T}{}_{\mathrm{2g}}\text{→}{}^3\text{T}{}_{\mathrm{2g}}$ transitions respectively.     

Remarks on Mc Bryan's convergence proof for (α-4(cos(αϕ)−1+α2ϕ2/2))2-quantum fields

With the help of Mc Bryan's method we prove the existence of F(?)₂-fields, where $\text{F(x) ?}\text{∑}\text{n=0}\text{∞}\text{a}{}_{\mathrm{2n}}\text{x}{}^{\mathrm{2n}}$ is a power series with fast decreasing coefficients. Hypercontractive estimates show the existence of fields with a superposition of exponential or cosine functions as interaction, similar to Mc Bryan's interaction.     

Phase transitions in ferroelectric ceramics of the type Sr0.5Ba0.5Nb2O6

The ferro-paraelectric transition in Sr_0.5Ba_0.5Nb₂O₆ ceramics has been studied by measuring the dielectric pennitivity as a function of temperature at different frequencies. Experimental results in the transition region over ?'_max fit the relation $\text{1}\text{?'}\text{?}\text{1}\text{?'}{}_{\max }\text{= A(T ?}\text{T}{}_0\text{)}{}^{\mathrm{\gamma }}$ with γ > 1, as is typical for dif transitions. In an interval of temperatures of 17°C over T₀ (=Tfor?'_max), γ = 2. Using the relaxors' model of Kirillov-Isupov an equation is inferred in order to compute the activation energy of the relaxors as a function of parameters directly obtained from the experimental results.     

Some effects of spin-orbit interaction on rotational levels and rotational line intensities in vibrationally unexcited 2A, 2E, and 2F electronic states of open-shell XY4 molecules

Rotational energy levels in vibronic ground states of ²A, ²E, and ²F electronic states of open-shell XY₄ molecules, as well as rotational line intensities for allowed transitions between such states, are discussed, including the effects of spin-orbit interaction and tetrahedral splittings. Jahn-Teller effects are assumed to be small, and are only taken into account implicitly, through their contributions to various parameters in the effective Hamiltonian. Qualitative information is obtained by considering several limiting-case coupling schemes among the electron spin angular momentum S, the electron orbital angular momentum L, and the pure rotational angular momentum R. These limiting cases are similar in spirit to Hund's coupling cases in diatomic molecules, but differ sufficiently from the latter to make detailed correspondences unhelpful. Quantitative information on rotational energy levels and line intensities is obtained numerically by diagonalizing a Hamiltonian matrix set up in a basis set characterized by uncoupled moleculefixed projections of S, L, and the total angular momentum J, and symmetrized so that all basis set functions belong to a definite species in the subgroup D_2d of the true point group T_d. Hamiltonian matrix elements are determined by ladder operator techniques. Three sample calculated spectra, corresponding to $\text{p(}{}^2\text{F}{}_2\text{)-s(}{}^2\text{A}{}_1\text{)}$, $\text{d(}{}^2\text{E)-p(}{}^2\text{F}{}_2\text{)}$, and $\text{d(}{}^2\text{F}{}_2\text{)-p(}{}^2\text{F}{}_2\text{)}$ are presented. As one might expect, when the spin-orbit constant A is set equal to zero, then both qualitative and quantitative aspects of the rotational-electronic problem in open-shell XY₄ molecules can be mapped easily onto discussions of the rotation-vibration problem from the CH₄ literature.     

The A-X system of Br2+ radical cations

The ²Π_u-X²Π_g transition in Br₂⁺ was reexamined using dispersed laser-induced fluorescence, and emission spectroscopy in a seeded molecular beam. New constants are derived, confirming the large difference between $\text{A}{}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{A}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and reconciling the emission spectrum with photoelectron data.     

The 5T2g → 5Eg absorption in MgO: Fe2+

At helium temperatures two sharp lines at 9350 and 9510 cm^?1 have been observed for the first tune on the low-energy side of the broad double-peaked absorption corresponding to the ${}^5\text{T}{}_{\mathrm{2g}}\text{→}{}^5\text{E}{}_{\mathrm{g}}$ transition in Fe²⁺ at the octahedral site in MgO. The lower energy line has a half width of 4 cm^?1; Zeeman measurements show that it is of magnetic dipole origin. The Zeeman spectra are consistent with those expected for a pure electronic transition from the (⁵T_2g)T_2g ground state to the ⁵E_g excited state. The second line, with a halfwidth of ~ 35 cm^?1, a vibrational sideband.     

Electrical conductivity of the system Y2O3CeO2

The electrical conductivity of the system Y₂O₃CeO₂ was measured in the temperature range 500–1100°C and P_o2 range 10^–7?10^?1 atm. Possible defect models were suggested on the basis of conductivity data, which were investigated as a function of temperature and of P_o2. The observed activation energies were 0.40 eV and 1.79 eV in the low- and high-temperature regions, respectively. The observed conductivity dependences on P_o2 were in the temperature range 500–750°C and at temperatures from 750–1100°C. It is suggested that the system Y₂O₃CeO₂ shows a mixed ionic plus hole conduction due to an O^″_i defect and an electronic hole conduction due to a V^'''_Y defect in the low- and high-temperature regions, respectively.     

