src.Atomic.LTELib.Saha_distribution

src.Atomic.LTELib.Saha_distribution(_gi, _gk, _chi, _ne, _Te)

calculate the population ratio between the ground states of two subsequent ionization stage under LTE.

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

Parameters

• _gk (np.uint8 or array-like) – statistical weight of the ground state in ionization stage I+1, [-]

• _gi (np.uint8 or array-like) – statistical weight of the ground state in ionization stage I, [-]

• _chi (np.double or array-like) – ionization energy from ground state in ionization stage I to ground state in ionization stage I, [\(erg\)]

• _ne (np.double or array-like) – electron density, [\(cm^{-3}\)]

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

Returns

_rt – \(n_k / n_i\), \(n_k\) the population of the ground state of ionization stage I+1 and \(n_i\) the population of the ground state of ionization stage I. [-]

Return type

np.double or array-like

Notes

The population ratio according to Saha’s equation 1.

a factor contains physics constants only,

\[f = 2(\frac{2 \pi m_e k}{h^2})^{3/2}\]

then the population ratio is,

\[\frac{n_{0,k}}{n_{0,i}} = f \cdot \frac{g_{0,k}}{g_{0,i}} e^{\frac{-\chi_{ki}}{kT}} T^{3/2} / n_e\]

References

1

Ivan Hubeny, Dimitri Mihalas, “Theory of Stellar Atmosphere: An Introduction to Astrophysical Non-equilibrium Quantitative Spectroscopic Analysis”, Princeton University Press, pp. 94, 2015.