Simultaneous Measurement of Refractive Index and Thickness by Low Coherence Interferometry Considering Chromatic Dispersion of Index

Low coherence interferometry can provide simultaneous measurement of refractive index n and thickness t of a transparent plate, as reported recently by some research groups. Precise measurement of n and t is impossible unless chromatic dispersion of index is taken into account. We then proposed and demonstrated a unique technique for simultaneous measurement of phase index n_p, group index n_g and thickness t using a special sample holder. This paper describes a novel technique for simultaneous measurement of n_p, n_g and t using an approximate expression of the chromatic dispersion in terms of n_p. The approximate expression of chromatic dispersion does not require use of the special sample holder, and n_p, n_g and t are determined from two measurable quantities with an accuracy of 0.3% or less, for the sample thickness was around 1 mm. In addition, it is possible to shorten the measurement time compared with the above method.     

A Pascal's triangle-like approach for the determination of characteristic polynomial coefficients of reciprocal graphs

Characteristic polynomial coefficients of three classes of graph, namely L_n + n(p), C_n + n(p) and K _1,n-1 + n(p), which are known to have reciprocal pairs of eigenvalues, have been shown to be generated by simple manipulation of the Pascal's triangle.     

Ba原子6pnd(J=1, 3)自电离光谱的实验研究

采用三台可调谐激光实施孤立实激发,分三步将处于基态的Ba原子激发到6p_1/2nd(J=1,3)和6p_3/2nd(J=1,3)自电离态上,获得了分别从6snd¹D₂(n=7—15)和6snd³D₂(n=7—12) 激发而得到的6p_1/2nd(J=1,3)和6p_3/2nd (J=1,3)自电离光谱,重点对主量子数n较低的自电离态进行了实验研究. 通过光谱的线形拟合得到了上述能级的位置和宽度等数据,进而获得了量子亏损和约化宽度等信息. 通过对不同系列的自电离光谱的分析和比较,详细讨论了这些自电离态的光谱特征及其复杂光谱结构的成因. 关键词： 孤立实激发 组态相互作用 自电离态     

A new theorem of information theory

Consider a random experiment whose possible outcomes arez ₁,z ₂,...,z _n. Let the prior probabilities be p₁ ⁰, ...,p_n ⁰, and let the posterior probabilities bep ₁,...,p _n. It is shown that, subject to certain prescribed and intuitively reasonable conditions, the expressionI =k p _i In (p _i/p _i ⁰), wherek is a positive constant, is the unique expression for the information contained in a message which alters the probabilities from thep _i ⁰ to thep _i.     

Relaxation of post-illumination electric fields in strongly biased high-resistance structures with a single deep impurity level

This paper examines how an electric field relaxes when a discontinuous large carrier-depleting voltage applied to high-resistance symmetric metal-semiconductor-metal (MSM) and metal-insulator-semiconductor-insulator-metal (MISIM) structures having a single impurity level, and how its energy level ɛ _t=E _c−E _t and the tunneling transparency T _n,p of the metal-semiconductor or metal-insulator boundary affect the relaxation. It is shown that the relaxation of the field and the form of its steady-state distribution depend on the ratio of the time constant t _p in the majority-carrier (hole) region to the ionization time τ _t ⁻¹ =α _n (n _*+n ₁)+α _p (p _*+p ₁) of a deep trap in the bulk. This ratio determines the relative contributions of free ρ _p,n and bound charge dnsities ρ _t (where α _n,p is the coefficient for capture by an impurity, and p _*, n _*, p ₁, n ₁ are equilibrium concentrations and Shockley-Read constants in the bulk). For τ _t ≈(τ _t )_max≫t _p ,ρ _t ≫ it is found that ρ _p,n and ρ _t ≫ρ _p,n , which corresponds to a trap energy close to , independent of the value of T _n,p , decaying oscillations arise in the concentration distribution, bulk charge, and field appear in the bulk. The amplitude of these oscillations reaches a maximum at time t≈0.4τ _t. Decreasing the ratio α _p/α_n causes τ _t to deviate from (τ _t)_max. When this happens, the field no longer oscillates; instead, it increases with positive curvature in the cathode portion of the bulk. The quantity T _n,p determines the behavior of the field in the neighborhood of the anode. The value of (dE/dx)₀ is positive for MSM structures (T _n,p ≈1), and negative for MISIM structures (T _n,p ≈0). For transparencies close to a critical value T _n,p ⁰ , the field in the structure remains almost uniform over an impurity ionization time. Fiz. Tverd. Tela (St. Petersburg) 39, 1775–1782 (October 1997)     

Scaling assumption for lattice animals in percolation theory

A scaling assumption for the numberg _ns of different cluster configurations with perimeters and sizen leads to the desired cluster numbers near the percolation threshold. The perimeter distribution function has a mean square width proportional ton for largen. The relation between the average perimeter and the cluster sizen for percolation has three different forms atp _c, belowp _c, and abovep _c and is closely related to the shape of the cluster size distribution.     

