H 2 + molecular ion in a strong magnetic field: Ground state
H 2 + molecular ion in a strong magnetic field: Ground state
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DOI：
10.1103/physreva.68.012504
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发表时间：
2002-12
影响因子：
2.9
通讯作者：
J. Vieyra;A. Turbiner
中科院分区：
文献类型：
--
作者：
J. Vieyra;A. Turbiner
从${10}^{9}\char21{}4.414\ifmmode\times\else\texttimes\fi{}{10}^{13}\mathrm{G}$理论出发，对磁场中两质子一电子系统进行了详细的定量分析。本文主要研究磁场中分子离子的存在问题。采用矢量势形式最优化(最优规范确定)的变分方法作为工具。结果表明，在非相对论近似的适用范围内，Born-Oppenheimer近似下的(PPE)系统在有限质子间距离处的总能量有一个非常明显的最小值，从而证明了${\mathm{H}}_{2}^{+}的存在。$对于$B确保数学{\gtrsim}{10}^{11}\mathm{G}$，最小值消失，因此分子离子${\mathm{H}}_{2}^{+}$不存在。结果表明，最稳定的组态总是位于磁力线上的质子。随着磁场的增大，离子的束缚越来越紧密，电子分布由双峰演化为单峰。离子存在的倾斜域随着磁场的增加而减小，最终在与化学反应开始有关的一些质子间距离的变分参数的$0\ifmmode^\circ\else\textdegree\fi{}\char21{}25\ifmmode^\circ\else\textdegree\fi{}$相变型行为在$B=4.414\ifmmode\times\else\texttimes\fi{}{10}^{13}\mathrm{G}.$找到了H}}_{2}^{+}\ensuremath{\leftrightarrow}\mathrm{H}+p$。
A detailed quantitative analysis of the system of two protons and one electron (ppe) placed in magnetic field ranging from ${10}^{9}\char21{}4.414\ifmmode\times\else\texttimes\fi{}{10}^{13}\mathrm{G}$ is presented. The present study is focused on the question of the existence of the molecular ion ${\mathrm{H}}_{2}^{+}$ in a magnetic field. A variational method with an optimization of the form of the vector potential (optimal gauge fixing) is used as a tool. It is shown that in the domain of applicability of the nonrelativistic approximation the (ppe) system in the Born-Oppenheimer approximation has a well-pronounced minimum in the total energy at a finite interproton distance for $B\ensuremath{\lesssim}{10}^{11}\mathrm{G},$ thus manifesting the existence of ${\mathrm{H}}_{2}^{+}.$ For $B\ensuremath{\gtrsim}{10}^{11}\mathrm{G}$ and large inclinations (of the molecular axis with respect to the magnetic line) the minimum disappears and hence the molecular ion ${\mathrm{H}}_{2}^{+}$ does not exist. It is shown that the most stable configuration of ${\mathrm{H}}_{2}^{+}$ always corresponds to protons situated along the magnetic line. With magnetic field growth the ${\mathrm{H}}_{2}^{+}$ ion becomes more and more tightly bound and compact, and the electronic distribution evolves from a two-peak to a one-peak pattern. The domain of inclinations where the ${\mathrm{H}}_{2}^{+}$ ion exists reduces with magnetic field increase and finally becomes $0\ifmmode^\circ\else\textdegree\fi{}\char21{}25\ifmmode^\circ\else\textdegree\fi{}$ at $B=4.414\ifmmode\times\else\texttimes\fi{}{10}^{13}\mathrm{G}.$ Phase-transition-type behavior of variational parameters for some interproton distances related to the beginning of the chemical reaction ${\mathrm{H}}_{2}^{+}\ensuremath{\leftrightarrow}\mathrm{H}+p$ is found.