.. 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_zero_IPD_limit.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_zero_IPD_limit.py>`
        to download the full example code

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

.. _sphx_glr_gen_examples_form_factors_plot_ffl_zero_IPD_limit.py:


Zero IPD limit for effective charge when using 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`.

Since the form of the 1s form factor is identical, and the only change is the
effective change, this value is plotted.

.. GENERATED FROM PYTHON SOURCE LINES 12-111



.. image-sg:: /gen_examples/form_factors/images/sphx_glr_plot_ffl_zero_IPD_limit_001.svg
   :alt: blue: H-like, green: He-like
   :srcset: /gen_examples/form_factors/images/sphx_glr_plot_ffl_zero_IPD_limit_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python


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

    import jaxrts

    ureg = jaxrts.ureg

    plt.style.use("science")

    Z_A = jnp.arange(2, 36)


    # Pauling
    # =======

    Zeff_pauling_H_like = Z_A
    Zeff_pauling_He_like = (
        Z_A - jaxrts.form_factors.pauling_size_screening_constants(Z_A)[0]
    )

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

    Zeff_ffl_H_like = []
    Zeff_ffl_He_like = []

    Zeff_ffl_H_like_corr = []
    Zeff_ffl_He_like_corr = []
    for Zs in Z_A:
        binding_E = jnpu.sort(jaxrts.Element(Zs).ionization.energies)[-2:][::-1]
        H_like, He_like = jaxrts.form_factors.form_factor_lowering_Zeff_10(
            binding_E, Zs, Z_squared_correction=False
        )
        Zeff_ffl_H_like.append(H_like)
        Zeff_ffl_He_like.append(He_like)

        H_like, He_like = jaxrts.form_factors.form_factor_lowering_Zeff_10(
            binding_E, Zs, Z_squared_correction=True
        )
        Zeff_ffl_H_like_corr.append(H_like)
        Zeff_ffl_He_like_corr.append(He_like)

    Zeff_ffl_H_like = jnp.array(Zeff_ffl_H_like)
    Zeff_ffl_He_like = jnp.array(Zeff_ffl_He_like)

    Zeff_ffl_H_like_corr = jnp.array(Zeff_ffl_H_like_corr)
    Zeff_ffl_He_like_corr = jnp.array(Zeff_ffl_He_like_corr)


    fig, ax = plt.subplots()


    ax.plot(
        Z_A,
        Zeff_ffl_H_like - Zeff_pauling_H_like,
        color="C0",
        ls="none",
        marker="o",
        label="ff lowering - Pauling",
        markerfacecolor="none",
        markeredgewidth=2,
    )
    ax.plot(
        Z_A,
        Zeff_ffl_H_like_corr - Zeff_pauling_H_like,
        color="C0",
        ls="none",
        marker="s",
        label="ff lowering (corr.) - Pauling",
    )

    ax.plot(
        Z_A,
        Zeff_ffl_He_like - Zeff_pauling_He_like,
        color="C1",
        ls="none",
        marker="o",
        markerfacecolor="none",
        markeredgewidth=2,
    )
    ax.plot(
        Z_A,
        Zeff_ffl_He_like_corr - Zeff_pauling_He_like,
        color="C1",
        ls="none",
        marker="s",
    )
    ax.plot(Z_A, jnp.zeros_like(Z_A), color="black", ls="dashed")

    ax.set_ylabel("$\\Delta Z_{eff}$")
    ax.set_xlabel("$Z$")
    ax.set_title("blue: H-like, green: He-like")

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


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

   **Total running time of the script:** (0 minutes 5.199 seconds)


.. _sphx_glr_download_gen_examples_form_factors_plot_ffl_zero_IPD_limit.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_zero_IPD_limit.ipynb <plot_ffl_zero_IPD_limit.ipynb>`

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

      :download:`Download Python source code: plot_ffl_zero_IPD_limit.py <plot_ffl_zero_IPD_limit.py>`


.. only:: html

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

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