# Download Atomic Spectra by W.R. Hindmarsh and D. ter Haar (Auth.) PDF

By W.R. Hindmarsh and D. ter Haar (Auth.)

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**Example text**

IK(r2)dti + ií «α* (r,)u* ir^)(e^r,2) « α ( Γ 2 Κ ( Γ ι ) dr, άτ, dx, + i J " a * ( r i K ( « - 2 ) ( e > , 2 ) " « ( r 2 K ( r . ) d T , dx^ + έ í " * (^2)"»* (ri)(«'/r, 2) = {r,)u, (r^) d t , d t ^ J+X where J is equal to each of the first two of the four integrals into which //js is decomposed and Κ is equal to each of the second two integrals. (ri)] V / r , 2 ) [ « . (Γΐ)"6 (••2) - W« (j2)Ub (Γι)] dXi dX2 = J+K-K-J = 0 Likewise H„ = 0 . The secular equation then reduces to J+K+E°-E 0 0 J-K+E°-E = 0 where we have put £ ^ = £ f = E°, since the unperturbed singlet and triplet energy levels coincide.

This discrepancy is partly because Racah used a value of ΔΓΟ/ΓΟ some 10 times too large, and partly because his value of |iA(0)|^ was also too large. 15)) for |i/^(0)|^ is on the whole much more reliable than the results of numerical calculations. The modification known as the Goudsmit -Fermi-Segré expression (see Paper 12) is better still: When such values are used, and the electron configuration responsible for the spectral lines concerned correctly identified, there is order of magnitude agreement between theory and observation.

1 -0-329I- Fio. 8. Fine structure of the a-line of hydrogen Lamb-shifted levels Dirac levels Transitions allowed in Sommerfeld's scheme shown by full vertical lines Transitions forbidden in Sommerfeld's scheme but allowed in Dirac*s scheme shown by dotted vertical lines 46 ATOMIC SPECTRA Thus even in a vacuum, where there are no photons, there is a **zero-point" electromagnetic energy of amount ^ i ^ v . V T o calculate the fields due to these zero point fluctuations we recall that the number of standing-wave modes in an enclosure of volume V in the frequency range ν to v + t/v is (Sn/c^)v^dvV, Hence the electromagnetic energy is (El+B',)dT = ^EiV where El is the mean square value, and E^ is the amplitude, of the component of electric field of frequency v.