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 The previously unpublished rotational levels of Dieke and Heath for the $\text{A}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, B³Π_g and C³Π_u states are referenced to the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.     

Spectrum and structure of the He2 molecule: Characterization of the singlet and triplet states associated with the UAO's 4s, 4dσ, 4dπ, and 4dδ

The emission spectrum of the He₂ molecule has been rephotographed in the ～4000–～5700 Å region and the $\text{4d(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$, $\text{4d(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^1\text{Π}{}_{\mathrm{u}}\text{,}{}^1\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$, $\text{4s}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$ and $\text{4s}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$ transitions analyzed. The 4dδj³Δ_u, 4dπj³Π_u, $\text{4dσj}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{4sh}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states have been characterized through v = 2 and the 4dδJ¹Δ_u, 4dπJ¹Π_u, $\text{4dσJ}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{4sH}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states for v = 0. The term levels for these perturbed and l-uncoupled states have been confirmed (a) by analyses of bands with common levels from Δv = 0, ±1 sequences and (b) by analyses of the transitions between the above states from 4d and 4s and the $\text{c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ and $\text{C}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ states associated with 3pσ. Molecular constants are reported which have been partially corrected for the effects of l-uncoupling and the homogeneous perturbations between the state pairs J, H and j, h.     

Reorientational motion of the OH− ion in cubic sodium hydroxide

The rotational motion of the OH^? ion was studied in cubic NaOH at 575 K with quasielastic incoherent neutron scattering. The data are compared to two simple models yielding values for the radius of rotation R, the translational mean square displacement 〈u²〉_H, the rotational jump rate τ^?1 and the rotational diffusion coefficient D_R. The following parameter values are obtained: (a) rotational jump model: $\text{R = 0.95}\text{A}\text{?}$, $\text{〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.052}\text{A}\text{?}{}^2\text{, τ}{}^{\mathrm{?1}}\text{= 2}\text{meV}$, (b) rotational diffusion model: $\text{R = 0.99}\text{A}\text{?}\text{, 〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.046}\text{A}\text{?}{}^2\text{, D}{}_{\mathrm{R}}\text{= 0.72}\text{meV}$.     

Dual model for dislocation and disclination melting

We show that defect melting involving dislocations and disclinations is dually equivalent to an extension of an XY model with an energy of the type Σ_{i, j}{[cos(?_iu_j + ?_ju_i) + ? cos ?_iω_j] }, where $\text{ω}{}_{\mathrm{t}}\text{=}\text{1}\text{2}\text{?}{}_{\mathrm{tjk}}\text{?}{}_{\mathrm{j}}\text{u}{}_{\mathrm{k}}$ is the local rotation field. The. model clarifies the proper choice of defect core energies arising from nonlinear elasticity. These permit the pile-up of dislocations to disclinations which is essential for the first order of the melting transition.     

3Σu−-3Σu+ coupling in the O2B3Σu− predissociation

The role of $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{-2}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ spin-orbit mixing in the O₂ Schumann-Runge predissociation is investigated. The $\text{2}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state is found to cross the $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ state near 2.0 Å with an interaction matrix element of approximately 55 cm^?1. This state contributes to the widths of the Bv ≥ 6 levels, but introduces only small level shift perturbations. When the partial widths due to the ${}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{-}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ interaction are added to the previously calculated widths due to the ⁵Π_u, ³Π_u, and ¹Π_u states, reasonable agreement is obtained with experimental measurements on O¹⁶O¹⁶ and O¹⁸O¹⁸. The possibility of non-Lorentzian line profiles and the dependence of the width on rotational quantum number is investigated. The approximation of the spin-orbit matrix element by its value at the crossing point is shown to be a good approximation for calculating the second difference perturbations.     

