On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

Theory of second harmonic generation at a metal surface with surface plasmon excitation

Theory of second harmonic generation at a metal surface is developed, when surface plasmon-polaritons are resonantly excited by the incident electromagnetic field. For harmonic generation from small metallic spheres characterized by the dielectric function ?₁(ω) + i?₂(ω), the resonant enhancement of the second harmonic intensity is predicted to be of the order of ($\text{?}{}_1\text{?}{}_2\text{)}{}^4$. The resonant enhancement is much smaller for the case of a metallic grating.     

νW2 at small ω′ and resonance form factors in a quark model with broken SU(6)

The small ω′ behaviour of F₂^en/F₂^ep and the apparent difference in the q² dependences of the magnetic form factor of the proton and of the transition to Δ⁺(1236) are quantitatively correlated in a model where nucleon consistes of a quarks and a scalar or vector core. The proton and Δ transition form factors suggest that only the scalar core contributes at large q² and small ω′. As a result the ω′ dependence of $\text{F}{}_2{}^{\mathrm{<mtext>en</mtext>}}\text{F}{}_2{}^{\mathrm{<mtext>ep</mtext>}}$ is obtained for ω′ < 3 and predictions for the weak structure functions and polarisation asymmetries at smallω′ are presented. We predict $\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>n</mtext><mtext>\omega \prime \to 1</mtext><mtext>0</mtext>}}$ asymmetries $\text{ω′→1}\text{1}$ and also expect that $\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>n</mtext>}}\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>p</mtext>}}\text{→}\text{?1}\text{2}$ as q²→∞.     

Thickness dependence of the surface-polariton relaxation rates in a crystal slab

A few useful formulas are derived concerning the damping properties of long-wavelength surface polaritons (SP) in a crystal slab. For example, it is shown that the SP propagation length in a metal slab with thickness 2a satisfying $\text{ω}{}_{\mathrm{p}}\text{a}\text{c}\text{< 1}$ (c is the velocity of light and ω_p the electronic plasma frequency) is increased by the factor $\text{3}\text{2}\text{(}\text{c}\text{ω}{}_{\mathrm{p}}\text{a}\text{)}{}^4$ in comparison with the corresponding value for SP in a semi-infinite metal.     

Polariton modes at the interface between two conducting or dielectric media

A review of polariton modes at interfaces composed of two semiinfinite, homogeneous, and isotropic media is given. Both media are characterized by frequency-dependent dielectric functions ?_i(ω), i = 1, 2, and may become “interface-wave-active” in different frequency regions. The conditions for the existance of propagation windows are analyzed and applied to two particular cases: an interface composed of (a) two dielectrics with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{?\infty i}}\text{(}\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>Li</mtext>}}{}^2\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>T</mtext><mtext>i</mtext>}}{}^2$, where ?_t8i are the dielectric constants for very large frequencies and ωTi and ωLi are the transverse and longitudinal phonon frequencies; (b) two conductors with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{\infty i}}\text{(}\text{1 ?ω}{}_{\mathrm{i}}{}^2\text{ω}{}^2\text{)}$, where ω_iare the plasma frequencies. In the first case there exist two propagation windows in the infrared region, while in the second case there is one propagation window in the ultraviolet, visible, or infrared region. The dispersion relations of the modes and their decay distances into the two media are presented, and various damping effects are discussed. The review is concluded with theoretical results on the optical excitation and detection (ATR) of the interface modes.     

