By taking full account of the non-orthogonality of the orbitals between the low-lying doubly excited states ^1po and the singly excited states ^1S^e and ^1D^e of He, the corresponding radiative decay rates have been i...By taking full account of the non-orthogonality of the orbitals between the low-lying doubly excited states ^1po and the singly excited states ^1S^e and ^1D^e of He, the corresponding radiative decay rates have been investigated theoretically via analytic generalized Laguerre-type atomic orbitals at a nearly numerical multi-conflguration self-consistent field accuracy in a general non-orthogonal configuration interaction scheme. From these rates, we calculate the VUV photon emission and metastable atom spectra, and both are found to be in good qualitative agreement with recent excellent measurements. We obtain, successfully, the enhancement of the VUV photon spectrum, experimentally observed at the energy of （2s4p-4s2p）/（2p,3d） ^1po as compared with other nearby lying states. The mechanism proposed by Odling-Smee et al is verified, implying that taking appropriate account of the overlap existing between orbitals of the low-lying doubly excited and singly excited states （especially important for the compact orbitals） can reveal basic physical dominant mechanism and is crucial in understanding these spectra.展开更多
A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. ...A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. It spans simultaneously wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to solve different problems and compared with analytical and published results. The comparison exhibits the strengths and accuracy of the presented basis set.展开更多
Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet ...Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10347126）, National High Technology Development Program of China （Grant No 2004AA306H10） and the Program ＂Excellence in the Research Institutes Supervised by the General Secretariat for Research and Technology / Ministry of Development＂, Greece.Acknowledgments Xiong Zhuang would like to express his appreciation for the partial support from the Greek State Scholarship Foundation （I.K.Y.） and the National Hellenic Research Foundation Scholarship for this work.
文摘By taking full account of the non-orthogonality of the orbitals between the low-lying doubly excited states ^1po and the singly excited states ^1S^e and ^1D^e of He, the corresponding radiative decay rates have been investigated theoretically via analytic generalized Laguerre-type atomic orbitals at a nearly numerical multi-conflguration self-consistent field accuracy in a general non-orthogonal configuration interaction scheme. From these rates, we calculate the VUV photon emission and metastable atom spectra, and both are found to be in good qualitative agreement with recent excellent measurements. We obtain, successfully, the enhancement of the VUV photon spectrum, experimentally observed at the energy of （2s4p-4s2p）/（2p,3d） ^1po as compared with other nearby lying states. The mechanism proposed by Odling-Smee et al is verified, implying that taking appropriate account of the overlap existing between orbitals of the low-lying doubly excited and singly excited states （especially important for the compact orbitals） can reveal basic physical dominant mechanism and is crucial in understanding these spectra.
文摘A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. It spans simultaneously wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to solve different problems and compared with analytical and published results. The comparison exhibits the strengths and accuracy of the presented basis set.
基金the National Natural Science Foundation of China (Nos.11571238,11601332,91130014,11471312 and 91430216).
文摘Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.