Thioformaldehyde: Vibrational analysis of the Ã1A2-X̃1A1 visible absorption system

The electronic absorption spectra of thioformaldehyde and thioformaldehyde-d₂ have been obtained. A vibrational analysis of the discrete band system in the 6100-4400-Å region is reported. The type A origin bands are at $\text{16 394}\text{16 484}\text{cm}{}^{\mathrm{?1}}$ for $\text{CH}{}_2\text{S}\text{CD}{}_2\text{S}$, and are magnetic dipole allowed. The electronic transition is $\text{A}\text{?}{}^1\text{A}{}_2\text{-}\text{X}\text{?}{}^1\text{A}{}_1$ under the C_2v point group. Most of the intensity of the system is in type B bands, and is due to vibronic mixing with higher ¹B₂ states when the inversion mode ν₄ is excited. The molecule in the excited ¹A₂ state is “floppy-planar,” having a broad potential function with a barrier of the order of 20 cm^?1 to the inversion motion.     

The infrared part of the C2 Phillips system (2.3–0.9 μm)

Line positions and molecular constants for the 0-0, 1-0, 2-0, 0-1, 2-1, 3-1, 0-2, 1-2, and 4-2 bands of the C₂ Phillips system ($\text{A}{}^1\text{Π}{}_{\mathrm{u}}\text{-X}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$) are reported. Among them, five bands have not been reported previously. Rotational perturbations have been observed in the previously unobserved v = 1 level of the $\text{A}{}^1\text{Π}{}_{\mathrm{u}}$ state. This state is perturbed by the $\text{c}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state which was discovered by Ballik and Ramsay. These observations provide new information regarding the perturbing state. In particular, the minimum of the potential energy for the $\text{c}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state has been found to be at 9227.4 cm^?1 instead of 13 310 cm^?1, which was the previous T_e value for this electronic state.     

S1-S0 fluorescence after narrow band excitation of glyoxal: Single rotational level fluorescence and a technique for deconvolution of Doppler congested absorptions

Individual rovibronic transitions are isolated at high resolution from a crowded absorption feature with a fluorescence excitation technique which is based on detection of fluorescence from one and only one rovibronic level. The method is illustrated by resolving four rovibronic transitions from the single rotational line-like feature in the 0, 0 band of the ${}^1\text{A}{}_{\mathrm{u}}\text{←}{}^1\text{A}{}_{\mathrm{g}}$ (S₁ ← S₀) absorption of glyoxal vapor. The rotational structure of the 5₁⁰ fluorescence band is studied as a function of tuning a narrow-band laser line (linewidth < 10^?4 cm^?1) to various positions in and near this absorption feature. The fluorescence structure proves an extremely sensitive tool for detecting small absorptions, with emission from 12 rovibronic levels being identified. One of the spectra so obtained is a close approximation of true single rotational level fluorescence.     

Acetylene fluorescence

Previously unobserved acetylene ${}^1\text{A}{}_{\mathrm{u}}\text{(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{) →}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ fluorescence occurs following 1933-Å ArF laser excitation of C₂H₂ or C₂H₄ and their deuterated analogs in solid Ne and Ar hosts at 4.2 K. Acetylene is a photolysis product of matrix-isolated ethylene. Ground-state vibrational levels as high as ν″₃ = 30 of the degenerate ν₃ bending vibration are observed for C₂D₂. Only ν₃ is appreciably active in the fluorescence. The negative ν₃ anharmonicity, previously observed in the gas phase, also occurs in Ne host. Consideration of rotational selection rules indicates that the Ne host strongly hinders free rotation about the low-moment-of-inertia $\text{a}\text{?}$ axis in the excited state.     