Spectrum and structure of the He2 molecule: Characterization of the triplet states associated with (1σg)2(1σu)nsσ, ndσ, ndπ, and ndδ (n = 5–12)

Emission spectra for the electronic transitions $\text{ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ b}{}^3\text{Π}{}_{\mathrm{g}}\text{(n = 5–12)}$, $\text{nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ b}{}^3\text{Π}{}_{\mathrm{g}}\text{(n = 5–12)}$, $\text{ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 3pσ c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{(n = 5–10)}$, $\text{nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 3pσ c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{(n = 5–11)}$, $\text{ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 3pπ e}{}^3\text{Π}{}_{\mathrm{g}}\text{(n = 6–11)}$, $\text{nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 3pπ e}{}^3\text{Π}{}_{\mathrm{g}}\text{(n = 6–11)}$, $\text{nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 4pσ g}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{(n = 9–11)}$, and $\text{10dδ}{}^3\text{Δ}{}_{\mathrm{u}}\text{→ 4pσ g}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ of ⁴He₂ are reported and the electronic structure of the triplet states associated with v = 0 of (1σ_g)²(1σ_u) nsσ and ndλ characterized. The energy levels comprising the $\text{(1σ}{}_{\mathrm{<mtext>g</mtext>}}\text{)}{}^2\text{(1σ}{}_{\mathrm{<mtext>u</mtext>}}\text{)ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{)}$ and the $\text{(1σ}{}_{\mathrm{<mtext>g</mtext>}}\text{)}{}^2\text{(1σ}{}_{\mathrm{<mtext>u</mtext>}}\text{)ndλ(}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{)}$ manifolds exhibit strong channel mixing, while the mixing of the $\text{(1σ}{}_{\mathrm{<mtext>g</mtext>}}\text{)}{}^2\text{(1σ}{}_{\mathrm{<mtext>u</mtext>}}\text{)nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ with the $\text{nd(}{}^3\text{λ}\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{)}$ channel structure is relatively minor. Models based on multichannel quantum defect theory are used to aid in the spectral assignments and to correlate the observed level structures. We show that three-limit and two-limit models adequately represent the bulk of the observed $\text{ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{)}$ and $\text{ndλ(}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{)}$ channel structures, respectively.     

Silver-compensated germanium center in α-quartz

A synthetic germanium-doped crystal of α-quartz was subjected to an electro-diffusion process $\text{ca. 600}\text{V}\text{cm}$, 625°K), in which Ag⁺ ions were introduced along the crystal's optic axis (c). A 9800MHz electron paramagnetic resonance spectrum at room temperature, taken after room temperature x-irradiation, revealed the presence of a silver-compensated germanium center A_Ge?Ag with large, almost isotropic ¹⁰⁷Ag and ¹⁰⁹Ag hyperfine splittings (26.078, 30.112 mT for magnetic field B∥c). Measurement of the spin-Hamiltonian (i.e. matrices $\text{g}$, $\text{A}{}^{73}{}_{\mathrm{<mtext>Ge</mtext>}}$, $\text{A}{}^{107}{}_{\mathrm{<mtext>Ag</mtext>}}$ and $\text{A}{}^{109}{}_{\mathrm{<mtext>Ag</mtext>}}\text{)}$ discloses that a suitable model for the observed center utilizes germanium, substituted for silicon, with the accompanying silver interstitial in a nearby c-axis channel, and with electronic structure in which an appreciable admixture Ge⁴⁺?Ag⁰ to Ge³⁺?Ag⁺ exists. Estimates of the unpaired electron orbital are presented.     

Electron paramagnetic resonance of 61Ni+ in CuGaS2

EPR of ⁶¹Ni⁺ doped CuGaS₂ at 4.2 K leads to the following experimental data: $\text{g = 1.918 ± 0.006 A  < 12 × 10}{}^{-4}\text{cm}{}^{-1}\text{, g}{}_{\mathrm{\perp }}\text{= 2.328±0.006 A}{}_{\mathrm{\perp }}\text{= (65±2) × 10}{}^{-4}\text{cm}{}^{-1}$. High axial field splitting of ²T₂ state stabilizes the center against Jahn-Teller interaction. Covalency reduction factor k is 0.76.     

Solving φ1,24 field theory with Monte Carlo

We study lattice g₀φ⁴ field theory for all g₀ and fixed renormalized mass M in one and two dimensions using Monte Carlo techniques. We calculate the dimensionless renormalized coupling constant $\text{g}{}_{\mathrm{<mtext>R</mtext>}}\text{=}\text{g}{}_{\mathrm{<mtext>R</mtext>}}\text{M}{}^{\mathrm{4?d}}\text{,}\text{where}\text{d}$ is the dimension of space—time, at fixed small values of the lattice spacing a for various g₀ and lattice sizes. Our results are in quantitative agreement with the analyses of high temperature and strong coupling series which rely on extrapolation from large to small lattice spacing.