耦合通道光学势方法研究正电子与锂原子碰撞的共振现象
摘要
20世纪30年代,Dirac在理论上预言正电子的存在,Anderson在实验上探测到正电子,成为20世纪物理学最惊人的发现之一。自此,正电子物理一直是物理学家感兴趣的课题,特别是,20世纪80年代,由于强正电子束的出现,使正电子物理成为近二十年最活跃的一个研究领域。正电子是电子的反粒子,正电子同原子分子的碰撞是反物质同普通物质的相互作用,为我们更好的了解原子内部的电子结构和相互作用以及碰撞的准确物理机制提供了重要的手段。
在实验方面,尽管相应的实验技术正在逐渐发展,但是由于正电子与原子碰撞过程比较复杂,对实验条件要求非常高,所以目前仅有少量关于碰撞截面的实验数据,这使得对正电子与与原子碰撞的研究更加依赖于理论。
在理论方面,过去的十年里,对正电子与原子的碰撞的研究上取得了相当大的进步。在正电子碰撞的理论研究中,人们往往首先从单电子原子入手,即氢原子和冻结核近似下的碱金属原子。研究过程中把碱金属原子看作一个最外层电子围绕包括内层电子在内的冻结核做运动的单电子体系。目前,变分法成功地处理了低能下的正电子与简单原子碰撞问题。畸变波玻恩近似方法(DWBA)对正电子与原子分子碰撞问题的研究主要集中在高能区域,早期的密耦法(close-coupling)经过理论工作者的不断发展被应用于中等能量范围内的正电子与原子碰撞问题,其中收敛的密耦方法(CCC)和动量空间耦合通道光学势方法(CCO)在近几年的理论工作中取得了一定的成功。
在本论文中,我们运用动量空间耦合通道光学势方法(CCO)研究了正电子与锂原子在低能(1.45-4.5eV)情况下散射过程中的共振现象。动量空间耦合通道光学势方法是基于周雅君所发展的正电子同氢原子碰撞的耦合通道光学势方法,将耙空间的组态空间分成互补的P和Q两个空间。我们在P空间解耦合积分方程,发展了一个Q空间的复的等价局部的光学势来描述,部分分立态,碰撞过程中电离以及正负电子耦素形成。应用这种方法我们计算了正电子与锂原子碰撞的总散射截面以及L=0-10的十一个分波散射截面,并给出了共振的位置和形状,并对共振形成的原因做了简单的分析。
Positron which was predicted by Dirac’s equations and shown by Anderson’s continuing studies was one of the most surprising discoveries in physics last century. Since then physicists have always been attracted deeply by the positron physics. Particularly, there has been a spurt of theoretical studies on positron-atom processes with the appearance of stable and intensive beams of positron in the last two decades. Positron is the antimatter of electron, and the scattering of positrons with atoms or molecules is one kind of interactions between antimatter and common matter, which provides us an important measure for understanding the electron structure and the mutual disposition in atoms and the exact physical mechanism of scattering.
There are few experimental reports about the data of total scattering cross section in positron-atom collisions because of the more complexity in the system of positron and atom which asks for the complexity in the impacting experiment, which makes the research of positron-atom collision depend on the theory research.
In the past decade, considerable advances of the studies in positron atomic collisions have seen achieved in the theoretical area. People used to start with one-electron atom,such as atomic hydrogen and the alkali atoms in the frozen core approximation. Variational method can successfully dispose the scatting problem between positron in low energy and single atom. The research of scatting between positron and atom with DWBA focused on the high energy area. The early close-coupling which has been developed by theoretical workers can now be used in the media medial energy area among them the convergent close-coupling (CCC) method and close-coupling optical method (CCO) acquired certain success in recently theoretical work.
In this thesis, we studied the resonances in positron-Li collisions under the circumstance of low energy (1.45-4.5eV) with the momentum-space coupled-channel optical (CCO) method. In this method, the whole space is split into P and Q spaces by the rejection vector P and Q. We got the solution of coupling integral equation in P space, and in Q space, we developed a plural equal local optical potential description. The P space consists of some discrete channels, and the rest discrete channels and the ionization continuum are included in the Q space. We reckoned the total scattering cross section between positron-Li collisions and eleven partial waves scattering cross section, and the position and shape of resonance is given and so is the simple analyze of it.
