An experimental study of the form factor in the decay K+ → πoe+ν

The q² variation of the factor $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)}$ in the decay K⁺→π⁰e⁺ν has been studied using a sample of even detected in the CERN 1.1 m³ heavy-liquid bubble chamber. The data are consistent with a linear development $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)=?}{}_{\mathrm{+}}\text{(0) (1+λ}{}_{\mathrm{+}}\text{q/m}{}^2{}_{\mathrm{\pi }}\text{)}$ with λ₊=0.027±0.008.     

Analysis of the Raman spectrum of SF6

The Raman active fundamentals ν₁(A1g), ν₂(Eg), ν₅(F2g), and the overtone 2ν₆ of SF₆ have been investigated with a higher resolution and the band origins were estimated to be: ν₁ = 774.53 cm^?1, ν₂ = 643.35 cm^?1, ν₅ = 523.5 cm^?1, and 2ν₆ = 693.8 cm^?1. Raman and infrared data have been combined for estimation of several anharmonicity constants. The ν₆ fundamental frequency is calculated as 347.0 cm^?1. From the analysis of the ν₂ Raman band, the following rotational constants of both the ground and upper states have been calculated:

$\text{B}{}_0\text{= 0.09111 ± 0.00005}\text{cm}{}^{\mathrm{?1}}\text{; D}{}_0\text{= (0.16±0.08)10}{}^{\mathrm{?7}}\text{cm}{}^{\mathrm{?1}}$

;

$\text{B}{}_2\text{= 0.09116 ± 0.00005}\text{cm}{}^{\mathrm{?1}}\text{; D}{}_2\text{= (0.18±0.04)10}{}^{\mathrm{?7}}\text{cm}{}^{\mathrm{?1}}$

.     

The bending vibration bands ν4 and ν5 of HCCI

The bending vibration bands ν₄ and ν₅ of HCCI were studied. From the observed rotational structure the rotational constant B₀ and the centrifugal distortion constant D₀ were obtained. The results were B₀ = 0.105968(7) cm^?1 and D₀ = 1.96(7) × 10^?8 cm^?1 from ν₄ and B₀ = 0.105948(8) cm^?1 and D₀ = 1.96(11) × 10^?8 cm^?1 from ν₅. The structure of the hot bands 2ν₅(Δ) ← ν₅(Π) and 3ν₅(φ) ← 2ν₅(Δ) was also resolved and hence the values α₅ = ?3.033(8) × 10^?4 cm^?1 and q₅ = 9.3(3) × 10^?5 cm^?1 could be derived. The other most intense hot bands following ν₅ could be explained in terms of the Fermi diads $\text{ν}{}_3\text{2ν}{}_5{}^0$ and $\text{ν}{}_3\text{+}\text{ν}{}_5{}^{\mathrm{\pm 1}}\text{3ν}{}_5{}^{\mathrm{\pm 1}}$. Of the numerous hot bands accompanying ν₄, only those between different excited states of ν₄ could be assigned. Then estimates for α₄ and q₄ were also obtained. In addition, several vibrational constants were derived.     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

Rotation-vibration analysis of the Coriolis-coupled ν5g, ν6g, ν8g and ν9 bands of H2CCO

Medium resolution infrared grating spectra of gaseous ketene, H₂CCO were recorded between 1000 and 400 cm^?1, both at instrument temperature (40°C) and with cooling (?40°C). Interferometric Fourier spectra were also measured at ?70°C with resolution 0.22 cm^?1 between 450 and 330 cm^?1. The K structure of the fundamentals ν₅, ν₆, ν₈, and ν₉ was assigned. These fundamentals are coupled by a-axis Coriolis interactions. These couplings were analysed on the symmetric top basis for setting up the perturbation matrix and by utilizing the K-dependent Coriolis shifts of levels. A preliminary analysis of the Coriolis intensity anomalies was also undertaken.Band center values from combination differences are $\text{ν}{}_5{}^0\text{= 587.30 (27)}$ and $\text{ν}{}_6{}^0\text{= 528.36 (39)}\text{cm}{}^{\mathrm{?1}}$. Synthetic spectra indicate the band origins of ν₈ and ν₉ to be close to 977.8 and 439.0 cm^?1, respectively. Estimates of Coriolis coupling constants obtained from synthetic spectra are $\text{ζ}{}_{58}{}^{\mathrm{a}}\text{= + 0.33 (5)}$, $\text{ζ}{}_{68}{}^{\mathrm{a}}\text{= + 0.714 (20)}$, $\text{ζ}{}_{59}{}^{\mathrm{a}}\text{= ? 0.774 (20)}$, and $\text{ζ}{}_{69}{}^{\mathrm{a}}\text{= ? 0.30 (2)}$. Approximate ratios of unperturbed vibrational transition moments obtained from spectral simulations are $\text{M}{}_8{}^0\text{:±iM}{}_5{}^0\text{:±iM}{}_6{}^0\text{:M}{}_9{}^0\text{≈ +2:?9:+10:+0.5}$.     

