原子的光电离截面及电子碰撞散射截面的理论研究
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摘要
原子(离子)的光电离截面以及带电粒子(特别是电子)与原子(离子)的弹性和非弹性碰撞散射截面数据是天体物理、空间和大气物理、等离子体物理等领域研究中必不可少的物理参数。
我们用最新发展的Breit-Pauli R-矩阵程序计算了基态Na原子的光电离截面。我们计算的靶态能级以及第一电离阈值都和实验值符合在1%以内。在光子能量比较低的区域(5?13 eV),我们计算的光电离截面以及吸收窗口位置是目前和实验值符合最好的计算结果。在吸收窗口以上,实验测量结果中有个奇异的隆起,这是理论和实验研究之间一个长期无法解释的矛盾。有趣地是我们发现Na+2分子离子的光电离截面(即光解离截面)中也存在一个吸收窗口,这个吸收窗口为这个长期存在的矛盾提供了一个合理的解释。此外,用上面经过检验的靶态和单轨道波函数基计算了激发态Na原子的光电离截面。我们的计算结果和最新的实验结果符合很好。因此,这说明Breit-Pauli近似下的R-矩阵方法以及相应的程序能同时处理好中Z元素原子光电离过程中的电子关联作用和相对论效应(主要是自旋-轨道相互作用)。
我们用分波法计算了Na原子与低能电子的碰撞散射截面,研究了分波散射截面随激发能以及轨道角动量变化的性质。此外,在一阶波恩近似下,我们用最新发展的R-矩阵程序计算了He原子与高能电子碰撞的广义振子强度以及广义振子强度密度曲面,我们的计算结果和最新的实验结果符合很好。进一步,我们提出了一个计算中能电子碰撞散射截面的方案。
经过最新的实验严谨检验的R-矩阵方法以及相应的程序预期能为天体物理、空间和大气物理、等离子体物理、聚变物理、激光物理等领域的研究提供大量精密的原子物理参数。
Photoabsorption (including the photoexcitation and photoionization) and electroncollision scattering cross sections are the indispensable physical parameters in laserphysics, radiation physics, plasma physics, atmospheric physics and astrophysics.
Using our modified Breit-Pauli R-matrix code, the photoionization cross sectionsof ground Na are calculated. Our calculated cross sections and minimum position in thelow photon energy range (5?13 eV) are in excellent agreement with the experimentalresults. In the high energy range, there is an abnormal bump in the experimental mea-surements, which is a long-standing experimental puzzle. It is interesting to note thatthere is also an absorption window in the photoabsorption (i.e. photodissociation) crosssections of Na2+ . Such absorption window provides an answer to the puzzle. Based onthe same target and orbital bases, we calculated the photoionization cross sections ofexcited Na. Our calculated branching ratios of the J-resolved partial cross sectionsare in good agreement with the recent measurements within the experimental uncer-tainties. The excellent agreement between our theoretical results and the experimentalresults demonstrates that both the electron correlations and the relativistic effects canbe treated adequately on equal footing by the theoretical method and modified codes.
Using the partial wave method we calculated the scattering cross sections of Naimpacted by the low-energy electron. We studied the features of the partial wave scat-tering amplitudes. Using the modified R-matrix code we calculated the GOSs of He-lium impacted by the high-energy electron within the First Born Approximation. TheGOSD surfaces of 1S, 1P and 1D channels are calculated and tested stringently by therecent experiments. In addition to the low- and high-energy electron impact excitationcross sections, a scheme to calculate the cross sections in the entire incident energyrange is discussed.
