areas#

Cross-sectional areas of silicon subshells for photon interactions.

Examples

Plot the cross-section areas of each silicon subshell as a function of photon energy.

import numpy as np
import matplotlib.pyplot as plt
import astropy.units as u
import astropy.visualization
import fano

# Define of grid of photon energies to sample
energy = np.geomspace(1, 10000, num=1001) * u.eV

# Evaluate the area of each subshell for the given
# photon energy.
area_k1 = fano.photons.areas.area_photoionization_k1(energy)
area_l1 = fano.photons.areas.area_photoionization_l1(energy)
area_l2 = fano.photons.areas.area_photoionization_l2(energy)
area_l3 = fano.photons.areas.area_photoionization_l3(energy)
area_m1 = fano.photons.areas.area_photoionization_m1(energy)
area_m2 = fano.photons.areas.area_photoionization_m2(energy)
area_m3 = fano.photons.areas.area_photoionization_m3(energy)
area = fano.photons.areas.area_photoionization(energy)

# Plot the areas as a function of photon energy.
with astropy.visualization.quantity_support():
    fig, ax = plt.subplots()
    ax.loglog(energy, area_k1, label="$K_1$")
    ax.loglog(energy, area_l1, label="$L_1$")
    ax.loglog(energy, area_l2, label="$L_2$")
    ax.loglog(energy, area_l3, label="$L_3$")
    ax.loglog(energy, area_m1, label="$M_1$")
    ax.loglog(energy, area_m2, label="$M_2$")
    ax.loglog(energy, area_m3, label="$M_3$")
    ax.loglog(energy, area, label="total")
    ax.set_xlabel(f"photon energy ({ax.get_xlabel()})")
    ax.set_ylabel(f"cross-sectional aread ({ax.get_ylabel()})")
    ax.legend()
../_images/fano.photons.areas_0_0.png

Functions

area_photoionization_k1(energy)

Calculate the cross-section area of the \(K_1\) shell for a photon of a given energy.

area_photoionization_l1(energy)

Calculate the photoionization cross-sectional area of the \(L_1\) subshell.

area_photoionization_l2(energy)

Calculate the photoionization cross-sectional area of the \(L_2\) subshell.

area_photoionization_l3(energy)

Calculate the photoionization cross-sectional area of the \(L_3\) subshell.

area_photoionization_m1(energy)

Calculate the photoionization cross-sectional area of the \(M_1\) subshell.

area_photoionization_m2(energy)

Calculate the photoionization cross-sectional area of the \(M_2\) subshell.

area_photoionization_m3(energy)

Calculate the photoionization cross-sectional area of the \(M_3\) subshell.

area_photoionization(energy)

Calculate the total photoionization cross-sectional area of silicon.
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