In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecule...In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecules have not been clearly elucidated.In this work,based on the molecular point group,the selection rules for the electric multipolarities of the electronic transitions of triatomic molecules are derived and summarized into several tables with the variation of molecular geometry in the transition process being considered.Based on the summarized selection rules,the electron energy loss spectra of H2O,CO2,and N2O are identified,and the momentum transfer dependence behaviors of their valence-shell excitations are explained.展开更多
After considering Kerr nonlinear effect, group velocity dispersion of host and gain distribution of active particle in laser amplifying medium, a basic equation describing propagation of the coupling optical pulse und...After considering Kerr nonlinear effect, group velocity dispersion of host and gain distribution of active particle in laser amplifying medium, a basic equation describing propagation of the coupling optical pulse under the multi-photon nonlinear Compton scattering in the laser amplifying medium has been deduced. Besides, the profile and power spectrum of a picosecond-level super-Gaussian coupling pulse in the laser amplifying medium have been discussed when its central frequency coincides with the gain peak frequency of the laser amplifying medium.展开更多
The knowledge of the energy level structures of atoms and molecules is mainly obtained by spectroscopic experiments. Both photoabsorption and photoemission spectra are subject to the electric dipole selection rules （...The knowledge of the energy level structures of atoms and molecules is mainly obtained by spectroscopic experiments. Both photoabsorption and photoemission spectra are subject to the electric dipole selection rules （also known as optical selection rules）. However, the selection rules for atoms and molecules in the scattering experiments are not identical to those in the optical experiments. In this paper, based on the theory of the molecular point group, the selection rules are derived and summarized for the electric monopole, electric dipole, electric quadrupole, and electric octupole transitions of diatomic molecules under the first Born approximation in scattering experiments. Then based on the derived selection rules, the electron scattering spectra and x-ray scattering spectra of H2, N2, and CO at different momentum transfers are explained, and the discrepancies between the previous experimental results measured by different groups are elucidated.展开更多
It is of both the theoretical and practical importance to reduce the storage andCPU time of moment methods by utilizing the geometrical and physical features of the scatterer.An unified approach based on the group the...It is of both the theoretical and practical importance to reduce the storage andCPU time of moment methods by utilizing the geometrical and physical features of the scatterer.An unified approach based on the group theory is presented to deal with the EM scattering fromsymmetric and anti-symmetric structures.展开更多
In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The id...In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: vp.vg = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ, i.e. to vgt ± σ/ω, where ω is the particle angular frequency. This is the first time the phase range has been described for a massive particle.展开更多
A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities signifi...A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.展开更多
We introduce the concept of transmission eigenvalues in scattering theory for automorphic forms on fundamental domains generated by discrete groups acting on the hyperbolic upper half complex plane. In particular, we ...We introduce the concept of transmission eigenvalues in scattering theory for automorphic forms on fundamental domains generated by discrete groups acting on the hyperbolic upper half complex plane. In particular, we consider Fuchsian groups of Type Ⅰ. Transmission eigenvalues are related to those eigen-parameters for which one can send an incident wave that produces no scattering. The notion of transmission eigenvalues, or non-scattering energies, is well studied in the Euclidean geometry, where in some cases these eigenvalues appear as zeros of the scattering matrix. As opposed to scattering poles,in hyperbolic geometry such a connection between zeros of the scattering matrix and non-scattering energies is not studied, and the goal of this paper is to do just this for particular arithmetic groups.For such groups, using existing deep results from analytic number theory, we reveal that the zeros of the scattering matrix, consequently non-scattering energies, are directly expressed in terms of the zeros of the Riemann zeta function. Weyl's asymptotic laws are provided for the eigenvalues in those cases along with estimates on their location in the complex plane.展开更多