Spectroscopic information on ground-state Ar2, Kr2, and Xe2 from interatomic potentials

Calculations of vibrational and rotational level spacings of homonuclear inert gas diatomic molecules by numerical integration of the radial Schrödinger equation are presented. The potentials which were used for the ground states of Ar₂, Kr₂, and Xe₂ were obtained from accurate fits to the molecular beam scattering data. From the calculated $\text{Δ}\text{G}{}_{\mathrm{<mtext>v+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{'}\text{s}$ and B_v's, the following spectroscopic constants (in cm^?1) were fitted: for Ar₂ω_e = 31.92, ω_ex_e = 3.31, ω_ey_e = 0.11, B_e = 0.060, α_e = 0.004; for $\text{Kr}{}_2\text{ω}{}_{\mathrm{e}}\text{? 23.99}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 1.30}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.021}$, $\text{B}{}_{\mathrm{e}}\text{? 0.024}$, $\text{α}{}_{\mathrm{e}}\text{? 0.001}$; for $\text{Xe}{}_2\text{ω}{}_{\mathrm{e}}\text{? 21.26}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 0.75}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.008}$, $\text{B}{}_{\mathrm{e}}\text{? 0.013}$, $\text{α}{}_{\mathrm{e}}\text{? 0.0004}$.     

Zero field steps in short Josephson junction

A theoretical investigation is carried out on the zero field current steps of a short Josephson junction under both the d.c. voltage V_d.c. and a.c. voltage V_a.c. cos ωt. The steps occur when the condition $\text{Ω + pω = 2Nω}{}_{\mathrm{n}}$ is fulfilled, where $\text{Ω = 2eV}{}_{\mathrm{d.c.}}\text{/}\text{h}\text{?}$, ω_n is the nth eigenfrequency in the eigenfrequency in the junction cavity, p and N are integers.     

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 [$\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)}\text{(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$]     

Phenomenological predictions of the SO(10) supersymmetric grand unified model

The phenomenological predictions of the SO(10) supersymmetric grand unified model (SO(10) SGUM) for the mass scales M₁, M₂, weak angle ifsin²θ_w, quark-leptons mass ratios $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, $\text{m}{}_{\mathrm{t}}\text{m}{}_{\mathrm{<mtext>b</mtext>}}$, $\text{m}{}_{\mathrm{\tau }}\text{m}{}_{\mathrm{\nu }}{}_{\mathrm{\tau }}$ and proton lifetime τ_p are estimated by using renormalization group analysis at one-loop level. In contrast with SU(5) SGUM, we find that the SO(10) SGUM still has problems with τ_p but not with sin²θ_w and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, which may suggest that supersymmetry would be bro at a mass scale $\text{?10}{}^7\text{GeV}$.     

Exact derivative interband dielectric function at Van Hove singularities

Interpretations of derivative spectra obtained by wavelength or thermal modulation have been based on universal lineshape functions that include only the resonant term, $\text{(ω}{}_{\mathrm{g}}\text{? ω ?iη)}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$, obtained from differentiating ε(ω) with respect to ω or ω_g, and that neglect the (ω + iη)^?2 prefactor. We find the following differences between the approximate universal lineshape functions and the exact results obtained by including the nonresonant terms. dε/dω and dε₂/dω are no longer simply related to each other; two entirely different functions are obtained. Wavelength and temperature modulation no longer have identical lineshapes. Either dε₁/dω or dε₂/dω has a resonant derivative lineshape according to whether j is even or odd, respectively, in contrast to the approximate universal function, which has no zeros, dε₁/dω for a pure M₁ singularity has positive and negative peaks of approximately equal strength, which would agree with the experimental results without invoking hyperbolic excitons (admixtures of M_j and m_j+1 lineshapes). On the other hand, the nonexcitonic exact result fails to reproduce other experimental features. At the very least, our results call into question the extraction of numbers from detailed curve fits to the approximate functions.     

Inverse solutions to the inelastic scattering problem

Exact inverse solutions to the integral equation $\text{φ(r}{}_{\mathrm{s}}\text{|r}{}_0\text{, k) = ?}{}_{\mathrm{D}}{}^3\text{f (r, ω)g(r|r}{}_0\text{, k)g(r|r, k)d}{}^3\text{r}$, where g(r|r_j, k); j = 0 or s is the free space Green function, are derived in plane and cylindrical coordinates for fixed ω. These solutions allow an inelastic scattering potential f(r, ω) which is of compact support r ? $\text{D}$³ to be recovered from scattering data collected over the surfaces of a plane and cylinder respectively.     