Flavour symmetry breaking in antiquark distributions

We show that knowledge of the valence quark distribution of a proton at one value of q², enables one to calculate a contribution to the difference between the distribution of anti-up quarks $\text{(}\text{u}{}_{\mathrm{<mtext>p</mtext>}}\text{)}$ and anti-down quarks $\text{(}\text{d}{}_{\mathrm{<mtext>p</mtext>}}\text{)}$ in the sea of the proton at higher values of q². This difference can be expressed as a linear combination of the structure functions F₁, for νp → νX and e^?p → e^?p (for which one knows the q² behaviour of the moments) and for $\text{ν}\text{p}\text{→ μ}{}^{\mathrm{?}}\text{X}\text{and}\text{ν}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{X}$ (for which one knows the q² behaviour of the odd moments). The calculable contribution involves a non-trivial continuation of the even (odd) moments of the neutral (charged) current structure functions to odd (even) moments. We calculate this contribution and although we find that its sign is negative we point out that this cannot be interpreted as a consequences of the Pauli exclusion principle. We discuss the constraints our results impose on antiquark distributions.     

Activation energy of field emission flicker noise power due to adsorbed potassium on tungsten

The temperature dependence of the field emission flicker noise spectral density functions has been investigated for potassium adsorbed on tungsten (112) planes by a probe hole technique. By integration of the spectral density functions $\text{W(?) = B}{}_{\mathrm{i}}\text{?}{}^{\mathrm{?ge}}\text{i}$ the noise power $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ for different frequency intervals Δ? is obtained. From the exponential temperature dependence of $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ noise power “activation energies” q_Δ? are determined. Plots of these energies versus coverage show a similar “oscillating” behaviour as recently found for $\text{W(?}{}_{\mathrm{j}}\text{)}$ or which indicates phase transitions of the adsorbed potassium submonolayers. The noise activation energies are discussed in terms of existing models and a comparison is made between the experimental q values and surface diffusion energies E_d as determined by conventional methods.     

Reflection of long waves by interfaces

We derive comparison identities for waves satisfying the equation d²Ψ/dz²+q²(z)Ψ=0. One of these identities is used to show that to second order in the product (wavenumber component normal to interface) × (interface thickness), the reflection amplitude is given by $\text{r=(1?2q}{}_1\text{q}{}_2\text{l}{}^2\text{)}\text{(q}{}_1\text{?q}{}_2\text{)}\text{(q}{}_1\text{+q}{}_2\text{)}$, where l is a legnth determined by the deviation of the interface profile from a step, and q₁, q₂ are the normal components of the wave numbers in media 1 and 2 on either side of the interface. For the continuous interfaces discussed, l is about two-fifths of the 10–90 interface thickness. The corresponding formula for the transmission amplitude is $\text{t=(1+}\text{1}\text{2}\text{(q}{}_1\text{?q}{}_2\text{)}{}^2\text{l}{}^2\text{)}\text{2q}{}_1\text{(q}{}_1\text{+q}{}_2\text{)}$.     

