.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gen_examples/form_factors/plot_ffl_H_He-like.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gen_examples_form_factors_plot_ffl_H_He-like.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gen_examples_form_factors_plot_ffl_H_He-like.py:


Zero IPD limit form factor lowering
===================================

This examples compares the limits of the Form Factor lowering reported by
:cite:`Doppner.2023` (:py:class:`jaxrts.models.FormFactorLowering`) for zero
IPD to the form factors by :cite:`Pauling.1932`.

We compare the form factors for a beryllium ion. Due to screening, there are
light differences between Hydrogen- and Helium-like ions. For a fractional
charge, we interpolate linearly between these two states.

.. GENERATED FROM PYTHON SOURCE LINES 13-69



.. image-sg:: /gen_examples/form_factors/images/sphx_glr_plot_ffl_H_He-like_001.svg
   :alt: $f_{1s}$ for beryllium
   :srcset: /gen_examples/form_factors/images/sphx_glr_plot_ffl_H_He-like_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python

    import jax.numpy as jnp
    import matplotlib.pyplot as plt
    import scienceplots  # noqa:F401

    import jaxrts

    ureg = jaxrts.ureg

    plt.style.use("science")

    Z_A = 4
    k = jnp.linspace(0, 17, 100) / (1 * ureg.angstrom)


    fig, ax = plt.subplots()
    for idx, Z in enumerate([1.5, 2.0, 2.5, 3.0, 3.5]):
        Z_C = Z_A - Z

        # Pauling
        # =======
        Zeff_pauling = (
            Z_A - jaxrts.form_factors.pauling_size_screening_constants(Z_C)[0]
        )
        f_pauling = jaxrts.form_factors.pauling_f10(k, Zeff_pauling)

        # Form Factor lowering
        # ====================

        binding_E = jaxrts.Element(Z_A).ionization.energies[::-1][:2]
        f_ffl = jaxrts.form_factors.form_factor_lowering_10(
            k, binding_E, Z_C, Z_A, Z_squared_correction=True
        )

        ax.plot(
            k.m_as(1 / ureg.angstrom),
            f_pauling.m_as(ureg.dimensionless),
            color=f"C{idx}",
            ls="dotted",
            lw=2 if idx in [1, 2, 3] else 1,
            label=f"Pauling, Z={Z}" if idx == 0 else f"Z={Z}",
        )
        ax.plot(
            k.m_as(1 / ureg.angstrom),
            f_ffl.m_as(ureg.dimensionless),
            color=f"C{idx}",
            ls="dashed",
            lw=2 if idx in [1, 2, 3] else 1,
            label="FFL" if idx == 0 else None,
        )
    ax.set_ylabel("$f_{1s}$")
    ax.set_xlabel("$k$ [1/angstrom]")

    ax.legend()
    plt.tight_layout()
    plt.title("$f_{1s}$ for beryllium")
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 2.624 seconds)


.. _sphx_glr_download_gen_examples_form_factors_plot_ffl_H_He-like.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_ffl_H_He-like.ipynb <plot_ffl_H_He-like.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_ffl_H_He-like.py <plot_ffl_H_He-like.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_