On the cyclotron resonance width of an electron impurity system in two dimensions

Using the proper connected diagram expansion which incorporates the quasi-particle effect naturally we calculated the cyclotron resonance width γ in the extreme quantum limit.(a) γ ∝n

$\text{1}\text{2}$

_s B

$\text{1}\text{2}$

for a short range interaction, and (b) γ = π

$\text{1}\text{2}$

ze² κ^-1 <?crossed h.c.h;^-1 n

$\text{1}\text{2}$

_s for Coulomb interaction, are obtained. The field (B) and concentration (n_s)-dependence is in satisfactory agreement with experimental data. The variation γ = (γ²₁ + γ²₂ + …)

$\text{1}\text{2}$

of Matthiessen's rule γ = γ₁ + γ₂ + …, holds when there exist scattering centers of different kinds in the system.     

On the theory of the low-temperature electrical resistivity of potassium

Expressing the residual resistivity ?₀ as a force-force correlation, a first-principles basis is afforded for the low temperature expansion of the electrical resistivity ? as

(I)$\text{? = ?}{}_0\text{[1 +}\text{λ1}\text{λ}\text{+ … ]}$

where λ = const T^-2 is the non-resistive mean free path arising from electron-electron scattering. λ¹ is found to reflect directly long-range correlations in the electronic motions via the off-diagonal behaviour of the local density of states at the Fermi energy.     

Pionic X-rays from 12, 13C

The energies and widths of pionic 2p-1s and 3d-2p X-rays have been measured in ^12,13C. Values obtained are

${}^{12}\text{C: 2p-1s E=93.221(55)}\text{keV}\text{, τ=2077(14)}\text{keV}$

$\text{3d-2p E=18.400(6)}\text{keV}\text{, τ=1.17(11)}\text{eV}$

${}^{13}\text{C: 2p-1s E=92.227(27)}\text{keV}\text{, τ=2.59(11)}\text{keV}$

$\text{3d-2p E=18.427(5)}\text{keV}\text{, τ=0.97(10)}\text{eV}$

The muonic 2p-1s X-ray energies in ^12,13C have also been measured. The strong interaction effects are discussed in relation to recent low-energy pion scattering measurements.     

Temperature and pressure dependence of the elastic property of GeS2 glass

The sound velocities in GeS₂ glass have been measured by means of ultrasonic interferometry as a function of temperature or pressure up to 1.8 kbar. The bulk modulus K_s = 117.6 kbar and shear modulus G = 60.60 kbar were obtained for GeS₂ glass at 15°C and 1 atm. The temperature derivatives of both sound velocities and elastic moduli are negative :

$\text{(}\text{?ν}{}_1\text{?T}\text{)}$

_p =

$\text{?1.54 × 10}{}^{\mathrm{?4}}\text{km}\text{sec}$

°C,

$\text{(}\text{?ν}{}_1\text{?T}\text{)}$

_p =

$\text{?1.27× 10}{}^{\mathrm{?4}}\text{km}\text{sec}$

°C and

$\text{(}\text{?K}{}_{\mathrm{s}}\text{?T}\text{)}$

_p =

$\text{?1.27 × 10}{}^{\mathrm{?2}}\text{kbar}\text{°C}$

,

$\text{(}\text{?G}\text{?T}\text{)}$

_p = ?1.23 × 10^?2 kbar/°C,

$\text{(}\text{?Y}\text{?T}\text{)}$

_p = ?2.93 × 10^?2 their pressure derivatives are positive:

$\text{(}\text{?ν}{}_1\text{?P}\text{)}$

_T = 4.43× 10^?2km/kbar,

$\text{(}\text{?ν}{}_1\text{?P}\text{)}$

_T =

$\text{0.633 × 10}{}^{\mathrm{?2}}\text{km}\text{kbar}$

and (?K_s?P0)_T=6.81,

$\text{(}\text{?G}\text{?P)}{}_{\mathrm{T}}$

= 1.03, (?Y?T_T= 3.57. The Grüneisen parameter, γ_th= 0.298, and the second Grüneisen parameter, δ_s = 3.27, have also been calculated from these data. The elastic behavior of GeS₂ glass has proved to be normal despite the structural similarity among the tetrahedrally coordinated SiO₂, GeO₂ and GeS₂ glasses.     

