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Physical Review A

Evolution of Electron Angular Momentum due to Spin-Exchange Collisions Involving Nuclear Spin

S. B. Crampton

Published Jan 1, 1971• 4 citations
Publisher

Abstract

The evolution of electronic angular momentum due to spin-exchange collisions between two species of ground-state alkali atoms is shown to depend substantially on nuclear spin when the effects of spin precession between collisions are included with the effects of the collisions themselves. General results are illustrated for nuclear spin \textonehalf{} and 1.

DOI
10.1103/physreva.3.515

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Effect of Spin-Exchange Collisions on Density Matrices Which Include Nuclear Spin

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The equation of motion for the electronic polarization of a ground-state alkali atom undergoing spin-exchange collisions is derived. It is shown that the equation of motion for the electronic polarization is unaffected by the inclusion of nuclear spin. A simple interpretation of the spin-exchange frequency shift is also given.

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Interaction between spin polarized alkali atoms

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Collisions of alkali-metal atoms in the ground state with the electron spin S = 1/2 are accompanied by exchange of electron coordinates between colliding particles, which leads to polarization transfer between them (i.e., to the well-known phenomenon of spin exchange). In addition, along with the polarization transfer from one partner to another, the magnetic resonance lines of colliding atoms are broadened and shifted in spin-exchange collisions. In particular the last two processes depend on the complex spin-exchange cross section. The real part of the cross section determines the so-called "spin-exchange cross section," which is responsible for the broadening of magnetic resonance lines, while the imaginary part determines the shift cross section, which governs the frequency shift of magnetic resonance. In order to describe the spin-exchange process one have to know complex spin-exchange cross sections. Complex spin-exchange cross sections are calculated on the basis of the data on the singlet (X 1 Σ + ) and triplet (a 3 Σ + ) potentials describing the interaction alkali-metal atoms in the ground state. Collisions of alkali-metal atoms Cs, Rb, K, Na in the ground state are considered in the energy interval of 10 −4 −10 −2 au.

Journal of Physics Conference Series•Dec 1, 2018•0 citations

Nuclear-Spin Effects Are Important in Analyzing Spin-Exchange Experiments

Hyatt M. Gibbs

Lambert's proof that the inclusion of nuclear spin does not alter the equation of motion for the electronic polarization is shown to be valid only when the hyperfine interaction is negligible. Usually the hyperfine frequency is much greater than the frequency of spin-exchange collisions; then the effect of the hyperfine interaction between collisions invalidates Lambert's proof. In general, spin exchange with a second depolarized species relaxes the electronic polarization as the sum of two exponentials, as shown by Gibbs and Grosset\^ete.

Physical Review A•Jan 1, 1971•5 citations
The evolution of electronic angular momentum due to spin-exchange collisions between two species of ground-state alkali atoms is shown to depend substantially on nuclear spin when the effects of spin precession between collisions are included with the effects of the collisions themselves. General results are illustrated for nuclear spin \textonehalf{} and 1.
We consider electron spin-exchange collisions between an atom with an electron spin of \textonehalf{} and a target atom with an arbitrary electron spin. The cross sections that describe the collision are expressed in terms of generalized direct and exchange amplitudes and are shown to depend only on the electron spin, polarization, and alignment of the target atom. We include the effects of an external magnetic field and the nuclear spin of the spin-\textonehalf{} atom on the collision. We calculate the cross sections connecting the initial and final states of the free Hamiltonian describing the spin-\textonehalf{} atom, with analytic results being displayed for the two limiting cases of the external magnetic field. For the general case, graphical results are presented for several common values of nuclear spin that allow the cross sections to be evaluated for arbitrary magnetic fields. The results are applied to several situations of current interest.
Les collisions d'echange de spin sont un processus tres efficace pour transferer du moment angulaire a partir d'atomes qui ont ete polarises par un pompage optique de type Kastler, au spin electronique ou nucleaire d'atomes qui ne peuvent pas etre polarises directement par pompage optique. Dans cet article sont discutes l'histoire, l'etat actuel et quelques possibilites futures de l'echange de spin. Abstract. — Spin exchange collisions have been a very effective mechanism for transferring angular momentum from atoms which have been polarized by Kastler's optical pumping method to electron and nuclear spins of species which cannot be directly polarized by optical pumping. The history, current status and some of the future possibilities of spin exchange are discussed in this paper.
The theory of spin exchange between optically pumped alkali-metal atoms and noble-gas nuclei is presented. Spin exchange with heavy noble gases is dominated by interactions in long-lived van der Waals molecules. The main spin interactions are assumed to be the spin-rotation interactions $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\mathrm{N}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ between the rotational angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{N}}$ of the alkali-metal---noble-gas pair and the electron spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ of the alkali-metal atom, and the contact hyperfine interaction $\ensuremath{\alpha}\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ between the nuclear spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$ of the noble-gas atom and the electron spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$. Arbitrary values for KKK and for the nuclear spin III of the alkali-metal atom are assumed. Precise formal expressions for spin transfer coefficients are given along with convenient approximations based on a perturbation expansion in powers of ${(\frac{\ensuremath{\alpha}}{\ensuremath{\gamma}N})}^{2}$, a quantity which has been shown to be small by experiment.
Collisions of alkali-metal atoms in the ground state with the electron spin S = 1/2 are accompanied by exchange of electron coordinates between colliding particles, which leads to polarization transfer between them (i.e., to the well-known phenomenon of spin exchange). In addition, along with the polarization transfer from one partner to another, the magnetic resonance lines of colliding atoms are broadened and shifted in spin-exchange collisions. In particular the last two processes depend on the complex spin-exchange cross section. The real part of the cross section determines the so-called "spin-exchange cross section," which is responsible for the broadening of magnetic resonance lines, while the imaginary part determines the shift cross section, which governs the frequency shift of magnetic resonance. In order to describe the spin-exchange process one have to know complex spin-exchange cross sections. Complex spin-exchange cross sections are calculated on the basis of the data on the singlet (X 1 Σ + ) and triplet (a 3 Σ + ) potentials describing the interaction alkali-metal atoms in the ground state. Collisions of alkali-metal atoms Cs, Rb, K, Na in the ground state are considered in the energy interval of 10 −4 −10 −2 au.
Lambert's proof that the inclusion of nuclear spin does not alter the equation of motion for the electronic polarization is shown to be valid only when the hyperfine interaction is negligible. Usually the hyperfine frequency is much greater than the frequency of spin-exchange collisions; then the effect of the hyperfine interaction between collisions invalidates Lambert's proof. In general, spin exchange with a second depolarized species relaxes the electronic polarization as the sum of two exponentials, as shown by Gibbs and Grosset\^ete.