We present a new potential function with an exactly solvable Ｓｃｈｒ?ｄｉｎｇｅｒ equation. At the same time, we propose a new variable transformation to show that the hyperbolic Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ molecular potential is also exactly solvable. The form of the solutions is not only closed, but also very simple. The normalized wave functions are expressed by the hypergeometric series. All the results of the Hulthéｎ potential and the modified Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ potential as well as the reflectionless potential in the existing literature are contained in the more general conclusions of this paper as special cases. Finally, practical applications of the potentials in this paper to diatomic molecules are discussed.
We present a new potential function with an exactly solvable Ｓｃｈｒ?ｄｉｎｇｅｒ equation. At the same time, we propose a new variable transformation to show that the hyperbolic Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ molecular potential is also exactly solvable. The form of the solutions is not only closed, but also very simple. The normalized wave functions are expressed by the hypergeometric series. All the results of the Hulthéｎ potential and the modified Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ potential as well as the reflectionless potential in the existing literature are contained in the more general conclusions of this paper as special cases. Finally, practical applications of the potentials in this paper to diatomic molecules are discussed.
A computer simulation model of one-dimensional random successive nucleation growth is presented. A series of patterns and their fractal dimensions are obtained for three near-neighbor conditions. The simulated structures are similar to those of porous silicon. The properties of the D-X curve and the critical threshold of the cluster change from fractal to uniform structure are also discussed briefly.
A computer simulation model of one-dimensional random successive nucleation growth is presented. A series of patterns and their fractal dimensions are obtained for three near-neighbor conditions. The simulated structures are similar to those of porous silicon. The properties of the D-X curve and the critical threshold of the cluster change from fractal to uniform structure are also discussed briefly.
We have observed crises with new characteristics induced by discontinuity in a one-dimensional discontinuous map describing relaxation oscillators. There are four critical lines characterizing different types of new crises in the parameter plane(Id,Ii). These have a common convergence at a non-differentiable vertex, near which a small parameter perturbation may induce drastic dynamical changes of the system.
We have observed crises with new characteristics induced by discontinuity in a one-dimensional discontinuous map describing relaxation oscillators. There are four critical lines characterizing different types of new crises in the parameter plane(Id,Ii). These have a common convergence at a non-differentiable vertex, near which a small parameter perturbation may induce drastic dynamical changes of the system.
Based on the Relativistic Multichannel Theory,we have systematically studied the fine structure of nf Rydberg states of alkali atoms. Our calculated differences between the quantum defects μj+ and μj- are in good agreement with measured values, namely normal for Li and Na while inverted for Rb and Cs. We also predict a normal fine-structure for K and an inverted one for Fr, which still have no experimental data currently. Our theoretical calculation shows that the exchange between excited electron and core electrons is responsible for the inversion, which is a purely relativistic effect, while electron correlation is unimportant.
Based on the Relativistic Multichannel Theory,we have systematically studied the fine structure of nf Rydberg states of alkali atoms. Our calculated differences between the quantum defects μj+ and μj- are in good agreement with measured values, namely normal for Li and Na while inverted for Rb and Cs. We also predict a normal fine-structure for K and an inverted one for Fr, which still have no experimental data currently. Our theoretical calculation shows that the exchange between excited electron and core electrons is responsible for the inversion, which is a purely relativistic effect, while electron correlation is unimportant.
Based on the X-ray diffraction theory, the X-ray diffraction patterns of C60 crystals with various stacking patterns have been simulated. The origin of amorphous scattering in C60 crystals has been discussed. It is suggested that there are two kinds of movements for a C60 molecule. The amorphous scattering of the crystals displays an intrinsic strutural characteristic of C60 crystals.
Based on the X-ray diffraction theory, the X-ray diffraction patterns of C60 crystals with various stacking patterns have been simulated. The origin of amorphous scattering in C60 crystals has been discussed. It is suggested that there are two kinds of movements for a C60 molecule. The amorphous scattering of the crystals displays an intrinsic strutural characteristic of C60 crystals.
