论文标题
静止磁场中的两体中性库仑系统：从氢原子到正电子
Two-body neutral Coulomb system in a magnetic field at rest: from Hydrogen atom to positronium
论文作者
论文摘要
A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field for the states of positive and negative parity, ${(1s_0)}$ and ${(2p_0)}$, respectively.结果表明，通过保持一个固定的物体的质量和电荷，所有具有不同体重不同的系统都是相关的。这使人们可以将第二个身体视为无限质量的，并将这样的系统视为基本。详细考虑了三个物理系统：具有（in）的氢原子（deuteron，triton）和阳性原子$（ - e，e）$。我们得出了分别描述小和大距离的域的riccati-bloch和广义式方程。基于波函数对数的小距离行为的插值，提出了一个紧凑的10参数函数。作为一个变异试验功能，它提供了不少于6个有效数字（s.d.）（$ \ lyssim 10^{ - 6} $的相对偏差）的准确性，用于整个被考虑的磁场的总能量$ [0 \ ,, \ ,, 10^4] $ A.U.而且不少于3 s.d.对于四极力矩$ q_ {zz} $。为了获得参考点，使用16k网格点的拉格朗日网格方法从10到6 s.d。在从小到大磁场的能量中。基于riccati-bloch方程，计算了以理性数字的形式的能量的前100个扰动系数，并使用Padé-borel重新点击步骤，发现能量的能量不少于10 s.d。在磁场上，$ \ leq 1 $ \，A.U。
A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field for the states of positive and negative parity, ${(1s_0)}$ and ${(2p_0)}$, respectively. It is shown that by keeping the mass and charge of one of the bodies fixed, all systems with different second body masses are related. This allows one to consider the second body as infinitely-massive and to take such a system as basic. Three physical systems are considered in details: the Hydrogen atom with (in)-finitely massive proton (deuteron, triton) and the positronium atom $(-e,e)$. We derive the Riccati-Bloch and Generalized-Bloch equations, which describe the domains of small and large distances, respectively. Based on the interpolation of the small and large distance behavior of the logarithm of the wavefunction, a compact 10-parametric function is proposed. Taken as a variational trial function it provides accuracy of not less than 6 significant digits (s.d.) ($\lesssim 10^{-6}$ in relative deviation) for the total energy in the whole domain of considered magnetic fields $[0\,,\,10^4]$ a.u. and not less than 3 s.d. for the quadrupole moment $Q_{zz}$. In order to get reference points the Lagrange Mesh Method with 16K mesh points was used to get from 10 to 6 s.d. in energy from small to large magnetic fields. Based on the Riccati-Bloch equation the first 100 perturbative coefficients for the energy, in the form of rational numbers, are calculated and, using the Padé-Borel re-summation procedure, the energy is found with not less than 10 s.d. at magnetic fields $\leq 1$\,a.u.
