低能情况下正电子与氦碰撞的共振现象
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摘要
低能情况下尤其是电离阈值以下的电子同原子的散射,存在着一种重要的物理现象:共振,即入射电子和靶原子形成暂时的不稳定的束缚态(quasi-boundstates),共振态会在相移和散射截面上引起剧烈的变化。正电子与原子散射的共振现象没有电子普遍,但是同样吸引着人们的兴趣。
氦是最简单的多电子靶原子,是检验一种理论方法有效的工具。在本论文中,我们对原有的动量空间耦合通道光学势方法作了进一步的发展,将极化势模型扩展到了正电子与氦原子的碰撞问题,对该体系的共振进行了研究。我们得到了位于20.160eV的尖锐的共振结构。在加入了一个复的等价局域近似的光学势来描述电离连续态和电子偶素形成通道的影响以后,共振的位置并没有发生改变。
由于高分辨率正电子束的限制,目前还没有关于正电子共振的实验研究。关于正电子-氦原子散射体系共振的理论研究也少有报道,现有的结果也没有出现过相互符合的情况。人们目前还不清楚共振的机制。
The interaction of positrons with atoms and moleculars has attracted a lot of attention with the development of new experimental technology during the past decades.Positron-atom and-molecule scattering is different from the electron counterpart since there is no exchange and the short-range interaction is repulsive, which leads to some new phenomena to challenge the theorists.Studying the mechanism is also very important for us to learn about the anti-matter.
Resonance is the quasi-bound state formed by the atom and incident positron at a certain energy which shows itself as a rapid change in the phase shift or cross section. That there is no exchange symmetry between positron and the electrons of target atom and we don't need to consider Pauli principle doesn't make it an easy problem since the collision system is of two-center interaction with a special rearrangement channel, namely the positronium formation.
Hydrogen atom is a good model to investigate with its simple atomic structure. Several theories,such as close-coupling[25-27],complex-coordinate rotation and hyperspherical coordinates[28-29],R-matrix method[31-32],stabilization method[37], and stochastical variational method[39],have all been applied to study the positron-hydrogen scattering system and many resonances have been reported[25-29]. On the other hand,there were only few experimental study of the system[40-42]as atomic hydrogen was not easy to prepare.There are also some reported resonances in positron scattering by alkali atoms theoretically,using polarization potential method[43],close-coupling method[44-45],and stabilization method[46-48]. Resonances in positron scattering from some other tagets,such as alkaline earth atoms[49-50],copper[51],zinc[52]and helium ion[53-58],have been reported too.
Helium atom is an ideal target for both experiments and theoretical calculations since it is the simplist many-electron atom and very stable,but there are not many resonances reported by far.
In this paper,we investigate the resonance structure in positron-helium scattering applying the momentum-space coupled-channel optical potential(CCO) method with a complex equivalent local optical potential describing the ionization continuum and positronium formation.CCO is an ab-initial method developed by McCarthy and Stebovics[67-68,78-80]for electron scattering.In this method,the whole space is split into P and Q spaces by the rejection vector P and Q.The P space consists of some discrete channels,and the rest discrete channels and the ionization continuum are included in the Q space.We can get the T-matrix elements by solving the deduced coupled integral Lippman-Schwinger equations in P space and the contribution of Q space is described by a complex optical potential.This method has been successfully applied in the electron collisions with atoms and molecules.In the past few years,a polarization potential for the positronium rearrangement contribution has been developed by Zhou to extend the CCO method to positron scattering from atomic hydrogen and alkali-metal atoms.In this paper,we extend the CCO method to calculate the resonance in positron-helium scattering.
