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46 Helium Now we need to calculate the perturbation produced by the electron– electron repulsion. The system has the spatial wav ...
3.2 Excited states of helium 47 Another wavefunction has the same energy, namely ψspace=u1s(2)unl(1). (3.9) These two states are ...
48 Helium Fig. 3.1The direct integral in a 1sns configuration of helium corresponds to the Coulomb repulsion between two spheric ...
3.2 Excited states of helium 49 (a) (b) (c) Fig. 3.3An illustration of degenerate perturbation in a classical system. (a) Two ha ...
50 Helium − 25 − 20 − 10 − 5 − 15 −13.6 0 5 768 9 4 3 2 1 Helium H Fig. 3.4The energy levels of the helium atom with those of hy ...
3.2 Excited states of helium 51 to construct the symmetrised wavefunctionsψAspaceandψSspace.^13 In this^13 For two electrons, sw ...
52 Helium are^1 Land^3 L, e.g. the 1s2s configuration in helium gives rise to the (^16) The letter ‘S’ appears over-used in term ...
3.3 Evaluation of the integrals in helium 53 − − − − − Fig. 3.5The allowed transitions be- tween the t ...
54 Helium The spherical symmetry of s-electrons means that the charge in the regionr 1 <r 2 acts like a point charge at the o ...
3.3 Evaluation of the integrals in helium 55 did the calculation as described in Bethe and Salpeter (1957) or Bethe and Salpeter ...
56 Helium unlm=Rnl(r)Ylm(θ, φ) only the radial part depends onZ.Wewrite the exchange integral as (cf. eqn 3.28) K1snl= e^2 4 π ...
3.3 Evaluation of the integrals in helium 57 electrons; and (b) a discussion of the influence of identical particles on the stat ...
58 Helium Exercises More advanced problems are indicated by a *. (3.1)Estimate of the binding energy of helium (a) Write down th ...
Exercises for Chapter 3 59 otic particles bound to a helium nucleus (and no electrons). [Hint.It is not necessary to specify the ...
The alkalis 4 4.1 Shell structure and the periodic table 60 4.2 The quantum defect 61 4.3 The central-field approximation 64 4.4 ...
4.2 The quantum defect 61 Table 4.1Ionization energies of the inert gases and alkalis. Element Z IE (eV) He 2 24.6 Li 3 5.4 Ne 1 ...
62 The alkalis Fig. 4.1The probability density of the electrons in a sodium atom as a func- tion ofr. The electrons in then=1 an ...
4.2 The quantum defect 63 − − − − − − Fig. 4.2The energies of the s, p, d and f configurations in ...
64 The alkalis Table 4.2The effective principal quantum numbers and quantum defects for the ground configuration of the alkalis. ...
4.3 The central-field approximation 65 S(r). This follows because the closed sub-shells within the core have a spherical charge ...
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