Physics:Quantum Hyperfine structure - Revision history

Maintenance script: Normalize quantum page header order

2026-05-22T11:31:54Z

Normalize quantum page header order

← Older revision		Revision as of 11:31, 22 May 2026
Line 2:		Line 2:
	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
	{{Quantum article nav\|previous=Physics:Quantum Fine structure\|previous label=Fine structure\|next=Physics:Quantum Isotopic shift\|next label=Isotopic shift}}		{{Quantum article nav\|previous=Physics:Quantum Fine structure\|previous label=Fine structure\|next=Physics:Quantum Isotopic shift\|next label=Isotopic shift}}

	<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

Maintenance script: Clean Book label remnants and backlink spacing

2026-05-22T11:10:11Z

Clean Book label remnants and backlink spacing

← Older revision		Revision as of 11:10, 22 May 2026
Line 1:		Line 1:
	{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}		{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
	{{Quantum article nav\|previous=Physics:Quantum Fine structure\|previous label=Fine structure\|next=Physics:Quantum Isotopic shift\|next label=Isotopic shift}}		{{Quantum article nav\|previous=Physics:Quantum Fine structure\|previous label=Fine structure\|next=Physics:Quantum Isotopic shift\|next label=Isotopic shift}}

Maintenance script: Remove hidden BOM characters and direct Book label after Short description

2026-05-22T11:02:23Z

Remove hidden BOM characters and direct Book label after Short description

← Older revision		Revision as of 11:02, 22 May 2026
Line 1:		Line 1:
	{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}~~Book I~~		{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}

