Abstract
The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li<sup>+</sup>, and Be<sup>2+</sup> in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.
Highlights
The most atomic theories arise from the independent electron shell model which assumes that every electron is moving in a field combined of the nucleus and the mean distribution of the other electrons
The results provided good alternative approaches for the calculation of the ground state energy for a strongly confined helium atom
The results of calculating the ground state energies of the helium and helium like ions by using the first trial wave function showed that the best value of the energy obtained for (F = − 0.14) and (S = 0.26)
Summary
The most atomic theories arise from the independent electron shell model which assumes that every electron is moving in a field combined of the nucleus and the mean distribution of the other electrons In this model, the effect of two-electron repulsion neglected. The ground state of helium and its ions calculated by using wave functions from the orbital product times correlated function depending on the distance between the two electrons. These wave functions depend on several variable parameters, which should satisfy the variational principle to give improved values for energies.
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