正电子与原子散射共振现象的研究
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摘要
原子分子物理是最重要的基础学科之一，其基本任务就是对物质的微观结构和粒子相互作用提供更详细准确的描述。目前原子分子物理面临的最大挑战就是对多体问题和电子关联的处理。近年来，随着正电子实验技术的提高，正电子与原子分子的碰撞受到越来越广泛的关注。正电子作为电子的反物质，其质量和所带电荷量与电子相等，而电性相反。在碰撞过程中正电子受到原子核的排斥和价电子的吸引力作用，与靶原子的电子之间没有交换相互作用，这就决定了正电子-原子散射与电子-原子散射有很大的区别。例如，正电子碰撞除了存在普通的弹性、激发、电离、形成束缚态等散射通道外，还有正负电子偶素形成和正负电子湮灭通道。由于正电子的这些独特性质，对正电子与原子的散射过程的研究，不仅能够给我们提供研究物质与反物质相互作用的重要手段，而且能够用于研究新的散射物理过程，具有非常重要的学术意义。
在正电子与原子碰撞过程中存在一个非常重要的现象就是形成共振态。与形成束缚态不同，正电子会暂时地束缚于靶原子，形成一个不稳定的准束缚态，称为共振态。共振态一般在原子的激发阈值以及激发态正负电子偶素阈值以下形成，其原因是由于入射正电子在激发态原子能级或者末态形成的激发态正负电子偶素能级简引起的势场中运动，受到势的吸引作用与靶原子形成临时的束缚态。由于正电子所感受到的这个势是电子-电子关联引起的极化势，因此对正电子共振现象的研究能够为我们提供正电子与原子散射中更详细的电子关联信息。
共振态的存在会在散射相移和散射截面中表现出剧烈的变化，因而研究散射截面能够预言共振位置和宽度等重要参数。目前广泛用于研究正电子原子碰撞散射截面的方法主要为密耦方法，在之前的理论模型中，一部分只考虑了靶的分立态之间的耦合而忽略连续态的作用，另外的大部分理论方法用伪态来描述连续态的作用。在研究共振时引入伪态会引起计算上的伪共振，并且由于需要大量的伪态来使结果达到收敛，因而计算会存在一定困难。本文的主要工作就是用发展的耦合通道光学势方法研究正电子与氢原子以及复杂原子散射的共振现象。在我们的方法中，引入一个极化势来描述碰撞过程中的连续态作用。使用Feshbach投影算符P和Q将整个反应空间分为P和Q两个互补的子空间，其中P空间包含靶原子基态在内的有限个分立态，Q空间包含剩余的分立态和连续态，其作用通过在势能项中附加一个复的极化势来描述。在描述正负电子偶素连续态的极化势中，我们发展了一种包含激发态正负电子偶素形成过程的计算方法，考虑了第一激发态正负电子偶素极化势对散射截面和共振的影响。为了计算的可行性，我们对这个极化势引入一个等价局域近似和角动量投影近似，通过联立求解P子空间中的通道耦合积分方程，得到各散射通道的T矩阵元，然后对T矩阵元进行积分得到各散射截面。
在本论文中，我们由简单到复杂依次研究了正电子与氢原子、碱金属中的钠原子和惰性气体中的氦原子散射中的共振现象。目前实验上受正电子束强度和精度的限制，对正电子散射共振的测量还存在一定的困难。对于理论方面的研究，大部分工作都集中在正电子与氢原子散射的研究，并且前人的主要工作都集中在S、P和D等低分波共振的研究。本文我们计算了正电子与氢原子碰撞的分波散射截面，研究了不同分波的共振位置和宽度。我们不仅确定了之前其它理论方法所预言的共振，还发现了许多新的共振，找到了目前为止能量位置最低的共振。除此之外我们还给出了F、G、H和I等高分波的共振。氢原子共振形成的主要原因是由激发态正负电子偶素和激发态氢原子能级简并形成的偶极极化势引起的。我们还研究了正电子碰撞氢原子的微分散射截面中的共振现象，首次给出了各共振态在散射空间中的角度分布情况。
在氢原子研究工作的基础上我们进一步研究了正电子与碱金属纳原子以及惰性气体氦原子散射的共振，分析了通道耦合数量、连续态极化势以及正负电子偶素形成通道对共振参数的影响。对于钠原子的研究表明共振位置随着耦合通道数量的增加而向低能区域移动，最终达到收敛。对于氦原子我们首次预言了正电子与氦原子碰撞的P和D分波散射截面中的共振。此外，在正负电子偶素形成阈值和激发阈值的附近，我们还发现了分波散射截面以及总散射截面中的Wigner Cusp阈值行为，并对这些阈值结构形成的原因进行了分析。
Atomic and molecular physics is one of the most fundamental area in science and itsmost important task is to help us accurately understand the microcosmic structure ofmaterials and the basic interactions in many-body systems. Up to now, the accuratedescription of the many-body system and electron correlation effects is still a significantchallenge for the theorists in atomic and molecular physics. The study of positroncollisions with atoms and molecules is more an more interesting with the development ofthe positron experiment techniques in recent years. As an antimatter of electron, positronhas the exactly same mass, same but opposite charge with electron. The interactionsbetween the incident positron and target atom are much different from ones inelectron-atom scattering. The coulomb interaction between the nucleus and the projectileis repulsive, while the interaction between valcene electron and projectile is attractive,and most importantly, the exchange effect in electron-atom scattering is absent inpositron-atom scattering. Therefore, several new reaction channels exist in positron-atomscattering, such as the positronium formation process, positron-electron annihilation andelectron capture to continuum state, et al.. Due to the uniqe properties of positron, thepositron-atom scattering not only help us to understand the matter-antimatter interactions,but also provide us an useful tool to investigate the new scattering processes.