Maintenance script: Clean Short description prefix and add Book I label

2026-05-22T10:47:25Z

Clean Short description prefix and add Book I label

← Older revision		Revision as of 10:47, 22 May 2026
Line 1:		Line 1:
	~~~~{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}		{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}Book I

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}

Maintenance script: Apply Quantum previous-next navigation

2026-05-20T12:23:52Z

Apply Quantum previous-next navigation

← Older revision		Revision as of 12:23, 20 May 2026
Line 1:		Line 1:
	{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}		{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
			{{Quantum article nav\|previous=Physics:Quantum Fine structure\|previous label=Fine structure\|next=Physics:Quantum Isotopic shift\|next label=Isotopic shift}}

	<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

Maintenance script: Improve Book I intro quality

2026-05-20T09:03:16Z

Improve Book I intro quality

← Older revision		Revision as of 09:03, 20 May 2026
Line 1:		Line 1:
	{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}		{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
Line 10:		Line 10:

	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	'''Hyperfine structure''' ~~is a Book I topic in the Quantum Collection. Hyperfine~~ structure refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the nucleus and the surrounding electron cloud. These shifts are typically much smaller than those of fine structure and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments. Hyperfine structure refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the nucleus and the surrounding electron cloud. These shifts are typically much smaller than those of fine structure and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments.		'''Hyperfine structure''' hyperfine structure refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the nucleus and the surrounding electron cloud. These shifts are typically much smaller than those of fine structure and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments. Hyperfine structure refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the nucleus and the surrounding electron cloud. These shifts are typically much smaller than those of fine structure and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments. In atomic systems, hyperfine structure originates from:
	</div>		</div>

Maintenance script: Clean Book I red links, intro, and image slots

2026-05-20T08:13:11Z

Clean Book I red links, intro, and image slots

← Older revision		Revision as of 08:13, 20 May 2026
Line 1:		Line 1:
	{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}		{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
Line 10:		Line 10:

	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	'''Hyperfine structure''' refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the ~~[[Physics:Atomic~~ nucleus\|nucleus]] and the surrounding electron cloud.		'''Hyperfine structure''' is a Book I topic in the Quantum Collection. Hyperfine structure refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the nucleus and the surrounding electron cloud. These shifts are typically much smaller than those of fine structure and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments. Hyperfine structure refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the nucleus and the surrounding electron cloud. These shifts are typically much smaller than those of fine structure and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments.

	These shifts are typically much smaller than those of ~~[[Physics:Fine structure\|~~fine structure]] and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments.
	</div>		</div>

Line 25:		Line 23:
	In atomic systems, hyperfine structure originates from:		In atomic systems, hyperfine structure originates from:

	* interaction between the ~~[[Physics:Nuclear magnetic moment\|~~nuclear magnetic dipole moment]] and magnetic fields produced by electrons		* interaction between the nuclear magnetic dipole moment and magnetic fields produced by electrons
	* interaction between the ~~[[Physics:Quadrupole\|~~nuclear electric quadrupole moment]] and the electric field gradient		* interaction between the nuclear electric quadrupole moment and the electric field gradient

	In molecules, additional contributions arise from:		In molecules, additional contributions arise from:
Line 62:		Line 60:
	* <math>\mathbf{F} = \mathbf{I} + \mathbf{J}</math> = total angular momentum		* <math>\mathbf{F} = \mathbf{I} + \mathbf{J}</math> = total angular momentum

	This interaction satisfies the ~~[[Physics:~~Landé interval rule~~\|Landé interval rule]]~~.		This interaction satisfies the Landé interval rule.

	==Electric quadrupole interaction==		==Electric quadrupole interaction==
Line 101:		Line 99:
	* atomic spectra		* atomic spectra
	* molecular spectroscopy		* molecular spectroscopy
	* ~~[[Physics:Electron paramagnetic resonance\|~~electron paramagnetic resonance]]		* electron paramagnetic resonance
	* ~~[[Physics:Nuclear magnetic resonance\|~~nuclear magnetic resonance]]		* nuclear magnetic resonance

	A key example is the 21 cm hydrogen line in astrophysics.		A key example is the 21 cm hydrogen line in astrophysics.
Line 128:		Line 126:
	==History==		==History==

	Hyperfine structure was first described theoretically by ~~[[Biography:~~Enrico Fermi~~\|Enrico Fermi]]~~ in 1930.<ref>E. Fermi (1930), "Über die magnetischen Momente der Atomkerne". Z. Physik 60, 320–333.</ref>		Hyperfine structure was first described theoretically by Enrico Fermi in 1930.<ref>E. Fermi (1930), "Über die magnetischen Momente der Atomkerne". Z. Physik 60, 320–333.</ref>

	The nuclear quadrupole moment was introduced in 1935 by H. Schüler and T. Schmidt.<ref>H. Schüler & T. Schmidt (1935), "Über Abweichungen des Atomkerns von der Kugelsymmetrie". Z. Physik 94, 457–468.</ref>		The nuclear quadrupole moment was introduced in 1935 by H. Schüler and T. Schmidt.<ref>H. Schüler & T. Schmidt (1935), "Über Abweichungen des Atomkerns von der Kugelsymmetrie". Z. Physik 94, 457–468.</ref>

Harold: Arrange page top as TOC lead image columns