我们用最新发展的Breit-Pauli R-矩阵程序计算了基态Na原子的光电离截面。我们计算的靶态能级以及第一电离阈值都和实验值符合在1%以内。在光子能量比较低的区域(5?13 eV),我们计算的光电离截面以及吸收窗口位置是目前和实验值符合最好的计算结果。在吸收窗口以上,实验测量结果中有个奇异的隆起,这是理论和实验研究之间一个长期无法解释的矛盾。有趣地是我们发现Na+2分子离子的光电离截面(即光解离截面)中也存在一个吸收窗口,这个吸收窗口为这个长期存在的矛盾提供了一个合理的解释。此外,用上面经过检验的靶态和单轨道波函数基计算了激发态Na原子的光电离截面。我们的计算结果和最新的实验结果符合很好。因此,这说明Breit-Pauli近似下的R-矩阵方法以及相应的程序能同时处理好中Z元素原子光电离过程中的电子关联作用和相对论效应(主要是自旋-轨道相互作用)。
我们用分波法计算了Na原子与低能电子的碰撞散射截面,研究了分波散射截面随激发能以及轨道角动量变化的性质。此外,在一阶波恩近似下,我们用最新发展的R-矩阵程序计算了He原子与高能电子碰撞的广义振子强度以及广义振子强度密度曲面,我们的计算结果和最新的实验结果符合很好。进一步,我们提出了一个计算中能电子碰撞散射截面的方案。
经过最新的实验严谨检验的R-矩阵方法以及相应的程序预期能为天体物理、空间和大气物理、等离子体物理、聚变物理、激光物理等领域的研究提供大量精密的原子物理参数。
Photoabsorption (including the photoexcitation and photoionization) and electroncollision scattering cross sections are the indispensable physical parameters in laserphysics, radiation physics, plasma physics, atmospheric physics and astrophysics.
Using our modified Breit-Pauli R-matrix code, the photoionization cross sectionsof ground Na are calculated. Our calculated cross sections and minimum position in thelow photon energy range (5?13 eV) are in excellent agreement with the experimentalresults. In the high energy range, there is an abnormal bump in the experimental mea-surements, which is a long-standing experimental puzzle. It is interesting to note thatthere is also an absorption window in the photoabsorption (i.e. photodissociation) crosssections of Na2+ . Such absorption window provides an answer to the puzzle. Based onthe same target and orbital bases, we calculated the photoionization cross sections ofexcited Na. Our calculated branching ratios of the J-resolved partial cross sectionsare in good agreement with the recent measurements within the experimental uncer-tainties. The excellent agreement between our theoretical results and the experimentalresults demonstrates that both the electron correlations and the relativistic effects canbe treated adequately on equal footing by the theoretical method and modified codes.
Using the partial wave method we calculated the scattering cross sections of Naimpacted by the low-energy electron. We studied the features of the partial wave scat-tering amplitudes. Using the modified R-matrix code we calculated the GOSs of He-lium impacted by the high-energy electron within the First Born Approximation. TheGOSD surfaces of 1S, 1P and 1D channels are calculated and tested stringently by therecent experiments. In addition to the low- and high-energy electron impact excitationcross sections, a scheme to calculate the cross sections in the entire incident energyrange is discussed.
引文
[1] 马丁.哈威. 天体物理学概论. 北京:科学出版社, 1981.
[2] P.L.Smith, W.L.Wiese. Atomic and molecular data for space astronomy-needs,analysis andavailability. Berlin:Springer-Verlag, 1992.
[3] A.Dalgarno, D.Lagyer. Spectrocopy of astrophysical plasmas. Cambridge: Univers. Press,1987.
[4] 美国物理学评述委员会. 90年代物理学-原子、分子物理学和光学. 北京:科学出版社, 1993.
[5] 国家自然科学基金委员会. 自然科学学科发展战略报告-原子、分子物理学和光学.北京:科学出版社, 1991.
[6] E.H.阿弗雷特. 天体物理学前沿. 北京:科学出版社, 1982.
[7] 欧阳自远. 天体化学. 北京:科学出版社, 1988.
[8] M.J.Seaton. Atomic data for opacity calculations. I. General description. J. Phys. B.:At.Mol. Opt. Phys., 1987, 20:6363–6378.
[9] P.W.B.Pearse, A.G.Gaydon. The identification on molecular spectra. London:Chapman andHall, 1992.
[10] D.R.Hartree. The wave mechanics of an atom with a non-Coulomb central field. Part I.Theory and methods. Proc. Camb. Phil. Soc., 1928, 24:89–110.
[11] D.R.Hartree. The wave mechanics of an atom with a non-Coulomb central field. Part II.Some results and discussion. Proc. Camb. Phil. Soc., 1928, 24:111–132.
[12] V.Fork. Approximate method of solution of the problem of many bodies in quantum me-chanics. Z. Physik., 1930, 61:126–148.
[13] J.C.Slater. Note on Hartree’s Method. Phys. Rev., 1930, 35:210–211.
[14] F.A.Parpia, C.F.Fischer, I.P.Grant. GRASP92: a package for large-scale relativistic atomicstructure calculations. Comput. Phys. Commun., 1996, 94:249–271.
[15] Hibbert A. CIV3?A general program tO calculate configuration interaction wave funtionand election-dopole oscillator strengs. Comput. Phys. Commun., 1975, 9:141–172.