The electronic structures of 13-atom Ru clusters with three possible high-symmetry geometries have been studied using the discrete-variational local-spin-density-functional method. The results indicata that all clusters with different symmetry at their equilibrium configuration have two magnetie solutions, and the low-spin solutions of the clusters are energetically more stable than the high-spin solutions of the clusters for each kind of symmetry. The ground state is the ＩhRu13 cluster, and has the magnetic moment of ４μB, or ０.３１μB per atom, which is in good agreement with the upper limit of experimental observation, ０.２９μB per atom. The reason for the contradiction of the magnetic moments between previous theory and experiment is that multiple magnetic solutions exist for the Kohn-Sham equations. The calculated results are compared and discussed with those of the previous theory. The real geometry of the Ru13 cluster is suggested to be a distorted icosahedron.
The electronic structures of 13-atom Ru clusters with three possible high-symmetry geometries have been studied using the discrete-variational local-spin-density-functional method. The results indicata that all clusters with different symmetry at their equilibrium configuration have two magnetie solutions, and the low-spin solutions of the clusters are energetically more stable than the high-spin solutions of the clusters for each kind of symmetry. The ground state is the ＩhRu13 cluster, and has the magnetic moment of ４μB, or ０.３１μB per atom, which is in good agreement with the upper limit of experimental observation, ０.２９μB per atom. The reason for the contradiction of the magnetic moments between previous theory and experiment is that multiple magnetic solutions exist for the Kohn-Sham equations. The calculated results are compared and discussed with those of the previous theory. The real geometry of the Ru13 cluster is suggested to be a distorted icosahedron.
Based on an empirical potential,we have performed calculations of bond lengths of carbon bucky-balls with high symmetry. Bond length of a monolayer graphite, considered as an extremely large bucky-ball, has also been calculated. The calculated bond lengths of single bonds and double bonds dectrease and increase with increasing bucky-ball size, respectively, and both smoothly connects with the corresponding value of the monolayer graphite.
Based on an empirical potential,we have performed calculations of bond lengths of carbon bucky-balls with high symmetry. Bond length of a monolayer graphite, considered as an extremely large bucky-ball, has also been calculated. The calculated bond lengths of single bonds and double bonds dectrease and increase with increasing bucky-ball size, respectively, and both smoothly connects with the corresponding value of the monolayer graphite.
It is shown that multiwave mixing of the beam itself in high-gain photorefractive crystals is also a possible cause of beam fanning. Through the multiwave coupling of the beam itself the power can asymmetrically transfer from low to high spatial frequencies. This leads to a broad-angled profile of light. Thus amplified noise and amplified spatial frequencies of the beam both play an important role in producing the fanning effect.
It is shown that multiwave mixing of the beam itself in high-gain photorefractive crystals is also a possible cause of beam fanning. Through the multiwave coupling of the beam itself the power can asymmetrically transfer from low to high spatial frequencies. This leads to a broad-angled profile of light. Thus amplified noise and amplified spatial frequencies of the beam both play an important role in producing the fanning effect.
Normally, when an imperfectly mode-locked 532nm ps laser is incident upon a Cu:KNSBN photorefractive crystal, no self-pumped phase conjugation can occur. We report however, for the first time to our knowledge, that if a photorefractive waveguide is first created in the crystal by a mode-locked beam of the same wavelength, then self-pumped phase conjugation can be induced for the imperfectly mode-locked beam.
Normally, when an imperfectly mode-locked 532nm ps laser is incident upon a Cu:KNSBN photorefractive crystal, no self-pumped phase conjugation can occur. We report however, for the first time to our knowledge, that if a photorefractive waveguide is first created in the crystal by a mode-locked beam of the same wavelength, then self-pumped phase conjugation can be induced for the imperfectly mode-locked beam.