An important phenomeneon in positron-atom scattering is the resonance formation.Unlike the bound state formation, the positron is temporarily bound to the target atomand form an unstable qusi-bound state, i.e. resonance state. The primary reason for theresonance formation is that the positron moves in the attactive potential formed by theenergy degeneracy of excited target states and excited positronium bound states. As aresult, the resonance appears mostly below the atomic excitation thresholds and excitedpositronium formation thresholds. Such attactive potential is very sensitive to theelectron-elctron correlation and target polarization effects, thus the investigation of theresonance phenomenon would sheld light on the detailed information about the collisiondynamics, electron correlation and positron-atom interactions, et al..
The formation of these resonance states will lead to dramatical changes in thescattering cross sections and phase shifts, consequently, the study on the scattering crosssections would be an efficient and convinent way to predict the resonnace parameters.The close-coupling method is the most widly used method to calculate the positron-atomscattering cross sections until now. However, the omitting of the continuum states andutilizing pseudo-states in previous methods would cause significant difficults in predicting the resonances, such as the appearing of the pseudo-resonances anddemanding in computational time owing to the large number of pseudo-states. In thepresent work, we have investigated the resonance phenomena in positron scattering withhydrogen and complex atoms using the momentum-space coupled-channel opticalmethod. In the present model, the whole reaction space is split into P and Q space usingthe Feshbach projection vector P and Q. The states in P space are a finite set of discretechannels including the target ground state. The rest of discrete channels, the ionizationcontinuum and the positronium formation channels are included in the Q space. Thecross sections are obtained by solving the coupled-integral equations in P space and thecontribution of the Q space is included by introducing a complex polarization potentialW(Q). This method can take all the reaction channels into account and has been applied tocalculate various scattering cross sections. In the positronium polarization potential, wehave developed a new method to calculate the excited positronium formation. Forcomputational feasibility, we also use the equivalent local approximation and angularprojection approximation to solve the coupled-integral equations in P space. Finally thescattering cross sectons are obtained by intergrating the T-matrix elements.
In the present thesis, we have studied the resonance phenomena in the positronscattering with atomic hydrogen, alkali atom sodium and noble gas atom helium. Due tothe limitations on the intensity and accuracy of positron beam in experimentalinstruments, there is no direct observation of resonances in positron atom scattering. Fortheoretical part, many investigations have been focused on the resonances inpositron-hydrogen system and most of their work was limited to the lower partial waves,such as S-, P-and D-wave resonances. In the present investigations, we have calculatedthe partial-wave scattering cross sections and extracted the resonance position and widthin various partial waves. We have also predicted several new resonances, including thelowest S-wave resonance that has not been found by previous work, and located higherpartial-wave resonances, i.e. F-, G-, H-and I-wave. These resonances inpositron-hydrogen system are mostly caused by the attractive potential formed by theenergy degeneracy of excited hydrogen atom and positronium states. In addition, theresonance phenomena in differential cross sections of positron-hydrogen scattering havealso been investigated. This will give us more detailed information about the angulardistribution of the resonances.