[16] I.P.Grant, B.J.McKenzie, P.H.Norrington, et al. An atomic multiconfigurational Dirac-Fockpackage. Comput. Phys. Commun., 1980, 21:207–231.
[17] J.P.Desclaux. A multiconfiguration relativistic Dirac-Fock program. Comput. Phys. Com-mun., 1975, 9:31–45.
[18] Fano U, Cooper J. Spectral distribution of atomic oscillator strengths. Rev. Mod. Phys.,1968, 40:441–507.
[19] Davenport J W, Cosgrove G J, Zangwill A. Electronic structure and photoionization crosssections of Li2, Na2, and K2. J. Chem. Phys., 1968, 78:1095–1103.
[20] 梁晓玲, 李家明. 激发态原子振子强度密度极小点. 物理学报, 1985, 11:105–113.
[21] Manson S J. Minima in atomic continuum generalized oscillator strengths. Phys. Rev. A.,1971, 3:1260–1267.
[22] Weisheit J C. Photoabsorption by ground-state alkali-metal atoms. Phys. Rev. A., 1972,5:1621–1630.
[23] Dasgupta A, Bhatia A K. Photoionization of sodium atoms and electron scattering fromionized sodium. Phys. Rev. A., 1985, 31:759–771.
[24] Isenberg E M, Carter S L, Kelly H P, et al. Photoionization cross section and resonancestructure of atomic sodium. Phys. Rev. A., 1985, 32:1472–1479.
[25] Saha H P, Froese-Fischer C, Langhoff P W. Numerical multiconfiguration Hartree-Fockstudies of atomic photoionization cross sections: Dynamical core-polarization effects inatomic sodium. Phys. Rev. A., 1988, 38:1279–1285.
[26] Hudson R D, Carter V L. Atomic absorption cross sections of Lithium and sodium between600 and 1000 A. J. Opt. Soc. Am., 1967, 4:651–654.
[27] Cubaynes D, Meyer M, Crum-Crzhimailo A N, et al. Dynamically and quasiforbidden tran-sitions in photoionization of open-shell atoms: A combined experimental and theoreticalstudy. Phys. Rev. A., 2004, 92:233002–1–233002–4.
[28] Burke P G, Hibbert A, Robb W D. Electron scattering by complex atoms. J. Phys. B.:At.Mol. Opt. Phys., 1971, 4:153–161.
[29] Berrington K A, Chang J J, Chivers A T, et al. A general program to calculate atomiccontinum processes using the R-matrix method. Comput. Phys. Commun., 1974, 8:149–198.
[30] Berrington K A, Burke P G, Le Dourneuf M, et al. A new version of the general pro-gram to calculate atomic continuum processes using the R-matrix method. Comput. Phys.Commun., 1978, 14:367–412.
[31] Berrington K A, Burke P G, Butler K, et al. Atomic data for opacity calculations. II. Com-putational methods. J. Phys. B.:At. Mol. Opt. Phys., 1987, 20:6379–6397.
[32] Voky L, Saraph H E, Eissner W B, et al. Inner-shell photoionization of beryllium. Phys.Rev. A., 1992, 46:3945–3958.
[33] Berrington K A, Eissner W B, Norrington P H. RMATRX1: Belfast atomic R-matrix codes.Comput. Phys. Commun., 1995, 92:290–420.
[34] Yan J, Qu Y Z, Voky L, et al. Polarization effect on He doubly excited states below the N=2threshold of He+. Phys. Rev. A., 1998, 57:997–1005.
[35] Chen G X, Pradhan A K, Eissner W B. Breit-Pauli R-matrix calculations for electron impactexcitation of Fe XVII: a benchmark study. J. Phys. B.:At. Mol. Opt. Phys., 2003, 36:453–477.
[36] Scott N S, Burke P G. Electron scattering by atoms and ions using the Breit-Pauli Hamilto-nian: an R-matrix approach. J. Phys. B.:At. Mol. Opt. Phys., 1980, 13:4299–4314.
[37] NIST Atomic Spectra Database Levels Form. http://physics.nist.gov/PhysRefData/ASD/levels form.html.
[38] Xia D, Li J M. Relativistic channel theory: abnormal fine structures of n2D Rydberg statesfor alkali atoms. Chin. Phys. Lett., 2001, 18(10):1334–1336.