On the theory of localized spin and phonon excitations in amorphous ferromagnets

Within the framework of a perturbation theory and a quasicrystalline approximation we have solved the linearized equation of motion for the circular spin component S⁺_j = S^x_j + iS^y_j in a one-dimensional amorphous ferromagnet with periodic external excitation of the spin S⁺₀ at site j = 0. It is shown that localized spin modes of the simple form $\text{«S}{}^{\mathrm{+}}{}_{\mathrm{j}}\text{a}\text{?}\text{= S}{}^{\mathrm{+}}\text{(q0) exp[iq}{}_0\text{· R}{}_{\mathrm{j}}\text{- iω(q0) t] exp (-gk?R}{}_{\mathrm{j}}\text{?)}$ with fall-off-length κ^-1 are solutions of the ensemble-averaged equation of motion. On the other hand, we have a damping of extended spin waves according to exp(-Γt). A simple relation is derived between the fall-off-length κ^-1 of localized spin modes and the damping factor Γ of extended spin waves. Analogous results hold for phonons in amorphous materials.     

Microwave spectrum of the C4v molecule IF5 in the excited vibrational states v5(B1) = 1 and v9(E) = 1: Analysis of the ν5-ν9 Coriolis resonance

Measurements of the microwave spectrum of the C_4v molecule IF₅ in the excited vibrational states v₅(B₁) = 1 and v₉(E) = 1 are reported for the transitions J4 → 5, 5 → 6, 6 → 7, 8 → 9, and 9 → 10 (27–55 GHz). The Coriolis resonance interaction between these two states is analyzed by diagonalization of Hamiltonian matrices of dimension 3 × (2J + 1) in which all (Δl,Δk) = (±2, ±2)(q⁺), (±2, ±2)(q^?), and (0, ±4)(R₆) interactions are included as off-diagonal terms in addition to the v₅ = 1 ? v₉ = 1, l₉ = ±1(R₅₉) Coriolis interaction. In the v₉ = 1 state spectra, the $\text{B}{}_1\text{B}{}_2$l-doubling of the kl = ?1 transitions and $\text{A}{}_1\text{A}{}_2$ splittings of the kl = ?3 transitions and $\text{B}{}_1\text{B}{}_2$ splittings of the kl = +3 transitions, all enhanced by the Coriolis resonance, have been observed and measured. Least-squares refined rovibrational parameters for the v₅ = 1 and v₉ = 1 states are reported and a preliminary value for the rotational constant C₉ has been obtained.     

Nonadiabatic effects in the B, C, B′, and D states of H2

The Kolos-Wolniewicz potentials for the H₂$\text{B}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and C¹Π_u states were used together with the hypothesis of pure precession for the rotation-electronic interaction, to calculate the nonadiabatic energy levels of these states for J = 1 to 5. The complete coupling matrix was computed using accurate numerical vibrational wavefunctions. The calculated Λ-doubling of the v = 0 to 12 C vibrational levels generally agrees well with experimental values, and the nonadiabatic shifts in the B rotational constants qualitatively explain the difference between the theoretical and RKR potentials for this state.The interaction of the B′${}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and D¹Π_u states was also investigated, but only qualitatively since adiabatic potentials of sufficient accuracy do not exist for these states. The Λ-doubling of the Dv = 0 rotational levels agrees well with the experimental values. An appreciable “background” nonadiabatic shift in the B′ rotational constants was found. This shift, which is nearly 5 percent of B_v, is in addition to that of strong local two-level interactions and was not “deperturbed” in constructing the B′ RKR potential. The result is that the RKR turning points differ by about 0.04 au from the “true” adiabatic turning points. This conclusion is supported by a Hartree-Fock calculation of the B′ potential to the left of R_e.     

Information on the dynamics of the reaction KN → K1N from KLN interactions

If $\text{K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{is a K}{}^1$ resonance decaying into K_S,L (the short- and long-lived kaon) and a neutral system S^o of pions, one can isolate the C-even and C-odd, crossed-channel contributions to $\text{KN → K}{}^1\text{N}$ by using the reactions $\text{K}{}_{\mathrm{L}}\text{N → K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{N}$ whether S^o is a C-eigenstate, or a mixture of C-even and C-odd states. Applications to the production of K¹(890) and the Q-meson are discussed, and simple numerical predictions made for Q_S,L production. Q-production data indicate approximate t-channel helicity conservation for the ω and P' exchanges at vertices involving a spin change, in similarity to the belief for the pomeron. Q_S,L production data can give information also on Q-decays.     