In the calculation,we include nine discrete channels in the P space,namely 1,2,3, 4 ~1S;2,3,4 ~1S;3,4 ~1S,without any triple states since no exchange involved.The target atom is described by configuration interaction(CI) wave function with the basis of nine Hartree-Fock orbits which are 1,2,3,4s;2,3,4p;3,4d.We calculate from 19.3eV incident energy to 24eV with 0.001eV interval and find a resonance structure at 20.160eV and the resonance width is 0.002eV.It is a S-wave resonance found for the first time.Then we add the coupled-channels in Q space with everything in P space unchanged.The polarization potential for ionization continuum is included in the coupled-terms 1~1 S-1~1 S,1~1 S-2~1 S,2~1S-2~1S and the one for positronium is in the 1~1 S-1~1 S term which describes the lowest three states of positronium.The higher the incident energy is,the more the total cross section is found to increase.The location of the resonance changes very slightly to 20.159eV,only 0.001 eV lower and the width remains the same 0.002eV. There are some theoretical researches on resonances of the positron-helium scattering system.Kahali er al[61]found a resonance in the S-wave capture cross section at about 84eV with the close coupling(CC) approach in 1995,but the position of resonance shifted when they applied different bases.Adhikari et al[59]found an S-wave resonance at 19.267eV of width 0.001 eV in the close-coupling approximation calculation in 1996.The resonance energy is below the lowest inelastic threshold,but it is surprizingly close to a similar S-wave resonance at about 19.3eV in the electron-helium system.They presume the closeness of these energies suggests that similar long-range polarization potentials are responsible for the appearance of these two resonances.Chaudhuri et al[60]found a S-wave resonance at 30eV of width 2eV using the close-coupling approach in 1997.They claim,for a correct representation of the resonance,both He(1s2p) and Ps atom states are required.The He(1s2p) state forms the long-range polarization potential in positron-helium,and the coupling between it and Ps atom states in the scheme builds a long-range multichannel effective potential with long-range repulsion and short-range attraction which is responsible for the resonance.Kar and Ho[62]found two S-wave resonances at 22.509eV and 22.788eV using the stabilization method in 2004.They presume resonances existing below the excited positronium thresholds are the result of an attractive induced dipole potential created between an excited positronium atom and a positively charged ion or nucleus.
We don't confirm the resonances found by Kar and Ho.The polarization potential only affects the position of our resonance slightly.We will improve our calculation model to include more channels and find out the mechanism for resonance in future.
氦是最简单的多电子靶原子,是检验一种理论方法有效的工具。在本论文中,我们对原有的动量空间耦合通道光学势方法作了进一步的发展,将极化势模型扩展到了正电子与氦原子的碰撞问题,对该体系的共振进行了研究。我们得到了位于20.160eV的尖锐的共振结构。在加入了一个复的等价局域近似的光学势来描述电离连续态和电子偶素形成通道的影响以后,共振的位置并没有发生改变。
由于高分辨率正电子束的限制,目前还没有关于正电子共振的实验研究。关于正电子-氦原子散射体系共振的理论研究也少有报道,现有的结果也没有出现过相互符合的情况。人们目前还不清楚共振的机制。
The interaction of positrons with atoms and moleculars has attracted a lot of attention with the development of new experimental technology during the past decades.Positron-atom and-molecule scattering is different from the electron counterpart since there is no exchange and the short-range interaction is repulsive, which leads to some new phenomena to challenge the theorists.Studying the mechanism is also very important for us to learn about the anti-matter.
Resonance is the quasi-bound state formed by the atom and incident positron at a certain energy which shows itself as a rapid change in the phase shift or cross section. That there is no exchange symmetry between positron and the electrons of target atom and we don't need to consider Pauli principle doesn't make it an easy problem since the collision system is of two-center interaction with a special rearrangement channel, namely the positronium formation.
Hydrogen atom is a good model to investigate with its simple atomic structure. Several theories,such as close-coupling[25-27],complex-coordinate rotation and hyperspherical coordinates[28-29],R-matrix method[31-32],stabilization method[37], and stochastical variational method[39],have all been applied to study the positron-hydrogen scattering system and many resonances have been reported[25-29]. On the other hand,there were only few experimental study of the system[40-42]as atomic hydrogen was not easy to prepare.There are also some reported resonances in positron scattering by alkali atoms theoretically,using polarization potential method[43],close-coupling method[44-45],and stabilization method[46-48]. Resonances in positron scattering from some other tagets,such as alkaline earth atoms[49-50],copper[51],zinc[52]and helium ion[53-58],have been reported too.
