In
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, spin-exchange is an interaction process between two particles mediated by an
exchange interaction
In chemistry and physics, the exchange interaction (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in an analogy to classical ...
. It preserves
total angular momentum
In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin).
If s is the particle's s ...
of the system but may allow other aspects of the system to change. When two spin-polarized
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, and ...
s in their
ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
experience a spin-exchange collision, the total
spin
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
of the atoms is preserved yet the orientation of the individual spins may change. For example, if atoms
and
are oppositely
polarized, a spin-exchange collision reverses the spins:
:
In alkali metals
In a typical vapor of
alkali metal
The alkali metals consist of the chemical elements lithium (Li), sodium (Na), potassium (K),The symbols Na and K for sodium and potassium are derived from their Latin names, ''natrium'' and ''kalium''; these are still the origins of the names ...
atoms, spin-exchange collisions are the dominant type of interaction between atoms. The collisions happen so rapidly that they only alter the state of the electron spins and do not significantly affect the nuclear spins. Thus, spin-exchange collisions between alkali metal atoms can change the
hyperfine
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nuc ...
state of the atoms while preserving total
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
of the colliding pair. As a result, spin-exchange collisions cause
decoherence
Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wa ...
in ensembles of polarized atoms precessing in the presence of a
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
.
The time between spin-exchange collisions for a vapor of alkali metal atoms is
:
where the spin exchange cross section for alkali metals such as K, Rb, and Cs is
[
]
:
and where
is the vapor density and
is the average relative velocity given by the
Maxwell–Boltzmann distribution
In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann.
It was first defined and used ...
:
:
where
is the
ideal gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
,
is the temperature, and
is the molar mass of the atoms.
References
Quantum mechanics
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