Thermal X-ray radiation (PDF) - SRON

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ut of course the ion can also be in a higher state, for instance the valence electron can be in a 2p orbit or a 3d orbit. Suppose now that it is excited to a 3d orbit. This orbit has n = 3 and L = 2. The single electron produces S = 1/2. Therefore, the multiplicity r = 2S + 1 = 2, hence we have a 2 D term. Allowed values of J are 3/2 and 5/2. If the electron falls back to one of the n = 2 states, than it can be seen that only a transition to L = 1 is allowed (why?). It is easy to show that this is the 2p 2 P 1/2 , 2 P 3/2 doublet. Therefore, we will get the radiative transition triplet 2 P− 2 D as treated above. The three lines can be found easily in a simulated spectrum (Fig. 3.11). The lines are found at 11.029, 11.171 and 11.188 Å. The spectral region shows several other lines from other (mainly iron) ions, so knowing the predicted line ratios is helpfull in identifying these triplets. Verify the relative intensity of these lines. A more complex example is given by the following. Example 3.12. Transition from 3 D to 3 P. In the spectrum, this gives a sextet: a: 3 D 1 – 3 P 2 b: 3 D 2 – 3 P 2 c: 3 D 3 – 3 P 2 d: 3 D 1 – 3 P 1 e: 3 D 2 – 3 P 1 f: 3 D 1 – 3 P 1 Applying the sum rule we find: I c : (I b + I e ) : (I a + I d + I f ) = 7:5:3 (I a + I b + I c ) : (I d + I e ) : I f = 5:3:1 and this implies I a : I b : I c : I d : I e : I f = 1.2 : 17.9 : 100 : 17.9 : 53.6 : 23.8 (3.2) exercise 3.2. For the above example, make a plot similar to Fig. 3.10. Use Hund’s law to plot a realistic relative distance between the terms of the upper and lower multiplet. The spectroscopic notation is based on the LS-coupling, because that applies in the most simple cases. LS-coupling dominates whenever the distance between two multiplets (determined by the electrostatic interaction of the electrons) is much larger than the multiplet-splitting (= largest distance within one multiplet, caused by the spin-orbit interaction), which is the case for a low nuclear charge Z (the light elements). Because the spin-orbit interaction increases faster with Z than the electrostatic interaction, for the heavier elements in the end JJ-coupling will dominate, in particular for complicated term configurations, where there are many terms close together. In an excited state (with large principle quantum number n), where the electrostatic interaction decreases rapidly, already for lower values of Z JJ-coupling can occur. For example, for Pb, Sn and Ge for the ground term LS-coupling applies, while the higher excited states have JJ-coupling. 21
3.5 Abundances of the elements With high spectral resolution and sensitivity, optical spectra of stars sometimes show spectral features from almost all elements of the Periodic Table, but in practice only a few of the most abundant elements show up in X-ray spectra of cosmic plasmas. In several situations the abundances of the chemical elements in an X-ray source are similar to (but not necessarily equal to) the abundances for the Sun or a constant fraction of that. There have been many significant changes over the last several years in the adopted set of standard cosmic abundances. A still often used set of abundances is that of Anders & Grevesse (1989), but a more recent one is the set of proto-Solar abundances of Lodders (2003), that we list in Table 3.4 for a few of the key elements. Table 3.4: Proto-Solar abundances for the 15 most common chemical elements. Abundances A are given with respect to hydrogen. Data from Lodders (2003). Element abundance Element abundance Element abundance H ≡ 1 Ne 89.1 × 10 −6 S 18.2 × 10 −6 He 0.0954 Na 2.34 × 10 −6 Ar 4.17 × 10 −6 C 288 × 10 −6 Mg 41.7 × 10 −6 Ca 2.57 × 10 −6 N 79.4 × 10 −6 Al 3.47 × 10 −6 Fe 34.7 × 10 −6 O 575 × 10 −6 Si 40.7 × 10 −6 Ni 1.95 × 10 −6 In general, for absorption studies the strength of the lines is mainly determined by atomic parameters that do not vary much along an iso-electronic sequence, and the abundance of the element. Therefore, in the X-ray band the oxygen lines are the strongest absorption lines, as oxygen is the most abundant metal. The emissivity of ions in the X-ray band often increases with a strong power of the nuclear charge. For that reason, in many X-ray plasmas the strongest iron emission lines are often of similar strength to the strongest oxygen lines, despite the fact that the cosmic abundance of iron is only 6 % of the cosmic oxygen abundance. Without being complete or giving too many details, we give here a short list of situations where the abundances differ from proto-Solar, and where X-ray spectroscopic observations are key to determine these abundances: • Stellar coronae: here due to the (inverse) FIP effect (FIP = First Ionisation potential), abundances can be different from Proto-Solar. Elements with high FIP, for instance noble gases line Ne, remain longer neutral in the transition zones between photosphere and corona. Neutral particles are not tied to the magnetic field in stellar flares, hence segregration between neutral and ionised species is possible, leading to deviant abundances. • Some hot stars show strong effects of the CNO cycle, leading e.g. to enhnced nitrogen abundances in some O-stars like ζ Pup. • In several young supernova remnants (e.g. Cas A) one sees directly the freshly produced chemical elements lighten-up in X-rays 22
Page 1 and 2: High Energy Astrophysics Jelle Kaas
Page 3 and 4: 3.1 Introduction Thermal X-ray radi
Page 5 and 6: Figure 3.2: The observed X-ray spec
Page 7 and 8: Figure 3.6: X-ray spectrum of the S
Page 9 and 10: series of alkaline spectra). The no
Page 11 and 12: • The first atomic shell (n = 1)
Page 13 and 14: Z El 1s 2s 2p 3s 3p 3d 4s Ground te
Page 15 and 16: m l1 s 1 m l2 s 2 M L M S +1 + +1
Page 17 and 18: 3.3 Energy levels We have seen the
Page 19 and 20: 3.4 Transitions between different l
Page 21: Figure 3.10: Transitions between a
Page 25 and 26: 3.6 Basic processes In order to be
Page 27 and 28: leading to Here the constant S 0 is
Page 29: 3.6.3 Radiative transition probabil
Page 32 and 33: Figure 3.12: Fluorescence yield as
Page 34 and 35: The formula of Younger While the Lo
Page 36 and 37: 3.6.6 Excitation-Autoionisation In
Page 38 and 39: 3.6.7 Photoionisation Figure 3.20:
Page 40 and 41: 3.6.9 Radiative recombination Radia
Page 42 and 43: 3.6.10 Dielectronic recombination T
Page 44 and 45: 3.7 The ionisation balance In order
Page 46 and 47: of computing time. Therefore one us
Page 48 and 49: 3.8 Continuum emission processes Af
Page 50 and 51: decays back to the 1s orbit by a ra
Page 52 and 53: Inner-shell ionisation The third li
Page 54 and 55: 3.9.3 Line width For most X-ray spe
Page 56 and 57: Table 3.6: The strongest emission l
Page 58 and 59: Table 3.8: Some important iron line
Page 60 and 61: with τ(λ) = τ 0 ϕ(λ) (3.83) wh
Page 62 and 63: Table 3.9: The most important X-ray
Page 64 and 65: where the hydrogen column density N
Page 66 and 67: source itself. Fortunately, with hi
Page 68 and 69: Figure 3.35: Stability for the ioni
Page 70: Table 3.10: Wavelengths in Å of th

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