When a ５１４.５ｎｍＡｒ＋ laser beam was incident on a Cu-doped ＫＮＳＢＮ crystal, a cat type of self-pumped phase conjugation was observed. And when two collinear ５１４.５ and ４８８ｎｍ beams of Ａｒ＋ laser were incident on the crystal simultaneously, a phenomenon of self-pumped phase conjugation quenching was observed. Both theoretical and experimental results are presented and discussed.
When a ５１４.５ｎｍＡｒ＋ laser beam was incident on a Cu-doped ＫＮＳＢＮ crystal, a cat type of self-pumped phase conjugation was observed. And when two collinear ５１４.５ and ４８８ｎｍ beams of Ａｒ＋ laser were incident on the crystal simultaneously, a phenomenon of self-pumped phase conjugation quenching was observed. Both theoretical and experimental results are presented and discussed.
The phenomenon of photorefractive asymmetrical self-defocusing induced by thermal self-focusing is observed when a Gaussian beam at 532nm with high enough intensity is focused onto a KNSBN crystal. The spatial distribution and physical properties of the asymmetrical self-defocusing are different from those of stimulated noise scattering. It is found that asymmetrical self-defocusing has no contribution to self-pumped phase conjugation. The diameter of the beam when asymmetrical self-defocusing first appears in the crystal is estimated.
The phenomenon of photorefractive asymmetrical self-defocusing induced by thermal self-focusing is observed when a Gaussian beam at 532nm with high enough intensity is focused onto a KNSBN crystal. The spatial distribution and physical properties of the asymmetrical self-defocusing are different from those of stimulated noise scattering. It is found that asymmetrical self-defocusing has no contribution to self-pumped phase conjugation. The diameter of the beam when asymmetrical self-defocusing first appears in the crystal is estimated.
A pair of diffractive optical elements are desinged to implement the wavefront transformation from an elliptical-gaussian beam to a flat-top circular beam,with the aid of a new algorithm (SAIO) composed of a simulated annealing algorithm (SA) and an input-output(IO) algorithm. The energy transformation efficiency is up to 91.9%. SAIO performs better than SA or IO alone.
A pair of diffractive optical elements are desinged to implement the wavefront transformation from an elliptical-gaussian beam to a flat-top circular beam,with the aid of a new algorithm (SAIO) composed of a simulated annealing algorithm (SA) and an input-output(IO) algorithm. The energy transformation efficiency is up to 91.9%. SAIO performs better than SA or IO alone.
The surface anchoring of nematic liquid crystals is an important coefficient which expresses the effect of liquid crystal alignment and the mechanism of the surface alignment. The surface azimuthal anchoring energy can be obtained by measuring the twist angle in the twist cell and the surface torsional angle between the rubbing direction and the liquid crystal director at the substrate boundary. The temperature dependence of the surface anchoring energy at 5CB-polyimide (PI) interface was studied. The surface anchoring energy decreases with increase of the temperature from ５.０×１０－5Ｊ／ｍ2 at 25.５℃ to ５.０×１０－6Ｊ／ｍ2 at 35.0℃. Meanwhile, the extrapolation length ｄe increases from 80nm at 25.5℃ to ３７０ｎｍ at ０.５℃ below Ｔc. This result clearly signifies the important role of the ordered structure of the nematic interface in determining the temperature dependence of the anchoring strength at the ５ＣＢ-PI interface.
The surface anchoring of nematic liquid crystals is an important coefficient which expresses the effect of liquid crystal alignment and the mechanism of the surface alignment. The surface azimuthal anchoring energy can be obtained by measuring the twist angle in the twist cell and the surface torsional angle between the rubbing direction and the liquid crystal director at the substrate boundary. The temperature dependence of the surface anchoring energy at 5CB-polyimide (PI) interface was studied. The surface anchoring energy decreases with increase of the temperature from ５.０×１０－5Ｊ／ｍ2 at 25.５℃ to ５.０×１０－6Ｊ／ｍ2 at 35.0℃. Meanwhile, the extrapolation length ｄe increases from 80nm at 25.5℃ to ３７０ｎｍ at ０.５℃ below Ｔc. This result clearly signifies the important role of the ordered structure of the nematic interface in determining the temperature dependence of the anchoring strength at the ５ＣＢ-PI interface.
