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essential facts and formulae note: the content of this site derives largely from my own research in theoretical space plasma physics and the theory of radiative processes (light-atom interaction). this was done mainly in the area of ionospheric physics, but should be applicable to other areas as well (e.g. astrophysics and solar physics). it concentrates on fundamental topics and formulae that, from my own experience, are vital for a correct understanding and solving of corresponding theoretical and practical problems in these areas. there is no claim though that this would be comprehensive and cover all aspects of space plasma- or atomic physics. note also that in some cases the approach differs from corresponding treatments in standard textbooks where the latter can be shown to be flawed. it is indicated in the corresponding entry when this is the case. gaussian cgs-units are used unless otherwise stated; for conversion into practical- (si-) units see the conversion table . . search site print version index: absorption , atomic decay probability , auto- ionization , bohr- einstein radiation formula , boltzmann distribution , boltzmann equation , charge screening , collision frequency , continuous medium , continuum radiation coulomb scattering , cyclotron frequency , debye shielding , detailed balance , doppler broadening , effective quantum number , elastic collisions , emission rate , energy loss , exb- drift , induced emission , inelastic collisions , larmor frequency , level population , line broadening , lte , maxwell distribution , mean free path , natural broadening , optical depth , oscillator strength , overlap integral , photoionization , photons , planck radiation formula , plasma , plasma field fluctuations , plasma frequency , plasma oscillations , plasma polarization field , pseudo- oscillator , radiation pressure , radiative recombination , radiative transfer , resonance scattering , saha equation , scattering of radiation , spectral line shape , stark broadening , transition probability . absorption: light can be absorbed by photoionization of atoms (or photo-dissociation of molecules). in standard treatments, it is assumed that the cross section σ ion for this process is independent of the intensity of the radiation. however, for intensities below a certain threshold it is obvious that it will be reduced due to the disturbing influence of plasma field fluctuations . one can adopt the efficiency factor β(e w )= e w 2 /(e w 2 +δ{e} p 2 ) , where e w is the electric field strength of the radiation with frequency ν (as given by the intensity i= e w 2 /8π) and δ{e} p =δe p . √ (ζ ν ,e 2 +ζ ν ,i 2 ) the effective plasma fluctuation field (see plasma field fluctuations and stark broadening with t n replaced by 1/(2π ν )). this leads to the circumstance that the optical depth with regard to photoionization is not proportional to the column density any more but has to be determined through the integral τ(s)= σ ion (0) . 0 ∫ s ds' n(s') . β(e w (s')) . because generally the intensity i (i.e. e w 2 ) is subject to the exponential absorption law i(s)= i 0 . e -τ(s) , the optical depth is determined by an integral equation which can be solved numerically (see /research/nlabsorb.htm ). back to index atomic decay probability: atoms in excited states are not stable but decay to lower levels more or less rapidly. for dipole allowed transitions the problem can be treated as a radiatively damped oscillator with an amplitude given by the quantum mechanical overlap integral <r> i,k for the lower state i=(m, l ') and the upper state k=(n, l ) involved. by equating the decay rate of the energy of a classical oscillator of frequency ν i,k with the quantum mechanical decay rate a i,k . h . ν i,k (h=planck constant), one obtains for the atomic decay coefficient a i,k = 16π . e 4 /(3c 3 h) . ν i,k 3 . <r> i,k 2 . (one should note that this expression is smaller by a factor 1/4 compared to the usual value quoted in the literature which is however derived inconsistently from statistical equilibrium considerations). in general, <r> i,k can only be evaluated numerically, but for large values of the principal effective quantum numbers m and n it can be approximated by a power law in terms of these parameters, with the result a m,n = 1.3 . 10 9 . m -1.8 . (n-1) -3.2 [sec -1 ] (m,n >>1) a numerical summation over all lower levels m reveals furthermore that the total average atomic decay coefficient (i.e. the inverse average lifetime) of level n can be approximated by a n = 1.1 . 10 9 . (n-1) -3.6 [sec -1 ] (n >>1) (neglection of the angular momentum quantum number l in these approximations may lead to an error up to a factor 2 in the absolute values for a m,n and a n , the relative values for fixed l should be accurate to within a few percent however). note : the above formula for a m,n assumes of course that the transition is allowed by the l -selection rule δ l =±1. it should not be misunderstood as an expression averaged over l . this is not so much because of the l -dependence of the decay coefficient (which is quite weak and has therefore not been explicitly considered here) but because an electron with angular momentum l >m is unable to decay to level m due to the l -selection rule. in order to get the l -averaged decay coefficient, one would have to apply a corresponding correction factor (which obviously also depends on the relative population of the angular momentum substates of the upper level; see for instance the last paragraph regarding radiative recombination ). back to index auto- ionization: contrary to established opinion, atoms or molecules can ionize each other through collisions even if their translational energy is smaller than the ionization energy. this is because bound electrons can collide with each other when two atoms come together and one of these may gain enough energy in the process to become ionized, leaving the other with correspondingly less energy in the atom (this is a purely classical process and does not affect the quantum mechanical states the electrons occupy; one has to remember that the quantum mechanical wave function for a given energy is finite everywhere in space and allows the electron therefore to have any classical energy). this process should be strongly temperature dependent, having its highest efficiency if the corresponding velocity of the approaching atoms is equal to the velocity of the bound electrons (i.e. about 10 8 cm/sec). for smaller velocities the electron orbits will have time to adjust themselves mutually to the field of the other atom and ionizing collisions will become less likely. the proposed process could be the explanation for the relatively high plasma density of the nighttime f- region of the earth's ionosphere. this would lead to an effective cross section of 10 -20 cm 2 in this case (which is characterized by atom velocities of 10 5 cm/sec). in general this mechanism should result in a significant degree of ionization even in the absence of any uv- radiation sources, which should be highly relevant for some astrophysical problems like star formation (see /research/#a8 ). back to index bohr- einstein radiation formula: the internal electronic energy changes of an atom are connected to the frequency of the corresponding emitted radiation by the formula ε =h . ν , with h the planck constant. usually, this equation is assumed to determine uniquely the resulting intensity of the radiation. however, there is theoretical and observational evidence that this assumption is only valid if the broadening of the spectral line due to plasma field fluctuations (stark broadening) is small compared to the natural broadening. in general, one has to assume a relationship in the form ε rad =(1+δ ν m,n d /a m,n ) . h . ν , where δ ν m,n d is the dynamical stark broadening due to the plasma field fluctuations and a m,n the atomic decay probability (natural broadening). this could

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