[39] Fano U. Spin orientation of photoelectrons ejected by circularly polarized light. Phys. Rev.,1969, 178:131–136.
[40] Huber K P, Herzberg G. Molecular spectra and molecular structure. IV. constants of di-atomic moleculaes. New York:Van Nostrand Reinhold Company, 1979
[41] Dill D, Dehmer J L. Electron-molecule scattering and molecular photoionization using themultiple-scattering method. J. Chem. Phys., 1974, 61:692–699.
[42] Liang X L, Pan X C, Li J M. Ionization channal of superexited molecules. Chin. Phys.Lett., 1985, 2:545–548.
[43] Zhang P H, Li J M. Theoretical studies of excited states for Na3. Phys. Rev. A., 1996,54:665–669.
[44] 潘晓川, 梁晓玲, 李家明. 量子数亏损理论—多重散射计算方法. 物理学报, 1987,36:426–435.
[45] Liu L, Li J M. The electronic structure of molecular Rydberg states of diatomic molecules.J. Phys. B.:At. Mol. Opt. Phys., 1991, 24:1893–1898.
[46] Slater J C. Suggestions from solid-state theory regarding molecular calculations. J. Chem.Phys., 1965, 43:S228.
[47] Fano U. Quantum defect theory of l uncoupling in H2 as an example of channel-interactiontreatment. Phys. Rev. A., 1970, 2:353–365.
[48] Fano U. Unified treatment of perturbed series, continuous spectra and collisions. J. Opt.Soc. Am., 1975, 65:979–987.
[49] Seaton M J. Quantum defect theory. Rep. Prog. Phys., 1983, 46:167–257.
[50] Lee C M. Multichannel dissociative recombination theory. Phys. Rev. A., 1977, 16:109–122.
[51] Jungen C, Atabek O. Rovibronic interactions in the photoabsorption spectrum of molecu-lar hydrogen and deuterium: An application of multichannel quantum defect methods. J.Chem. Phys., 1977, 66:5584–5609.
[52] 李家明. 电子与类锂离子碰撞激发. 物理学报, 1980, 29(4):419–428.
[53] Peng Y L, Han X Y, Wang M S, et al. A theoretical study of dielectronic recombinationprocesses of C2+ ions in planetary nebulae. J. Phys. B.:At. Mol. Opt. Phys., 2005, 38:3825–3839.
[54] K.Siegbahn. Electron spectroscopy for atoms, molecules, and condensed matter. Rev. Mod.Phys., 1982, 54:709–728.
[55] H.Jbach, D.L.Mills. Electron energy loss spectroscopy and surface vibrations. NewYork:Academic Press, 1982.
[56] Messiah A. Quantum Mechanics, 1973.
[57] Bethe H. Theory of passage of swift corpuscular rays through matter. Annalen der Physik,1930, 5:325–400.
[58] 田伯刚, 李家明. 广义振子强度密度. 物理学报, 1984, 33(10):1401–1407.
[59] 潘晓川, 李家明. 等电子系列离子的广义振子强度密度之标度关系. 物理学报, 1985,34(11):1500–1508.
[60] Han X Y, Voky L, Li J M. Theoretical analysis of generalized oscillator strengths for Heliumby R-matrix method. Chin. Phys. Lett., 2004, 21(1):54–56.
[61] Inokuti M. Inelastic collisions of fast charged particles with atoms and molecules-the Bethetheory revisited. Rev. Mod. Phys., 1971, 43:297–347.
[62] Burke V M, Noble C J. FARM-a ?exible asymptotic R-matrix package. Comput. Phys.Commun., 1995, 85:471–500.
[63] D.W.Norcross. Application of scattering theory to the calculation of alkali negative-ionbound states. Phys. Rev. L., 1974, 32(5):192.
[64] A.Weiss. Theoretical electron affinities for some of the alkali and alkaline-earth elements.Phys. Rev., 1968, 166:70–74.
[65] W.H.E.Schwarz. Electron affinities of the alkali atoms. A model-potential calculation.Chem. Phys. L., 1971, 10:478.
[66] T.A.Patterson, H.Hotop, Kasdan A, et al. Resonances in alkali negative-ion photodetach-ment and electron affinities of the corresponding neutrals. Phys. Rev. L., 1974, 32(5):189–192.
[67] E.A.Gallagher. Electron Excitation of the Sodium D Lines. Phys. Rev. A., 1972, 6:192–205.
