【正文】 The twobody problem was analyzed by Johannes Kepler in 1609 and solved by Isaac Newton in 1687. The threebody problem, on the other hand, is much more plicated and cannot be solved analytically, except in some particular cases. In 1765, for instance, Leonhard Euler discovered a “collinear” solution in which three masses start in a line and remain linedup. Some years later, Lagrange discovered the existence of five equilibrium points, known as the Lagrange points. Even the most recent quests for solutions of the threebody scattering problem use similar mathematical tools and follow similar paths than those travelled by astronomers and mathematicians in the past three centuries. For instance, in the centerofmass reference system, we describe the threebody problem by any of the three possible sets of the spatial coordinates already introduced by Jacobi in 1836. All these pairs are related by lineal point canonical transformations, as described in [1]. In momentum space, the system is described by the associated pairs (kT,KT), (kP,KP) and (kN,KN). Switching to the Laboratory reference frame, the final momenta of the electron of mass m, the (recoil) target fragment of mass MT and the projectile of mass MP can be written in terms of the Jacobi impulses Kj by means of Galilean transformations [1]For decades, the theoretical description of ionization processes has assumed simplifications of the threebody kinematics in the final state, based on the fact that ? in an ion–atom collision, one particle (the electron) is much lighter than the other two,? in an electron–atom or positron–atom collision, one particle (the target nucleus) is much heavier than the other two.For instance, based on what is known as Wick’s argument, the overwhelming majority of the theoretical descriptions of ion–atom ionization collisions uses an impactparameter approximation, where the projectile follows an undisturbed straight line trajectory throughout the collision process, and the target nucleus remains at rest [2]. It is clear that to assume that the projectile follows a straight line trajectory makes no sense in the theoretical description of electron or positron–atom collisions. However, it is usually assumed that the target nucleus remains motionless. These simplifications of the problem were introduced in the eighteenth century. The unsolvable threebody problem was simplified, to the socalled restricted threebody problem, where one particle is assumed to have a mass small enough not to influence the motion of the other two particles. Though introduced as a means to provide approximate solutions to systems such as Sun–planet–et within a Classical Mechanics framework, it has been widely used in atomic physics in the socalled impactparameter approximation to ion–atom ionization collisions. Another simplification of the threebody problem widely employed in the nineteenth century assumes that one of the particles is much more massive than the other two and remains in the center of mass unperturbed by the other two. This approximation has been widely used in electron–atom or positron–atom ionization collisions. 2. The multiple differential cross section A kinematically plete description of a threebody continuum finalstate in any atomic collision would require, in principle, the knowledge of nine variables, such as the ponents of the momenta associated to each of the three particles in the final state. However, the condition of momentum and energy conservation reduces this number to five. Furthermore, whenever the initial targets are not prepared in any preferential direction, the multiple differential cross section has to be symmetric by a rotation of the threebody system around the initial direction of motion of the projectile. Thus, leaving aside the internal structure of the three fragments in the final state, only four out of nine variables are necessary to pletely describe the scattering process. Therefore, a plete characterization of the ionization process may be obtained with a quadruple differential cross section:There are many possible sets of four variables to use. For, instance, we can chose azimuthal angles of the electron and of one of the other two particles, the relative angle between the planes of motion, and the energy of one particle.Such a choice is arbitrary, but plete in the sense that any other set of variables can be related to this one. A similar choice of independent variables has been standard for the description of atomic ionization by electron impact, both theoretically and experimentally [3] and [4]. A picture of the very general quadruple differential cross section is not feasible. Thus, it is usually necessary to reduce the number of variables in the cross section. This can be achieved by fixing one or two of them at certain particular values or conditions. For instance, we might arbitrarily restrict ourselves to describe a coplanar (. Wannier。 Positron impact。 Electron spectra。 Collision dynamics。橫剖面也許會被很多巨大的困難所阻礙, 但值得高興的是, 我們一直沒有錯過對問題許多不同的全方位的觀察, 唯一的遺憾就是對總橫剖面的研究。 終于, 有被解釋對象由于所謂的備鞍點 電離機(jī)制的極小值。 你是知名的電子捕獲對連續(xù)流峰頂。 圖 58. 結(jié)論 總結(jié)結(jié)果提出了在這通信, 我們由正子的沖擊調(diào)查了分子氫的電離。 圖5 表示, 結(jié)構(gòu)完全出現(xiàn)從tp 期限。 圖3 和圖4 精確地設(shè)置早先條件在任何能量和角度三個微粒符合的那些點。 這個機(jī)制被描述在圖4. 因而, 檢查備鞍點的提案是正確的, 我們看是否我們的演算顯示與備鞍點電子生產(chǎn)的這個描述是一致的結(jié)構(gòu)。 能量和動量保護(hù)原則的應(yīng)用表示, 正子偏離在角度 終于, 為電子涌現(xiàn)在方向和正子一樣, 它必須遭受隨后碰撞以殘余中堅力量在a 托馬斯象過程。 在 離子原子碰撞案件, 查尋這個機(jī)制的理論和實驗性證據(jù)是陰暗由生動的爭論[ 1418 ] 。 想法是, 電子能從離子原子碰撞涌現(xiàn)由在在子彈頭和殘余的目標(biāo)離子潛力的備鞍點。7. 備鞍點機(jī)制  一定更難辨認(rèn)。 但有其它結(jié)構(gòu), 。 在這種情況下, 從電子和正子大量是相等的, 這兩個過程干涉在45 。 每個這些過程包括正子電子二進(jìn)制碰撞, 被偏折跟隨被90 輕的微粒的當(dāng)中一個被重的中堅力量。6. 托馬斯機(jī)制 現(xiàn)在讓我們走回到H2 的電離由1 keV 正子沖擊。 他們第一次測量了四倍有差別的電離橫剖面在collinear 幾何為離子原子碰撞, 并且發(fā)現(xiàn)ECC 尖頂和在正子沖擊在大角度。 從目標(biāo)反沖不充當(dāng)在這個實驗性情況的重大角色, 當(dāng)前一般理論給結(jié)果相似與那些由Berakdar [ 11 ] 獲得, 并且兩個跟隨嚴(yán)密實驗性價值。Kover 和Laricchia 測量了在1998 dr/dEedXkdXK 橫剖面在一個collinear 情況在零的程度, 為H2 的電離分子由100 keV 正子沖擊[ 10 ] 。 因而, 觀察這結(jié)構(gòu)它是必要增加橫剖面的維度。 并且這一定是如此。 這爭執(zhí)的原因是那, 與離子對比盒, 正子外出的速度與那不是相似沖擊