The Zeeman effect in doublet-quartet transitions in orthorhombic rotating molecules

Theoretical predictions on the effect of magnetic fields of variable strength on the rotational structure of doublet-quartet transitions in orthorhombic near symmetric top molecules are reported, with the assistance of computer simulations of line profiles. Low-field profiles are discussed, and it is shown that low-field linewidths are approximately equal to 2gβH|ΔJ ? ΔN| for transitions between states of any spin multiplicity. In a high field, transitions allowed by direct spin-orbit contamination of the combining states give rise to three lines with ΔM_s = 0, ±1, whereas two additional lines, with ΔM_s = ±2, are found if the combining states are appreciably contaminated also by indirect coupling to the active states, through intermediate levels. Computed Zeeman profiles are reported and discussed for several typical cases, with emphasis on the effects of different light polarizations. Prospectives of applicability are briefly outlined.     

Forbidden pure rotational Raman spectra of C3v and Td molecules

Some of the pure rotational Raman transitions of polyatomic molecules that are forbidden according to rigid rotor selection rules may acquire intensity by a centrifugal distortion mechanism. These are analogous to forbidden rotational electric dipole transitions which recently have been studied extensively (1–6). A simple technique to obtain the intensity factors leading to the line strengths of such Raman transitions is presented. The intensity factors $\text{b}{}_{\mathrm{J\prime k\prime }}{}^{\mathrm{Jk}}$ and $\text{b}{}_{\mathrm{J\prime }}{}^{\mathrm{J}}$ of the Q, R, and S branches of molecules with C_3v and T_d symmetry are obtained. For C_3v molecules, in addition to the usual selection rules for J, those for k are found to be Δk = ±3 and ±6. There is a modification of intensity of the normally allowed Δk = 0 transitions. T_d molecules, which normally do not have pure rotational spectra, now give rise to weak Raman transitions due to centrifugal distortion.     

Variation Angulaire,Transitions Interdites Dans Le Spectre De R.P.E. Des Ions Mn2+ Dans L'alumine α

The spin Hamiltonian with trigonal symmetry for Mn²⁺ in Al₂O₃ has been derived. The line positions have been calculated using perturbation theory up to third order. Three groups of forbidden transitions ΔM = ± 1 Δm = ± 1 have been investigated. Q′ and γ have been deduced from for forbidden hyperfine doublets. The two evaluations of the spin Hamiltonian parameters from allowed (Δm = 0) and forbidden lines (Δm = 1) are discussed.     

The Δk = ±2 perturbation-allowed ν4 band and inversion-rotation energy levels of 15NH3

More than 800 Δk = ±2 and 60 Δk = ±3 forbidden transitions to the ν₄ and 2ν₂ vibrational levels, respectively, have been assigned in the Fourier transform spectra of ¹⁵NH₃, recorded with a pathlength of 96 m. Combination differences derived from these transitions provide information on the spacing between the ground state energy levels with different rotational quantum numbers K in the interval from 0 to 16. These data along with wavenumbers of all the available allowed transitions pertaining to the ground and ν₂ states have been subjected to a simultaneous least-squares analysis using two different parametrization models to obtain precise values of the inversion-rotation energy levels.     

Third-order theory of the line intensities in the allowed and forbidden vibrational-rotational bands of C3v molecules

A third-order theory of the intensities of the allowed and “forbidden” (perturbation-allowed) transitions to the fundamental vibrational levels of C_3v semirigid molecules has been worked out by using the method of contact transformations applied to the electric dipole moment operator. Explicit expressions have been obtained for the linestrengths of the allowed (Δk = 0, ±1) as well as forbidden (Δk = ±2, ±3, ±4) transitions from the ground vibronic state to the fundamental vibrational levels of C_3v molecules. The treatment takes into account all the important Coriolis and anharmonic interactions in a C_3v molecule, including the effect of the “2, 2” and “2, −1” l-type interactions and the Δk = ±3 interactions on the intensities of the allowed and forbidden vibrational-rotational transitions. The expressions for the linestrengths of the allowed and forbidden transitions are given here in a form suitable to fit the experimental data on the intensities in the vibrational-rotational spectra of C_3v molecules.     

