A detailed quantitative analysis of the system $(ppe)$ placed in magnetic field ranging from $0 - 4.414 \times 10^{13} G$ is presented. The present study is focused on the question of the existence of the molecular ion $H_2^{+}$ in a magnetic field. As a tool, a variational method with an optimization of the form of the vector potential (optimal gauge fixing) is used. It is shown that in the domain of applicability of the non-relativistic approximation the system $(ppe)$ in the Born-Oppenheimer approximation has a well-pronounced minimum in the total energy at a finite interproton distance for $B \lesssim 10^{11} G$, thus manifesting the existence of $H_2^{+}$. For $B \gtrsim 10^{11} G$ and large inclinations (of the molecular axis with respect to the magnetic line) the minimum disappears and hence the molecular ion $H_2^{+}$ does not exist. It is shown that the most stable configuration of $H_2^{+}$ always corresponds to protons situated along the magnetic line. With magnetic field growth the ion $H_2^{+}$ 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 $H_2^{+}$ ion exists reduces with magnetic field increase and finally becomes $0^o - 25^o$ at $B = 4.414 \times 10^{13} G$. Phase transition type behavior of variational parameters for some interproton distances related to the beginning of the chemical reaction $H_2^{+} \leftrightarrow H + p$ is found.
展开▼
机译:给出了对放置在磁场中的系统$(ppe)$的详细定量分析,该磁场的范围为$ 0-4.414×10 ^ {13} G $。本研究集中在磁场中存在分子离子$ H_2 ^ {+} $的问题。作为一种工具,使用了一种变分方法,该方法优化了矢量电势的形式(最佳量规固定)。结果表明,在非相对论近似的适用范围内,Born-Oppenheimer近似中的系统$(ppe)$在$ B \ lesssim 10 ^的有限质子距离处的总能量中具有最低的发音。 {11} G $,因此表明存在$ H_2 ^ {+} $。对于$ B \ gtrsim 10 ^ {11} G $和(分子轴相对于磁力线的)大倾角,最小值消失了,因此分子离子$ H_2 ^ {+} $不存在。结果表明,最稳定的$ H_2 ^ {+} $构型始终对应于沿磁力线分布的质子。随着磁场的增长,离子$ H_2 ^ {+} $变得越来越紧密且紧密,电子分布从两峰到一峰。随着磁场的增加,存在$ H_2 ^ {+} $离子的倾斜范围减小,最终在$ B = 4.414×10 ^ {13} G $时变为$ 0 ^ o-25 ^ o $。发现与化学反应的开始有关的一些质子距离的变参数的相变类型行为$ H_2 ^ {+} \ leftrightarrow H + p $。
展开▼