Atomic models¶
Atomic models have to be defined in in order to carry out a
calculation. This section describes the model atom file in detail by
using the example helium.mod that is included in the present version
of Hazel. The atom model for He I is given by:
2
5
1 0
0.00
2 2
0.00
-0.987913
-1.064340
3 0
0.00
4 2
0.00
-0.270647
-0.292616
5 4
0.00
-0.044187
-0.046722
4
1 1 2 1.022d7 10829.0911 1.0000000 1.0000000 0.0000000
2 1 4 9.478d6 3888.6046 0.2000000 1.0000000 0.0000000
3 2 3 2.780d7 7065.7085 1.0000000 1.0000000 0.0000000
4 2 5 7.060d7 5875.9663 1.0000000 1.0000000 0.0000000
The first two numbers define the general properties of the atom. The first line of the file is equal to \(2S\), where \(S\) is the value of the spin of the terms. In the example, \(S=1\). At present, the code does not treat transitions between terms of different multiplicity which are, otherwise, of reduced importance due to their small transition probability. The second line contains the number of terms included in the model atom. This example represents the triplet system of He i with the lowest five terms, 2s\(^3\)S, 3s\(^3\)S, 2p\(^3\)P, 3p\(^3\)P and 3d\(^3\)D
Then, the following lines define the term levels included in the model. The information for each term consist of a line with an index (0,1,2,…) that is used just to label each term and the value of \(2L\), where \(L\) is the value of the electronic orbital angular momentum. Then, for each term, we must supply a list containing the energy separation in cm\(^{-1}\) between each \(J\)-level and the level with the smallest absolute value of \(J\). In case only one value of \(J\) is possible in the term, just put 0 in the energy difference.
Finally, the list of transitions has to be supplied. The first number indicates the number of radiative transitions included in the model. Then, the list contains the following numbers for each transition: index number, index of lower level, index of upper level, Einstein coefficient for spontaneous emission \(A_{ul}\) of the transition, modification factor \(f(\bar{n})\), modification factor \(f(w)\) and value of \(J^1_0/J^0_0\). The modification factors \(f(\bar{n})\) and \(f(w)\) are multiplied by the mean number of photons per mode \(\bar{n}\) and the anisotropy factor \(w\), respectively. Since uses the value of \(\bar{n}\) and \(w\) calculated from the tabulated solar CLV and taking into account geometrical effects, these factors can be used to analyze the behavior of the emergent Stokes profiles when, for some reason, the anisotropy or the intensity of the radiation field is increased or decreased by an arbitrary factor. Finally, if the radiation illuminating the atoms has non-zero net circular polarization, it is possible to include its effect in the statistical equilibrium equations by giving the value of \(J^1_0/J^0_0\).