Reexamination of the I2 spectrum near the B(3Π0u+) state dissociation limit

The disagreement of Danyluk and King's (Chem. Phys.25, 343 (1977)) rotational constants for levels lying near the dissociation limit of B-state I₂ with the mechanical behavior predicted by near-dissociation theory is investigated. The discrepancies are shown to be much too large to be explained by either the neglect of centrifugal distortion effects in the original analysis or by rotational or spin-rotation coupling to a nearby repulsive 1_u state. These differences are therefore attributed to experimental error, a conclusion which is confirmed by more recent experimental results. A reanalysis of the best available data for levels near the dissociation limit of B-state I₂ then yields improved values for the B-state dissociation limit $\text{D}$ = 20 043.16 (±0.02) cm^?1 of the vibrational index at dissociation v_$\text{D}$ = 87.32 (±0.04) and of the long-range potential constant $\text{C}{}_5\text{= 2.88 (±0.03) × 10}{}^5\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^5$. This in turn implies a slightly improved ground-state dissociation energy of $\text{D}$₀ = 12 440.18 (±0.02) cm^?1.     

Analysis of the 2770-Å emission system in I2

A weak emission spectrum of I₂ near 2770 Å is reanalyzed and found to to minate on the A(1u³Π) state. The assigned bands span v″ levels 5–19 and v′ levels 0–8. The new assignment is corroborated by isotope shifts, band profile simulations, and Franck-Condon calculations. The excited state is an ion-pair state, probably the 1g state which tends toward $\text{I}{}^{\mathrm{?}}\text{(}{}^1\text{S) +}\text{I}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_1\text{)}$. In combination with other results for the A state, the analysis yields the following spectroscopic constants: T″_e = 10 907 cm^?1, $\text{D}$″_e = 1640 cm^?1, ω″_e = 95 cm^?1, $\text{R″}{}_{\mathrm{e}}\text{= 3.06}\text{A}\text{?}$; T′_e = 47 559.1 cm^?1, ω′_e = 106.60 cm^?1, $\text{R′}{}_{\mathrm{e}}\text{= 3.53}\text{A}\text{?}$.     

Diode laser spectroscopy of the CCl radical

Vibration-rotation transitions of the fundamental band have been observed for both C³⁵Cl and C³⁷Cl in the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ states by using an infrared diode laser spectrometer with Zeeman modulation. A few lines of the “hot” band (v = 2 ← 1) have also been recorded for C³⁵Cl. From an analysis of the observed spectra improved values were obtained for the vibrational harmonic frequency and anharmonicity constant, rotational constants, and Λ-doubling parameters. It was found necessary to take into account centrifugal distortion effects on the spin-orbit coupling constant A in the analysis, which gave $\text{(}\text{dA}\text{dr}\text{)}{}_{\mathrm{<mtext>e</mtext>}}\text{r}{}_{\mathrm{<mtext>e</mtext>}}$ to be ?176 ± 38 or ?125 ± 38 cm^?1, depending upon whether ²Σ^? or ²Σ⁺ states contribute more to the Λ-type doubling. The equilibrium internuclear distance r_e was calculated from the derived rotational constants to be 1.64506 ± 0.00016 Å.     

An algebraic approach to (3, 3)⊕(3, 3)⊕(8, 8) chiral-symmetry breaking

We examine the Hamiltonian

$\text{H = H}{}_0\text{+ε}{}_0\text{u}{}_0\text{+ε}{}_8\text{u}{}_8\text{+A S}{}_{\mathrm{\alpha \alpha }}\text{+B d}{}_{\mathrm{8\alpha \beta }}\text{S}{}_{\mathrm{\alpha \beta }}$

, where u_o, u₈ belong to $\text{(3,}\text{3}\text{)+(}\text{3}\text{,3)}$ and S_αα, S_αβ belong to (8,8), following a purely algebraic approach due to Michel and Radicati and obtain B/A = 2√3 if ε₈/ε₀ = ?√2.     

