The （e, 2e） triple differential cross sections of 2s orbitals of neon and neonic ions （Z = 11-14） are calculated using a distorted-wave Born approximation under coplanar asymmetric geometry. The calculated results...The （e, 2e） triple differential cross sections of 2s orbitals of neon and neonic ions （Z = 11-14） are calculated using a distorted-wave Born approximation under coplanar asymmetric geometry. The calculated results show that, with the increase in the nuclear charge number Z, the amplitude of triple differential cross sections decreases. The angle difference between the binary peak position and the direction of momentum transfer gradually increases with the increase in the nuclear charge Z, and a new structure appears at an ejected angle 90° 〈 θ2 〈 120°. Three kinds of collision processes are proposed to illustrate the formation mechanism of such collision peaks.展开更多
This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be a...This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.展开更多
The standard distorted wave Born approximation （DWBA） method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order...The standard distorted wave Born approximation （DWBA） method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections （TDCS） of coplanar doubly symmetric （e, 2e） collisions for the alkali target potassium at excess energies of 6 eV-60 eV. Compared with the previous first-order DWBA calculations, the present theoretical model improves the degree of agreement with experiments, especially for the backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric （e, 2e） problems in low and intermediate energy ranges.展开更多
The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient sc...The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient scattering problem.However,so far,the research on the generalized Born approximation has only stayed in theory,and its implementation techniques are rarely reported.In order to fill this gap,the basic theory of generalized Born approximation is reviewed,and the implementation method of generalized Born approximation is discussed in this paper.In particular,the problem of calculating boundary effect elimination is discussed in detail.Finally,through model trial calculation,the calculation of gradient scattering,by comparing Born approximation and finite difference method,shows that using the generalized Born approximation to calculate gradient scattering achieves higher computational accuracy.展开更多
We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating w...We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.展开更多
Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relat...Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, and , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on inverse square law of quantum action (Planck’s constant). Born approximation is revisited for quantum mechanical scattering. Using Bessel and Neumann asymptotic functions and response of nuclear surface potential barrier, born approximations were modified. The coulombic fields inside the nucleus of the atom are studied for reflection and transmission with corresponding wave vectors, phase shifts and eigenfunctions Bulk quantum mechanical tunneling and reflection scattering, both for ruptured and unruptured nucleus of the atom, are deciphered with corresponding wave vectors, phase shifts and eigenfunction. Similar calculation ware accomplished for quantum surface tunneling and reflection scattering with corresponding wave vectors, phase shifts and eigenfunctions. Such diverse quantum mechanical scattering cross-section with corresponding wave vectors for tunneling and reflection, phase shifts and eigenfunctions will pave a new dimension to understanding the behavior of exchange fields in the nucleus of the atom with insides layers both ruptured and unruptured. Phase shifts, δ<sub>l</sub> for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.展开更多
An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for di...An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for dimensionless frequency responses to a heterogeneous alluvial valley where the velocity is perturbed randomly in the range of 5 %–25 %,compared with the full-waveform numerical solution. Then,the scheme is extended to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies Numerical experiments indicate that the convergence rate of this method decreases gradually with increasing velocity perturbations. The method has a fast convergence for velocity perturbations less than 15 %. However,the convergence becomes slow drastically when the velocity perturbation increases to 20 %. The method can hardly converge for the velocity perturbation up to 25 %.展开更多
本文讨论了 Born 近似与 Rytov 近似的相互关系,并对地面反射、VSP、井间和四周观测系统在异常体速度与背景速度相差5%、10%以及15%的条件下,用这两种近似方法作了重建图像的实验。其结果表明,速度差低于10%时,无论 Born 近似或 Rytov ...本文讨论了 Born 近似与 Rytov 近似的相互关系,并对地面反射、VSP、井间和四周观测系统在异常体速度与背景速度相差5%、10%以及15%的条件下,用这两种近似方法作了重建图像的实验。其结果表明,速度差低于10%时,无论 Born 近似或 Rytov 近似,更射层析均优于透射层析。此时,Rytov 近似的透射层析优势消失,这一结论与传统观点相悖。当速度差大于10%时,Rytov 近似透射层析优于 Born 近似。实验结果还说明,在地面激发、四周观测时,波动理论层析效果最佳,此点与射线理论是一致的。展开更多
基金Project supported by the Fundamental Research Funds for the Central University of China(Grant No.13CX02019A)
文摘The （e, 2e） triple differential cross sections of 2s orbitals of neon and neonic ions （Z = 11-14） are calculated using a distorted-wave Born approximation under coplanar asymmetric geometry. The calculated results show that, with the increase in the nuclear charge number Z, the amplitude of triple differential cross sections decreases. The angle difference between the binary peak position and the direction of momentum transfer gradually increases with the increase in the nuclear charge Z, and a new structure appears at an ejected angle 90° 〈 θ2 〈 120°. Three kinds of collision processes are proposed to illustrate the formation mechanism of such collision peaks.