Algebraic study of a class of relativistic wave equations

First-order relativistic wave equations are considered whose irreducible matrix coefficients satisfy the simplest (except for the Dirac algebra) unique mass condition, (β · p)³ = p²(β · p), which is also sufficient to guarantee causality in a minimally coupled external electromagnetic field. All of the associated representations of SL(2, ©) are classified and studied up to and including those which are the direct sum of four irreducible components, (n, m), with either n or m less than two. A large number of families of representations are found which permit the algebraic condition to be satisfied. These are tabulated according to whether a Hermitian choice for β⁰ is possible and their spin content is given. If a unique spin is described, then the only possible representations are

$\text{(1) (}\text{n}\text{,0) ⊕ (}\text{n}\text{? 1/2, 1/2)}$

$\text{(2) (}\text{n}\text{,0) ⊕ (}\text{n}\text{+ 1/2, 1/2)}$

$\text{(3) (}\text{n}\text{+ 1/2, 1/2) ⊕ (}\text{n}\text{,0) ⊕ (}\text{n}\text{? 1/2, 1/2)}$

$\text{(4) (1,0) ⊕ (1/2, 1/2) ⊕ (0,1)}$

and their conjugates. If, in addition, the representation is assumed to be self-conjugate, then only the Dirac and Petiau-Duffin-Kemmer equations survive.     

Forbidden lines of the ν3 band of 13CH4: Ground-state constants

The ν₃ fundamental vibration-rotation band of carbon-13 enriched methane (¹³CH₄) was recorded using a high-resolution vacuum infrared grating spectrograph. Forbidden transitions of this band are reported for the first time. Of the nearly 900 transitions identified, 560 are forbidden transitions and 347 of the forbidden transitions have 11 ≤ J ≤ 18. Pairs of forbidden and allowed transitions having the same upper-state energy levels were used to calculate 550 independent differences between ground-state term values. From these data, a least-squares analysis was used to calculate the following values for ground-state structure constants and their standard deviations (in cm^?1):

$\text{β}{}^{\mathrm{O}}\text{hc}\text{= 5.240820 ± 0.000056}$

,

$\text{λ}{}^{\mathrm{O}}\text{hc}\text{=?(1.0856 ± 0.0015) × 10}{}^{\mathrm{?4}}$

,

$\text{?}{}^{\mathrm{O}}\text{hc}\text{= ?(1.4174 ± 0.0034) × 10}{}^{\mathrm{?4}}$

,

$\text{η}\text{hc}\text{= ?(1.73 ± 0.37) × 10}{}^{\mathrm{?11}}$

. The 550 values for the ground-state combination differences retained for analysis can be reproduced with an overall standard deviation of 0.0155 using the stated values for the structure constants. The note added in proof refines the above constants by including the newly observed microwave data.     

The ground state of propynal

The millimeter wave spectrum of propynal, HCCCHO, has been studied in the ground vibrational state. A detailed centrifugal distortion analysis has been carried out on the combined data of newly assigned millimeter wave rotational transitions (up to 200 GHz) together with the microwave transitions reported earlier. A total of 90 transitions as high as J = 20 and K = 12 could be fitted with a standard deviation of 87 kHz. This analysis yielded a complete set of ground state rotational and centrifugal distortion constants. The rotational constants are in MHz:

$\text{A = 68 035.2994 ± 0.0429,}$

$\text{B =}\text{4826.3014 ± 0.0073,}$

$\text{C =}\text{4499.5107 ± 0.0069.}$

     

Etude de l'autodiffusion dans la phase cubique centree de l'europium et du gadolinium

The self-diffusion coefficient follows a relation of the form : D = (1,0_?0.4^+0.7)exp (?shape=case>34400RT±700)

$\text{cm}{}^2\text{sec}$

for b.c.c. europium D = (1,0_?0.3^+0.5) × 10^?2 exp(?

$\text{32700 ±4000}\text{RT}\text{)}$

$\text{cm}{}^2\text{sec}$

for β-b.c.c. gadolinium.Whereas europium has normal self-diffusion parameters, β-b.c.c. gadolinium must be set in the class of the anomalous b.c.c. rare-earth metals.From these results we conclude that there exists no evident connexion between the instability of the 4f shell and the activation energies anomalously low in the b.c.c. phases of the rare-earth metals.     

