Helium atom variation treatment

The value of the polarizability a of an atom or molecule can be calculated by evaluating the second-order Stark effect energy — %aF2 by the methods of perturbation theory or by other approximate methods. A discussion of the hydrogen atom has been given in Sections 27a and 27e (and Problem 26-1). The helium atom has been treated by various investigators by the variation method, and an extensive approximate treatment of many-electron atoms and ions based on the use of screening constants (Sec. 33a) has also been given.3 We shall discuss the variational treatments of the helium atom in detail. 

Hass6 has considered five variation functions of this form, shown with their results in Table 47-2. The success of his similar treatment of the polarizability of helium (function 6 of Table 29-3) makes it probable that the value — 1.413e2aj /i28 for W" is not in error by more than a few per cent. Slater and Kirkwood1 obtained values 1.13, 1.78, and 1.59 for the coefficient of — e2al/R6 by the use of variation functions based on their helium atom functions mentioned in Section 29e. An approximate discussion of dipole-quadrupole and quadrupole-quadrupole interactions has been given by Margenau.1... 

Table 47-2.—Variation Treatment of van der Waals Interaction of Two Helium Atoms...

The best orbitals which have been obtained were found by a different method of approach. This method is similar to that used in the variational treatment of the helium atom hydrogenlike orbitals are given up completely. For the [2" ion, the natural coordinates to use are the elliptical coordinates /x, v, [Pg.201]

The Bohr model gave the correct energies for the hydrogen atom but failed when applied to helium. Hence, in the early days of quantum mechanics, it was important to show that the new theory could give an accurate treatment of helium. The pioneering work on the helium ground state was done by Hylleraas in the years 192 1930. To allow for the effect of one electron on the motion of the other, Hylleraas used variational functions that contained the interelectronic distance ri2- One function he used is... 

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