A Derivative Formula for the Free Energy Function

We consider bond percolation on the Z ^d lattice. Let M _n be the number of open clusters in B(n)=[−n,n] ^d . It is well known that E _p M _n /(2n+1) ^d converges to the free energy function κ(p) at the zero field. In this paper, we show that s²_p(M_n)/(2n+1)^d\sigma^{2}_{p}(M_{n})/(2n+1)^{d} converges to −p(1−p)κ′(p).     

Spin structure of the “Forward” nucleon charge-exchange reaction <Emphasis Type="Italic">n</Emphasis> + <Emphasis Type="Italic">p</Emphasis> → <Emphasis Type="Italic">p</Emphasis> + <Emphasis Type="Italic">n</Emphasis> and the deuteron charge-exchange breakup

The structure of the nucleon charge-exchange process n + p → p + n is investigated basing on the isotopic invariance of the nucleon-nucleon scattering. Using the operator of permutation of the spin projections of the neutron and proton, the connection between the spin matrices, describing the amplitude of the nucleon charge-exchange process at zero angle and the amplitude of the elastic scattering of the neutron on the proton in the “backward” direction, has been considered. Due to the optical theorem, the spin-independent part of the differential cross section of the process n + p → p + n at zero angle for unpolarized particles is expressed through the difference of total cross sections of unpolarized proton-proton and neutron-proton scattering. Meantime, the spin-dependent part of this cross section is proportional to the differential cross section of the deuteron charge-exchange breakup d + p → (pp) + n at zero angle at the deuteron momentum k _d = 2 k _n (k _n is the initial neutron momentum). Analysis shows that, assuming the real part of the spin-independent term of the “forward” amplitude of the process n + p → p + n to be smaller or of the same order as compared with the imaginary part, in the wide range of neutron laboratory momenta k _n > 700 MeV/c the main contribution into the differential cross section of the process n + p → p + n at zero angle is provided namely by the spin-dependent term.     

Preparation and characterization of p–n heterojunction photocatalyst p-CuBi2O4/n-TiO2 with high photocatalytic activity under visible and UV light irradiation

In this article, the p-type CuBi₂O₄ powder was prepared by the solid-state reaction method. The p–n heterojunction photocatalyst p-CuBi₂O₄/n-TiO₂ was prepared by ball milling. The photocatalyst was characterized by X-ray powder diffraction (XRD), UV–Vis diffuse reflectance spectroscopy, scanning electron microscopy (SEM), and photoluminescence emission spectra. The photocatalytic activity of the photocatalyst was evaluated by photocatalytic reduction of Cr₂O₇ ²⁻ and photocatalytic oxidation of methyl orange (MO). The results showed that the photocatalytic activity of the p–n heterojunction photocatalyst p-CuBi₂O₄/n-TiO₂ was much higher than that of TiO₂ and the mixture of p-CuBi₂O₄–n-TiO₂ without ball milling under visible and UV light irradiation. The optimal percentage of doped p-CuBi₂O₄ is 20 wt%. Compared with pure TiO₂, the photoabsorption wavelength range of the photocatalyst is extended greatly toward visible light and improves the utilization of the total spectrum. The effect of ball milling time on the photocatalytic activity of the photocatalyst was also investigated. The optimum ball milling time is 6 h. The mechanisms of influence of p-CuBi₂O₄ on the photocatalytic activity of p-CuBi₂O₄/n-TiO₂ were also discussed by the p–n junction principle and the valance band theory.     