Measurements of the high frequency resistence of a deuterium plasma near the lower hybrid resonance

The resistance of a deuterium plasma generated by a radio frequency discharge near the lower hybrid resonance —power transfer into the plasma between 400W and 1500W — is measured and compared with the theory of a bounded cold plasma. Reasonable agreement is found between measurement and theory only by introducing an effective collision frequency in the range from $\text{ν}{}^1\text{= 0.01 ω}{}_{\mathrm{p}}$ up to $\text{ν}{}^1\text{= 0.1 ω}{}_{\mathrm{p}}$. The effective collision frequency introduced in this manner exhibits an almost linear dependence on the power transferred into the plasma ($\text{ν}{}^1\text{ω}{}_{\mathrm{p}}\text{～?P}$).     

Combination tones in the response of single degree of freedom systems with quadratic and cubic non-linearities

The method of multiple scales is used to analyze the response of a single-degree-of-freedom system to either the combination resonance of the additive type $\text{Ω}{}_2\text{+ Ω}{}_1\text{≈ ω}{}_0$ or the combination resonance of the difference type $\text{Ω}{}_2\text{? Ω}{}_1\text{≈ ω}{}_0$, where $\text{Ω}{}_1$ and $\text{Ω}{}_2$ are the frequencies of the excitation and ω₀ is the linear undamped natural frequency of the system. To the second approximation, the combination resonance of the additive type has three effects on the steady state response. First, it produces terms having the frequencies $\text{Ω}{}_1\text{, Ω}{}_2$ and $\text{Ω}{}_2\text{+ Ω}{}_1$ at first order and terms having the frequencies 0, $\text{2Ω}{}_1\text{, 2Ω}{}_2\text{, Ω}{}_2\text{? Ω}{}_1$, $\text{2(Ω}{}_2\text{+ Ω}{}_1\text{), Ω}{}_2\text{+ 2Ω}{}_1$ and $\text{2Ω}{}_2\text{+ Ω}{}_1$ at second order. Second, it produces a shift in the natural frequency of the system. Third, it produces a virtual primary-resonant excitation having the frequency $\text{Ω}{}_2\text{+ Ω}{}_1\text{≈ ω}{}_0$ that makes the component having the frequency $\text{Ω}{}_2\text{+ Ω}{}_1$ be of first rather than second order. Similar effects are produced by a combination resonance of the difference type or a superharmonic resonance of order two.     

Effect of constant mismatch on stimulated scattering in laser plasma interactions

The presence of a constant wave number mismatch (Δk) renders the asymptotic steady of the backward scattered wave time dependent. While the pump wave is unaffected by the mismatch, the excited waves (with group velocities v₂, v₃) are modulated at the frequency $\text{[}\text{v}{}_2\text{v}{}_3\text{(v}{}_2\text{+ v}{}_3\text{)}\text{] Δk}$.     

Pressure dependence of elastic behaviour and force constants of GaP

The six third order elastic constants of GaP have been obtained from measurements of the effect of hydrostatic and uniaxial pressures on ultrasonic wave velocities. The valence force field model has been used to obtain the bond-bending and stretching force constants. Confirmatory evidence is added to the hypotheses that zinc blende structure crystals undergo the densification transition under pressure when (1) a modified Born stability criterion that $\text{1}\text{2}\text{(C}{}_{11}\text{? C}{}_{12}\text{)}\text{B}$ equals about 0.2 is reached at the phase transition pressure P_t, and (2) the ratio $\text{β}{}_{\mathrm{t}}\text{α}{}_{\mathrm{t}}$ of the second order bond-bending β_t to bond-stretching α_t, force constants is about 0.1. These findings suggest that a macroscopic shear takes place at the transition     