Necessary and sufficient conditions for the existence of a lagrangian. The case of quasi-linear field equations

Necessary and sufficient conditions for the existence of the Lagrangian associated with given field equations of motion are investigated. For the quasi-linear equations A_ab^μν(x^λ, φ^c, φ_?^c)φ_μν^b + B_a(x^μ, φ^b, φ_ν^b) = 0, the complete necessary and sufficient conditions are obtained, resorting to the formalism of an exterior derivative. It is emphasized that, to find expressions of these conditions, the anti-symmetric parts of the second derivatives of a Lagrangian, $\text{R}{}_{\mathrm{\mu \nu }}{}^{\mathrm{ab}}\text{= (}\text{?}{}^2\text{L}\text{?φ}{}_{\mathrm{\mu }}{}^{\mathrm{a}}\text{?φ}{}_{\mathrm{\nu }}{}^{\mathrm{b}}\text{?}\text{?}{}^2\text{L}\text{?φ}{}_{\mathrm{\nu }}{}^{\mathrm{a}}\text{?φ}{}_{\mathrm{\mu }}{}^{\mathrm{b}}\text{)/2}$, which disappear in the field equations, take an important role. The procedure to construct the Lagrandian associated with the field equations is also presented.     

Charge density wave commensurability in 2H-TaS2 and AgxTaS2

The charge density wave transition in 2H-TaS₂near 75 K has been observed to be incommensurate, using electron diffraction, with $\text{q}{}^1\text{= (}\text{0.338}\text{±}\text{0.002}\text{)a}{}^1{}_0$ along the 〈10.0〉 directions which, within the experimental uncertainty, remains temperature independent to about 14 K. Incommensurate charge density formation is also observed in Ag_xTaS₂ samples for $\text{x?}\text{0.26}$ with an increase in q¹ to $\text{(}\text{0.347}\text{±}\text{0.002}\text{)a}{}^1{}_0$ when x?0.26. Within the experimental error q¹ appears to be temperature independent to 25 K.     

Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.     

The ã3A2 ← X̃1A1 absorption spectrum of thioformaldehyde: A vibrational and rotational analysis

The results of a vibrational and rotational analysis of the banded $\text{a}\text{?}{}^3\text{A}{}_2\text{←}\text{X}\text{?}{}^1\text{A}{}_1$ transition in $\text{CH}{}_2\text{S}\text{CD}{}_2\text{S}$ are presented. Only three of the six vibrational modes are active in the spectrum with $\text{ν′}{}_2\text{=}\text{1320}\text{1012}$, $\text{ν′}{}_3\text{=}\text{859}\text{798}$, and $\text{2ν′}{}_4\text{=}\text{711}\text{516}\text{cm}{}^{\mathrm{?1}}$. The spin forbidden transition gains intensity primarily by a mixing of the ${}^1\text{A}{}_1\text{(π}{}^1\text{,π)}$ and ${}^3\text{A}{}_2\text{(π}{}^1\text{,n)}$ states. This is confirmed by a rotational analysis of the 0₀⁰ band of both isotopes. The rotational analysis shows that the coupling in the $\text{a}\text{?}{}^3\text{A}{}_2$ state is near Hund's case b and that the spin constants are nearly 10 times greater than those observed for CH₂O. A $\text{CNDO}\text{2}$ calculation shows that this difference is due to the greater spin orbit coupling of S in CH₂S and to the smaller energy differences between the $\text{B}\text{?}{}^1\text{A}{}_1\text{(π}{}^1\text{,π)}$, $\text{b}\text{?}{}^3\text{A}{}_1\text{(π}{}^1\text{,π)}$, $\text{X}\text{?}{}^1\text{A}{}_1$, and the $\text{a}\text{?}{}^3\text{A}{}_2\text{(π}{}^1\text{,n)}$ states. The r₀ structure calculated from the rotational constants is $\text{r}{}_{\mathrm{<mtext>CS</mtext>}}\text{= 1.683}\text{A}\text{?}$, $\text{r}{}_{\mathrm{<mtext>CH</mtext>}}\text{= 1.082}\text{A}\text{?}$, β_HCH = 119.6°, and α (out of plane) = 16.0°. A simultaneous fit of the vibrational levels in ν′₄ of CH₂S and CD₂S to a double minimum potential function yielded a barrier to molecular inversion of 13 cm^?1 and an equilibrium out-of-plane angle of 15°.     

