Analysis of the B1Πu → X1Σg+ band system of 7Li2 molecule excited by the 4545- and 5287-Å visible lines of the argon ion laser

Two new fluorescence series have been excited by the two lines at the extreme ends of the range of visible Ar⁺ transitions, 4545 and 5287 Å. In each case the B¹Π_u electronic state of ⁷Li₂ is excited, to levels $\text{v′ = 12, J′ = 13 (4545}\text{A}\text{?}\text{)}$ and $\text{v′ = 2, J′ = 58 (5287}\text{A}\text{?}\text{)}$. Fluorescence to the ground state can be detected in the range 2 ≤ v″ ≤ 23 and 0 ≤ v″ ≤ 8, respectively. Measured relative intensities agree well with calculated radiative transition probabilities reported herein.     

The A3Π(1) ← X1Σ+ absorption spectrum of ICl: Rotational analysis of bands in the v″ = 2, 3, 4, 5 progressions (λ > 7000 Å) and a reexamination of published data for individual bands in the v″ = 0, 1, 2 progressions

Molecular constants are reported for the A³Π(1) and X¹Σ⁺ states of I³⁵Cl (0 ≤ v″ ≤ 5, 3 ≤ v′ ≤ 35) and of I³⁷Cl (v″ = 0, 11 ≤ v′ ≤ 32) from least-squares fits to individual bands. The constants are based on analyses of new bands photographed at $\text{λ > 7000}\text{A}\text{?}$ and on data previously reported in the literature. Attention is given to the choice of adequate models. The application of long-range theory to the levels of A³Π(1) near convergence indicates a homogeneous perturbation in addition to the heterogeneous perturbations established in previous work. However, there is no evidence of any discontinuities in the manifold of vibrational levels near v′ = 6 or 9 of the type suggested in previous work.     

Rotational analysis of the B2Σ+ → X2Σ+ system of the aluminum monoxide radical,AlO

Twenty-five bands of the B²Σ → X²Σ system of AlO with 0 ≤ v′ ≤ 9 and 0 ≤ v″ ≤ 6 have been photographed at high resolution. The measured positions of the assigned lines of each band have been fitted by least-squares to obtain estimates of the constants (B′, D′, B″, D″), the band origin, and Δγ_v′,v″, which is the difference of the upper and lower state spin-doubling constants (γ′_v and γ″_v). The parameters from individual bands have been merged to single-valued estimates, as well as to polynomial representations in ($\text{v +}\text{1}\text{2}$). Although the spin-doubling constants are not found absolutely for either state, their vibrational dependences are well determined. The data are employed in the computation of RKR potential energy curves and an array of Franck-Condon factors and r-centroids.     

Λ-Doubling in the v = 2 ← 0 overtone band in the infrared spectrum of NO

Λ-doubling in the first overtone, v = 2 ← 0, vibration-rotation band of ¹⁴N¹⁶O has been measured with Doppler-limited resolution using a tunable difference-frequency laser spectrometer. P- and R-branch Λ-splittings for $\text{1}\text{2}\text{<- J ≤}\text{53}\text{2}$ in the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ electronic state and for $\text{47}\text{2}\text{≤ J ≤}\text{57}\text{2}$ in the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state have been determined by least squares fitting of the spectral profiles to Gaussian doublets with a precision of better than ±1.5 MHz for the stronger, well-resolved lines. The Λ-doubling parameters obtained from a least square Hamiltonian analysis of the data for the v = 2 level are p₂ = 349.542 (60) MHz and q₂ = 2.754 (5) MHz with the error limits representing three standard deviations. These precise v = 2 parameters are combined with excellent v = 1 constants available in the literature to calculate the Λ-splittings expected in the v = 2 ← 1 hot band of NO for comparison with recently reported measurements. The effect of nuclear hyperfine structure on the lineshapes of some of the low J overtone transitions has also been observed.     

Hyperfine and Λ-doubling parameters for the v = 1 state of NO from infrared-radiofrequency double resonance

Hyperfine Λ-doubling transitions have been measured for a number of rotational levels with 2.5 ≤ J ≤ 20.5 in the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{v = 0}\text{and}\text{1}$ states of ¹⁴N¹⁶O. The measurements were made with infrared-radiofrequency double-resonance spectroscopy, utilizing close coincidences between CO laser lines and NO 1-0 band transitions in the 5.4-μm region. A combined fit of the present and previous data gives new information for NO in the v = 1 state: greatly improved Λ-doubling parameters and the first determination of hyperfine interaction parameters.     

Charm production by weak neutral currents

We discuss quantitatively the production of charm in $\text{v}\text{N and}\text{v}\text{N}$ neutral current interactions, and the anomalous lepton events that follow from semi-leptonic charm decay. Diagonal neutral currents, in the Weinberg-Salam model and similar models, predict associated charm production with small cross sections: e.g. $\text{σ(v}\text{N}\text{→ vcc}{}^{\mathrm{?}}\text{X}\text{)/σ(v}\text{N}\text{→ μ}{}^{\mathrm{?}}\text{X}\text{) ? 10}{}^{\mathrm{?2}}$ at high energy. The meagre data on vN → ve⁺X are consistent with a rate of this order. Non-diagonal neutral currents, if present, could give larger cross sections via valence p → c transitions. It should be possible to distinguish diagonal from non-diagonal contributions by their x- or u-dependences, where u = x(1 ? y). We calculate the expected energy distributions of the leptons in characteristic vN → v?⁺X and vN → v?⁺?^?X charm decay events using simple models, and discuss some practical problems in neutral current measurements.     