Helium atom is an ideal target for both experiments and theoretical calculations since it is the simplist many-electron atom and very stable,but there are not many resonances reported by far.
In this paper,we investigate the resonance structure in positron-helium scattering applying the momentum-space coupled-channel optical potential(CCO) method with a complex equivalent local optical potential describing the ionization continuum and positronium formation.CCO is an ab-initial method developed by McCarthy and Stebovics[67-68,78-80]for electron scattering.In this method,the whole space is split into P and Q spaces by the rejection vector P and Q.The P space consists of some discrete channels,and the rest discrete channels and the ionization continuum are included in the Q space.We can get the T-matrix elements by solving the deduced coupled integral Lippman-Schwinger equations in P space and the contribution of Q space is described by a complex optical potential.This method has been successfully applied in the electron collisions with atoms and molecules.In the past few years,a polarization potential for the positronium rearrangement contribution has been developed by Zhou to extend the CCO method to positron scattering from atomic hydrogen and alkali-metal atoms.In this paper,we extend the CCO method to calculate the resonance in positron-helium scattering.
In the calculation,we include nine discrete channels in the P space,namely 1,2,3, 4 ~1S;2,3,4 ~1S;3,4 ~1S,without any triple states since no exchange involved.The target atom is described by configuration interaction(CI) wave function with the basis of nine Hartree-Fock orbits which are 1,2,3,4s;2,3,4p;3,4d.We calculate from 19.3eV incident energy to 24eV with 0.001eV interval and find a resonance structure at 20.160eV and the resonance width is 0.002eV.It is a S-wave resonance found for the first time.Then we add the coupled-channels in Q space with everything in P space unchanged.The polarization potential for ionization continuum is included in the coupled-terms 1~1 S-1~1 S,1~1 S-2~1 S,2~1S-2~1S and the one for positronium is in the 1~1 S-1~1 S term which describes the lowest three states of positronium.The higher the incident energy is,the more the total cross section is found to increase.The location of the resonance changes very slightly to 20.159eV,only 0.001 eV lower and the width remains the same 0.002eV. There are some theoretical researches on resonances of the positron-helium scattering system.Kahali er al[61]found a resonance in the S-wave capture cross section at about 84eV with the close coupling(CC) approach in 1995,but the position of resonance shifted when they applied different bases.Adhikari et al[59]found an S-wave resonance at 19.267eV of width 0.001 eV in the close-coupling approximation calculation in 1996.The resonance energy is below the lowest inelastic threshold,but it is surprizingly close to a similar S-wave resonance at about 19.3eV in the electron-helium system.They presume the closeness of these energies suggests that similar long-range polarization potentials are responsible for the appearance of these two resonances.Chaudhuri et al[60]found a S-wave resonance at 30eV of width 2eV using the close-coupling approach in 1997.They claim,for a correct representation of the resonance,both He(1s2p) and Ps atom states are required.The He(1s2p) state forms the long-range polarization potential in positron-helium,and the coupling between it and Ps atom states in the scheme builds a long-range multichannel effective potential with long-range repulsion and short-range attraction which is responsible for the resonance.Kar and Ho[62]found two S-wave resonances at 22.509eV and 22.788eV using the stabilization method in 2004.They presume resonances existing below the excited positronium thresholds are the result of an attractive induced dipole potential created between an excited positronium atom and a positively charged ion or nucleus.
We don't confirm the resonances found by Kar and Ho.The polarization potential only affects the position of our resonance slightly.We will improve our calculation model to include more channels and find out the mechanism for resonance in future.
引文
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