Helium atom theory

In this section we examine the ground-state energy of the helium atom by means of both perturbation theory and the variation method. We may then compare the accuracy of the two procedures. 

Modem atomic theory teaches that an atom is made up of positively charged protons, an equal number of negatively charged, i much, much tinier electrons, and varying numbers of uncharged j neutrons. Each element has a definite number of protons, and no other element can have that same number. For example, the element hydrogen has one, helium has two, lithium, three, and so on. The number of protons in the nucleus, or center, of each atom, is called the atomic number of the element. 

Bohr next applied his theory to helium ions—helium atoms in which one of the two electrons is removed—and again the predictions of the theory exactly matched results obtained in experiments. The scientific world was convinced. For example, when Einstein heard of the results, he reversed himself and said, This is a tremendous achievement—Bohr s theory must be right. ... 

The corrugation of the charge density on metal surfaces can be obtained from first-principles calculations or helium scattering experiments. The theory and the experiments match very well. A helium atom can reach to about 2.5-3 A from the top-layer nuclei. At that distance, the repulsive force between the helium atom and the surface is already strong. The corrugation at that distance is about 0.03 A, from both theory and experiments. For STM,... 

Peterson (reference listedl reported in early 1991 dial researchers at Harvard University made what is considered a remarkable prediction regarding the energy-level transitions that occur in a helium atom. The agreement between theoretical calculations and experimental results show lhat computational methods lor constructing a model of a Iwo-cleciron atom am work, thus bridging the gap between theory and practice. 

One of the more important conclusions from kinetic-molecular theory comes from assumption 5—the relationship between temperature and EK, the kinetic energy of molecular motion. It can be shown that the total kinetic energy of a mole of gas particles equals 3RT/2 and that the average kinetic energy per particle is thus 3RT/2Na, where NA is Avogadro s number. Knowing this relationship makes it possible to calculate the average speed u of a gas particle. To take a helium atom at room temperature (298 K), for example, we can write... 

The classical theory of a many-electron atom would be an even harder proposition. At least with the planets, their gravitational forces on each other are much smaller than the attraction to the Sun. Atomic forces ate electrostatic, not gravitational, and proportional therefore to the charges on particles. The repulsion between negatively charged electrons is comparable in its combined effect to their attraction to the nucleus. Even in a two-electron helium atom, the classical trajectories of electrons would be extraordinarily complicated, and would not even approximately resemble the elliptical motion of the single particle. 

Following the development of quantum theory by Heisenberg [1] and Schrodinger [2] and a few further discoveries, the basic principles of the structure of atoms and molecules were described around 1930. Unfortunately, the complexity of the Schrodinger equation increases dramatically with the number of electrons involved in a system, and thus for a long time the hydrogen and helium atoms and simple molecules as H2 were the only species whose properties could really be calculated from these first principles. In 1929, Dirac [3] wrote ... 

He, because a helium atom is much smaller than a sulfur hexafluoride molecule, which better approximates the first tenet of the kinetic molecular theory of gases. 

The study of the interactions among closed shell systems (van der Waals forces) represents a benchmark for theories of electron correlation. We report here the results of our variational MO-VB study of the interaction between two helium atoms [70]. Up to n=10 optimal virtuals are calculated and employed to generate MO-VB final wavefunctions of higher and higher accuracy, in the usual MO-VB form ... 

With the recent advances in atomic theories and experimental techniques, the value of the information obtained from studies of atoms that are different from but similar to atomic hydrogen have increased. These studies include atomic helium, muonic hydrogen, positronium, muonium, antihydrogen, moderate Z ions, high Z ions, antiprotonic atoms and muonic atoms. 

Abstract. Laser spectroscopy of hydrogen-like and helium-like ions is reviewed. Emphasis is on the fast-beam laser resonance technique, measurements in moderate-/ ions which provide tests of relativistic and quantum-electrodynamic atomic theory, and future experimental directions. 

Precision measurement of energy intervals in hydrogen and helium has been fundamental to the development of atomic theory. Relativistic and quantum-electrodynamic contributions scale with various powers of Z. Hence more information is gained by extending precise measurements to one- and two-electron ions. Laser spectroscopy is restricted to certain special transitions which fall in the infrared, visible or near-ultraviolet, and from which a useful signal can be obtained. However, where applicable, it provides precision tests of theory. The focus of this review is laser spectroscopy of the n = 2 levels of moderate-Z helium-like and hydrogen-like ions. Previous reviews may be found in [1,2,3],... 

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