The "fine structure" of X-ray levels refers to the detailed characteristics and properties associated with the energy levels of X-rays. Here are some key points regarding the fine structure of X-ray levels:

Energy Levels: X-rays are electromagnetic radiation with energies typically in the range of 100 eV (electron volts) to several MeV (mega electron volts). The energy of an X-ray photon corresponds to the difference in energy between atomic or molecular energy levels.
Shell Structure: X-rays are often emitted or absorbed when electrons transition between different energy levels within atoms or molecules. In atoms, electrons occupy various shells (e.g., K, L, M shells), each characterized by discrete energy levels.
Characteristic X-rays: When inner-shell electrons are ejected from an atom (e.g., by collision with high-energy particles or X-rays), outer-shell electrons can transition to fill the vacancy. This transition results in the emission of X-rays with energies specific to the difference in energy between the initial and final electron states. These are known as characteristic X-rays and their energies depend on the atomic number of the element involved.
Fine Structure Splitting: This refers to small energy differences between closely spaced energy levels within a shell due to various interactions such as spin-orbit coupling or relativistic effects. These small energy differences can affect the precise energies at which X-ray transitions occur and can be resolved with high-resolution X-ray spectroscopy.
Absorption Edges: X-rays can be absorbed by atoms or molecules at energies corresponding to the binding energies of electrons in their inner shells. This absorption creates characteristic features in X-ray absorption spectra known as absorption edges, which are associated with transitions from core levels to higher energy states.
X-ray Emission Lines: X-rays emitted by atoms following excitation can exhibit lines corresponding to transitions between different energy levels. These emission lines are typically sharp due to the narrow energy distribution of the emitted photons.
Experimental observation shows that X ray levels are not singlet. They have their own fine structure. Eg: L levels have 3 sub levels, m levels have 5 sub levels etc and so on.
To account the fine structure of X ray level we consider the screening effect and effect of spin motion of electrons.
For L electrons which move in approximate coulomb field, the K electrons behave as if they have merged into the nucleus and thereby reducing the nuclear charge by two. The reduction of nuclear charge by the near electrons is called screening effect. If we consider only screening effect then total energy of system can be taken as like H atom ie
T = R (z-b)² / n²
When an electron in an atom moves in an orbit of low quantum number in the field of nucleus, the velocity of electron is enough so that relativistic variation of mass can be taken into account with the argument Sommerfield and Wentzal show the energy of the system.

where 𝛼 = 2𝜋e²/ ch is fine structure constant

k = sommerfield Azimuthal quantum number

d = sommerfield screening constant

The first screening constant b depends upon the distribution of electron in the shells both outside and inside the shell considered electron whereas screening constant d depends upon variation of mass with velocity and spin motion of electron.

Each energy level is divided into n sublevels by the effect of screening constant "b", and the corresponding terms are called reduced terms. If we add a second screening constant "d" to that effect, then each sublevel, except the ground level, splits into two levels as shown in figure.

Understanding the fine structure of X-ray levels is crucial in various scientific disciplines, including X-ray spectroscopy, materials science, and medical imaging. High-resolution techniques allow scientists to precisely measure and analyze X-ray energies, providing detailed information about the atomic and electronic structure of materials.

This note is a part of the Physics Repository.

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