论文标题
强磁场中氢原子能量水平的饱和
Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field
论文作者
论文摘要
我们证明，在无限制的磁场生长下，嵌入该原子的氢原子的较低能级的限制值已经在磁场近似Euler-Heisenberg的局部作用的近似值内计算出来。我们发现，当通过毛茸茸的图片中的Feynman图计算VP时，这种饱和的机制与表演的机制不同。我们研究了利用绝热（对角线）近似来解决schrödinger方程时出现的有效潜力，以在原子中最低的Landau水平上的纵向电子自由度。我们发现，由于VP提供的增长筛选，点状电荷的（有效）潜力仍然是非发挥作用的。正规化长度被证明为$ \ sqrt {α/3π} \ lambdabar _ {\ mathrm {c}} $，其中$ \ lambdabar _ {\ mathrm {c}} $是电子综合长度。有效电位的家族被磁场的增长值凝结到一定限制的，磁场无关的电势距离曲线。使用Karnakov-Popov方法确定了四个磁量子数的〜限制值。
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.