Δk = ±3 “forbidden” infrared transitions in the ν2-band of NH3

Two Δk = ±3 “forbidden” vibration-rotation transitions in the ν₂-band of NH₃ have been measured by using infrared-microwave two-photon spectroscopy and laser Stark spectroscopy. Combining these results with Rao's recent measurement of the band, we have obtained the C₀ rotational constant of 6.2280 ± 0.0008 cm^?1.     

Rotational analysis of the 7390- and 7937-Å bands of NO2 by means of Fourier transform spectroscopy

We have extended to higher N and to K_a = 3 and 4 the rotational analysis of the 7390-Å band of NO₂ performed by K. E. Hallin and A. J. Merer (Canad. J. Phys.55, 2101–2112 (1977)). The lines belong to a perturbed parallel band for which Hallin and others have proposed the vibrational assignment (2 13 1)-(0 0 0) within the electronic ground state. These authors presumed that this band borrows its intensity through a vibronic coupling (spin-orbit and/or Coriolis coupling) from the stronger (0 2 0)-(0 0 0) band of the $\text{A}\text{?}\text{-}\text{X}\text{?}$ electronic system at 7460 Å. We have observed about 900 transitions belonging to the K_a = 0, 1, 2, 3, 4 subbands of the (2 13 1)-(0 0 0) band for N values going up to about 23, and 300 lines of the “hot” band (2 13 1)-(0 1 0). We have also looked for spin-orbit-induced transitions and we have detected about 400 transitions with ΔN ≠ ΔJ. Among them ΔN = ±2 transitions with ΔK_a = 0 or ± 2 have been observed, indicating that N and K_a are no longer good quantum numbers, and demonstrating clearly the existence of rovibronic interactions perturbing the upper levels of the transitions.     

M-dependence of collisional transfer of rotational energy in OCS mixtures

Collision-induced transitions between rotational levels of OCS in the ground vibrational state have been investigated by steady-state microwave double resonance, with the M sublevels separated by a Stark field. The (2 ← 1)_P-(1 ← 0)_S, (3 ← 2)_P-(1 ← 0)_S, and (4 ← 3)_P-(1 ← 0)_S systems have been studied for pure OCS and for mixtures with excess CH₃OH, He, and H₂. For four-level systems having dipolar connections (ΔJ = 1; ΔM = 0, ± 1; parity ± ? ?) between pump and signal levels, it is found for OCS and the OCS-CH₃OH mixture that the dipole-type ΔJ = 1 transitions always dominate the collisional transfer, but for the OCS-He and OCS-H₂ mixtures that ΔJ = 2 quadrupole-type transitions are dominant. For all four collision partners, significant ΔJ = 2 and ΔJ = 3 collisional transfer is observed in some systems, indicating the presence of high-order terms in the collisional interaction.     

Spin forbidden transitions in the Ka = 0 subband of NO2 in the λ = 592.5 nm region

In a high resolution laser excitation spectrum of NO₂, lines were recorded which do not follow the selection rule ΔN = ΔJ = ΔF of “spin allowed” transitions. Line positions and intensities of these “spin forbidden” lines were investigated for all rotational lines up to N″ = 12 of the K_a = 0 subband around λ = 592.5 nm. While the observed line intensities of “spin allowed” transitions can be well described by the J-coupling scheme, neither the J- nor the G-coupling scheme sufficiently describes the “spin forbidden” transitions. The observations can be fitted satisfactorily by perturbation theory, in which the Fermi interaction in ²A₁ is treated as the perturber. This looks similar to a superposition of J and G scheme in the ²A₁ ground state.     

Far infrared spectrum and spectroscopic constants of AsH3 in the ground state

The far ir spectrum of arsine, AsH₃, was recorded in the range 25–100 cm^?1 with a resolution of approximately 0.004 cm^?1. ΔJ = +1, ΔK = 0 rotational transitions were measured and assigned up to J″ = 12. These transitions, together with the presently available microwave and submillimeter-wave data and ground state combination differences, were analyzed on the basis of a rotational Hamiltonian which includes Δk = ±3 and Δk = ±6 interaction terms. The derived ground state molecular parameters reproduced the transition frequencies of both allowed and “perturbation allowed” transitions within the accuracy of the measurements. The equilibrium structure was determined for the AsH₃ molecule.     

