Hyperfine

THEORY

According to classical thinking, the electron moving around the nucleus has a magnetic dipole moment, because it is charged. The interaction of this magnetic dipole moment with the magnetic moment of the nucleus (due to its Spin ) leads to hyperfine splitting.

However, due to the electron's spin, there is also hyperfine splitting for s-shell electrons, which have zero orbital angular momentum. In this case, the magnetic dipole interaction is even stronger, as the electron probability density does not vanish inside the nucleus (

~r=0~

).

The amount of correction to the Bohr Energy levels due to hyperfine splitting of the hydrogen atom is on the order of

:

rac{m}{m_{
m p}} \alpha^4 m c^2

where
:

~m~

is the mass of an electron,
:

~m_{
m p}~

is the mass of a proton,
:

~\alpha~

is the Fine Structure Constant

~(~\alpha \approx 1/137.036~)~

, and
:

~c~

is the Speed Of Light .

For atoms other than hydrogen, the Nuclear Spin

ec{I}

and the Total Electron Angular Momentum

ec{J} = ec{L} + ec{S}

get coupled, giving rise to the total angular momentum

ec{F} = ec{J} + ec{I}

.
The hyperfine splitting is then
:

\Delta E_{
m hfs} = - ec{\mu}_I ec{B}_J = rac{a}{2} F(F+1) - I(I+1) - J(J+1),

where
:

a = rac{g_I ec{\mu}_{
m N} ec{B}_J}{\sqrt{J(J+1)}},

ec{\mu}_{
m N}

the Magnetic Dipole Moment of the nucleus, and
:

ec{B}_J

is the atomic Magnetic Field .

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	CATEGORIES ABOUT HYPERFINE STRUCTURE

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Information About

Hyperfine