Constraints on the reaction νμ(νμ) + Z → νμ(νμ) + μ− + μ+ + Z in theories with neutral currents

In the presence of neutral lepton currents, the characteristics of the reaction $\text{ν}{}_{\mathrm{\mu }}\text{(}\text{ν}{}_{\mathrm{\mu }}\text{) +}\text{Z}\text{→ ν}{}_{\mathrm{\mu }}\text{(}\text{ν}{}_{\mathrm{\mu }}\text{) + μ}{}^{\mathrm{?}}\text{+ μ}{}^{\mathrm{+}}\text{+}\text{Z}$ are modified from those expected in the conventional V-A theory. We show that in a very general class of intermediate boson theories, the modification produced can be specified entirely in terms of the cross sections for $\text{ν}{}_{\mathrm{\mu }}\text{(}\text{ν}{}_{\mathrm{\mu }}\text{) +}\text{e}{}^{\mathrm{?}}\text{→ ν}{}_{\mathrm{\mu }}\text{(}\text{ν}{}_{\mathrm{\mu }}\text{) +}\text{e}{}^{\mathrm{?}}$. Such a constraint does not necessarily exist in models with four-fermion interaction.     

Infrared spectrum of acetonitrile: Analysis of Coriolis resonance

The Coriolis resonance between ν₄ and ν₇ in CH₃CN and between ν₁ and ν₅, ν₃ and ν₆, and ν₄ and ν₇ in CD₃CN has been analyzed, applying the technique developed by DiLauro and Mills, to obtain the signs of [$\text{ζ}{}_{\mathrm{r,sa}}{}^{\mathrm{y}}\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$] and the ratio of $\text{?μ}\text{?Q}{}_{\mathrm{r}}$ to $\text{?μ}\text{?Q}{}_{\mathrm{s}}$ for the interacting pairs in CD₃CN. For (ν₄, ν₇) in both CH₃CN and CD₃CN, the sign of [$\text{ζ}{}_{\mathrm{r,sa}}{}^{\mathrm{y}}\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$] is found to be negative as it is also for (ν₁, ν₅) in CD₃CN. For (ν₃, ν₆) the sign of this interaction term is found to be positive. For a given definition of normal coordinates the signs of these interaction terms give the relative signs of $\text{?p}\text{?Q}{}_{\mathrm{r}}$ and $\text{?p}\text{?Q}{}_{\mathrm{sa}}$; our study also gives approximate values for the corresponding ratio [$\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)}\text{(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$]     

The 2780 Å absorption system of thiophosgene

The vapor phase absorption spectrum of thiophosgene (Cl₂CS) in the 2500–2900 Å region consists of a broad intense band ($\text{log}\text{?}{}_{\mathrm{<mtext>max</mtext>}}\text{= 3.5}\text{at}\text{2540}\text{A}\text{?}$. On the red side of this a vibrationally discrete structure is found which becomes increasingly diffuse and merges into the broad band as the wavelength is decreased. It is shown that this vibrational structure can be explained as due to a $\text{π → π}{}^1$, ${}^1\text{A}{}_1\text{-}\text{X}\text{?}{}^1\text{A}{}_1$ electronic transition between a planar ground state and a pyramidal excited state of the molecule. In the latter state, the CS stretching mode ν₁′(a₁) = 681 cm^?1 and the CCl bending mode ν₃′(a₁) = 147 cm^?1. From the inversion doublet splitting of the out-of-plane mode ν₄′(b₁), the barrier to inversion is calculated to be ～126 cm^?1, with an equilibrium out-of-plane angle of ～20°.     

Vibrational spectra and force constants of symmetric tops: High resolution spectra of monoisotopic H3SiCl in the 2200-cm−1 region and rovibrational analysis of the ν1 and ν4 fundamentals