基金supported by the Explore Foundation of Weapon Development (Grant No 7130620)
文摘This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11174066)
文摘The standard distorted wave Born approximation （DWBA） method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections （TDCS） of coplanar doubly symmetric （e, 2e） collisions for the alkali target potassium at excess energies of 6 eV-60 eV. Compared with the previous first-order DWBA calculations, the present theoretical model improves the degree of agreement with experiments, especially for the backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric （e, 2e） problems in low and intermediate energy ranges.
基金Supported by Project of the National Natural Science Foundation of China(No.41974135)
文摘The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient scattering problem.However,so far,the research on the generalized Born approximation has only stayed in theory,and its implementation techniques are rarely reported.In order to fill this gap,the basic theory of generalized Born approximation is reviewed,and the implementation method of generalized Born approximation is discussed in this paper.In particular,the problem of calculating boundary effect elimination is discussed in detail.Finally,through model trial calculation,the calculation of gradient scattering,by comparing Born approximation and finite difference method,shows that using the generalized Born approximation to calculate gradient scattering achieves higher computational accuracy.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10975181 and 11175247)the National Basic Research Program of China(Grant No.2012CB922104)
文摘We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.
文摘Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, and , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on inverse square law of quantum action (Planck’s constant). Born approximation is revisited for quantum mechanical scattering. Using Bessel and Neumann asymptotic functions and response of nuclear surface potential barrier, born approximations were modified. The coulombic fields inside the nucleus of the atom are studied for reflection and transmission with corresponding wave vectors, phase shifts and eigenfunctions Bulk quantum mechanical tunneling and reflection scattering, both for ruptured and unruptured nucleus of the atom, are deciphered with corresponding wave vectors, phase shifts and eigenfunction. Similar calculation ware accomplished for quantum surface tunneling and reflection scattering with corresponding wave vectors, phase shifts and eigenfunctions. Such diverse quantum mechanical scattering cross-section with corresponding wave vectors for tunneling and reflection, phase shifts and eigenfunctions will pave a new dimension to understanding the behavior of exchange fields in the nucleus of the atom with insides layers both ruptured and unruptured. Phase shifts, δ<sub>l</sub> for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41204097 and 41130418)the China National Major Science and Technology Project (2011ZX05023-005-004)
文摘An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for dimensionless frequency responses to a heterogeneous alluvial valley where the velocity is perturbed randomly in the range of 5 %–25 %,compared with the full-waveform numerical solution. Then,the scheme is extended to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies Numerical experiments indicate that the convergence rate of this method decreases gradually with increasing velocity perturbations. The method has a fast convergence for velocity perturbations less than 15 %. However,the convergence becomes slow drastically when the velocity perturbation increases to 20 %. The method can hardly converge for the velocity perturbation up to 25 %.
文摘本文讨论了 Born 近似与 Rytov 近似的相互关系,并对地面反射、VSP、井间和四周观测系统在异常体速度与背景速度相差5%、10%以及15%的条件下,用这两种近似方法作了重建图像的实验。其结果表明,速度差低于10%时,无论 Born 近似或 Rytov 近似,更射层析均优于透射层析。此时,Rytov 近似的透射层析优势消失,这一结论与传统观点相悖。当速度差大于10%时,Rytov 近似透射层析优于 Born 近似。实验结果还说明,在地面激发、四周观测时,波动理论层析效果最佳,此点与射线理论是一致的。