Based on the previous work on hydrogen atom, we have also calculated theresonances in positron-sodium and positron-helium scatterings in the following twochapters. The effects of channel-coupling scheme, continuum polarization potential andpositronium formation channels on resonance parameters are investigated detailedly. Ithas been shown that the resonance positions moves to lower energies with increasing the channel-coupling scheme, which represents the convergence of the present calculations.For helium atom as target, we have firstly predicted the P-and D-wave resonances inpartial-wave scattering cross sections. The Winger Cusps, i.e. the threshold effect thatopening a new scattering channel may influence the cross sections in old channels, werefound just near the positronium formation and target excitation thresholds inpositron-helium scattering. The probably reason of such cusp behaviour was analysed inthe final chapter.
在正电子与原子碰撞过程中存在一个非常重要的现象就是形成共振态。与形成束缚态不同，正电子会暂时地束缚于靶原子，形成一个不稳定的准束缚态，称为共振态。共振态一般在原子的激发阈值以及激发态正负电子偶素阈值以下形成，其原因是由于入射正电子在激发态原子能级或者末态形成的激发态正负电子偶素能级简引起的势场中运动，受到势的吸引作用与靶原子形成临时的束缚态。由于正电子所感受到的这个势是电子-电子关联引起的极化势，因此对正电子共振现象的研究能够为我们提供正电子与原子散射中更详细的电子关联信息。
共振态的存在会在散射相移和散射截面中表现出剧烈的变化，因而研究散射截面能够预言共振位置和宽度等重要参数。目前广泛用于研究正电子原子碰撞散射截面的方法主要为密耦方法，在之前的理论模型中，一部分只考虑了靶的分立态之间的耦合而忽略连续态的作用，另外的大部分理论方法用伪态来描述连续态的作用。在研究共振时引入伪态会引起计算上的伪共振，并且由于需要大量的伪态来使结果达到收敛，因而计算会存在一定困难。本文的主要工作就是用发展的耦合通道光学势方法研究正电子与氢原子以及复杂原子散射的共振现象。在我们的方法中，引入一个极化势来描述碰撞过程中的连续态作用。使用Feshbach投影算符P和Q将整个反应空间分为P和Q两个互补的子空间，其中P空间包含靶原子基态在内的有限个分立态，Q空间包含剩余的分立态和连续态，其作用通过在势能项中附加一个复的极化势来描述。在描述正负电子偶素连续态的极化势中，我们发展了一种包含激发态正负电子偶素形成过程的计算方法，考虑了第一激发态正负电子偶素极化势对散射截面和共振的影响。为了计算的可行性，我们对这个极化势引入一个等价局域近似和角动量投影近似，通过联立求解P子空间中的通道耦合积分方程，得到各散射通道的T矩阵元，然后对T矩阵元进行积分得到各散射截面。
在本论文中，我们由简单到复杂依次研究了正电子与氢原子、碱金属中的钠原子和惰性气体中的氦原子散射中的共振现象。目前实验上受正电子束强度和精度的限制，对正电子散射共振的测量还存在一定的困难。对于理论方面的研究，大部分工作都集中在正电子与氢原子散射的研究，并且前人的主要工作都集中在S、P和D等低分波共振的研究。本文我们计算了正电子与氢原子碰撞的分波散射截面，研究了不同分波的共振位置和宽度。我们不仅确定了之前其它理论方法所预言的共振，还发现了许多新的共振，找到了目前为止能量位置最低的共振。除此之外我们还给出了F、G、H和I等高分波的共振。氢原子共振形成的主要原因是由激发态正负电子偶素和激发态氢原子能级简并形成的偶极极化势引起的。我们还研究了正电子碰撞氢原子的微分散射截面中的共振现象，首次给出了各共振态在散射空间中的角度分布情况。
在氢原子研究工作的基础上我们进一步研究了正电子与碱金属纳原子以及惰性气体氦原子散射的共振，分析了通道耦合数量、连续态极化势以及正负电子偶素形成通道对共振参数的影响。对于钠原子的研究表明共振位置随着耦合通道数量的增加而向低能区域移动，最终达到收敛。对于氦原子我们首次预言了正电子与氦原子碰撞的P和D分波散射截面中的共振。此外，在正负电子偶素形成阈值和激发阈值的附近，我们还发现了分波散射截面以及总散射截面中的Wigner Cusp阈值行为，并对这些阈值结构形成的原因进行了分析。
Atomic and molecular physics is one of the most fundamental area in science and itsmost important task is to help us accurately understand the microcosmic structure ofmaterials and the basic interactions in many-body systems. Up to now, the accuratedescription of the many-body system and electron correlation effects is still a significantchallenge for the theorists in atomic and molecular physics. The study of positroncollisions with atoms and molecules is more an more interesting with the development ofthe positron experiment techniques in recent years. As an antimatter of electron, positronhas the exactly same mass, same but opposite charge with electron. The interactionsbetween the incident positron and target atom are much different from ones inelectron-atom scattering. The coulomb interaction between the nucleus and the projectileis repulsive, while the interaction between valcene electron and projectile is attractive,and most importantly, the exchange effect in electron-atom scattering is absent inpositron-atom scattering. Therefore, several new reaction channels exist in positron-atomscattering, such as the positronium formation process, positron-electron annihilation andelectron capture to continuum state, et al.. Due to the uniqe properties of positron, thepositron-atom scattering not only help us to understand the matter-antimatter interactions,but also provide us an useful tool to investigate the new scattering processes.