Inverse Laplace transforms of osculatory and hyperosculatory interpolation polynomials

In the numerical calculation of f(t), the inverse Laplace transform of F(p), where f(′) = (1/2πi) °_c−i∞^c+i∞ e^pt F(p)dp, sufficient accuracy is usually obtainable when p³F(p), s > 0, is replaced by an interpolating polynomial in 1/p. From the values of F(p) with F′(p), or with F′(p) and F″(p), for p at points equally spaced on the real axis, an osculatory or hyperosculatory interpolation polynomial for p⁸F(p), namely L_2n−1(x) or L_3n−1(x), where x = 1/p, is obtained in barycentric form. Then f(t) is calculated by a Gaussian-type quadrature formula employing complex values of L_2n−1 or L_3n−1 and instead of p^sF(p) which may be unknown or more difficult to compute. For calculating L_2n−1 and L_3n−1, auxiliary coefficients, suitable for economical storage in the program, are given exactly for n = 2(1)11 and n = 2(1)7, furnishing up to 21st and 20th degree accuracy, respectively.     

Energy levels of perturbed 6p<Emphasis Type="Italic">n</Emphasis>d <Emphasis Type="Italic">J</Emphasis>=2 Rydberg states of Pb I by multichannel quantum defect theory

Energy levels of the odd-parity 6pnd J=2 Rydberg states of atomic lead are analyzed by the multichannel quantum defect theory (MQDT) with previous experimental energy levels. The obtained. Using these parameters, admixture coefficients for each level are calculated to designate the level denotations. The results show that strong channel mixings exist for the levels near the 6pnd (3/2)[5/2]₂ ⁰ and 6p6d (3/2)[3/2]₂ ⁰ pertubers. The five-channel model different from that in literature is used to predict 21 energy positions of 6pnd (1/2)[3/2]₂ ⁰ levels and to determine the denotations of all the 6pnd J=2 Rydberg states under 59788 cm⁻¹ for Pb I.     

Divergence of the bulk resistance at criticality in disordered media

Consider the electrical resistancer _n (p) of a hypercubic bond lattice [O,n] ^d inZ ^d , where the bonds have resistance 1 with probabilityp or with probability 1-p. Letp _n (p)=n ^2-d r _n (p) andp(p)=lim_np_n(p). It is well known thatp(p)< ifp>p _c andp(p)= ifp<p _c , wherep _c is the percolation threshold. Here we show thatp(p _c )=, and .     

Thermostatistical properties of a q-deformed bosonic exciton gas

We present the calculations of the electronic structure and transport properties on the filled-skutterudites LaFe₄Sb₁₂ and CeFe₄Sb₁₂ using the full-potential linearized augmented plane-wave method and the semi-classical Boltzmann theory. Our calculation indicates that LaFe₄Sb₁₂ and CeFe₄Sb₁₂ have the large density of states near the Fermi level. The obtained Seebeck coefficient and the magnetic susceptibilities are in good agreement with experimental results. It is found that n-type doping in the CeFe₄Sb₁₂ compound may be more favorable than p-type doping below 900 K and p-type doping in the CeFe₄Sb₁₂ compound may be more favorable than n-type doping above 900 K. It is also seen that n-type doping in the LaFe₄Sb₁₂ compound may be more favorable than p-type doping below 700 K and p-type doping in the LaFe₄Sb₁₂ compound may be more favorable than n-type doping above 700 K. Ultimately, we found that LaFe₄Sb₁₂ is more suitable for thermoelectric applications than CeFe₄Sb₁₂.     

Multiple Intersection Exponents for Planar Brownian Motion

Let p≥2, n ₁≤⋅⋅⋅≤n _p be positive integers and be independent planar Brownian motions started uniformly on the boundary of the unit circle. We define a p-fold intersection exponent ς _p (n ₁,…,n _p ), as the exponential rate of decay of the probability that the packets , i=1,…,p, have no joint intersection. The case p=2 is well-known and, following two decades of numerical and mathematical activity, Lawler et al. (Acta Math. 187:275–308, 2001) rigorously identified precise values for these exponents. The exponents have not been investigated so far for p>2. We present an extensive mathematical and numerical study, leading to an exact formula in the case n ₁=1, n ₂=2, and several interesting conjectures for other cases.     

Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis

A criterion for the existence of a continuous embedding of a weighted Sobolev class in a weighted L _p space is obtained, i.e., the existence of an index n for which the Kolmogorov n-diameter is finite. For the case in which a continuous embedding exists, the reduced Sobolev class is constructed together with a continuous operator of a natural embedding of the class in a weighted L _p -space.     

Geometric form of the equations for the phase changes on reflection and transmission at a thin absorbing film

Abelès' equations for the phase changes on reflection and transmission, F_s, F_p, X_s and X_p at thin films have been rearranged into geometrical form in the ε₁, ε₂ plane. The contours of constant F_s and F_p are a series of circles whilst X_s and X_p can be represented by straight lines. When considering the same functions in the n, k plane, f_s and F_p become quartics in new axes, n′ and k′, obtained by rotating the n and k axes through an angle a given by tan . A similar transformation applied to X_s and X_p generates hyperbolae in the n′, k′ plane.     

