Calculation of the angular dependence of the multi-center auger matrix element

The multi-center Auger matrix element as it may occur in the theory of Auger transitions in solids is calculated. Bound state wave functions are described by a linear combination of Gaussian-type orbitals while the continuum wave function is expressed in a series of plane waves. No approximations are necessary throughout the calculation. As an application of the theory the system Ni(100)?c(2 × 2)S is treated in a similar way as done by Gadzuk.     

Physical model of the dependence of the Nusselt number on the Rayleigh number

The dependence of the Nusselt number on the Rayleigh number at the stage preceding the turbulent regime of convection is substantiated and obtained in analytic form. At this stage, the Nusselt number can be described by the power dependence on the Rayleigh number, which contains five constants. One of these constants is the same for all liquids and is the critical Rayleigh number Ra_cr = 1700 ± 51. The remaining four constants are strictly individual for each type of liquid. For liquid helium, the critical Rayleigh number Ra_cr = 35000 ± 4000 has the threshold value (Ra₁^mix)th = 37 085.75. This value is determined by the small ratio of the diameter of the vessel to its height, as well as the formation of a cylindrical convection cell at the bottom of the vessel with a mode number of 2 and a radial number determined by the fourth root of the firstorder Bessel function of the first kind.     

Exciton level densities with spin and parity based on random matrix model

Level densities for fixedJ ^π and the exciton number are evaluated for closed shell nuclei⁴⁰Ca and²⁰⁸Pb. The single particle spectra and wave functions are generated by Woods-Saxon potentials. The effects of the residual interaction are taken into account statistically by the method of generating function and Grassmann integral. The matrix elements for the residual interaction are assumed to be random variables with Gaussian distributions whose second moments are calculated by using a zero range interaction. The second moments are evaluated for fixedJ ^π by ignoring the Pauli principle between active nucleons and the spectator. This approximation is shown numerically to be very good. The partial level densities are calculated using the second moments as well as independent particle model spectra. The resulting level densities spread over wider energy ranges, have a smoother energy dependence and are enhanced at low energies compared with the independent particle model densities, although the total level densities do not differ by much.     

Cross-section energy dependence of planar and non-planar two-body hypercharge-exchange reactions

The energy dependence of total cross sections for twenty-three two-body hypercharge-exchange reactions is studied. It is found that the planar reactions have in general a less steep fall-off with increasing energy than the non-planar reactions. Explanations of the difference in terms of kinematics and dynamics (baryon exchange and t-channel exchange effects) are discussed and found highly improbable. Implications of the effects observed are discussed.     

Off-energy-shell continuation of the two-body transition matrix in the impact parameter representation

In the impact parameter representation, the symmetric part σ(k′, b, k) of the half-shell T-matrix, H, can be given arbitrarily. This in turn determines the entire T-matrix. Since σ(k, b, k) is essentially the impact parameter phase shift, the arbitrary part of the T-matrix appears to be a continuation into two dimensions of the phase shift function with symmetry being the only restriction. Since we can work with the T-matrix instead of the potential V, our formalism stays closer to experiments. Only two assumptions are necessary, namely, high energy and small intermediate angles.     

Interband transition matrix element and temperature dependence of the lasing threshold for GaN laser structures

By comparing experimental and theoretical radiative recombination spectra, we have determined the values of the square of the matrix element for interband optical transitions |M|² in epitaxial GaN at different temperatures T. The data obtained were used to analyze the mechanism for the temperature dependence of the lasing threshold for a GaN laser. In the experiments, we used epitaxial layers of GaN with a wurtzite crystal structure, grown on Al₂O₃ (0001) substrates and excited by a focused beam from a nitrogen laser. We have shown that the spontaneous emission spectra near the lasing threshold of a GaN laser are consistent with the model of optical interband transitions not obeying a selection rule for the electron wave vector. As we have established, the parameter |M|² practically does not vary for T = 300–470 K: 5.4·10⁻⁷³ kg²·m⁵/sec². Further increase in the temperature leads to an exponential fall-off in |M|² down to 3.4·10⁻⁷³ kg²·m⁵/sec² at T ≈ 520 K. Such behavior of |M|² as a function of temperature correlates with the sudden increase in the nonradiative recombination rate at T > 470 K, and may be connected with a change in the recombination mechanisms in the active layer of the GaN laser in the high temperature region. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 6, pp. 790–794, November–December, 2007.     

全同粒子两体算符的另一类非对角矩阵元

推导了玻色子和费米子两体算符在占有数表象下的另一类非对角矩阵元.     

Energy-scale dependence of the lepton flavor-mixing matrix

We study an energy-scale dependence of the lepton flavor-mixing matrix in the minimal supersymmetric standard model with the effective dimension-five operators, which give Majorana masses of neutrinos. We analyze the renormalization group equations of the coefficients () of these effective operators under an approximation that neglects terms of order . We find that only (where is the generation number) real independent parameters in the lepton flavor-mixing matrix depend on the energy scale. In particular, all the phases in are scale-independent. Received: 10 April 1999 / Revised version: 23 May 1999 / Published online: 28 September 1999     

原子模型势中任意算符矩阵元的递推关系

运用升降算子和超维里定理计算出原子模型势中任意算符Af^U2(r)的矩阵元〈n′1l′1|Af^U2(r)|n1l1〉的递推关系.     