在实验方面,尽管相应的实验技术正在逐渐发展,但是由于正电子与原子碰撞过程比较复杂,对实验条件要求非常高,所以目前仅有少量关于碰撞截面的实验数据,这使得对正电子与与原子碰撞的研究更加依赖于理论。
在理论方面,过去的十年里,对正电子与原子的碰撞的研究上取得了相当大的进步。在正电子碰撞的理论研究中,人们往往首先从单电子原子入手,即氢原子和冻结核近似下的碱金属原子。研究过程中把碱金属原子看作一个最外层电子围绕包括内层电子在内的冻结核做运动的单电子体系。目前,变分法成功地处理了低能下的正电子与简单原子碰撞问题。畸变波玻恩近似方法(DWBA)对正电子与原子分子碰撞问题的研究主要集中在高能区域,早期的密耦法(close-coupling)经过理论工作者的不断发展被应用于中等能量范围内的正电子与原子碰撞问题,其中收敛的密耦方法(CCC)和动量空间耦合通道光学势方法(CCO)在近几年的理论工作中取得了一定的成功。
在本论文中,我们运用动量空间耦合通道光学势方法(CCO)研究了正电子与锂原子在低能(1.45-4.5eV)情况下散射过程中的共振现象。动量空间耦合通道光学势方法是基于周雅君所发展的正电子同氢原子碰撞的耦合通道光学势方法,将耙空间的组态空间分成互补的P和Q两个空间。我们在P空间解耦合积分方程,发展了一个Q空间的复的等价局部的光学势来描述,部分分立态,碰撞过程中电离以及正负电子耦素形成。应用这种方法我们计算了正电子与锂原子碰撞的总散射截面以及L=0-10的十一个分波散射截面,并给出了共振的位置和形状,并对共振形成的原因做了简单的分析。
Positron which was predicted by Dirac’s equations and shown by Anderson’s continuing studies was one of the most surprising discoveries in physics last century. Since then physicists have always been attracted deeply by the positron physics. Particularly, there has been a spurt of theoretical studies on positron-atom processes with the appearance of stable and intensive beams of positron in the last two decades. Positron is the antimatter of electron, and the scattering of positrons with atoms or molecules is one kind of interactions between antimatter and common matter, which provides us an important measure for understanding the electron structure and the mutual disposition in atoms and the exact physical mechanism of scattering.
There are few experimental reports about the data of total scattering cross section in positron-atom collisions because of the more complexity in the system of positron and atom which asks for the complexity in the impacting experiment, which makes the research of positron-atom collision depend on the theory research.
In the past decade, considerable advances of the studies in positron atomic collisions have seen achieved in the theoretical area. People used to start with one-electron atom,such as atomic hydrogen and the alkali atoms in the frozen core approximation. Variational method can successfully dispose the scatting problem between positron in low energy and single atom. The research of scatting between positron and atom with DWBA focused on the high energy area. The early close-coupling which has been developed by theoretical workers can now be used in the media medial energy area among them the convergent close-coupling (CCC) method and close-coupling optical method (CCO) acquired certain success in recently theoretical work.
In this thesis, we studied the resonances in positron-Li collisions under the circumstance of low energy (1.45-4.5eV) with the momentum-space coupled-channel optical (CCO) method. In this method, the whole space is split into P and Q spaces by the rejection vector P and Q. We got the solution of coupling integral equation in P space, and in Q space, we developed a plural equal local optical potential description. The P space consists of some discrete channels, and the rest discrete channels and the ionization continuum are included in the Q space. We reckoned the total scattering cross section between positron-Li collisions and eleven partial waves scattering cross section, and the position and shape of resonance is given and so is the simple analyze of it.
引文
1 C. D. Anderson. The Positive Electron. Phys. Rev. 1933, 43:491~494.
2 M. Deutsch. Evidence for the Formation of Positronium in Gases. Phys. Rev. 1951, 82:455~456.
3 A. P. Mills Jr. Observation of the Positronium Negative Ion. Phys. Rev. Lett. 1981, 46:717~720.
4 S. J. Gilbert, L. D. Barnes, J. P. Sulivan and C. M. Surko. Vibrational-Resonance Enhancement of Positron Annihilation in Molecules. Phys. Rev. Lett. 2002, 88:043201/1~043201/4.
