Relationships in infrared intensity theories,in particular the Mayants-Averbukh theory

A brief survey is given of the Mayants-Averbukh infrared intensity theory in relation to the more well-known but equivalent polar tensor theory. In addition, the appearances of the symmetry invariant parameter matrices D_n⁰ of the Mayants-Averbukh theory were derived and tabulated for various symmetries about the midpoint of bond n. The use of these matrices and a single bond coordinate system will offer a convenient alternative to the Mayants-Averbukh treatment of a central, symmetric bond. The rotational mode equations of the Mayants-Averbukh and polar tensor theories have been investigated to elucidate the constrainsts which they impose on infrared intensity theories based on the bond dipole moment model and the atomic point charge model. It was found that the valence-optical theory is in full conformity with the rotational modes only if all electrooptical parameters $\text{?μ}{}_{\mathrm{n}}\text{?γ}{}_{\mathrm{i}}$ are neglected, where γ_i is the ith internal angular coordinate. The constraints imposed on the equilibrium charge-charge flux theory correspond to neglect of all charge flux parameters. The generalized valence-optical theory was found to be incompatible with the rotational mode equations of the Mayants-Averbukh theory. However, its basic dipole moment equation was found useful for suggesting a unique interpretation of a set of d parameters (elements of D_n⁰) in terms of bond dipole moment components.     

Interpretation of the d-parameters,occurring in the Mayants-Averbukh theory of infrared intensity,in terms of the bond dipole moment concept: Equivalence with the valence-optical theory in the zeroth approximation for linear and planar molecules

From a comparison with the valence-optical theory of infrared intensity in the zeroth approximation, it is suggested that the d-parameters (elements of the effective charge tensor D_n⁰ of a bond) occurring in the Mayants-Averbukh theory can be expressed in terms of bond dipole moment components and their derivatives with respect to components of the Cartesian bond displacement vector. With this interpretation, which may be suitable for practical application, the Mayants-Averbukh theory formally appears as a combination of the “special” and the generalized valence-optical theory. In particular, it is found that for linear molecules the Mayants-Averbukh theory is equivalent to the “special” valence-optical theory in the zeroth approximation. For planar molecules the Mayants-Averbukh theory is equivalent to the generalized valence-optical theory (zeroth approximation) for in-plane modes and to the “special” valence-optical theory for out-of-plane modes.     

The irreducible Raman scattering tensor operator for the 32 crystallographic point groups and its application to the resonance and electronic Raman effect

The irreducible components of the Raman scattering tensor operator $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ under the symmetry of a general point group are calculated. The unitary transformations U(Γ_γΓ_ksΓ_k′s′, ρσ) from the Cartesian $\text{α}\text{?}{}_{\mathrm{\rho \sigma }}$ and spherical $\text{α}\text{?}{}_{\mathrm{Q}}{}^{\mathrm{K}}$ components, respectively, to the irreducible components $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ for the 32 crystallographic point groups are collected in tables. As an example the unitary transformation U(Γ_γΓ_ksΓ_k′s′, ρσ) is used to discuss the behavior of the scattering tensor in a resonance Raman experiment. With the help of the general formalism the scattering tensor for electronic Raman transitions of transition metal ions is calculated. As an example the scattering tensors of electronic Raman transitions within the ⁵T₂ state of the high-spin trigonal distorted octahedral Fe²⁺ are calculated and the refinement of the selection rules is discussed.     

Light composite fermions in a dynamical subquark model of pregauge interactions

The masses of composite leptons and quarks are discussed in a “dynamical subquark model of pregauge interactions”. In this model, the leptons and quarks are made of a spinor and scalar subquark with equal mass, M, and the gauge bosons and Higgs scalar of the SU(3)_c×SU(2)_L×U(1)_Y model are made of a subquark-antisubquark pair. The SU(2)_L×U(1)_Y symmetry is spontaneously broken by the composite Higgs scalar and the (scalar) subquark mass parameter is in turn bounded as $\text{M > 5.4}\text{TeV}\text{(=2π(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{where}\text{G}{}_{\mathrm{<mtext>F</mtext>}}$ is the Fermi coupling constant). The spontaneously generated mass of a lepton or quark, m_i⁽ⁿ⁾ (i = 1, 2; n = 1 ～ N_g), is calculated to be: $\text{m}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{× (4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)α}{}_{\mathrm{<mtext>e.m.</mtext>}}\text{(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/3}\text{6}\text{(=0.35r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{(4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)}\text{GeV}\text{),}\text{where}\text{r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}$ are the parameters satisfying that 0 ? r_i⁽ⁿ⁾ ? 1 and Σ (r_i⁽ⁿ⁾)² = 1;N_g is the total number of generations of the leptons and quarks; α_e.m. is the fine structure constant. The appearance of light composite fermions is related to a specific mechanism of generating global chiral symmetries of the leptons and quarks. Global symmetries of scalar subquarks yield chiral symmetries of the leptons and quarks. Our model turns out to satisfy 't Hooft's anomaly conditions on massless composite fermions.     