Microwave l-type resonance transitions of the v4 = 1 state in PF3: Detailed interactions and molecular structure

Observation of the direct l-type resonance transitions in the microwave spectrum of the v₄ = 1 state of PF₃ has been extended to J = 36. The w-type interaction, (Δl = 0, ΔK = 6), has been found from measurements on the “forbidden” Stark trasitions in the $\text{K}\text{= 3}$ series. Also in this series a close accidental degeneracy was found between J = 30, $\text{K}\text{= 3}$ and 0, leading to new zero-field “forbidden” transitions through the r-type interaction (Δl = 2, ΔK = ?1) and to the determination of the C rotational constant. Nine spectroscopic parameters were determined using 140 observed frequencies including two “forbidden” trasitions. After suitable correction the B and C constants were used to determine the r₀, r_z, and r_e structures for PF₃. The equilibrium structure is estimated to be P-F = 1.561 ± 0.001 Å and ∠FPF = 97.7 ± 0.2°.     

Microwave spectrum and selenol internal rotation of 2-propaneselenol

Microwave spectra of 2-propaneselenol and its deuterated species were measured and assigned for the gauche and trans isomers. The double minimum splittings of the gauche isomers were directly observed from b-type transitions, which were assigned with the aid of a double resonance technique. Rotational constants and torsional splitting of the gauche isomer of the parent species were determined to be A = 7802.50 ± 0.75, B = 2847.68 ± 0.04, C = 2242.03 ± 0.03, ΔA = ?2.52 ± 0.74, ΔB = 0.02 ± 0.05, ΔC = ?0.34 ± 0.03, and Δν = 368.91 ± 0.94 MHz, where ΔA, and ΔB, and ΔC are the differences of the rotational constants between the (+) and (?) states. From the torsional splittings and the energy differences of the two isomers of the parent and SeD species, Fourier coefficients of the selenol internal rotation potential function were determined to be V₂ = ?88 ± 15, V₃ = 1543 ± 29 cal/mole on the assumption of V₁ = 0. Dipole moments and their components were also obtained for the two isomers.     

Selection rules for matrix elements of the generalized momentum operator π at the Γ point in III–V semiconductors

Exact selection rules for matrix elements of the generalized momentum operator π at the Γ point in semiconductors of the GaAs-type without an inversion center are deduced for the first time with thorough account of spin-orbit interaction, which manifests itself in both splitting and mixing of orbital states. In particular, selection rules are obtained for forbidden optical transitions Γ₇ → Γ₈ in the valence band. The selection rules are formulated in terms of Clebsch-Gordan coefficients and reduced matrix elements. The relation between the reduced matrix elements and the mixing parameters of the wave functions is derived.     

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.     

Forbidden rotational spectra of polyatomic molecules

Some of the pure rotational transitions of polyatomic molecules that are forbidden according to the rigid rotor selection rules may acquire intensity by a centrifugal distortion mechanism, in which the intensity depends on the dipole derivatives and on the displacements in the normal coordinates produced by centrifugal distortion. The structures of the predicted spectra are discussed for nonpolar molecules belonging to the point groups D_3h, D_n (n > 2), D_2d, and T_d. Some of the calculated R-branch lines of methane are stronger than some of the lines of HD already observed in the same frequency range. For polar molecules extra contributions to the intensity must be considered and are exemplified for the Δk = ±3 transitions of C_3v molecules. These forbidden rotational transitions may have some astrophysical importance.     

Stark splitting of the optically pumped 118.8-μm CH3OH laser line

We report the first observation that the optically pumped 118.8-μm CH₃OH laser line splits into two components corresponding to ΔM = ±1 transitions in the presence of the Stark field. The splitting shows linear dependence on the Stark field and well amounts to about 34 MHz at the Stark field of 1300 V/cm. The cases are discussed in which a far infrared laser line splits into ΔM = ± 1 components in the presence of the Stark field. Stark field dependence of the 118.8- and 170.6-μm output power is also given.     