On the super symmetry charges in the theory of scalar and spinor free fields

It is shown that for spinorial charges Q^(L))_α (α = 1, 2, L = 1, …, S) satisfying the commutation relations

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)}}{}_{\mathrm{\beta }}\text{} = ε}{}_{\mathrm{\alpha }}\text{βa}{}^{\mathrm{LM}}\text{Q,}$

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)+}}{}_{\mathrm{\beta }}\text{} = cσ}{}^{\mathrm{\mu }}{}_{\mathrm{\alpha \beta }}\text{P}{}_{\mathrm{\mu }}\text{δ}{}^{\mathrm{LM}}\text{,}$

$\text{[Q}{}^{\mathrm{(L)}}\text{)}{}_{\mathrm{\alpha }}\text{, P}{}^{\mathrm{\mu }}\text{] = 0,}$

where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields.     

Comparison of the lattice Λ parameter with the continuum Λ parameter in massless QCD

The ratio of the scale parameter Λ in massless QCD defined on a lattice to the one in the continuum theory is determined by performing one-loop renormalization of the coupling constant. Our calculation method on a lattice directly relates Λ^lattice to the continuum one in the minimal subtraction scheme. The effect of incorporation of massless quarks depends on a parameter λ which is introduced to avoid trouble with fermions on a lattice. For λ=1, which is Wilson's value, the ratio previously calculated by Hasenfratz in the pure gauge theory is changed as follows:

$\text{Δ}{}_{\mathrm{\alpha =1}}{}^{\mathrm{MOM}}\text{Δ}{}^{\mathrm{lattice}}\text{=83.5}\text{for pure SU(3) gauge theory;}$

$\text{Δ}{}_{\mathrm{\alpha =1}}{}^{\mathrm{MOM}}\text{Δ}{}^{\mathrm{lattice}}\text{=105.7}\text{for QCD with 3 flavors;}$

$\text{Δ}{}_{\mathrm{\alpha =1}}{}^{\mathrm{MOM}}\text{Δ}{}^{\mathrm{lattice}}\text{=105.7}\text{117.0 for QCD with 4 flavors.}$

Critical properties of the lattice QCD will also be discussed briefly.     

Ground-state molecular constants of bideuterated methane

A rotational analysis of the satellite bands of the β system of ZrO gives the splittings in the triplet states. For the lowest triplet state X′³Δ, these splittings are:

$\text{δF}{}_{\mathrm{1,2}}\text{= 287.9 ± 0.1 cm}{}^{\mathrm{?1}}\text{,}$

$\text{δF}{}_{\mathrm{2,3}}\text{= 337.6 ± 0.4 cm}{}^{\mathrm{?1}}\text{.}$

     

Vacuum polarization test and search for muonhadron interactions from muonic X-rays:: Crystal-spectrometer experiments

We have measured the wavelengths of the $\text{3}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{?2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and the $\text{3}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{-2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ X-ray transitions in μ-²⁴Mg, -²⁸Si and -³¹P with the bent-crystal spectrometer at the SIN muon channel. The X-rays are measured relative to the wavelengths of the 84 keV and the 63 keV γ-rays of ¹⁷⁰Tm and ¹⁶⁹Yb which have recently been calibrated to about 1 ppm. The measured X-ray wavelengths λ_exp are compared with theoretical values λ_th, as obtained from QED calculations. The relative difference, averaged over all six measured transitions, is

$\text{λ}{}_{\mathrm{<mtext>exp</mtext>}}\text{?λ}{}_{\mathrm{<mtext>th</mtext>}}\text{λ}{}_{\mathrm{<mtext>th</mtext>}}\text{= (2 ± 8) × 10}{}^{\mathrm{?6}}$

This result corresponds to a test of the vacuum polarization effect in QED of (0.6 ± 2.4) × 10^?3. Assuming the QED calculations to be correct, we can use the result to put limits on additional muon-nucleon interactions (as required by gauge theories). If such an interaction is mediated by a scalar, isoscalar boson with a mass smaller than 1 MeV, the coupling constant is found to be

$\text{g}{}_{\mathrm{<mtext>N</mtext>}}\text{g}{}_{\mathrm{\mu }}\text{4π}\text{= (?4 ± 17) × 10}{}^{\mathrm{?9}}$

Alternatively, we can deduce from our experiments the most accurate direct value to date for the negative muon mass,

$\text{m}{}_{\mathrm{\mu }}\text{- = 105.65906(91)}\text{MeV}$

.     

