The "screening doublet law" in X-ray spectroscopy refers to a specific empirical relationship observed in the energies of characteristic X-ray emission lines from elements. This law describes how the energy difference between two closely spaced X-ray emission lines (known as a doublet) depends on the atomic number (Z) of the element emitting the X-rays.

Here’s an explanation of the screening doublet law:

Origin: The screening doublet law arises due to the shielding effect of inner electrons in an atom. When an inner-shell electron is ejected (for example, by incident X-rays or electrons), an outer-shell electron can transition to fill the vacancy left in the inner shell. This transition results in the emission of characteristic X-rays.
Energy of Emission Lines: The energies of these emitted X-rays are characteristic to the element and depend on the binding energies of electrons in the involved atomic shells.
Doublet Structure: In many cases, the X-ray emission lines appear as closely spaced pairs (doublets) due to fine structure splitting caused by factors such as spin-orbit coupling and relativistic effects.
Empirical Law: The screening doublet law empirically states that the energy difference (ΔE) between the two lines in the doublet is inversely proportional to the fourth power of the atomic number Z:
ΔE∝Z41
Here, ΔE represents the energy difference between the higher and lower energy lines in the doublet, and Z is the atomic number of the element emitting the X-rays.
Explanation: The inverse fourth power dependence on Z arises from the electrostatic screening effect by inner-shell electrons. As Z increases (i.e., for heavier elements), the electrons in inner shells shield the outer electrons more effectively from the nuclear charge. This shielding reduces the binding energy of the outer electrons and thus decreases the energy difference between the X-ray emission lines in the doublet.

Applications: The screening doublet law is utilized in X-ray spectroscopy for identifying elements and determining their atomic numbers based on the energies of characteristic X-ray emission lines. It provides a quantitative relationship that helps in interpreting and analyzing X-ray spectra in various scientific and industrial applications, including materials analysis, mineralogy, and biomedical imaging.

In general, the term screening doublet refer to the part of energy levels which have same n and j but different l values. In X ray energy levels the pair (L_I, L_II), (M_I, M_II), (M_III, M_IV) have same n and j values but different l values. So there are called screening doublet or irregular doublet.

Taking only screening effect into account, we have the total energy formula as

T = R/ n² (z -b)²

(T/R)^1/2 = z-b / n ...1

Considering the doublet

For L_I, we have n= 2

(T/R)^1/2 = z-b_1 / 2 ...2

For L_I, we have n= 2

(T/R)^1/2 = z-b_2 / 2 ...3

Now difference between square root of term value will be

Equation 4 is irregular doublet law which states that the difference between square root of term values for irregular doublet is constant and is independent of atomic number z. This holds good for L_I - L_II levels of 6 elements (Cs, Ba, La, Ce, Pr and Na)

In summary, the screening doublet law is a fundamental empirical relationship in X-ray spectroscopy that describes the energy separation between characteristic X-ray emission lines in terms of the atomic number Z of the emitting element.

This note is a part of the Physics Repository

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