On the temperature dependence of the mean number of clusters

The random variable number of cluster defined on the configurations of a ferromagnetic Ising model at zero field and inverse temperature on a graphG is considered. The Gibbs average at=0 is proved to be greater than the one at>0 if the degree ofG is not greater than 3.     

On the Mach number and temperature dependence of jet noise: Results from a simplified numerical model

Numerical simulations of sound radiation from perturbed round jets are used, firstly to explore the structure of the sound sources and then to carry out a parametric study of the effect of jet Mach number and jet temperature. The simplified model problem includes a steady base jet flow, maintained in the absence of disturbances, superimposed with instability waves that are free to interact nonlinearly. Simulations over a range of subsonic jet Mach numbers show that a nonlinear mechanism dominates over a linear mechanism for low-frequency sound radiation, while for supersonic Mach numbers the linear mechanism is dominant. Additional insight is gained from a frequency-wavenumber analysis, including a transformation in the radial direction. With this decomposition, the acoustic field is located by the arc of a circle in plots of radial against streamwise wavenumber for discrete frequencies. The transformation is applied to both the pressure field, showing the sound directivity, and to selected source terms, showing characteristic directivity patterns for the streamwise and radial quadrupole terms. Decreasing the Mach number leads to a reduction in amplitude of the sources and of the sound radiation. Simulations with broadband forcing show that the qualitative effects of Mach number and jet heating are captured by this approach, which requires less resolution than a direct numerical simulation. A significant increase in the strength of the acoustic radiation for cold jets is observed, which is worthy of further investigation.     

The dependence of the fermi energy on the atomic number

Taking a general fenomenological pseudopotential, a connection between the Fermi energy and the atomic number is established. This simple relation is valid not only for simple but also for complex metals.     

Can the Isgur-Karl model be successfully applied to meson-baryon two-body reactions?

Via the additivity assumption, the model of baryon structure formulated by Isgur and Karl is applied to quasi-two-body meson-baryon scattering. The model offers no improvement over the strictSU (6) case, nor will other configuration-mixing models which do not alter the relative weight of the two diquark components of the nucleon. The features of the Isgur-Karl model are compared to those of a diquark model which has been successful in this area.     

Exact matrix elements for general two-body central-force interactions,expressed as sums of products

ABSTRACT

In a manner similar to but distinct from concurrent tensor efforts in electronic structure, it is shown that the Laplace transform can serve as a generator for a sum-of-products (SOP) form that allows one to write essentially any function of distance between two particles (i.e. any central force potential) as an exact two-body matrix. In particular, exact expressions for the Coulomb, Yukawa and long-range Ewald two-body operators are evaluated in a band-limited (Sinc function) basis. The resultant exact, full-basis, SOP representations for these interaction potentials – acting in conjunction with an external harmonic confining field – are validated via comparison with energy eigenstate solutions obtained via an independent calculation based on separation of variables. The new two-body matrix representations may have substantial impact in any of the many disciplines in which pair-wise central force interactions are relevant – especially, electronic structure and dynamics.     

Calculating the characteristics of neutron-deuteron and proton-deuteron systems in a two-body potential model

³H and ³He nuclei are considered in a two-body model (³H = n + d; ³He = p + d). Two independent approaches are used: in the first, interaction is described by the folding potential, while NN potentials are taken in the Hulthen form with allowance for violations of isotopic invariance. The second approach features phenomenological Hulthen and Yukawa Nd potentials used as Nd interaction. In both approaches, the binding energies, vertex constants, and asymptotic normalization coefficients in the N+d channel are calculated.     

An autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination

Fundamental frequency (f0) difference limens (DLs) were measured as a function of f0 for sine- and random-phase harmonic complexes, bandpass filtered with 3-dB cutoff frequencies of 2.5 and 3.5 kHz (low region) or 5 and 7 kHz (high region), and presented at an average 15 dB sensation level (approximately 48 dB SPL) per component in a wideband background noise. Fundamental frequencies ranged from 50 to 300 Hz and 100 to 600 Hz in the low and high spectral regions, respectively. In each spectral region, f0 DLs improved dramatically with increasing f0 as approximately the tenth harmonic appeared in the passband. Generally, f0 DLs for complexes with similar harmonic numbers were similar in the two spectral regions. The dependence of f0 discrimination on harmonic number presents a significant challenge to autocorrelation (AC) models of pitch, in which predictions generally depend more on spectral region than harmonic number. A modification involving a "lag window"is proposed and tested, restricting the AC representation to a limited range of lags relative to each channel's characteristic frequency. This modified unitary pitch model was able to account for the dependence of f0 DLs on harmonic number, although this correct behavior was not based on peripheral harmonic resolvability.     

Speckle intensity mean value dependence on the number of scatterers

The number of scatterers contributing to the speckle amplitude can be determined by the spot size of the incident light or by the amplitude point spread function of the optical system. The speckle intensity mean value measurement results with two methods of choosing the number of scatterers applied are presented. The values of the rms phase deviation and correlation length obtained from two methods agree well. The properties of both methods are discussed. The possibilities for the roughness measurement are suggested.