[68] W.K.Trail, M.A.Morrison, H.L.Zhou, et al. Low-energy-electron collisions with sodium:Elastic and inelastic scattering from the ground state. Phys. Rev. A., 1994, 49(5):3620–3645.
[69] Liu X J, Zhu L F, Yuan Z S, et al. The generalized oscillator strengths for the valence shellexcitations in helium by fast electron impact. J. Electron Spectrosc. Relat. Phenom., 2004,135:15–20.
[70] Cann N M, Thakkar A J. First Born differential cross-sections for electronic excitation inthe helium atom. J. Electron Spectrosc. Relat. Phenom., 2002, 123:143–159.
[71] Dillon M A, Lassettre E N. A collision cross section study of the 11S? >21P and 11S? >21S transitions in helium at kinetic energies from 200–700 eV. Failure of the Born approx-imation at large momentum changes. J. Chem. Phys., 1975, 62:2373–2390.
[72] Cartwright D C, Csanak G, Trajmar S, et al. Electron-impact excitation of the n1P levels ofhelium: Theory and experiment. Phys. Rev. A., 1992, 45:1602–1624.
[73] Xu K Z, Feng R F, Wu S L, et al. Absolute generalized oscillator strengths of 21S and 21Pexcitations of helium measured by angle-resolved electron-energy-loss spectroscopy. Phys.Rev. A., 1996, 53:3081–3086.
[74] Zhong Z P, Feng R F, Wu S L, et al. Electron-impact study for the 31S and n1P ( n = 3 - 6)excitations in helium. J. Phys. B.:At. Mol. Opt. Phys., 1997, 30:5305–5315.
[75] Suzuki T Y, Suzuki H, Currell F J, et al. Measurements of the electron-impact differentialcross sections and generalized oscillator strengths for excitation of the 21S and 31S statesin helium at small scattering angles. Phys. Rev. A., 1998, 57:1832–1848.
[76] Pochat A, Rozuel D, Peresse J. Determination of the absolute differential cross sectionfor the 11S? >41S,41D,51S, and 51D transitions in helium atoms. J. Phys. (Paris), 1973,34:701–709.
[77] Dierckx,P. Curve and surface fitting with splines. New York:Oxford University Press, 1993.
[78] C.M.Lee. Spectroscopy and collision theory. III. Atomic eigenchannel calculation by aHartree-Fock-Roothaan method. Phys. Rev. A., 1974, 10:584–600.
[79] K.T.Lu. Spectroscopy and collision theory. The Xe absorption spectrum. Phys. Rev. A.,1971, 4:579–596.
[80] C.M.Lee, K.T.Lu. Spectroscopy and collision theory II, The Ar absorption spectrum. Phys.Rev. A., 1973, 8:1241–1257.
[81] J.C.Slater. Quantum Theory of Molecules and Solids, volume 4. New York:McGraw-HillCo., 1974.
[82] 潘毓刚, 李俊清, 祝继康. Xα方法的理论和应用. 北京:科学出版社, 1987.
[83] K.H.Johnson. Scattered-wave theory of the chemical bond, in Advances in Quantum Chem-istry, volume 9. New York:Academic Press, 1973.
[84] J.C.Slater, K.H.Johnson. Self-Consistent-Field XαCluster Method for PolyatomicMolecules and Solids. Phys. Rev. B., 1972, 5:844–853.
[85] Lee C M. Multichannel photodetachment theory. Phys. Rev. A., 1975, 11:1692–1699.
[2] P.L.Smith, W.L.Wiese. Atomic and molecular data for space astronomy-needs,analysis andavailability. Berlin:Springer-Verlag, 1992.
[3] A.Dalgarno, D.Lagyer. Spectrocopy of astrophysical plasmas. Cambridge: Univers. Press,1987.
[4] 美国物理学评述委员会. 90年代物理学-原子、分子物理学和光学. 北京:科学出版社, 1993.
[5] 国家自然科学基金委员会. 自然科学学科发展战略报告-原子、分子物理学和光学.北京:科学出版社, 1991.
[6] E.H.阿弗雷特. 天体物理学前沿. 北京:科学出版社, 1982.
[7] 欧阳自远. 天体化学. 北京:科学出版社, 1988.
[8] M.J.Seaton. Atomic data for opacity calculations. I. General description. J. Phys. B.:At.Mol. Opt. Phys., 1987, 20:6363–6378.
