jaxrts.form_factors.form_factor_lowering_Zeff_10
- jaxrts.form_factors.form_factor_lowering_Zeff_10(binding_E: Quantity, Z_A: float, Z_squared_correction: bool) Array[source]
Calculate the form factor lowering for the 1s orbital. See [Döppner et al., 2023].
For hydrogen-like ions, the binding energy has to be compared to 13.6eV. He-like ions use a corrected ground-state value, instead, to account for screening. This has to be chosen to reproduce the known form factors
pauling_f10()in the case of no IPD, and scales with 1/Z_A\[E_n^\text{H-like} = 13.6 \text{eV} E_n^\text{He-like} = (13.6 - 12.13/Z_A)\text{eV}\]We noted that with growing Z, the simple functions above start to deviate from the values given by [Pauling and Sherman, 1932].
We fitted an additional correction term:
\[\Delta E_n = 1.77 \times 10^{-4} \text{eV} \cdot Z_A^2\]- Parameters:
binding_E (Quantity) – The binding energies of the two 1s electrons. Has to be an array with 2 entries. Note that this potentially has to be reduced by the IPD.
Z_A (float) – Atomic number of the element, i.e., number of protons in the core.
Z_squared_correction (bool) – If
True, the quadratic correction term discussed above is added to better match the zero IPD limit.
Examples using jaxrts.form_factors.form_factor_lowering_Zeff_10
Zero IPD limit for effective charge when using form factor lowering