In this paper, we present an analytical procedure to determine the effective charge and ground-state energy of a four-electron beryllium atom. The procedure followed is based on a variant of variational technique using modified hydrogenic one-electron wave function to calculate effective charge in 1s and 2s states of beryllium atom. The effective charge in 1s state is 3.68609 and in 2s state is 1.82362. Further, we have used these values in non-relativistic Hamiltonian with interaction terms to calculate the ground-state energy of beryllium atom. The estimated value of ground-state energy (− 14.3423 au) is in good agreement with the experimental results and with other theoretically obtained values. The calculated results without using any computationally intensive technique are the essence of this research work.

在本文中，我们提出了一种分析程序，以确定四电子铍原子的有效电荷和基态能量。遵循的程序基于变分技术的一种变体，使用改进的氢一电子波函数计算铍原子在1s和2s状态下的有效电荷。1s状态下的有效电荷为3.68609，2s状态下的有效电荷为1.82362。此外，我们已使用非相对论哈密顿量中的这些值以及相互作用项来计算铍原子的基态能。基态能量的估计值（− 14.3423 au）与实验结果以及其他理论上获得的值非常吻合。不使用任何计算密集型技术的计算结果是这项研究工作的本质。