Bafia Group is part of the southernmost portion of the Central African Fold Belt (CAFB) in Cameroon. The geological feature of the group is characterized by the presence of metamorphic rocks in which tourmaline had be...Bafia Group is part of the southernmost portion of the Central African Fold Belt (CAFB) in Cameroon. The geological feature of the group is characterized by the presence of metamorphic rocks in which tourmaline had been recognized among accessory minerals. In the present study, attention is focus on the tourmaline bearing quartzite to the southeast of Kombé II. Structure refinement shows that tourmaline is a Fe-dravite with the formula X(Na<sub>0.95</sub>[]<sub>0.05</sub>)Y(Mg<sub>2.39</sub>Fe<sub>0.61</sub>)Z(Al<sub>5.10</sub>Mg<sub>0.90</sub>)(BO<sub>3</sub>)<sub>3</sub>T[Si<sub>6</sub>O<sub>18</sub>](OH)<sub>3</sub>[(O,OH)<sub>0.88</sub>F<sub>0.12</sub>]. The Fe-dravite is hosted in a Ca-poor quartzite, which is made up, in addition to quartz and tourmaline, of biotite and muscovite. The structure of the dravites shows a low vacancy at the X site, which militates for a crystallization of the tourmaline at a high temperature > 750℃. This is in agreement with previous work which shows that the metamorphic peak in the associated biotite gneiss reaches 825℃. The R1 value of 1.24% means that the crystal structure of the tourmalines is of high quality. The genetical link between gold mineralization and tourmaline should stimulate exploration interest in the study area.展开更多
It is a very important issue to reduce computer storage and calculation time for matrix in solving scattering field by making use of geometric and physical symmetric features of a scattering body. A general definition...It is a very important issue to reduce computer storage and calculation time for matrix in solving scattering field by making use of geometric and physical symmetric features of a scattering body. A general definition for the symmetric and anti-symmetric structure is given by applying the group theory in mathematics and a general method for treating the electromagnetic scattering problems with symmetry is proposed. An example for applying the theory mentioned above is also given.展开更多
The symmetry of rotation vibration spectra of molecule SiO_2 is described by means of group U(5). Grouptheory approach is adopted to give the matrix elements of stimulated Raman scattering in fiber. The cross sections...The symmetry of rotation vibration spectra of molecule SiO_2 is described by means of group U(5). Grouptheory approach is adopted to give the matrix elements of stimulated Raman scattering in fiber. The cross sectionsand gain coefficients of stimulated Raman scattering are given. The results are in good agreement with the experi-mental values.展开更多
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0402300)the National Natural Science Foundation of China(Grant No.U1732133)the Science Fund from Chinese Academy of Sciences(Grant No.11320101003)
文摘In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecules have not been clearly elucidated.In this work,based on the molecular point group,the selection rules for the electric multipolarities of the electronic transitions of triatomic molecules are derived and summarized into several tables with the variation of molecular geometry in the transition process being considered.Based on the summarized selection rules,the electron energy loss spectra of H2O,CO2,and N2O are identified,and the momentum transfer dependence behaviors of their valence-shell excitations are explained.
文摘After considering Kerr nonlinear effect, group velocity dispersion of host and gain distribution of active particle in laser amplifying medium, a basic equation describing propagation of the coupling optical pulse under the multi-photon nonlinear Compton scattering in the laser amplifying medium has been deduced. Besides, the profile and power spectrum of a picosecond-level super-Gaussian coupling pulse in the laser amplifying medium have been discussed when its central frequency coincides with the gain peak frequency of the laser amplifying medium.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.U1332204,11274291,and 11320101003)
文摘The knowledge of the energy level structures of atoms and molecules is mainly obtained by spectroscopic experiments. Both photoabsorption and photoemission spectra are subject to the electric dipole selection rules （also known as optical selection rules）. However, the selection rules for atoms and molecules in the scattering experiments are not identical to those in the optical experiments. In this paper, based on the theory of the molecular point group, the selection rules are derived and summarized for the electric monopole, electric dipole, electric quadrupole, and electric octupole transitions of diatomic molecules under the first Born approximation in scattering experiments. Then based on the derived selection rules, the electron scattering spectra and x-ray scattering spectra of H2, N2, and CO at different momentum transfers are explained, and the discrepancies between the previous experimental results measured by different groups are elucidated.