The gas phase infrared spectra of monoisotopic H₃Si³⁵Cl and H₃Si³⁷Cl have been studied in the $\text{ν}{}_1\text{ν}{}_4$ region near 2200 cm^?1 with a resolution of 0.012 and 0.04 cm^?1, respectively, and rotational fine structure for ΔJ = ±1 branches has been resolved. In addition, some information on ν₃ + ν₄ of H₃Si³⁵Cl near 2750 cm^?1 has been obtained. ν₁ and ν₄ are weakly coupled by Coriolis x, y resonance, $\text{B}\text{Ω}{}_{14}\text{ζ}{}_{14}\text{～ 2 × 10}{}^{\mathrm{?3}}\text{cm}{}^{\mathrm{?1}}$, only the upper states K′ = 2, l = 0 and K′ = 1, l = ?1 being substantially affected. Local perturbation due to rotational l(±1, ±1)-type resonance with ν₃ + ν₅⁺¹ + ν₆⁺¹ and ν₃ + ν₅⁺¹ + ν₆^?1 is revealed in the ΔK = +1 and ?1 branches, respectively. From a fit of the experimental line positions, standard deviations of 1.4 and 3.8 × 10^?3 cm^?1, respectively, to a model with five interacting levels conventional excited state parameters and interaction constants have been obtained. In $\text{H}{}_3\text{Si}{}^{35}\text{Cl}\text{H}{}_3\text{Si}{}^{37}\text{Cl}$ the fundamentals are ν₁, $\text{2201.94380(15)}\text{2201.9345(7)}$ and ν₄, $\text{2209.63862(8)}\text{2209.6254(2)}\text{cm}{}^{\mathrm{?1}}$, respectively. Q branches of the “hot” band (ν₃ + ν₄) ? ν₃ and of ν₄ of the ²⁹Si and ³⁰Si species have been detected.     

Vibronic coupling as a major cause of the anharmonicity of antisymmetric stretching in the ground state of NO2

Approximate experimental and theoretical information about vibronic coupling of the $\text{X}\text{?}{}^2\text{A}{}_1$ (ground) and $\text{A}\text{?}{}^2\text{B}{}_2$ electronic states of NO₂—by its antisymmetric vibration ν₃(b₂)—is tested in model calculations of the accurately known ground-state levels ν₃ = 0, 1, 2, 3. The test is positive and it is estimated that 64% of the very large observed anharmonic constant χ₃₃ has its origin in vibronic coupling. In this model, ν₃ in the à state is predicted at about 1200 cm^?1.     

Strengths and lorentz broadening coefficients for spectral lines in the ν3 and ν2 + ν4 bands of 12CH4 and 13CH4

Line strengths and self- and nitrogen-broadened half-widths were measured for spectral lines in the ν₃ and ν₂ + ν₄ bands of ¹²CH₄ and ¹³CH₄ from 2870–2883 cm^?1 using a tunable diode laser spectrometer. From measurements made over a temperature range from 215 to 297 K, on samples of ¹²CH₄ broadened with N₂, we deduced that the average temperature coefficients n, defined as $\text{b}{}_{\mathrm{<mtext>L</mtext>}}{}^0\text{(T) = b}{}_{\mathrm{<mtext>L</mtext>}}{}^0\text{(T}{}_0\text{)(}\text{T}\text{T}{}_0\text{)}{}^{\mathrm{?n}}$, of the Lorentz broadening coefficients for the ν₃ and ν₂ + ν₄ bands of ¹²CH₄ were 0.97 ± 0.03 and 0.89 ± 0.04, respectively. A smaller increase is observed in line half-width with increasing pressure for E-species lines, for both self- and nitrogen-broadening, than for other symmetry species lines over the range of pressures measured, 70 to 100 Torr.     

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.     

Consistent MFA correlation functions of Ising models for all temperatures

A correct calculation of the Ising model correlation function C(q) = 〈(S(q) ? 〈S(q)〉) (S(-q) ? 〈S(-q)〉)〉 in the MFA results in

$\text{C(q)=}\text{〈S}{}^2\text{〉?〈〉}{}^2\text{1?(〈S}{}^2\text{〉?〈S〉}{}^2\text{βJ(q}\text{1}\text{N}\text{∑}\text{q}\text{1}\text{1?〈S〉}{}^2\text{βJ(q)}{}^{\mathrm{?1}}\text{C(q) fulfills the exact sum rule N}{}^{-1}\text{Σ}{}_{\mathrm{q}}\text{C(q) = 〈S}{}^2\text{〉 ? 〈S〉}{}^2$

. Previous literature supposed a violation of this sum rule to be a characteristic disadvantage of this approximation.