The rotational analysis of the 1Π-X 1Σ+ system at 649.5 nanometers of zirconium oxide

A red-degraded band head, normally badly overlapped by the gamma system, $\text{A}{}^3\text{Φ}\text{- X′}{}^3\text{Δ}$, of zirconium oxide, appears in emission spectra of zirconium arcs and in absorption spectra of S-type stars and of frozen rare gas matrices containing zirconium. The emission band has been examined at high-resolution with the aid of separated zirconium isotopes. Identification of the band as 0-0 of a ${}^1\text{Π}\text{- X}{}^1\text{Σ}{}^{\mathrm{+}}$ system of zirconium oxide is confirmed by rotational analysis where the following constants (cm^?1) are obtained for ⁹⁰Zr¹⁶O:

$\text{B}{}_0\text{′(R,P) = 0.40142 D}{}_0\text{′(R,P) = 3.51 × 10}{}^{\mathrm{?7}}$

$\text{B}{}_0\text{′(Q) = 0.40166 D}{}_0\text{′(Q) =3.52 × 10}{}^{\mathrm{?7}}$

$\text{B}{}_0\text{″ = 0.42263 D}{}_0\text{″ =3.19 × 10}{}^{\mathrm{?7}}$

$\text{ν}{}_0\text{= 15383.81s}$

The Λ-type doubling in the ¹Π state and the question of whether $\text{X}{}^1\text{Σ}{}^{\mathrm{+}}$ or $\text{X′}{}^3\text{Δ}$ is the true ground state of ZrO are discussed.     

A new proof of the invariance principle in scattering theory

For free and interacting Hamiltonians, H₀ and H = H₀ + V(r) acting in L²(R³, dx) with V(r) a radial potential satisfying certain technical conditions, and for ? a real function on R with ?′ > 0 except on a discrete set, we prove that the Moller wave operators

exist and are independent of ?. The scattering operator

$\text{S = (Ω}{}^{\mathrm{+}}\text{)1Ω}{}^{\mathrm{?}}$

is shown to be unitary. Our proof utilizes time independent methods (eigenfunction expansions) and is effective in cases not previously analyzed, e.g. $\text{V(r) =}\text{sin}\text{r}\text{r}$ and many others.     

Systems of ordinary differential equations with nonlinear superposition principles

This work is concerned with the derivation of superposition rules which express the general solution of ordinary differential equations.

$\text{x}\text{?}\text{= η(x,t).}\text{(x, η ?}\text{R}{}^{\mathrm{n}}\text{, t ?}\text{R}\text{)}$

. in terms of a finite number of particular solutions. The point of departure is Lie's criterion according to which such a rule exists if and only if the vector fields η(x,t). ? generate a finite dimensional Lie algebra. We provide three different constructive methods for deriving superposition rules and apply them to systems of coupled Riccati equations of the projective and conformal types based, respectively, on the Lie algebra sl(n + 1, R) and o(p + 1, n ? p + 1).     

An analysis of the four nuclear quadrupole problem: The microwave spectrum of cyanogen azide

We have derived expressions for the Hamiltonian matrix elements for the coupling of any number of quadrupolar nuclei with the molecular rotation using the Wigner n-j formalism. These expressions have been used to analyse the nuclear quadrupole hyperfine structure of the rotational spectrum of cyanogen azide, NCN₃. The analysis was effected by comparing the experimental high resolution spectral traces with computer simulated traces from which the nuclear quadrupole coupling constants obtained are (MHz)

$\text{x}{}_{\mathrm{aa}}\text{(1) = 4.82 ± 0.02,}\text{x}{}_{\mathrm{bb}}\text{(1) = ?0.70±0.08,}$

$\text{x}{}_{\mathrm{aa}}\text{(2) = ?0.85 ± 0.07,}\text{x}{}_{\mathrm{bb}}\text{(2) = 0.70±0.08,}$

$\text{x}{}_{\mathrm{aa}}\text{(3) = ?0.75 ± 0.07,}\text{x}{}_{\mathrm{bb}}\text{(3) = 0.70±0.05,}$

$\text{x}{}_{\mathrm{aa}}\text{(4) = ?2.27 ± 0.04,}\text{x}{}_{\mathrm{bb}}\text{(4) = 0.70±0.07,}$

Small corrections to the previously reported rotational constants are given.     