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.     

On the difference between pp and pp topological cross sections up to 100 GeV/c

New 100 GeV/c$\text{p}$p data are used to find moments of the difference between the $\text{p}$p and pp topological cross sections. The mean multiplicity for annihilations at 100 GeV/c is estimated to be 9.06 ± 0.56, and the value of the quantity 〈n〉/D to be 2.75 ± 0.33. It is shown that $\text{R}{}_{\mathrm{n}}\text{= {σ}{}_{\mathrm{n}}\text{(}\text{p}\text{p) ? σ}{}_{\mathrm{n}}\text{(pp)}/σ}{}_{\mathrm{n}}\text{(pp)}$ appears at 100 GeV/c to have acquired an asymptotic form, R_n = s^?αβⁿ, with α and β constant.     

How to continue the predictions of perturbative QCD from the spacelike region where they are derived to the timelike regime where experiments are performed

The predictions of perturbative QCD are derived in the deep euclidean region, whereas the physical region for most observables is timelike. The confrontation of these predictions with experiment thus necessitates an analytic continuation. This we find introduces large higher order corrections in terms of α_s(|Q²|), the usual choice ofperturbative expansion parameter. These corrections are naturally absorbed by changing to the expansion parameter $\text{a}\text{(Q}{}^2\text{) = |α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|(}\text{Re}\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)/|α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|)}{}^{\mathrm{<mtext>(n?2)</mtext><mtext>3</mtext>}}$, where α_s(Q²)ⁿ is the leading term in the spacelike region. For the intermediate range of Q² experimentally accessible at present, where $\text{a}\text{(Q}{}^2\text{)}$ is significantly smaller than α_s(|Q²|), we find the resulting phenomenology is improved. In particular, we demonstrate how the values of $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}$ obtained from analyses of quarkonium decays become consistent.     

The fluorescence excitation spectrum of s-tetrazine cooled in a supersonic free jet

The fluorescence excitation spectrum of the ${}^1\text{B}{}_{\mathrm{3u}}\text{(v′ = 0) ←}{}^1\text{A}{}_{\mathrm{g}}\text{(v″ = 0)}$ transition in s-tetrazine has been observed and measured. The sample was cooled to a rotational temperature of <1 K by expansion in a supersonic free jet. In this way the rotational structure arising from asymmetry split low J lines could be observed. The rotational A and B axes of the ²H₁¹²C₂¹⁴N₄ isotope were observed to interchange upon electronic excitation and a theory describing the effect of this interchange upon the optical selection rules has been developed. Analysis of the resolved rotational structure suggests that the geometry change upon electronic excitation is smaller than that deduced from previous analysis of the room temperature optical spectrum.     

Gauge invariance and renormalization

The renormalization of Abelian and non-Abelian local gauge theories is discussed. It is recalled that whereas Abelian gauge theories are invariant to local c-number gauge transformations δA_μ(x) = ?_μ,…, with □Λ = 0, and to the operator gauge transformation δA_μ(x) = ?_μφ(x), …, δφ(x) = α^?1?·A(x), with □φ = 0, non-Abelian gauge theories are invariant only to the operator gauge transformations $\text{δA}{}_{\mathrm{\mu }}\text{(x) ～}\textcolor{red}{}{}_{\mathrm{\mu }}\text{C(x)}$, …, introduced by Becchi, Rouet and Stora, where