[9] P.W.B.Pearse, A.G.Gaydon. The identification on molecular spectra. London:Chapman andHall, 1992.
[10] D.R.Hartree. The wave mechanics of an atom with a non-Coulomb central field. Part I.Theory and methods. Proc. Camb. Phil. Soc., 1928, 24:89–110.
[11] D.R.Hartree. The wave mechanics of an atom with a non-Coulomb central field. Part II.Some results and discussion. Proc. Camb. Phil. Soc., 1928, 24:111–132.
[12] V.Fork. Approximate method of solution of the problem of many bodies in quantum me-chanics. Z. Physik., 1930, 61:126–148.
[13] J.C.Slater. Note on Hartree’s Method. Phys. Rev., 1930, 35:210–211.
[14] F.A.Parpia, C.F.Fischer, I.P.Grant. GRASP92: a package for large-scale relativistic atomicstructure calculations. Comput. Phys. Commun., 1996, 94:249–271.
[15] Hibbert A. CIV3?A general program tO calculate configuration interaction wave funtionand election-dopole oscillator strengs. Comput. Phys. Commun., 1975, 9:141–172.
[16] I.P.Grant, B.J.McKenzie, P.H.Norrington, et al. An atomic multiconfigurational Dirac-Fockpackage. Comput. Phys. Commun., 1980, 21:207–231.
[17] J.P.Desclaux. A multiconfiguration relativistic Dirac-Fock program. Comput. Phys. Com-mun., 1975, 9:31–45.
[18] Fano U, Cooper J. Spectral distribution of atomic oscillator strengths. Rev. Mod. Phys.,1968, 40:441–507.
[19] Davenport J W, Cosgrove G J, Zangwill A. Electronic structure and photoionization crosssections of Li2, Na2, and K2. J. Chem. Phys., 1968, 78:1095–1103.
[20] 梁晓玲, 李家明. 激发态原子振子强度密度极小点. 物理学报, 1985, 11:105–113.
[21] Manson S J. Minima in atomic continuum generalized oscillator strengths. Phys. Rev. A.,1971, 3:1260–1267.
[22] Weisheit J C. Photoabsorption by ground-state alkali-metal atoms. Phys. Rev. A., 1972,5:1621–1630.
[23] Dasgupta A, Bhatia A K. Photoionization of sodium atoms and electron scattering fromionized sodium. Phys. Rev. A., 1985, 31:759–771.
[24] Isenberg E M, Carter S L, Kelly H P, et al. Photoionization cross section and resonancestructure of atomic sodium. Phys. Rev. A., 1985, 32:1472–1479.
[25] Saha H P, Froese-Fischer C, Langhoff P W. Numerical multiconfiguration Hartree-Fockstudies of atomic photoionization cross sections: Dynamical core-polarization effects inatomic sodium. Phys. Rev. A., 1988, 38:1279–1285.
[26] Hudson R D, Carter V L. Atomic absorption cross sections of Lithium and sodium between600 and 1000 A. J. Opt. Soc. Am., 1967, 4:651–654.
[27] Cubaynes D, Meyer M, Crum-Crzhimailo A N, et al. Dynamically and quasiforbidden tran-sitions in photoionization of open-shell atoms: A combined experimental and theoreticalstudy. Phys. Rev. A., 2004, 92:233002–1–233002–4.
[28] Burke P G, Hibbert A, Robb W D. Electron scattering by complex atoms. J. Phys. B.:At.Mol. Opt. Phys., 1971, 4:153–161.
[29] Berrington K A, Chang J J, Chivers A T, et al. A general program to calculate atomiccontinum processes using the R-matrix method. Comput. Phys. Commun., 1974, 8:149–198.
[30] Berrington K A, Burke P G, Le Dourneuf M, et al. A new version of the general pro-gram to calculate atomic continuum processes using the R-matrix method. Comput. Phys.Commun., 1978, 14:367–412.
[31] Berrington K A, Burke P G, Butler K, et al. Atomic data for opacity calculations. II. Com-putational methods. J. Phys. B.:At. Mol. Opt. Phys., 1987, 20:6379–6397.
[32] Voky L, Saraph H E, Eissner W B, et al. Inner-shell photoionization of beryllium. Phys.Rev. A., 1992, 46:3945–3958.
[33] Berrington K A, Eissner W B, Norrington P H. RMATRX1: Belfast atomic R-matrix codes.Comput. Phys. Commun., 1995, 92:290–420.