An important phenomeneon in positron-atom scattering is the resonance formation.Unlike the bound state formation, the positron is temporarily bound to the target atomand form an unstable qusi-bound state, i.e. resonance state. The primary reason for theresonance formation is that the positron moves in the attactive potential formed by theenergy degeneracy of excited target states and excited positronium bound states. As aresult, the resonance appears mostly below the atomic excitation thresholds and excitedpositronium formation thresholds. Such attactive potential is very sensitive to theelectron-elctron correlation and target polarization effects, thus the investigation of theresonance phenomenon would sheld light on the detailed information about the collisiondynamics, electron correlation and positron-atom interactions, et al..
The formation of these resonance states will lead to dramatical changes in thescattering cross sections and phase shifts, consequently, the study on the scattering crosssections would be an efficient and convinent way to predict the resonnace parameters.The close-coupling method is the most widly used method to calculate the positron-atomscattering cross sections until now. However, the omitting of the continuum states andutilizing pseudo-states in previous methods would cause significant difficults in predicting the resonances, such as the appearing of the pseudo-resonances anddemanding in computational time owing to the large number of pseudo-states. In thepresent work, we have investigated the resonance phenomena in positron scattering withhydrogen and complex atoms using the momentum-space coupled-channel opticalmethod. In the present model, the whole reaction space is split into P and Q space usingthe Feshbach projection vector P and Q. The states in P space are a finite set of discretechannels including the target ground state. The rest of discrete channels, the ionizationcontinuum and the positronium formation channels are included in the Q space. Thecross sections are obtained by solving the coupled-integral equations in P space and thecontribution of the Q space is included by introducing a complex polarization potentialW(Q). This method can take all the reaction channels into account and has been applied tocalculate various scattering cross sections. In the positronium polarization potential, wehave developed a new method to calculate the excited positronium formation. Forcomputational feasibility, we also use the equivalent local approximation and angularprojection approximation to solve the coupled-integral equations in P space. Finally thescattering cross sectons are obtained by intergrating the T-matrix elements.
In the present thesis, we have studied the resonance phenomena in the positronscattering with atomic hydrogen, alkali atom sodium and noble gas atom helium. Due tothe limitations on the intensity and accuracy of positron beam in experimentalinstruments, there is no direct observation of resonances in positron atom scattering. Fortheoretical part, many investigations have been focused on the resonances inpositron-hydrogen system and most of their work was limited to the lower partial waves,such as S-, P-and D-wave resonances. In the present investigations, we have calculatedthe partial-wave scattering cross sections and extracted the resonance position and widthin various partial waves. We have also predicted several new resonances, including thelowest S-wave resonance that has not been found by previous work, and located higherpartial-wave resonances, i.e. F-, G-, H-and I-wave. These resonances inpositron-hydrogen system are mostly caused by the attractive potential formed by theenergy degeneracy of excited hydrogen atom and positronium states. In addition, theresonance phenomena in differential cross sections of positron-hydrogen scattering havealso been investigated. This will give us more detailed information about the angulardistribution of the resonances.
Based on the previous work on hydrogen atom, we have also calculated theresonances in positron-sodium and positron-helium scatterings in the following twochapters. The effects of channel-coupling scheme, continuum polarization potential andpositronium formation channels on resonance parameters are investigated detailedly. Ithas been shown that the resonance positions moves to lower energies with increasing the channel-coupling scheme, which represents the convergence of the present calculations.For helium atom as target, we have firstly predicted the P-and D-wave resonances inpartial-wave scattering cross sections. The Winger Cusps, i.e. the threshold effect thatopening a new scattering channel may influence the cross sections in old channels, werefound just near the positronium formation and target excitation thresholds inpositron-helium scattering. The probably reason of such cusp behaviour was analysed inthe final chapter.
引文
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