2026-05-17T14:00:09Z

Arrange page top as TOC lead image columns

← Older revision		Revision as of 14:00, 17 May 2026
Line 1:		Line 1:
			{{Short description\|Quantum Collection topic on Quantum Hyperfine structure}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}

			<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

			<div style="width:280px;">
			__TOC__
			</div>

			<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	'''Hyperfine structure''' refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the [[Physics:Atomic nucleus\|nucleus]] and the surrounding electron cloud.		'''Hyperfine structure''' refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the [[Physics:Atomic nucleus\|nucleus]] and the surrounding electron cloud.

	These shifts are typically much smaller than those of [[Physics:Fine structure\|fine structure]] and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments.		These shifts are typically much smaller than those of [[Physics:Fine structure\|fine structure]] and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments.
			</div>

			<div style="width:300px;">
			[[File:Fine hyperfine levels yellow.png\|thumb\|280px\|Quantum Hyperfine structure.]]
			</div>

	~~[[File:Fine hyperfine levels yellow.png\|thumb\|400px\|Fine and hyperfine structure in the hydrogen atom]]~~		</div>

	==Overview==		==Overview==

imported>WikiHarold: Repair Quantum Collection B backlink template

2026-05-08T19:51:12Z

Repair Quantum Collection B backlink template

← Older revision	Revision as of 19:51, 8 May 2026
(No difference)

imported>WikiHarold: Repair Quantum Collection B backlink template

2026-05-08T19:51:12Z

Repair Quantum Collection B backlink template

New page

{{Quantum book backlink|Atomic and spectroscopy}}
'''Hyperfine structure''' refers to small shifts and splittings of otherwise degenerate electronic energy levels in atoms, molecules, and ions due to interactions between the [[Physics:Atomic nucleus|nucleus]] and the surrounding electron cloud.

These shifts are typically much smaller than those of [[Physics:Fine structure|fine structure]] and arise from electromagnetic multipole interactions, primarily involving nuclear magnetic dipole and electric quadrupole moments.

[[File:Fine hyperfine levels yellow.png|thumb|400px|Fine and hyperfine structure in the hydrogen atom]]

==Overview==

In atomic systems, hyperfine structure originates from:

* interaction between the [[Physics:Nuclear magnetic moment|nuclear magnetic dipole moment]] and magnetic fields produced by electrons
* interaction between the [[Physics:Quadrupole|nuclear electric quadrupole moment]] and the electric field gradient

In molecules, additional contributions arise from:

* nuclear spin–spin interactions
* nuclear spin–rotation coupling

Hyperfine structure is fundamentally weaker than fine structure and reflects the coupling between nuclear and electronic degrees of freedom.

==Magnetic dipole interaction==

For a nucleus with spin <math>\mathbf{I}</math>, the magnetic dipole moment is

<math>\boldsymbol{\mu}_I = g_I \mu_N \mathbf{I}</math>

where <math>g_I</math> is the nuclear ''g''-factor and <math>\mu_N</math> the nuclear magneton.

The interaction Hamiltonian is:

<math>\hat{H}_D = -\boldsymbol{\mu}_I \cdot \mathbf{B}</math>

where <math>\mathbf{B}</math> is the magnetic field generated by electrons.

In the effective angular momentum form, this becomes:

<math>\hat{H}_D = \hat{A}\,\mathbf{I} \cdot \mathbf{J}</math>

leading to the hyperfine energy shift:

<math>\Delta E = \frac{1}{2}A\left[F(F+1) - I(I+1) - J(J+1)\right]</math>

where:

* <math>\mathbf{J}</math> = total electronic angular momentum
* <math>\mathbf{F} = \mathbf{I} + \mathbf{J}</math> = total angular momentum

This interaction satisfies the [[Physics:Landé interval rule|Landé interval rule]].

==Electric quadrupole interaction==

For nuclei with spin <math>I \ge 1</math>, an electric quadrupole moment exists.

The quadrupole Hamiltonian is:

<math>\hat{H}_Q = -e\,T^2(Q)\cdot T^2(q)</math>

where:

* <math>T^2(Q)</math> describes the nuclear quadrupole moment
* <math>T^2(q)</math> describes the electric field gradient

This interaction reflects deviations from spherical nuclear charge distributions.

==Molecular hyperfine structure==

In molecules, hyperfine structure includes additional contributions:

===Spin–spin interaction===
Magnetic coupling between nuclei:

<math>\hat{H}_{II} = -\sum_{\alpha \ne \alpha'} \boldsymbol{\mu}_\alpha \cdot \mathbf{B}_{\alpha'}</math>

===Spin–rotation interaction===
Coupling between nuclear spins and molecular rotation:

<math>\hat{H}_{IR} \propto \mathbf{I} \cdot \mathbf{T}</math>

These effects are important in rotational spectroscopy.

==Experimental observation==

Hyperfine structure is observed in:

* atomic spectra
* molecular spectroscopy
* [[Physics:Electron paramagnetic resonance|electron paramagnetic resonance]]
* [[Physics:Nuclear magnetic resonance|nuclear magnetic resonance]]

A key example is the 21 cm hydrogen line in astrophysics.

==Applications==

===Atomic clocks===
The SI second is defined via the hyperfine transition of caesium-133:

<math>f = \frac{\Delta E}{h}</math>

One second equals exactly:

9192631770 cycles of this transition.

===Astrophysics===
Hyperfine transitions probe the interstellar medium and molecular clouds.

===Quantum computing===
Hyperfine states serve as long-lived qubits in trapped-ion systems.

===Precision physics===
Measurements of hyperfine splitting provide tests of quantum electrodynamics.

==History==

Hyperfine structure was first described theoretically by [[Biography:Enrico Fermi|Enrico Fermi]] in 1930.<ref>E. Fermi (1930), "Über die magnetischen Momente der Atomkerne". Z. Physik 60, 320–333.</ref>

The nuclear quadrupole moment was introduced in 1935 by H. Schüler and T. Schmidt.<ref>H. Schüler & T. Schmidt (1935), "Über Abweichungen des Atomkerns von der Kugelsymmetrie". Z. Physik 94, 457–468.</ref>

==See also==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

==References==
{{reflist|3}}

{{Author|Harold Foppele}}
[[Category:Atomic physics]]
[[Category:Quantum mechanics]]

{{Sourceattribution|Physics:Quantum Hyperfine structure|1}}