src.Atomic.LTELib.Boltzmann_distribution

src.Atomic.LTELib.Boltzmann_distribution(_gi, _gj, _Eji, _Te)

calculate the population ratio between upper level j and lower level i under LTE.

with nb.vectorize( [nb.float64(nb.uint8, nb.uint8, nb.float64, nb.float64)]).

Parameters

• _gi (np.uint8 or array-like) – statistical weight of lower level i, [-]

• _gj (np.uint8 or array-like) – statistical weight of upper level j, [-]

• _Eji (np.double or array-like) – the gap of level energy between upper level j and lower level i, \(E_{ji}=E_j-E_i, \quad [erg]\)

• _Te (np.double or array-like) – electron temperature, [\(K\)]

Returns

_rt – population ratio of upper level j and lower level i. \(rt = n_j / n_i\), [-]

Return type

np.double or array-like

Notes

The population ratio according to Boltzmann distribution 1.

\[\frac{n_j}{n_i} = \frac{g_j}{g_i} e^{-(E_j-E_i)/{kT}}\]

References

1

Ivan Hubeny, Dimitri Mihalas, “Theory of Stellar Atmosphere: An Introduction to Astrophysical Non-equilibrium Quantitative Spectroscopic Analysis”, Princeton University Press, pp. 262, 2015.