5 D. B. Cassidy and A. P. Mills Jr. The Production of Molecular Positronium. Nature. 2007, 449:195~197.
6 George J. Schulz. Resonances in Electron Impact on Atoms. Reviews of Modern Physics. 1973, 45:379~411.
7 M. H. Mittleman. Resonances in Proton-Hydrogen and Positron-Hydrogen Scattering. Phys. Rev. 1966, 152:76~78.
8 G. D. Doolen, J. Nuttall and C. J. Wherry. Evidence for a Resonance in e+-H S-Wave Scattering. Phys. Rev. Lett. 1978, 40:313.
9 J. Mitroy. Close Coupling Calculations of Positron-Hydrogen Scattering at Low Energies. J. Phys. B: At. Mol. Opt. Phys. 1993, 26:4861~4869.
10 Z-C Yan and Y. K. Ho. D-Wave Resonances in e+-H Scattering. J. Phys. B: At. Mol. Opt. Phys. 2002, 35:1875~1883.
11 S. Kar and Y. K, Ho. S-wave resonances in e-He scattering below the Ps(=2) excitation threshold. J. Phys. B: At. Mol. Opt. Phys. 2004, 37:3177~3186.
12 Y. Zhou and C. D. Lin. Hyperspherical Close-coupling Calculation of Positronium Formation and Excitation Cross Section in Positron-Hydrogen Scattering at Energies below the H (n=4) Threshold. J. Phys. B: At. Mol. Opt. Phys. 1995, 28:4907~4925.
13 T. T. Gien. Accurate Calculation of Phase Shifts for Positron-He+ Collisions. J. Phys. B: At. Mol. Opt. Phys. 2001, 34 L535~L541.
14 M. T. McAlinden, A. A. Kernoghan and H. R. J. Walters. Cross-channelCoupling in Positron-atom Scattering. Hyperfine Interactions. 1994, 89:161~194.
15 J. Mitroy and A. T. Stelbovics. Resonances Structure in the Positron-Hydrogen System above the Ionization Threshold. J. Phys. B: At. Mol. Opt. Phys. 1994, 27:L55~L60.
16 A. Kernoghan M. T. McAlinden. An 18-state Calculation of Positron-Hydrogen Scattering. J. Phys. B: At. Mol. Opt. Phys. 1995, 28:1079~1094.
17 H. R. J. Walters, A. A. Kernoghan, and M. T. McAlinden. The Physics of Electronic and Atomic Collisions. Edited by Louis J. Dubé, J. Brain A. Mitchell, J. William McConkey and Chris E. Brion. AIP Conference Proceedings 360, Whistler, 1995. Canada.
18 I. Bray and A. Stelbovics. Explicit Demonstration of the convergence of the Close-coupling Method for a Coulomb Three-body Problem. Phys. Rev. Lett. 1992, 69:53~56.
19 I. E. McCarthy and Y. Zhou. Equivalent-Local Calculation of the Continuum Contributions to Electron and Positron Reactions on Atoms. Phys. Rev. A. 1994, 49:4597~4601.
20 Y. Zhou, K. Ratnavelu and I. E. McCarthy, Momentum-Space Couple-Channel Optical Method for Positron-Hydrogen Scattering. Phys. Rev. A. 2005, 71:042703/1~042703/6.
21 I. E. McCarthy and A. T. Stelbovics. Continuum in the Atomic Optical Model. Phys. Rev. A. 1980, 22:502~513.
22 Wu Yong and Zhou Yajun. Calculation of Total Cross Sections for Positron Scattering by Lithium at Intermediate Energies. Chin. Phys. Lett. 2005, 22:861~864.
23 Y. Ke, Y. Zhou and G. Nan. Optical Model for Positronium Formation in e+-Na Collision. Phys. Rev. A. 2004, 70:024702/1~024702/4.
24 G. Nan, Y. Zhou and Y. Ke. Optical Model for Positronium Formation Cross Section in e+-K Collisions at Low Impact Energies. Phys. Rev. A. 2005, 72:012709/1~012709/5.