_μ is the covariant derivative matrix and C is the vector of ghost fields. The renormalization of these gauge transformation is discussed in a formal way, assuming that a gauge-invariant regularization is present. The naive renormalized local non-Abelian c-number gauge transformation $\text{δA}{}_{\mathrm{\mu }}\text{(x) = (Z}{}_1\text{/Z}{}_3\text{)gA}{}_{\mathrm{\mu }}\text{(x) ×}\text{Λ}\text{(x)+?}{}_{\mathrm{\mu }}\text{Λ}\text{(x)}$, …, is never a symmetry transformation and is never finite in perturbation theory. Only for $\text{Λ}\text{(x) = (Z}{}_3\text{/Z}{}_1\text{)L}$ with L finite constants or for $\text{Λ}\text{(x) = Ω}\text{z}\text{?}{}_3\text{C(x)}$ with Ω a finite constant does it become a finite symmetry transformation, where $\text{z}\text{?}{}_3$ is the ghost field renormalization constant. The renormalized non-Abelian Ward-Takahashi (Slavnov-Taylor) identities are consequences of the invariance of the renormalized gauge theory to this formation. It is also shown how the symmetry generators are renormalized, how photons appear as Goldstone bosons, how the (non-multiplicatively renormalizable) composite operator A_μ × C is renormalized, and how an Abelian c-number gauge symmetry may be reinstated in the exact solution of many asymptotically fr ee non-Abelian gauge theories.     

Competition cusps in (α, γ) reactions

Absolute cross sections are presented for the reactions ³⁷Cl(α, γ)⁴¹K for 2.90 MeV ≦ E^lab_α ≦ 5.23 MeV, ${}^{62}\text{Ni}\text{(α, γ)}{}^{66}\text{Zn}\text{for}\text{5.07}\text{MeV}\text{≦ E}{}_{\mathrm{\alpha }}{}^{\mathrm{?2}}\text{lab}\text{≦ 8.64}\text{MeV}\text{,}{}^{62}\text{Ni}\text{(α,}\text{n}\text{)}{}^{65}\text{Zn}$ for energies near the (α, n₀) threshold at $\text{E}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>lab</mtext>}}\text{= 6.90}\text{MeV up to}\text{8.76}\text{MeV}\text{,}{}^{64}\text{Ni}\text{(α, γ)}{}^{68}\text{Zn for}\text{4.50 ≦ E}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>lab</mtext>}}\text{≦ 7.45}\text{MeV}$, and for ⁶⁴Ni(α, n)⁶⁷N from E_α^lab = 5.30 MeV up to E_α = 7.45 MeV. Substantial competition cusps were observed in the excitation function for all three (α, γ) reactions. The data were found to be in reasonable agreement with the predictions of the current versions of global Hauser-Feshbach models used in nucleosynthesis calculations. Including width fluctuation corrections and realistic neutron strength functions generally improves the ability of the models to predict the depth of the (α, γ) competition cusps; the depths of the predicted (α,γ) cusps are insensitive to the degree of isospin mixing. Taken together with studies of competition effects in proton-induced reactions, the present data confirm the importance of width fluctuation and strength function effects, and indicate essentially complete isospin mixing between T^< and T^> states in the compound nucleus.     

The QCD effective coupling constant in e+e− annihilation

The QCD effective coupling constant α_s(Q²) is determined by comparing the O(α_s)² jet-distributions with the high-energy e⁺e^? data from PETRA. We get α_s(Q² = 1225 GeV²) = 0.125 ± 0.01, which corresponds to $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}\text{= 110}{}^{\mathrm{+70}}{}_{\mathrm{?50}}\text{MeV}$ with five flavours.     

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:

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

;

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

.     

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.     

Extending the QCD leading logs up to reggeon field theory

The deep inelastic structure function D(ω, q²) is calculated in the leading log approximation for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{) 1}\text{n}\text{ω < 0.84 1}\text{n}\text{(}\text{1}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2\text{))}$. For larger ω up to ( the influence of reggeon cuts proves to slow down the growth of the structure function. A reggeon diagram technique is developed, and D is calculated up to a pre-exponent O(1), leading to D(ω, q²) ∝ q² for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2{}_0\text{) 1}\text{n}\text{ω ? 0.42}\text{α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{)}\text{α}{}_{\mathrm{<mtext>S</mtext>}}{}^2\text{(q}{}^2\text{)}$. By assuming the reggeon diagrams when ω is still greater, one can expect to obtain a strong coupling behaviour: D(ω, q²) ∝ q²(ln ω)^η (η <2).     

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.     

Temperature dependence of dispersive hopping transport and diffusion in disordered solids