The surface alignment of liquid crystals is very important in preparing liquid crystal cells. The orientational effect of liquid crystal and polymide molecules on Langmuir-Blodgett(LB) films has been studied. The degree of orientation of the polyimide chain in LB films is weaker than that in strong rubbing films. The orientational effect of liquid crystals on the polyimide LB films is worse than that on the strong rubbing films. The surface azimuthal anchoring energy of liquid crystals on the polyimide LB films was measured. The intermolecular interaction between liquid crystal and polymer molecules is considered to be very important for the alignment of liquid crystals on the polymer surface.
The surface alignment of liquid crystals is very important in preparing liquid crystal cells. The orientational effect of liquid crystal and polymide molecules on Langmuir-Blodgett(LB) films has been studied. The degree of orientation of the polyimide chain in LB films is weaker than that in strong rubbing films. The orientational effect of liquid crystals on the polyimide LB films is worse than that on the strong rubbing films. The surface azimuthal anchoring energy of liquid crystals on the polyimide LB films was measured. The intermolecular interaction between liquid crystal and polymer molecules is considered to be very important for the alignment of liquid crystals on the polymer surface.
The electronic structure of CdTe(111) surfaces with adsorbed alkali metals has been explored by synchrotron radiation and LMTO method. The experimental results showed that the surface states were redistributed when K-adsorbed and Fermi-pinning phenomena appeared. Theoretical calculations of K adsorbed on CdTe(111) surfaces agree well with the experiment. A systematic study of alkali metals adsorbed on CdTe(111) surfaces showed that the electronic structure characteristics not only depend on the atomic number of the alkali metals, but are also related to the core electron configurations.
The electronic structure of CdTe(111) surfaces with adsorbed alkali metals has been explored by synchrotron radiation and LMTO method. The experimental results showed that the surface states were redistributed when K-adsorbed and Fermi-pinning phenomena appeared. Theoretical calculations of K adsorbed on CdTe(111) surfaces agree well with the experiment. A systematic study of alkali metals adsorbed on CdTe(111) surfaces showed that the electronic structure characteristics not only depend on the atomic number of the alkali metals, but are also related to the core electron configurations.
Applying the effective-field theory with correlations, we study the phase transition of a periodically diluted Ising system in the presence or absence of a transverse field. We focus on the dependence of the critical temperature of the system on the modulation amplitude and transverse field. The interesting result is: the inhomogeneity of the concentration of magnetic atoms can cause an increase in the critical temperature of the system. However, as the modulation amplitude is increased, the bulk magnetic order of the system may change to a partial magnetic order.
Applying the effective-field theory with correlations, we study the phase transition of a periodically diluted Ising system in the presence or absence of a transverse field. We focus on the dependence of the critical temperature of the system on the modulation amplitude and transverse field. The interesting result is: the inhomogeneity of the concentration of magnetic atoms can cause an increase in the critical temperature of the system. However, as the modulation amplitude is increased, the bulk magnetic order of the system may change to a partial magnetic order.
Following the random magnetic anisotropy model proposed by Alben for amorphous ferromagnets and taking into consideration the two-phase microstructure of nanostructured soft magnetic alloys, we propose a two-phase random magnetic anisotropy model for nanostructured soft magnetic alloys. We obtain the relationship of the effective magnetic anisotropy density with the microstructure parameters and magnetic parameters of ferromagnetic phases in the alloy, and also the dependence of the magnetic propertics on the effective magnetic anisotropy density. The experimental results of X-ray diffraction and magnetic measurements of Ｆｅ７３.５Ｃｕ１.０Ｎｂ３.０Ｓｉ１３.５Ｂ９.０ nanostructured soft magnetic alloys give favourable support to the above theoretical research.