25 C. Cheng and Y. Zhou. Optical Model for the Positronium Formation in Positron-Mg Collision. Phys. Rev. A. 2006, 73:024701/1~024701/5.
26 Y. Cheng and Y. Zhou. Momentum-Space Coupled-Channel Calculation for Positron-Helium Scattering. Phys. Rev. A. 2007, 76:012704/1~012704/6.
27 Y. Cheng and Y. Zhou. Optical Potential Calculation for Positron Collision with Helium. Chin. Phys. Lett. 2005, 24:3408~3412.
28 Y.G. J. Seiler, R. S. Oberoi, and J. Callaway. Algebraic Close-Coupling Calculation of the Scattering of Electrons and Positrons by Hydrogen. Phys. Rev. A. 1971, 3:2006~2014.
29 S. E. A. Wakid. Resonances in Low-Energy Positron-Hydrogen Collisions. Phys. Lett. A. 1975, 54:103~105.
30 Y. K. Ho and Z. -C Yan, High Partial Wave Resonances in Positron Hydrogen Scattering. Phys. Rev. A. 2004, 70:032716/1~032716/10.
31 P. G. Burke and A. J. Taylor. The Excitation of He+ by Electron Impact. J. Phys. B: At. Mol. Opt. Phys. 1969, 2:44~51.
32 S. J. Ward, M. Horbatsch, R. P. Mceachran and A. D. Stauffer. Resonances in low-energy positron scattering from Li, Na and K. J. Phys. B: At. Mol. Opt. Phys. 1989, 22:3763~3774.
33 Utpal Roy and Y. K. Ho. Resonances in Positron–lithium Scattering. J. Phys. B: At. Mol. Opt. Phys. 2002, 35:2149~2157.
34 Utpal Roy and Y. K. Ho. P-wave Resonances in Positron-lithium Scattering. Nuclear Instr. and Methods in Phys. Research B. 2004, 221:36~40.
35 I. Bary, I. E. McCarthy, J. Mitroy and K. Ratnavelu. Coupled Channels in the Distorted-Wave Representation. Phys Rev. A. 1989, 39:4998~5009.
36 I. E. McCarthy and A. T. Stelbovics. Momentum-Space Coupled-Channel Optical Method for Electron-Atom Scattering. Phys. Rev. A. 1983, 28:2693~2707.
37吴奕初,胡懿,王少阶.基于正电子的反物质研究进展.物理学进展. 2008, 28:83~94.
38 Y. K. Ho. Atomic Resonances Involving Positrons. Nuclear Instr. and Methods in Phys. Research B. 2008, 226:516~521.
39 Stephen J. Buckman and Charles W. Clark. Atomic Negative-ion Resonances. Reviews of Modern Physics. 1994, 66:582~583.
40 J. Yuan, B. D. Esry, T. Morishita and C. D. Lin. Stable Bound States of e++Li and e++Na. Phys. Rev. A. 1998, 58:R4~R7.
41 G. G. Ryzhikh and J. Mitroy. Positronic Lithium, an Electronically Stable Li-e+ Ground State. Phys. Rev. Lett. 1997, 79:4124~4126.
42 S. J. Ward and J. Shertzer. Effect of the Core Polarization Term on Ps Formation in Low-Energy e+-Li Collisions. Nuclear Instr. and Methods in Phys. Research B. 2004, 221:206~209.
43 D. L. Moores and D. W. Norcross. The Scattering of Electrons by Sodium Atoms. J. Phys. B: At. Mol. Opt. Phys. 1972, 5:1482~1505.
44 A. C. Fung and J. J. Matese. Autoionization States of Li- and Na-. Phys. Rev. A. 1972, 5:22~26.
45 A. W. Weiss. Theoretical Electron Affinities for Some of the Alkali and Alkaline-Earth Elements. Phys. Rev. 1968, 166:70~74.
46曾谨言.量子力学卷Ⅰ.第三版.科学出版社. 2000, 650~681.
