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arXiv 0907.2614quant-ph
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双电子原子、离子和分子

Two-electron atoms, ions and molecules

Hallstein Hogaasen, Jean-Marc Richard, Paul Sorba

摘要:

从中心荷为$Z\ge 2$的氦原子和类氦离子基态出发,综述了双电子系统的量子力学。对于Z=1,证明负氢离子H $^-$的稳定性,不能仅仅使用单个电子波函数的乘积来实现,而是需要明确说明两个电子之间的相互关系。重新讨论了由Eschrasekhar提出的波函数,其中置换对称性首先被破缺,然后由一个反项恢复。用同样的策略可以研究更微妙的问题:质子与电子质量比$M/m$为任意值时,类氢离子$(M^+,m^-,m^-)$的稳定性;氦和类氦离子最低自旋三重态的能量;具有非自然宇称的双激发氢离子的稳定性。正电子素分子$(e^+,e^+,e^-,e^-)$在几年前就被预测到了,最近才被发现,它也可以被证明对自发解离是稳定的,尽管计算有点复杂。重点讨论了对称性破缺对系统稳定性的影响。

英文摘要:

The quantum mechanics of two-electron systems is reviewed, starting with the ground state of the helium atom and helium-like ions, with central charge $Z\ge 2$. For Z=1, demonstrating the stability of the negative hydrogen ion, H$^-$, cannot be achieved using a mere product of individual electron wave functions, and requires instead an explicit account for the anticorrelation among the two electrons. The wave function proposed by Chandrasekhar is revisited, where the permutation symmetry is first broken and then restored by a counter-term. More delicate problems can be studied using the same strategy: the stability of hydrogen-like ions $(M^+,m^-,m^-)$ for any value of the proton-to-electron mass ratio $M/m$; the energy of the lowest spin-triplet state of helium and helium-like ions; the stability of the doubly-excited hydrogen ion with unnatural parity. The positronium molecule $(e^+,e^+,e^-,e^-)$, which has been predicted years ago and discovered recently, can also be shown to be stable against spontaneous dissociation, though the calculation is a little more involved. Emphasis is put on symmetry breaking which can either spoil or improve the stability of systems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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