文摘It is of both the theoretical and practical importance to reduce the storage andCPU time of moment methods by utilizing the geometrical and physical features of the scatterer.An unified approach based on the group theory is presented to deal with the EM scattering fromsymmetric and anti-symmetric structures.
文摘In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: vp.vg = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ, i.e. to vgt ± σ/ω, where ω is the particle angular frequency. This is the first time the phase range has been described for a massive particle.
基金Supported by National Natural Science Foundation of China (50378063), Excellent Young Teachers Program of MOE and SRF for ROCS, MOE.
文摘A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.
基金Supported by AFOSR(Grant No.FA9550-17-1-0147)NSF(Grant No.DMS-1813492)
文摘We introduce the concept of transmission eigenvalues in scattering theory for automorphic forms on fundamental domains generated by discrete groups acting on the hyperbolic upper half complex plane. In particular, we consider Fuchsian groups of Type Ⅰ. Transmission eigenvalues are related to those eigen-parameters for which one can send an incident wave that produces no scattering. The notion of transmission eigenvalues, or non-scattering energies, is well studied in the Euclidean geometry, where in some cases these eigenvalues appear as zeros of the scattering matrix. As opposed to scattering poles,in hyperbolic geometry such a connection between zeros of the scattering matrix and non-scattering energies is not studied, and the goal of this paper is to do just this for particular arithmetic groups.For such groups, using existing deep results from analytic number theory, we reveal that the zeros of the scattering matrix, consequently non-scattering energies, are directly expressed in terms of the zeros of the Riemann zeta function. Weyl's asymptotic laws are provided for the eigenvalues in those cases along with estimates on their location in the complex plane.
文摘Bafia Group is part of the southernmost portion of the Central African Fold Belt (CAFB) in Cameroon. The geological feature of the group is characterized by the presence of metamorphic rocks in which tourmaline had been recognized among accessory minerals. In the present study, attention is focus on the tourmaline bearing quartzite to the southeast of Kombé II. Structure refinement shows that tourmaline is a Fe-dravite with the formula X(Na<sub>0.95</sub>[]<sub>0.05</sub>)Y(Mg<sub>2.39</sub>Fe<sub>0.61</sub>)Z(Al<sub>5.10</sub>Mg<sub>0.90</sub>)(BO<sub>3</sub>)<sub>3</sub>T[Si<sub>6</sub>O<sub>18</sub>](OH)<sub>3</sub>[(O,OH)<sub>0.88</sub>F<sub>0.12</sub>]. The Fe-dravite is hosted in a Ca-poor quartzite, which is made up, in addition to quartz and tourmaline, of biotite and muscovite. The structure of the dravites shows a low vacancy at the X site, which militates for a crystallization of the tourmaline at a high temperature > 750℃. This is in agreement with previous work which shows that the metamorphic peak in the associated biotite gneiss reaches 825℃. The R1 value of 1.24% means that the crystal structure of the tourmalines is of high quality. The genetical link between gold mineralization and tourmaline should stimulate exploration interest in the study area.
文摘It is a very important issue to reduce computer storage and calculation time for matrix in solving scattering field by making use of geometric and physical symmetric features of a scattering body. A general definition for the symmetric and anti-symmetric structure is given by applying the group theory in mathematics and a general method for treating the electromagnetic scattering problems with symmetry is proposed. An example for applying the theory mentioned above is also given.
文摘The symmetry of rotation vibration spectra of molecule SiO_2 is described by means of group U(5). Grouptheory approach is adopted to give the matrix elements of stimulated Raman scattering in fiber. The cross sectionsand gain coefficients of stimulated Raman scattering are given. The results are in good agreement with the experi-mental values.