2 M. Deutsch. Evidence for the Formation of Positronium in Gases. Phys. Rev. 1951, 82:455~456.
3 A. P. Mills Jr. Observation of the Positronium Negative Ion. Phys. Rev. Lett. 1981, 46:717~720.
4 S. J. Gilbert, L. D. Barnes, J. P. Sulivan and C. M. Surko. Vibrational-Resonance Enhancement of Positron Annihilation in Molecules. Phys. Rev. Lett. 2002, 88:043201/1~043201/4.
5 D. B. Cassidy and A. P. Mills Jr. The Production of Molecular Positronium. Nature. 2007, 449:195~197.
6 George J. Schulz. Resonances in Electron Impact on Atoms. Reviews of Modern Physics. 1973, 45:379~411.
7 M. H. Mittleman. Resonances in Proton-Hydrogen and Positron-Hydrogen Scattering. Phys. Rev. 1966, 152:76~78.
8 G. D. Doolen, J. Nuttall and C. J. Wherry. Evidence for a Resonance in e+-H S-Wave Scattering. Phys. Rev. Lett. 1978, 40:313.
9 J. Mitroy. Close Coupling Calculations of Positron-Hydrogen Scattering at Low Energies. J. Phys. B: At. Mol. Opt. Phys. 1993, 26:4861~4869.
10 Z-C Yan and Y. K. Ho. D-Wave Resonances in e+-H Scattering. J. Phys. B: At. Mol. Opt. Phys. 2002, 35:1875~1883.
11 S. Kar and Y. K, Ho. S-wave resonances in e-He scattering below the Ps(=2) excitation threshold. J. Phys. B: At. Mol. Opt. Phys. 2004, 37:3177~3186.
12 Y. Zhou and C. D. Lin. Hyperspherical Close-coupling Calculation of Positronium Formation and Excitation Cross Section in Positron-Hydrogen Scattering at Energies below the H (n=4) Threshold. J. Phys. B: At. Mol. Opt. Phys. 1995, 28:4907~4925.
13 T. T. Gien. Accurate Calculation of Phase Shifts for Positron-He+ Collisions. J. Phys. B: At. Mol. Opt. Phys. 2001, 34 L535~L541.
14 M. T. McAlinden, A. A. Kernoghan and H. R. J. Walters. Cross-channelCoupling in Positron-atom Scattering. Hyperfine Interactions. 1994, 89:161~194.
15 J. Mitroy and A. T. Stelbovics. Resonances Structure in the Positron-Hydrogen System above the Ionization Threshold. J. Phys. B: At. Mol. Opt. Phys. 1994, 27:L55~L60.
16 A. Kernoghan M. T. McAlinden. An 18-state Calculation of Positron-Hydrogen Scattering. J. Phys. B: At. Mol. Opt. Phys. 1995, 28:1079~1094.
17 H. R. J. Walters, A. A. Kernoghan, and M. T. McAlinden. The Physics of Electronic and Atomic Collisions. Edited by Louis J. Dubé, J. Brain A. Mitchell, J. William McConkey and Chris E. Brion. AIP Conference Proceedings 360, Whistler, 1995. Canada.
18 I. Bray and A. Stelbovics. Explicit Demonstration of the convergence of the Close-coupling Method for a Coulomb Three-body Problem. Phys. Rev. Lett. 1992, 69:53~56.
19 I. E. McCarthy and Y. Zhou. Equivalent-Local Calculation of the Continuum Contributions to Electron and Positron Reactions on Atoms. Phys. Rev. A. 1994, 49:4597~4601.
20 Y. Zhou, K. Ratnavelu and I. E. McCarthy, Momentum-Space Couple-Channel Optical Method for Positron-Hydrogen Scattering. Phys. Rev. A. 2005, 71:042703/1~042703/6.
21 I. E. McCarthy and A. T. Stelbovics. Continuum in the Atomic Optical Model. Phys. Rev. A. 1980, 22:502~513.
22 Wu Yong and Zhou Yajun. Calculation of Total Cross Sections for Positron Scattering by Lithium at Intermediate Energies. Chin. Phys. Lett. 2005, 22:861~864.
23 Y. Ke, Y. Zhou and G. Nan. Optical Model for Positronium Formation in e+-Na Collision. Phys. Rev. A. 2004, 70:024702/1~024702/4.