A study of sputter-induced defects in magnetron-sputtered CoSi2 and TiSi2 Schottky barriers on n- and p-type GaP

Magnetron-sputtered CoSi₂ and TiSi₂ Schottky barriers on n- and p-type GaP were investigated. Their hitherto unknown barrier heights were determined to be 0.98 eV (for CoSi₂/n-GaP and CoSi₂/p-GaP), 0.91 eV (for TiSi₂/n-GaP), and 0.90 eV (for TiSi₂/p-GaP). It was found that magnetron-sputtering induced a compensated layer near the surface, both for n- and p-type GaP, with a thickness of about 0.05 m. As the dependence of the shift of the Mott-Schottky intercept with the V-axis on the substrate dopant concentration obeyed some specific law, we proposed that the defects are neutral complexes of dopant ions and sputter-induced native defects. These native defects were assumed to depend on the Fermi level position, namely the P_Ga antisite and the V_P vacancy for p-GaP and the V_Ga vacancy for n-GaP. The conversion between these defects occurs by nearest neighbour hopping of a phosphorus atom. The Schottky barrier heights obtained on p-GaP could be explained by Fermi level pinning at the surface due to the P_Ga defects. This could not be confirmed by n-GaP as the energy level position of the V_Ga was not available. The defects could be annealed out between 200° C and 300° C and the associated change of the Schottky barrier height corroborated the proposed model.On leave from the Université de Burundi, Faculté des Sciences, Bujumbura, Burundi     

Response to the Comment: “On the computation of molecular auxiliary functions<Emphasis Type="Italic">A</Emphasis><Subscript>n</Subscript>and B<Subscript>n</Subscript>”

The Comment ‘on the computation of auxiliary functionsA _n(p) and B_n(pt)’ (FEHarris, Pramana - J. Phys. 61, C779 (2003)) is analysed in the arbitrary range of parametersn,p andpt. It is shown that our downward recursion approach forB _n(pt) in the range (n/pt) > 1 is more efficient than the well-known upward recursion method, and the upward recursion procedure forA _n(p) does not have merit for smaller non-zero values ofp (p < 001).     

Simple one-centre calculation of breathing force constants and equilibrium internuclear distances for NH3, H2O and HF

Total molecular energies, breathing force constants and equilibrium internuclear distances are determined for the NH₃, H₂O and HF molecules using a single determinant wave function of the simplified one-centre form s ² s′² p _x ² p _y ² p _z ², where each of the five Slater orbitals, s, s′, p _x , p _y , p _z , is characterized by an effective orbital exponent ζ and an effective principal quantum number n. Five different calculations are performed for each molecule: in (a) the orbitals are centred on the heavy atom, the parameters n are taken to be integral, and the orbitals p _x , p _y and p _z are given the same ζ values (the spherical approximation); in (b) the orbitals p _x , p _y and p _z are allowed to have different ζ values (the ellipsoidal approximation); (c) and (d) are the same as (a) and (b) except that non-integral n values are allowed; (e) is the same as (d) except that the orbital centre also is taken to be a variational parameter. The values obtained are compared with experimental values (the agreement is surprisingly good) and with values from previous one-centre wave functions. The electronic densities for the various spherical approximations are tabulated.     

Improvement of <Emphasis Type="Italic">n</Emphasis>-ZnO/<Emphasis Type="Italic">p</Emphasis>-Si photodiodes by embedding of silver nanoparticles

The photo-current of n-ZnO/p-Si heterojunction photodiodes was improved by embedding Ag nanoparticles in the interface (ZnO/nano-P_Ag/p-Si), and the ratio between photo- and dark-current increased by about three orders more than that of a n-ZnO/p-Si specimen. The improvement in the photo-current resulted from the light scattering of embedded Ag nanoparticles. The I–V curve of n-ZnO/p-Si degraded after thermal treatment (A-ZnO/p-Si) because the silicon robbed the oxygen from ZnO to form amorphous silicon dioxide and left an oxygen vacancy. Notably, the properties of ZnO/nano-P_Ag/p-Si were better in the time-dependent photoresponse under 10 V bias. Ag nanoparticles (15–20 nm) scattered the UV light randomly and increased the probability for the absorption of ZnO to enhance the properties of the photodiode.