[34] Yan J, Qu Y Z, Voky L, et al. Polarization effect on He doubly excited states below the N=2threshold of He+. Phys. Rev. A., 1998, 57:997–1005.
[35] Chen G X, Pradhan A K, Eissner W B. Breit-Pauli R-matrix calculations for electron impactexcitation of Fe XVII: a benchmark study. J. Phys. B.:At. Mol. Opt. Phys., 2003, 36:453–477.
[36] Scott N S, Burke P G. Electron scattering by atoms and ions using the Breit-Pauli Hamilto-nian: an R-matrix approach. J. Phys. B.:At. Mol. Opt. Phys., 1980, 13:4299–4314.
[37] NIST Atomic Spectra Database Levels Form. http://physics.nist.gov/PhysRefData/ASD/levels form.html.
[38] Xia D, Li J M. Relativistic channel theory: abnormal fine structures of n2D Rydberg statesfor alkali atoms. Chin. Phys. Lett., 2001, 18(10):1334–1336.
[39] Fano U. Spin orientation of photoelectrons ejected by circularly polarized light. Phys. Rev.,1969, 178:131–136.
[40] Huber K P, Herzberg G. Molecular spectra and molecular structure. IV. constants of di-atomic moleculaes. New York:Van Nostrand Reinhold Company, 1979
[41] Dill D, Dehmer J L. Electron-molecule scattering and molecular photoionization using themultiple-scattering method. J. Chem. Phys., 1974, 61:692–699.
[42] Liang X L, Pan X C, Li J M. Ionization channal of superexited molecules. Chin. Phys.Lett., 1985, 2:545–548.
[43] Zhang P H, Li J M. Theoretical studies of excited states for Na3. Phys. Rev. A., 1996,54:665–669.
[44] 潘晓川, 梁晓玲, 李家明. 量子数亏损理论—多重散射计算方法. 物理学报, 1987,36:426–435.
[45] Liu L, Li J M. The electronic structure of molecular Rydberg states of diatomic molecules.J. Phys. B.:At. Mol. Opt. Phys., 1991, 24:1893–1898.
[46] Slater J C. Suggestions from solid-state theory regarding molecular calculations. J. Chem.Phys., 1965, 43:S228.
[47] Fano U. Quantum defect theory of l uncoupling in H2 as an example of channel-interactiontreatment. Phys. Rev. A., 1970, 2:353–365.
[48] Fano U. Unified treatment of perturbed series, continuous spectra and collisions. J. Opt.Soc. Am., 1975, 65:979–987.
[49] Seaton M J. Quantum defect theory. Rep. Prog. Phys., 1983, 46:167–257.
[50] Lee C M. Multichannel dissociative recombination theory. Phys. Rev. A., 1977, 16:109–122.
[51] Jungen C, Atabek O. Rovibronic interactions in the photoabsorption spectrum of molecu-lar hydrogen and deuterium: An application of multichannel quantum defect methods. J.Chem. Phys., 1977, 66:5584–5609.
[52] 李家明. 电子与类锂离子碰撞激发. 物理学报, 1980, 29(4):419–428.
[53] Peng Y L, Han X Y, Wang M S, et al. A theoretical study of dielectronic recombinationprocesses of C2+ ions in planetary nebulae. J. Phys. B.:At. Mol. Opt. Phys., 2005, 38:3825–3839.
[54] K.Siegbahn. Electron spectroscopy for atoms, molecules, and condensed matter. Rev. Mod.Phys., 1982, 54:709–728.
[55] H.Jbach, D.L.Mills. Electron energy loss spectroscopy and surface vibrations. NewYork:Academic Press, 1982.
[56] Messiah A. Quantum Mechanics, 1973.
[57] Bethe H. Theory of passage of swift corpuscular rays through matter. Annalen der Physik,1930, 5:325–400.
[58] 田伯刚, 李家明. 广义振子强度密度. 物理学报, 1984, 33(10):1401–1407.
[59] 潘晓川, 李家明. 等电子系列离子的广义振子强度密度之标度关系. 物理学报, 1985,34(11):1500–1508.
[60] Han X Y, Voky L, Li J M. Theoretical analysis of generalized oscillator strengths for Heliumby R-matrix method. Chin. Phys. Lett., 2004, 21(1):54–56.
[61] Inokuti M. Inelastic collisions of fast charged particles with atoms and molecules-the Bethetheory revisited. Rev. Mod. Phys., 1971, 43:297–347.
