arXiv 2011.124222020-11-10quant-phhep-th

强磁场中氢原子能级的饱和

Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field

T. C. Adorno, D. M. Gitman, A. E. Shabad

备注：: 20 pages, 4 pictures. Published version
发表信息：: Universe 2020, 6, 204
DOI：: 10.3390/universe6110204

摘要：

我们证明了在磁场的无限制增长下氢原子的低能级极限值的有限性，当真空极化（VP）在欧拉-海森堡局域作用量近似下在磁场中计算时，已经实现了这个原子被嵌入其中。我们发现，这种饱和的机制是不同的，从一个代理，当VP计算通过费曼图在毛茸茸的图片。我们研究了在绝热（对角）近似下求解原子中最低朗道能级上电子纵向自由度的薛定谔方程时出现的有效势。我们发现，（有效）潜力的点状电荷保持非奇异感谢VP提供的日益增长的屏蔽。正则化长度是$\sqrt{α/3π}\lambdabar_{\mathrm{C}}$，其中$\lambdabar_{\mathrm{C}}$是电子康普顿长度。以磁场的增长值为标记的有效势族朝着某个极限的、与磁场无关的势-距离曲线凝聚。本文用Karnakov-Popov方法确定了四个磁量子数的偶基态能量的极限值。

英文摘要：

We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization (VP) is calculated in the magnetic field within the approximation of the local action of Euler--Heisenberg. We find that the mechanism for this saturation is different from the one acting, when VP is calculated via the Feynman diagram in the Furry picture. We study the effective potential that appears when the adiabatic (diagonal) approximation is exploited for solving the Schrödinger equation for the longitudinal degree of freedom of the electron on the lowest Landau level in the atom. We find that the (effective) potential of a point-like charge remains nonsingular thanks to the growing screening provided by VP. The regularizing length turns out to be $\sqrt{α/3π}\lambdabar_{\mathrm{C}}$, where $\lambdabar_{\mathrm{C}}$ is the electron Compton length. The family of effective potentials, labeled by growing values of the magnetic field condenses towards a certain limiting, magnetic-field-independent potential-distance curve. The~limiting values of even ground-state energies are determined for four magnetic quantum numbers using the Karnakov--Popov method.

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