24 G. Nan, Y. Zhou and Y. Ke. Optical Model for Positronium Formation Cross Section in e+-K Collisions at Low Impact Energies. Phys. Rev. A. 2005, 72:012709/1~012709/5.
25 C. Cheng and Y. Zhou. Optical Model for the Positronium Formation in Positron-Mg Collision. Phys. Rev. A. 2006, 73:024701/1~024701/5.
26 Y. Cheng and Y. Zhou. Momentum-Space Coupled-Channel Calculation for Positron-Helium Scattering. Phys. Rev. A. 2007, 76:012704/1~012704/6.
27 Y. Cheng and Y. Zhou. Optical Potential Calculation for Positron Collision with Helium. Chin. Phys. Lett. 2005, 24:3408~3412.
28 Y.G. J. Seiler, R. S. Oberoi, and J. Callaway. Algebraic Close-Coupling Calculation of the Scattering of Electrons and Positrons by Hydrogen. Phys. Rev. A. 1971, 3:2006~2014.
29 S. E. A. Wakid. Resonances in Low-Energy Positron-Hydrogen Collisions. Phys. Lett. A. 1975, 54:103~105.
30 Y. K. Ho and Z. -C Yan, High Partial Wave Resonances in Positron Hydrogen Scattering. Phys. Rev. A. 2004, 70:032716/1~032716/10.
31 P. G. Burke and A. J. Taylor. The Excitation of He+ by Electron Impact. J. Phys. B: At. Mol. Opt. Phys. 1969, 2:44~51.
32 S. J. Ward, M. Horbatsch, R. P. Mceachran and A. D. Stauffer. Resonances in low-energy positron scattering from Li, Na and K. J. Phys. B: At. Mol. Opt. Phys. 1989, 22:3763~3774.
33 Utpal Roy and Y. K. Ho. Resonances in Positron–lithium Scattering. J. Phys. B: At. Mol. Opt. Phys. 2002, 35:2149~2157.
34 Utpal Roy and Y. K. Ho. P-wave Resonances in Positron-lithium Scattering. Nuclear Instr. and Methods in Phys. Research B. 2004, 221:36~40.
35 I. Bary, I. E. McCarthy, J. Mitroy and K. Ratnavelu. Coupled Channels in the Distorted-Wave Representation. Phys Rev. A. 1989, 39:4998~5009.
36 I. E. McCarthy and A. T. Stelbovics. Momentum-Space Coupled-Channel Optical Method for Electron-Atom Scattering. Phys. Rev. A. 1983, 28:2693~2707.
37吴奕初,胡懿,王少阶.基于正电子的反物质研究进展.物理学进展. 2008, 28:83~94.
38 Y. K. Ho. Atomic Resonances Involving Positrons. Nuclear Instr. and Methods in Phys. Research B. 2008, 226:516~521.
39 Stephen J. Buckman and Charles W. Clark. Atomic Negative-ion Resonances. Reviews of Modern Physics. 1994, 66:582~583.
40 J. Yuan, B. D. Esry, T. Morishita and C. D. Lin. Stable Bound States of e++Li and e++Na. Phys. Rev. A. 1998, 58:R4~R7.
41 G. G. Ryzhikh and J. Mitroy. Positronic Lithium, an Electronically Stable Li-e+ Ground State. Phys. Rev. Lett. 1997, 79:4124~4126.
42 S. J. Ward and J. Shertzer. Effect of the Core Polarization Term on Ps Formation in Low-Energy e+-Li Collisions. Nuclear Instr. and Methods in Phys. Research B. 2004, 221:206~209.
43 D. L. Moores and D. W. Norcross. The Scattering of Electrons by Sodium Atoms. J. Phys. B: At. Mol. Opt. Phys. 1972, 5:1482~1505.
44 A. C. Fung and J. J. Matese. Autoionization States of Li- and Na-. Phys. Rev. A. 1972, 5:22~26.
45 A. W. Weiss. Theoretical Electron Affinities for Some of the Alkali and Alkaline-Earth Elements. Phys. Rev. 1968, 166:70~74.
46曾谨言.量子力学卷Ⅰ.第三版.科学出版社. 2000, 650~681.