High resolution FTIR spectra of AsD3 in the 20-1000 cm−1 region. The ground, 98, v2 = 1 and v4 = 1 states

The pure rotational spectrum of the near-spherical oblate symmetric top AsD₃ has been recorded in the 20–120cm^?′ region with a resolution of 2.3 × 10^?3 m^?1 employing an FT interferometer. Rotational transitions with 5 ? J ? 29 and 0 ? X ? 25 of the ground state (GS) and the v₂ = 1 and v₄ = 1 excited states have been assigned. Splittings were observed for the GS, 98, K = 3 and 6 levels, the K = 3 levels of v₂ and the kl = ?2, 1, 4 and 7 levels of v₄. Furthermore the x,y Coriolis coupled v₂ and v₄ bands, v ⁰ ₂ = 654.4149cm^?1, and v ⁰ ₄ = 714.3399 cm^?1, have been examined with a resolution of 2.4 × 10^?3 cm^?1, and ca. 2500 allowed and 336 ‘forbidden’ lines with J′_max = 31 and K′_max = 28 have been assigned. Appropriately weighted GS data comprising FIR lines, allowed and ‘forbidden’ (up to ΔK = ±6) GS combination differences, mmw data, and ΔJ = 0, ΔK = ±1 distortion moment transitions were fitted together, and GS parameters complete through H parameters have been determined. Two different reductions of the Hamiltonian, either with ΔK = ±6 (h₃) or ΔK = ±3 (ε) off-diagonal elements, have been employed. Equivalence of these reductions up to J = 22 was established while for J > 22 the ε reduction is superior. The v₂ and v₄ data have been fitted with two equivalent models based on different reductions of the rovibrational Hamiltonian. In addition to the dominating x,y Coriolis resonance, ζ ^y ₂₄ 0.520, Δ(k ? l) = ±3 and ±6 interactions are important and were accounted for by the models. The transition moment ratio |M₄: M₂| =0.75 has been determined, with a positive sign of the product M ₂ζ ^y ₂₄ M ₄. An improved r₀ structure, r₀(AsD) = 1.51753 Å and α₀(DAsD) = 92.000°, has been determined.     

Inelastic collision cross section of excited molecules

The (v′=6,J′=43) level in theB ¹Π _u electronic state of Na₂ has been selectively populated by excitation with the 4 880 Å line of the argon laser. Through collisions with He atoms energy is transferred to neighbouring rotational states in Na₂ and the density of these states is determined by observing fluorescence to electronic ground state. From previous measurement of the lifetime of theB ¹Π _u state and new measurements of the intensities of collision induced spectral lines as a function of He pressure, absolute collision cross sections for all rotational transitions up to ΔJ=±5 have been obtained. The total cross section for all rotational transitions observed is σ _rot ^total =65±15 Ų. Preliminary results about collision induced vibrational transitions are also presented.     

ΔK = 2 transitions in H2CO and D2CO

Weak transitions of the type ΔJ = ± 1, $\text{Δ}\text{K}{}_{\mathrm{a}}\text{= ? 2}$, ΔK_c = ± 3 have been observed in H₂CO and D₂CO by the millimeterwave double resonance method and also by direct absorption with a Stark modulated spectrometer. The addition of these new transitions in a least-squares analysis, in which all previously known microwave and millimeterwave data are also included, results in an improved set of rotational and distortion constants.     

The Zeeman effect in spin-allowed and forbidden doublet-doublet transitions in orthorhombic rotating molecules

Theoretical predictions of the Zeeman effect on spin-allowed and forbidden doublet-doublet transitions in near-symmetric top molecules are reported, with the assistance of computer simulations of band profiles. Bandwidths in the high-field limit have been determined. Marked differences have been found between the behavior of spin-allowed and forbidden transitions. The intermediate-field effect on spin-allowed transitions is sensitive to the relative energy order of the zero-field spin components of the rotational sublevels in the combining vibronic states. In the high-field limit the rotational components of spin-allowed transitions give rise to a single band, corresponding to ΔM_S = 0, whereas the bands with ΔM_S = ±1 are also expected in spin-forbidden transitions. The applicability to actual cases is finally discussed.