Abstract

A muonic hydrogen-like atom is formed when replacing the electron in it by a negative muon \(\mu ^-\). The Schrödinger equation corresponds to the one of the atoms with a binding particle \((\mu ^-)\) with mass \(M_{\mu } \approx 207m_e\), where \(m_e\) is the electron mass. The muon, in comparison with the electron, moves along an orbit which remains much closer to the nucleus and the associated binding energy is considerably increased. In this report, we have studied how the ground state energy changes for H, \(He^{+}\) and \(Li^{+2}\) muonic atoms when subjected to very high compression. In order to simulate such a compression regime for the atoms, we have considered two confinement models: In the first, we assume for each system a nuclear point mass, whereas in the second the nucleus consists of a finite volume with a uniformly distributed charge. The energy correction due to the nucleus finite size is carried out at first-order perturbation theory. We found that the maximum of the energy correction becomes more important as the confinement and mass number of the atom nucleus grow.

Graphic abstract

中文翻译：

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密闭的类氢原子

摘要

当用负μon （\ mu ^-\）替换其中的电子时，会形成一个类似氢的离子型原子。薛定ding方程对应于具有质量为\（M _ {\ mu} \ approx 207m_e \）的结合粒子\（（\ mu ^-）\）的原子之一，其中\（m_e \）为电子质量。与电子相比，该介子沿着保持更接近原子核的轨道运动，并且相关的结合能大大增加。在此报告中，我们研究了H，\（He ^ {+} \）和\（Li ^ {+ 2} \）的基态能量如何变化受到极高压缩的非离子原子。为了模拟原子的压缩方式，我们考虑了两个限制模型：第一个，我们为每个系统假设一个核点质量，而第二个，原子核由有限体积的电荷均匀分布组成。由于原子核尺寸有限而进行的能量校正是在一阶微扰理论下进行的。我们发现，随着原子核的约束和质量数的增长，能量校正的最大值变得越来越重要。

图形摘要