Atomic form factors of C, by Pauling and Sherman

Calculate the atomic form factors of carbon using a hydrogen-like atom, as presented in [Pauling and Sherman, 1932].

Note

Instead of calling the functions jaxrts.form_factors.pauling_f10() and so on, directly, you could also use jaxrts.form_factors.pauling_atomic_ff(), instead.

import matplotlib.pyplot as plt
import numpy as np

import jaxrts
import jaxrts.form_factors as ff

ureg = jaxrts.units.ureg

k = np.linspace(0, 10, 100) / ureg.angstrom

CZ1s, CZ2s, CZ2p = ff.pauling_effective_charge(6)[:3]

fC10 = ff.pauling_f10(k, CZ1s)
fC20 = ff.pauling_f20(k, CZ2s)
fC21 = ff.pauling_f21(k, CZ2s)

plt.style.use("science")
plt.plot(
    k.m_as(1 / ureg.angstrom),
    (fC10 + fC20 + fC21).m_as(ureg.dimensionless),
    label="Full form factor",
)

plt.plot(
    k.m_as(1 / ureg.angstrom),
    fC10.m_as(ureg.dimensionless),
    label=r"$1s$ electrons",
    color="grey",
    linestyle=((0, (1, 1))),
)
plt.plot(
    k.m_as(1 / ureg.angstrom),
    fC20.m_as(ureg.dimensionless),
    label=r"$2s$ electrons",
    color="grey",
    linestyle=((0, (5, 1))),
)
plt.plot(
    k.m_as(1 / ureg.angstrom),
    fC21.m_as(ureg.dimensionless),
    label=r"$2p$ electrons",
    color="grey",
    linestyle=(0, (3, 1, 1, 1, 1, 1)),
)

plt.title("Atomic form factors for Carbon\n(Pauling and Sherman)")

plt.xlabel(r"$k$ [1/$\AA$]")
plt.ylabel(r"$f_i$")

plt.legend()
plt.tight_layout()
plt.show()