Following the random magnetic anisotropy model proposed by Alben for amorphous ferromagnets and taking into consideration the two-phase microstructure of nanostructured soft magnetic alloys, we propose a two-phase random magnetic anisotropy model for nanostructured soft magnetic alloys. We obtain the relationship of the effective magnetic anisotropy density with the microstructure parameters and magnetic parameters of ferromagnetic phases in the alloy, and also the dependence of the magnetic propertics on the effective magnetic anisotropy density. The experimental results of X-ray diffraction and magnetic measurements of Ｆｅ７３.５Ｃｕ１.０Ｎｂ３.０Ｓｉ１３.５Ｂ９.０ nanostructured soft magnetic alloys give favourable support to the above theoretical research.
A structure for short wavelength spin wave mode excitation is developed, which is used to investigate a spin wave (Winter mode) bound to the domain wall in a magnetic bubble film with an rf magnetic field produced by a microstrip carrying rf current, a thin permalloy grating on the top of the magnetic specimen generates secondary magnetic fields which match the time frequency and spatial wavelength of the spin wave, and an efficient coupling between them is realized By means of phase lock-in techniques a differential absorption peak corresponding to the Winter mode has been observed at 318 MHz.
A structure for short wavelength spin wave mode excitation is developed, which is used to investigate a spin wave (Winter mode) bound to the domain wall in a magnetic bubble film with an rf magnetic field produced by a microstrip carrying rf current, a thin permalloy grating on the top of the magnetic specimen generates secondary magnetic fields which match the time frequency and spatial wavelength of the spin wave, and an efficient coupling between them is realized By means of phase lock-in techniques a differential absorption peak corresponding to the Winter mode has been observed at 318 MHz.
The femtosecond laser pulses and pump-probe method have been used to measure the transient change of transmissivity of metallic ultrafine particles(UFPs) embedded in semiconductor thin film (Ag-BaO). The phenomena that the optical absorption of the films decreases and then restores within 2ps have been observed. The phenomena are due to the fact that electrons near the Fermi energy level in Ag UFPs are excited by femtosecond laser pulses and then the generated nonequilibrium electrons undergo a transient relaxation. The relaxation includes includes two parts: first, nonequilibrium electrons from Ag UFPs enter the matrix;then,nonequilibrium electrons are scattered by the lattice and inter-face between the Ag UFPs and the matrix. The different diameters of Ag UFPs affter the relaxation time of nonequilibrium electrons.
The femtosecond laser pulses and pump-probe method have been used to measure the transient change of transmissivity of metallic ultrafine particles(UFPs) embedded in semiconductor thin film (Ag-BaO). The phenomena that the optical absorption of the films decreases and then restores within 2ps have been observed. The phenomena are due to the fact that electrons near the Fermi energy level in Ag UFPs are excited by femtosecond laser pulses and then the generated nonequilibrium electrons undergo a transient relaxation. The relaxation includes includes two parts: first, nonequilibrium electrons from Ag UFPs enter the matrix;then,nonequilibrium electrons are scattered by the lattice and inter-face between the Ag UFPs and the matrix. The different diameters of Ag UFPs affter the relaxation time of nonequilibrium electrons.
Nucleation and formation of barium titanate crystallites under hydrothermal conditions was studied using a mathematical model and calculation of the stabilization energy of the growth unit on the basis of synthesis experiments.
Nucleation and formation of barium titanate crystallites under hydrothermal conditions was studied using a mathematical model and calculation of the stabilization energy of the growth unit on the basis of synthesis experiments.
The compensate effect under the time-scale transformation for the Schwarzschild black hole and Vaidya black hole are studied. The gauge potential is the contraction of the affine connection. Both the Hawking temperature and the change of entropy of black holes can be regarded as the pure-gauge potentials of the compensate field.
The compensate effect under the time-scale transformation for the Schwarzschild black hole and Vaidya black hole are studied. The gauge potential is the contraction of the affine connection. Both the Hawking temperature and the change of entropy of black holes can be regarded as the pure-gauge potentials of the compensate field.