Microwave spectra of D217O and D218O

Forty lines of the microwave spectra of D₂¹⁷O and D₂¹⁸O have been measured in the region from 8 to 400 GHz and analyzed according to Watson's centrifugal distortion theory. Comparison of the results obtained for D₂¹⁶O, D₂¹⁷O, and D₂¹⁸O demonstrates their internal consistency. The transferability of the parameters according to the isotopic substitution rules is evidence for the validity of the model chosen for the study of the ground state of heavy water.The effective rotational constants deduced from the observed spectra are very close to the values calculated using Oka's second order theory. The values obtained in MHz are:

$\text{A = 456766.9,}\text{B = 218041.0,}\text{C = 144701.5}\text{(D}{}_2{}^{17}\text{O;)}$

$\text{A = 451891.9,}\text{B = 218045.2,}\text{C = 144201.7}\text{(D}{}_2{}^{18}\text{O;).}$

The hyperfine structure of the D₂¹⁷O lines has been analyzed using as a reference the corresponding quadrupole coupling tensor of HD¹⁷O with the appropriate rotation. The values of χ_gg in MHz used for the analysis are:

$\text{x}{}_{\mathrm{\chi \chi }}\text{= - 1.2104,}\text{x}{}_{\mathrm{yy}}\text{= 10.1068,}\text{x}{}_{\mathrm{zz}}\text{= - 8.8964.}$

     

Elastic scattering of 119 MeV 3He particles and energy and mass-number dependence of optical potential parameters

The elastic scattering of 119 MeV ³He particles by ¹²C, ²⁷Al, ^58,60,62,64Ni, ⁵⁹Co, ^90,92Zr and ⁸⁹Y has been investigated over a wide angular range in order to study the mass-number dependence of the optical potential and odd-even differences in the elastic scattering. The elastic scattering cross sections have been analyzed in terms of the optimal model. The data, except for ¹²C, ²⁷Al and ⁵⁹Co, were fitted with r_R = 1.21 fm, a_R = 0.76 fm and r_I = 1.17 fm, fixed at the average values. The following formulae were obtained for the three remaining parameters by combining with the energy dependence of the parameters (90–120 MeV) obtained previously:

$\text{V=111.4?0.173E+}\text{Z}\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{+14.9}\text{N?Z}\text{A}\text{(}\text{MeV}\text{)}$

$\text{W}{}_{\mathrm{<mtext>D</mtext>}}\text{=24.8?0.028E (}\text{MeV}\text{)}$

,

$\text{a}{}_{\mathrm{I}}\text{=0.754+0.78}\text{N?Z}\text{A}\text{(}\text{fm}\text{)}$

The depths of the valleys of the angular distribution in the case of ${}^{59}\text{Co}\text{(I =}\text{7}\text{2}\text{)}$ are considerably shallower than those for Ni isotopes, while the depths in the case of ${}^{89}\text{Y}\text{(I =}\text{1}\text{2}\text{)}$ are nearly the same as those for Zr isotopes. Thus it may be concluded that the odd-even differences are attributed to the scattering from the quadrupole moment of the odd-A nucleus (if $\text{I >}\text{1}\text{2}$).     

Unitary operators with discrete spectrum induced by measure preserving transformations

The purpose of this paper is to prove the following theorem.Theorem. Given a countable subset Λ on the circle K and an integer-valued function n(λ) on Λ, there exists a dynamical system with discrete spectrum (X,$\text{F}$,μ,T) such that Λ is the set of all eigenvalues of T and n(λ) is the multiplicity function of T if and only if there exist two systems of subgroups {G_i}_i∈N and $\text{{S}{}_{\mathrm{j}}\text{}}{}_{\mathrm{j\in M}}\text{(}\text{N}\text{??}{}_0\text{,}\text{M}\text{??}{}_0\text{)}$ of the circle such that Λ = G ∪ S and

$\text{n(λ)=}\text{∞}\text{for}\text{λ∈S,}\text{{i∈N; λ∈G}{}_{\mathrm{i}}\text{}}\text{for}\text{λ∈G?S,}$

where $\text{G =}\text{?}\text{i∈N}\text{G}{}_{\mathrm{i}}\text{, S =}\text{?}\text{j∈M}\text{S}{}_{\mathrm{j}}$.