Precise determination of the v and N dependence of the spin-rotation and hyperfine interactions in the CaF X2Σ12 ground state

The molecular-beam, laser-rf, double-resonance technique has been used to make high-precision measurements of both the v and N dependences of the spin-rotational and hyperfine splittings in the $\text{X}{}^2\text{Σ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ ground state of CaF. The precision (1 ppm) and scope (1 ≤ N″ ≤ 119, 0 ≤ v″ ≤ 4) of the data allow evaluation of many of the parameters (with the Dunham expansion) in the Hamiltonian. The results are compared with new ab initio calculations.     

Far-infrared LMR spectroscopy of NF a1Δ (v = 0, 1, 2)

Far-infrared LMR spectra of NF in its a¹Δ state have been detected and assigned. Lines in two rotational transitions of both v = 0 and v = 1 states were measured for analysis. The derived constants are in excellent agreement with earlier EPR work (hyperfine parameters, v = 0) and with diode laser spectroscopy (rotational constants for v = 0 and 1). Using the optimized parameters it is shown that there is a significant decrease in the fluorine hyperfine constant on vibrational excitation. One rotational transition from $\text{v = 2}\text{NF}{}^1\text{Δ}$ has also been assigned.     

On the definition of the pressure of an infinite system

A microcanonical system $\text{L}$^o_Λ is considered together with a manometer $\text{M}$_Λ. The thermodynamic limit Λ → ∞ is taken for the system $\text{L}$_Λ composed of $\text{L}$^o_Λ and $\text{M}$_Λ. This yields a definition of the pressure P(v, ε) of $\text{{}\text{L}{}^{\mathrm{o}}{}_{\mathrm{\Lambda }}\text{; Λ → ∞}}$ for given values ε and v of the energy and particle densities. P(v, ε) is shown to be equal to the thermodynamic function p(z, β) derived from the grand canonical ensemble for almost all values of ε and v provided the appropriate equilibrium values of the temperature β^?1 and the chemical potential μ = β^?1 log z are inserted.     

Thermodynamical information on quark matter from the nucleon valence quark distribution

If the valence quarks in the nucleon are considered as a gas of the non-interacting massless particles, an expression of the xF₃(x) structure function is obtained which reproduces very well the experimental $\text{v(}\text{v}\text{)}$N data in the range 0.1?x?0.8. The effective temperature of such a quark gas is found to be of the order of 50 MeV.     

Derivation of bonding distance and vibration frequency from field evaporation experiments

This paper extends the analysis of previously reported data, concerning the field evaporation of rhodium atoms that escape as Rh⁺ and are then post-ionised to Rh²⁺. A more general formula is derived for obtaining values of critical distance x^cr from correlated measurements of temperature, field (F), activation energy (Q), and onset appearance energy. A zkT-type correction is included. If prior to evaporation the surface atom is vibrating in an effectively parabolic potential well, and a Gomer-type escape mechanism operates, then experimental plots of $\text{Q}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ versus $\text{1}\text{F}$ and of x^cr versus $\text{Q}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ should be linear. Such plots may be used to obtain estimates of zero-Q evaporation field F^e, electrical bonding distance a, and vibrational force-constant k and frequency v. These formulae and methods are applicable to a range of materials and evaporation situations. For rhodium this paper establishes that escape takes place via a Gomer-type escape mechanism, and deduces the following values: F^e = 61 ± 20 V/nm; a = 0.13 ± 0.035 nm; v = (1.4_+0.5^?0.3) × 10¹²Hz.     

Overall width,mean peak width and the uncertainty principle

We define the overall width W and the mean peak width w of a normalized function ψ (x). We show W ≤ 2Δx and w > (2Δp)^?1, where Δx and Δp are standard deviations. Analogous relations hold for the Fourier transform. The uncertainty principle is expressed precisely by these relations, not by $\text{ΔxΔp ≥}\text{1}\text{2}$.     

Transition amplitudes and probabilities for the Weinberg-Salam model

Transition probabilities for the processes vv?vv, vv?, $\text{vv}$?$\text{vv}$, and spin-dependent transition amplitudes for the processes ve?ve, vē?vē, v?e?v?e, $\text{ve}$?$\text{ve}$ and vv??eē are calculated in lowest order for the Weinberg-Salam model.     