Global aspect of steady-states for competitive-diffusive systems with homogeneous Dirichlet conditions

This paper is concerned with the competitive-diffusive systems

$\text{u}{}_{\mathrm{t}}\text{=d}{}_{\mathrm{l}}\text{u}{}_{\mathrm{xx}}\text{+(a}{}_{\mathrm{l}}\text{?b}{}_{\mathrm{l}}\text{u?c}{}_{\mathrm{l}}\text{v)u}\text{v}{}_{\mathrm{t}}\text{=d}{}_2\text{v}{}_{\mathrm{xx}}\text{+(a}{}_2\text{?b}{}_2\text{u?c}{}_2\text{u)v}\text{(x, t) ? (0, 1) × (0, ∞)}$

, with homogeneous Dirichlet boundary conditions. From a global bifurcation view point, the dependency of steady-states on the parameters a_i, b_i, c_i and d_i (i = 1, 2) is investigated. In particular, bifurcation of coexist ence solutions amd their stabilities are our main interests.     

Laser-excited phosphorescence spectrum of C3S2 in an Ar matrix

The phosphorescence spectrum of C₃S₂ was observed in a low-temperature Ar matrix with excitation of an Ar⁺ laser. The spectrum consists of a very strong 0-0 band at 18 287 cm^?1 and well-resolved progressions in the ν₂, ν₅, ν₆, and ν₇ vibrations. Side bands were found on the high-energy sides of some transitions. The separation between the main and side bands is 23 cm^?1. Polarization analysis suggests that C₃S₂ is linear symmetric in the Phosphorescent state as in the ground electronic state. On the basis of symmetry considerations and a qualitative evaluation of spin-orbit coupling, the phosphorescent state is assigned to ³Σ_u^? with Σ_u⁺ and Π_u components split by spin-spin interaction. The Σ_u⁺ level is lower than the Π_u one by 23 cm^?1 and the main and side band emissions start from the Σ_u⁺ and Π_u levels, respectively. The Σ_u⁺ component seems to acquire allowed character from a ¹Σ_u⁺ state by spin-orbit coupling and from bent ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}\text{(}{}^1\text{B}{}_2\text{)}$ and ${}^1\text{Δ}{}_{\mathrm{g}}\text{(}{}^1\text{A}{}_1\text{+}{}^1\text{B}{}_2\text{)}$ states by ν₅ vibronic coupling. Mixing of the Σ_u⁺ and Π_u components through ν₅ is responsible for most of the side bands. The ν₅ frequency is estimated to be 160 ± 20 cm^?1 in the ³Σ_u^? state from the intensities of ν₅ progression bands and from the ground-state frequency, 411 cm^?1.     

Excess low frequency conduction noise in a granular composite

Granular composites consisting of 25% nickel as 8 nm diameter particles dispersed in an aluminium oxide matrix display excess conduction noise. Co-deposited films with resistance per square about 10⁵ ohms and negative temperature coefficient show a noise power spectral density $\text{S}{}_{\mathrm{v}}\text{(?) =}\text{S}{}_{\mathrm{v}}\text{(1)}\text{?}{}^{\mathrm{\alpha }}$ where α ? 1.10 ± 0.03 over the accessible spectral range of 0.1 Hz ? ? ? 5000 Hz. The amplitude 3 × 10^?15 ? S_v(1) ? 5 × 10^?12 V²Hz^?1, appears to increase approximately quadratically as the applied voltage V_s up to V_s ? 2.5 V and as the first power of V_s for 2.5 ? V_s < 35 V.