Sound attenuation in one-dimensional magnetic systems at finite temperatures

Sound attenuattion constants are calculated for the one-dimensional ferro- and antiferromagnetic systems at finite temperatures. Their frequency dependences, in both cases, turn out to be $\text{ω}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}_{\mathrm{<mtext>k</mtext>}}\text{if}\text{ω}{}_{\mathrm{<mtext>k</mtext>}}\text{? ω}{}_{\mathrm{c}}\text{and}\text{ω}{}^2{}_{\mathrm{<mtext>k</mtext>}}\text{if}\text{ω}{}_{\mathrm{<mtext>k</mtext>}}\text{?ω}{}_{\mathrm{c}}$, where ω_c is a “cut-off” frequency related to the three-dimensional anisotropic interactions.     

On proton-deuteron backward elastic scattering at medium energies (II)

We examine rescattering corrections to the single nucleon exchange model of backward p-d elastic scattering and find them to be important at all energies. Using realistic deuteron wave functions we conclude that the rise at E_p (lab) ～ 400–600 MeV results from another mechanism, possibly the opening of the $\text{p}\text{+}\text{d}\text{→}\text{NNN}{}_{33}{}^1$ channel.     

Rydberg atoms in crossed electric and magnetic fields. Experimental evidence for the Pauli quantization

The experimental evidence for the Pauli quantization obeyed by the Rydberg spectrum of rubidium, in crossed electric and magnetic fields, is reported. When the external field perturbation associated with Zeeman and linear Stark effects are of the same order but small compared to the Coulomb binding energy, the energy levels of the system are given by $\text{E}{}_{\mathrm{n,k}}\text{= -R/n}{}^2\text{+ ɡK (ω}{}^2{}_{\mathrm{L}}\text{+ ω}{}^2{}_{\mathrm{E}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where K is an integer ω_L, ω_E the Larmor and linear Stark frequencies respectively.     

Fourier spectrometry: Rovibrational analysis of an infrared 1Π → 1Σ system of yttrium monoiodide

The infrared spectrum of yttrium monoiodide has been excited in an electrodeless microwave discharge and explored between 2500 and 12 000cm^?1 with a high-resolution Fourier transform spectrometer. A unique system is observed (ν₀₀ = 9905.520 cm^?1), which we attribute to a ${}^1\text{Π}\text{→}{}^1\text{Σ}$ transition and an extensive analysis is made. Rovibrational constants are obtained for both states mainly from a simultaneous multiband fitting. This procedure is applied to the whole set of 2231 observed line wavenumbers in the 1-0, 0-0, and 0–1 bands, yielding a final weighted standard deviation of 0.0038 cm^?1. Furthermore, a partial analysis of the 2-0 and 3-1 bands is performed. The following equilibrium constants are derived (cm^?1):

$\text{ω′}{}_{\mathrm{e}}\text{=192.210 ω′}{}_{\mathrm{e}}\text{x′}{}_{\mathrm{e}}\text{=0.463}$

$\text{B′}{}_{\mathrm{e}}\text{=0.0399133 α′}{}_{\mathrm{e}}\text{=0.0001150}$

$\text{ω″}{}_{\mathrm{e}}\text{=215.815 ω″}{}_{\mathrm{e}}\text{x″}{}_{\mathrm{e}}\text{=0.514}$

$\text{B″}{}_{\mathrm{e}}\text{=0.0422163 α″}{}_{\mathrm{e}}\text{=0.0001125}$

High-order constants D_v and H_v are also calculated for the various vibrational levels (v′ = 0, 1, 2, 3; v″ = 0, 1).     

High-resolution proton scattering on 46Ti

Differential cross sections were measured for ⁴⁶Ti(p, p) and ⁴⁶Ti(p, p₁) at four angles between E_p = 1.5 and 3.1 MeV, with an overall energy resolution of about 300 eV. Spins, parities, total and partial widths were extracted for 144 resonances. Six analogue states were identified. The s-wave states have expected spacing and width distributions, while the $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ states behave anomalously. The $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ strength functions were determined.