[62] Burke V M, Noble C J. FARM-a ?exible asymptotic R-matrix package. Comput. Phys.Commun., 1995, 85:471–500.
[63] D.W.Norcross. Application of scattering theory to the calculation of alkali negative-ionbound states. Phys. Rev. L., 1974, 32(5):192.
[64] A.Weiss. Theoretical electron affinities for some of the alkali and alkaline-earth elements.Phys. Rev., 1968, 166:70–74.
[65] W.H.E.Schwarz. Electron affinities of the alkali atoms. A model-potential calculation.Chem. Phys. L., 1971, 10:478.
[66] T.A.Patterson, H.Hotop, Kasdan A, et al. Resonances in alkali negative-ion photodetach-ment and electron affinities of the corresponding neutrals. Phys. Rev. L., 1974, 32(5):189–192.
[67] E.A.Gallagher. Electron Excitation of the Sodium D Lines. Phys. Rev. A., 1972, 6:192–205.
[68] W.K.Trail, M.A.Morrison, H.L.Zhou, et al. Low-energy-electron collisions with sodium:Elastic and inelastic scattering from the ground state. Phys. Rev. A., 1994, 49(5):3620–3645.
[69] Liu X J, Zhu L F, Yuan Z S, et al. The generalized oscillator strengths for the valence shellexcitations in helium by fast electron impact. J. Electron Spectrosc. Relat. Phenom., 2004,135:15–20.
[70] Cann N M, Thakkar A J. First Born differential cross-sections for electronic excitation inthe helium atom. J. Electron Spectrosc. Relat. Phenom., 2002, 123:143–159.
[71] Dillon M A, Lassettre E N. A collision cross section study of the 11S? >21P and 11S? >21S transitions in helium at kinetic energies from 200–700 eV. Failure of the Born approx-imation at large momentum changes. J. Chem. Phys., 1975, 62:2373–2390.
[72] Cartwright D C, Csanak G, Trajmar S, et al. Electron-impact excitation of the n1P levels ofhelium: Theory and experiment. Phys. Rev. A., 1992, 45:1602–1624.
[73] Xu K Z, Feng R F, Wu S L, et al. Absolute generalized oscillator strengths of 21S and 21Pexcitations of helium measured by angle-resolved electron-energy-loss spectroscopy. Phys.Rev. A., 1996, 53:3081–3086.
[74] Zhong Z P, Feng R F, Wu S L, et al. Electron-impact study for the 31S and n1P ( n = 3 - 6)excitations in helium. J. Phys. B.:At. Mol. Opt. Phys., 1997, 30:5305–5315.
[75] Suzuki T Y, Suzuki H, Currell F J, et al. Measurements of the electron-impact differentialcross sections and generalized oscillator strengths for excitation of the 21S and 31S statesin helium at small scattering angles. Phys. Rev. A., 1998, 57:1832–1848.
[76] Pochat A, Rozuel D, Peresse J. Determination of the absolute differential cross sectionfor the 11S? >41S,41D,51S, and 51D transitions in helium atoms. J. Phys. (Paris), 1973,34:701–709.
[77] Dierckx,P. Curve and surface fitting with splines. New York:Oxford University Press, 1993.
[78] C.M.Lee. Spectroscopy and collision theory. III. Atomic eigenchannel calculation by aHartree-Fock-Roothaan method. Phys. Rev. A., 1974, 10:584–600.
[79] K.T.Lu. Spectroscopy and collision theory. The Xe absorption spectrum. Phys. Rev. A.,1971, 4:579–596.
[80] C.M.Lee, K.T.Lu. Spectroscopy and collision theory II, The Ar absorption spectrum. Phys.Rev. A., 1973, 8:1241–1257.
[81] J.C.Slater. Quantum Theory of Molecules and Solids, volume 4. New York:McGraw-HillCo., 1974.
[82] 潘毓刚, 李俊清, 祝继康. Xα方法的理论和应用. 北京:科学出版社, 1987.
[83] K.H.Johnson. Scattered-wave theory of the chemical bond, in Advances in Quantum Chem-istry, volume 9. New York:Academic Press, 1973.
[84] J.C.Slater, K.H.Johnson. Self-Consistent-Field XαCluster Method for PolyatomicMolecules and Solids. Phys. Rev. B., 1972, 5:844–853.
[85] Lee C M. Multichannel photodetachment theory. Phys. Rev. A., 1975, 11:1692–1699.