Helium nuclear charge

The value of C, as has been explained, depends upon the nuclear charge less the screening effect of other electrons. For the K series of X-ray frequencies it varies nearly as Z. As the degree of ionization of the atom increases with more intense methods of spectral excitation, for example, passage from flame spectra to spark spectra, G increases. For the spectrum of ionized helium (nuclear charge 2, one electron) it is four times the value for hydrogen (nuclear charge... 

The reactions of deuterium, tritium, and helium-3 [14762-55-17, He, having nuclear charge of 1, 1, and 2, respectively, are the easiest to initiate. These have the highest fusion reaction probabiUties and the lowest reactant energies. 

Since the nucleus has positive charge, it attracts electrons (each with negative charge). If a nucleus attracts the number of electrons just equal to the nuclear charge, an electrically neutral atom is formed. Consider a nucleus containing two protons, a helium nucleus. When the helium atom has two electrons as well (2— charge), an electrically neutral helium atom results ... 

The helium atom has the highest ionization potential of any atom. It has a nuclear charge of + 2, and the electrons reside in the lowest energy level close to the nucleus. 

Figure 5.10 The variation of the autoionization width of the helium nq = n2 = 2 resonances of even parity as a function of nuclear charge, Z. The three dashed lines show the widths for the 2p2 3P resonances that cannot autoionize nonrelativistically, short dashed line [J = 0), long dashed line (J = 1), and long-short dashed line (J = 2). The three solid lines show the width of the three resonances for which autoionization is nonrelativistically allowed for comparison. A logarithmic scale is used to highlight the Z-dependence.

As mentioned previously, parameter a may be viewed as the effective nuclear charge felt by either one of the two electrons. Such an interaction is commonly called the screening effect. Furthermore, as described by this wavefunction, the two electrons move independently of each other, i.e., angular correlation is ignored. Electron correlation may be taken as the tendency of the electrons to avoid each other. For helium, angular correlation describes the two electrons inclination to be on opposite sides of the nucleus. On the other hand, radial correlation, or screening effect, is the tendency for one electron to be closer to the nucleus, while the other one is farther away. A one-parameter trial function that does take angular correlation into account is... 

Recall i/fa assumes that both electrons in helium experience the same effective nuclear charge a. While this may be so in an average sense, such an approximation fails to take into account that, at a given instant, the two electrons are not likely to be equidistant from the nucleus and hence the effective nuclear charges they feel should not be the same. Taking this into consideration, C. Eckart proposed the following trial function in 1930 ... 

This equation cannot be solved exactly. The most often used approximation model to solve this equation is called the self-consistent field (SCF) method, first introduced by D. R. Hartree and V. A. Fock. The physical picture of this method is very similar to our treatment of helium each electron sees an effective nuclear charge contributed by the nuclear charge and the remaining electrons. 

There are two basic approaches to the theory of atomic helium, depending on whether the nuclear charge Z is small or large. For low-Z atoms and ions, the principal challenge is the accurate calculation of nonrelativistic electron correlation effects. Relativistic corrections can then be included by perturbation theory. For high-if ions, relativistic effects become of dominant importance and must be taken into account to all orders via the one-electron Dirac equation. Corrections due to the electron-electron interaction can then be included by perturbation theory. The cross-over point between the two regimes is approximately Z = 27... 

The nuclear charge in Fig. 10.2 is not specified in order to be able to describe any other member of the two-electron iso-electronic family, such as H , Li" ", etc. For helium, Z — 2. Even when focussing on a specific two-electron atom or ion we would like to keep the nuclear charge Z variable in order to study the sensitivity of bound states and resonances to small changes of Z. This topic is covered in Section 10.5.2. 

The apparent nuclear charge, or the effective nuclear charge, is designated Zeff. For a helium atom Zeff, the charge experienced by each electron, is less than 2. In general,... 

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