The time- and temperature-dependent drift mobility μ_d for dispersive transients in disordered solids is $\text{μ}{}_{\mathrm{d}}\text{(T,t) =}\text{L}\text{Et}{}_{\mathrm{T}}$ in terms of distance L, field E and transit time t_T. Since current I ∝ tsu?(1?α) for t <_Tand 0<α<1 by Scher-Montroll theory for hopping among localized states, it follows that $\text{μ}{}_{\mathrm{d}}\text{(T) = α[μ}{}_{\mathrm{d}}\text{(T,t)]}{}^{\mathrm{\alpha }}\text{(}\text{L}\text{Eτ}\text{)}{}^{\mathrm{1?\alpha }}$ where τ≈ 10^?13s is estimated. Further $\text{μ}{}_{\mathrm{d}}\text{(T) ∝ exp (}\text{?Δ}{}_0\text{KT}\text{)}$ and the activation energy Δ₀ is time independent. On this basis Δ for the carbazole polymers is ca. zero, that for a-Se is ca. 0.05 eV, and that for a-As₂Se₃ is 0.35 eV rather than 0.5, 0.3 and 0.6 eV respectively on a phenomenological basis for μ_d(T,t). Trap-controlled hopping transport may be excluded. Time-resolved optical studies of excess carrier recombination supplement mobility measurements in a-Si:H and a-As₂Se₃ as well as other systems. Combined results suggest a dielectric response mechanism in which the time-dependent hopping frequency of localized carriers ν ∝ t^α?1 arises from distortion of the medium at localization sites. This is satisfied by Δ(T,t) = Δ₀+(1?α)KTT ln(t/τ) where τ is the mean initial localization time of the carrier, 10^?13?10^?12s, Δio is the height of the barrier at T, and 0<α<l. Consequently ν = ν₀(t/τ)^α?1 exp(frsol|?Δ₀/KT) which applies also to bimolecular recombination.     

Deep inelastic sum rules at fixed hadron energy

Experimentally, it is much easier to measure structure functions at fixed hadron energy E_h, rather than at fixed Q². We prove the sum rules

,

$\text{h}{}_{\mathrm{NS}}\text{=}\text{4}\text{3}\text{(}\text{1}\text{6}\text{π}{}^2\text{?}\text{5}\text{8}\text{),}$

$\text{h}{}_{\mathrm{S}}\text{=}\text{4}\text{16+3n}{}_{\mathrm{<mtext>f</mtext>}}\text{(2π}{}^2\text{+}\text{1}\text{6}\text{π}{}^2\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{?}\text{65}\text{12}\text{?}\text{5}\text{72}\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{).}$

Here s = 2m_pE_h and F_2,3 are the standard functions for scattering of neutrinos on an isoscalar target. K is an unknown constant, and the corrections to the sum rules are O(α_s²), O(α_s^1.75), respectively.     

Microwave spectrum of the IO radical

The two lowest rotational transitions of the IO radical in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ ground electronic state have been observed by means of a Stark modulated spectrometer. The effective rotational constants in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state, the centrifugal distortion constant, the axial component of the magnetic hyperfine interaction, and the nuclear electric quadrupole coupling constant are determined accurately. It was necessary to take into account the second-order effects from the matrix elements off-diagonal in J for the analysis of the hyperfine structure. An equilibrium internuclear distance r_e is calculated to be 1.8677 ± 0.0028 Å from the effective rotational constant $\text{B}{}_0\text{(}{}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}$, combined with α₃ from the A²Π → X²Π transition.     

Laser-induced fluorescence spectroscopy of the E band of the Ã-X̃ transition of SO2 cooled rotationally in a supersonic jet

The rotationally resolved, laser-induced fluorescence spectrum of the E band of the $\text{A}\text{?}{}^1\text{A}{}_2\text{-}\text{X}\text{?}{}^1\text{A}{}_1$ transition of SO₂ seeded in a supersonic jet was observed, and each rotational line was assigned on the basis of the ground state combination differences and the relative intensity data as a function of the rotational temperature. It was demonstrated that the line congestion was reduced significantly in the spectrum of the jet, and some of the lines, e.g., ^rR₀(0), were assigned unambiguously. This makes it possible to determine the vibronic band origin with an error of less than 0.2 cm^?1.     

An inequality for the trace of matrix products

In this paper we consider a product of n complex m×m matrices A_k (k=1,…,n) with singular values ∝^(k)_i ordered in decreasing magnitude. Using the spectral resolution for the operators $\text{A}{}^{\mathrm{dagger;}}{}_{\mathrm{k}}\text{A}{}_{\mathrm{k}}$, it is shown that $\text{|}\text{Tr}\text{A}{}_1\text{…A}{}_{\mathrm{n}}\text{|≤}\text{∑}\text{i=1}\text{m}\text{Φ}\text{i=1}\text{n}\text{α}{}^{\mathrm{(k)}}{}_{\mathrm{i}}\text{.}$This inequality is an extension of an inequality of von Neumann in the simple case that n=2. The necessary and sufficient condition for the equality sign to hold is established. Application of Hölder's inequality leads to further inequalities which can be useful in statistical mechanics.