Relation between classical and quantum formulations of the Franck-Condon principle: The generalized r-centroid approximation

The classical transition point $\text{r}{}_{\mathrm{v\prime v″}}{}^1$ for the (v′, v″) band is introduced as the point where the kinetic energy does not change during the transition (classical statement of the Franck-Condon principle). It is shown that when the r-centroid approximation is valid, it implies that the r centroid $\text{r}{}_{\mathrm{v\prime v″}}$ equals $\text{r}{}_{\mathrm{v\prime v″}}{}^1$, allowing a new connection to be made between the classical and quantum statements of the Franck-Condon principle. The r-centroid approximation fails for some classically allowed bands having large Franck-Condon factors. This occurs when the (v′, v″) band has more than one classical transition point. A generalization of the r-centroid approximation permits such bands to be used in determining the variation of the electronic transition moment with internuclear distance.     

Radial matrix elements of rn for twofold and threefold isotropic simple harmonic oscillators

A generating function for associated Laguerre polynomials and Louck's recursion relations have been employed independently to formulate radial matrix elements of rⁿ for g-fold (g = 2, 3) isotropic simple harmonic oscillators in terms of quantum numbers v and l. This paper gives all relevant matrix elements (vl|rⁿ|v′l′) of rⁿ for n = 1,2, …, 7 and the diagonal element of r⁸. Introduction of the quantities, $\text{V =}\text{1}\text{2}\text{(v + v′ + g)}$ and $\text{L =}\text{1}\text{2}\text{(l + l′ + g ? 2)}$, simplifies the expressions and reveals symmetries and patterns occurring as n increases. Results are compared with those for the one-fold oscillator and sample computer routines have been prepared for numerical evaluation of the matrix elements for g = 1, 2, 3.     

Ultraviolet laser-induced fluorescence spectrum of fluorochlorocarbene in solid argon

CFCl has been produced for spectral investigation by matrix reactions of alkali metal atomic beams with CFCl₃ in argon followed by rapid quenching to 15°K on a tilted copper wedge. When these samples were irradiated with near uv light from a krypton ion laser, a very intense, highly structured fluorescence spectrum was observed. This emission system extended from about 25 000 cm^?1 to 15 000 cm^?1 and peaked in intensity at about 22 000 cm^?1. The three most intense progressions are assigned to transitions from a common excited state to ground state levels (0v₂0), (1v₂0) and (1v₂1). New molecular constants determined from these progressions include $\text{ω}{}_2{}^0\text{= 446}\text{cm}{}^{\mathrm{?1}}$, x₂₂ = ?1.2 cm^?1, x₁₂ = ?3 cm^?1, x₂₃ = ?4 cm^?1, and x₁₃ = ?6 cm^?1. CFCl was also produced by in situ photolysis of CFCl₃ using laser plasma emission and by alkali metal atom reactions with CF₂Cl₂, CF₂ClBr, and CHFCl₂.     

Laser-induced fluorescence spectrum of nitrogen dioxide in the neighborhood of 6125 Å

The resonance fluorescence spectrum of nitrogen dioxide has been excited by a tunable, cw dye laser in the neighborhood of 6125 Å. The rotational constants of the ²B₂ upper electronic state are determined as follows, in units of cm^?1: A_v′ = 7.2 ± 0.6; $\text{B}\text{?}{}_{\mathrm{v}}\text{′ = 0.454 ± 0.015}$; B_v′ = 0.496 ± 0.046; C_v′ = 0.412 ± 0.019. The band origin is at 16 325.1 ± 1.8. Quoted error limits are standard deviations obtained from the fit of the data. The vibrational assignment of the upper state is (0, 5, 0), and by combination with the data of other workers, we estimate for its vibrational constants, in cm^?1: ω₁′ + x₁₁′ = 1425.7; ω₂′ = 876.6; x₂₂′ = ?0.83; x₁₂′ = ?8.1. The molecular geometry in the upper state is briefly discussed.     

Scale breaking in inclusive charged particle production by e+e− annihilation

The scale cross section $\text{s}\text{d}\text{σ}\text{d}\text{x}{}_{\mathrm{<mtext>p</mtext>}}$ for inclusive charged-particle production in e⁺e^? annihilation has been studied for c.m. energies W between 12.0 and 36.7 GeV. Scale breaking is observed. For x_p>0.2 the cross section decreases by ≈20% when W increases from 14 to 35 GeV. The production angular distribution was used to separate the longitudinal and transverse cross-section contributions and to determine the ratio of the structure functions $\text{m}\text{W}{}_1$ and $\text{v}\text{W}{}_2$.     

High vibrational levels of the X state of ICl,and the electronic-coriolis coupling of the X and A states

Ro-vibrational levels of the ground state of ICl have been measured in the range v_x = 35–73 and J_x < 55 using three-stage polarization-labeling spectroscopy. When merged with established microwave and fluorescence data for the lower levels, these results lead to a self-consistent set of spectroscopic constants G_v, B_v, D_v and H_v for all levels v_x ≤ 73. The highest G_v and G_v + F_J term values recorded are, respectively, 52.7 and 1.37 cm^?1 below the dissociation limit. Coefficients of the long-range interaction I + Cl are determined by analysis of the outer wings of the RKR potentials for the X(0⁺) and A′(2) states. Electronic rotational interaction between X and the well-known A(1) state of ICl is shown to account for at least a major part of the $\text{Ω-doubling}$ splitting observed in A: the electronic matrix element characterizing this interaction is shown to be strongly r-dependent, and reasons for this are reviewed.