﻿ Spin polarization

# Spin polarization

In a collection of identical particles such as electrons, atoms or ions is spin polarization - usually simply called polarization in practice - when the spin vectors of the particles are more or less aligned, the directions are therefore not randomly distributed.

## Basics

The axial vector of a spin described by the quantum number S can an elected quantization axis 2 S 1 are taking different directions (see directional quantization, multiplicity ). These are designated by a "spin magnetic" quantum number ms:

In the simplest case S = ½, the two values ​​ms = result - ½ and ms = ½ (multiplicity 2).

States that differ only in the value of ms, although are quantum mechanically different. However, they usually have the same energy, ie are " degenerate." In an ensemble of identical particles, these states ( with the exception of the electrons and positrons of the beta radiation, see below) are therefore generally up to random statistical fluctuations equally busy.

A polarization, ie deviation from the uniform distribution, can be at Spin-1/2-Teilchen described by the degree of polarization P:

Here, Nu and Nd, the numbers of particles with the two spin states ("up " and "down" ) for the selected axis. Also, the degree of polarization is often referred to as " polarization ". P is for an unpolarized ensemble 0, for a maximum of ± 1 polarized, often expressed as ± 100 %. The description by a polarization vector is possible; this is the vector sum of all spins in the ensemble divided by the number of particles and is usually also normalized to the magnitude 1 for maximum polarization. In particles having a higher spin than 1/2, that is, three or more possible orientations, the description of the polarization is complicated and generally requires a tensor appropriate stage.

Spin polarization is therefore not a property of a single particle, but the ensemble. In quantum mechanics, it can be described by the density matrix formalism.

## Spin polarization in a magnetic field

The spinning of particles is connected to a magnetic moment. Bring to the ensemble of particles in a magnetic field, so the energy of each state varies depending on the position to the field direction, the degeneracy is lifted. Hence the name " magnetic" quantum number stirred. The corresponding observable resolution of optical spectral lines is called the Zeeman effect.

As the particles accumulate preferentially in states of small energy, the magnetic field is already without further measures to a certain spin polarization. However, this is at ambient temperature is usually low because the magnetic energy differences are small compared to the thermal energy of the particles ( this is especially true for atomic nuclei with their small magnetic moments ). Using methods to much higher polarizations can be achieved. This is referred to in some, but not all cases hyperpolarization.

## Spin -orbit interaction in scattering processes

If an interest first flying on a straight track particles with spin deflected from its direction of flight, the interaction effect between spin and orbital angular momentum of the movement, much like in atoms and atomic nuclei (see spin-orbit coupling). Displays for example the spin vector in the x - direction, while the particles flying in the z- direction, the vectors of spin and orbital angular momentum are at deflection ( scattering) in the y- direction anti-parallel to the y- direction parallel to each other (see diagram). The differential cross-section is characterized differently with the same scattering angle, depending on the scattering of the Y side or the -Y - side is carried out. More generally, it depends not only on the scattering angle and the azimuth angle (see spherical coordinates ), the angle between the orbital plane and the xz plane decreases. For a polarized particle beam, the scattering process in this way, an analyzer is because two symmetrically to each other left and right of the xz plane established detectors register a different number of particles. On the other hand, in an unpolarized beam, the particles are scattered according to a specific page, a more or less strongly polarized ensemble; the scattering process thus acts as a polarizer.

Because of conservation of angular momentum is also evident in nuclear reactions corresponding behavior as scattering. Scattering and reaction experiments with observation of the polarization of the emitted particles or with polarized beam and target are therefore in nuclear physics an important means of closer determination of the spin -orbit interaction. Before you could produce polarized particle beams, polarized targets, delivered double -scattering experiments in which the same particles underwent two scatterings consecutively information. When you put the first scattering polarizer, the second the analyzer dar.

## Preparation of the spin polarization

### Neutral matter

In solids, liquids or gases polarization of the nuclei is generated by a magnetic field, often with the aid of lower temperature in order to keep the thermal energy of the particles is small (see Boltzmann distribution ). With this technique, for example, was Wu experiment at 10 mK, a polarization degree of the cobalt -60 seeds of about 60 % was reached.

Instead of a strong external field, the field caused by the electron spin to a paramagnetic ion can be used to polarize the cores in some cases, so that a relative weak external field is sufficient, which aligns the ions.

Another method is to line up atoms by optical pumping with circularly polarized light, and the coupling torque of the electron with the nucleus (see hyperfine ) utilize.

### Ion beams

Polarized ion beams for use in particle accelerators can be prepared by the advanced concept of the Stern-Gerlach experiment produced: from an atomic beam, eg, hydrogen or deuterium, in the inhomogeneous magnetic field of a polarized beam component is obtained and this then - in the simplest case - in a weak magnetic field ionized taking advantage of the hyperfine splitting.

Another type of " polarized ion sources " makes use of the splitting of the energy levels by the Lamb shift.

### Neutron

Polarized slow neutrons for neutron scattering are obtained (see neutron supermirror ) by reflection at the aligned atoms of a ferromagnetic mirror.

## Applications

• Spin polarized neutrons can be used to examine the magnetic structure of solids.
• In photoelectron spectroscopy, the spin polarization of the emitted electrons can provide information on the magnetic orientation of the sample and the polarization of the exciting radiation.
• In nuclear physics help scattering and nuclear reaction experiments with polarized particles to explore details of certain states of the nuclei, since the cross sections of the processes depend on the spin orientation.
• Possibly, the reaction yield can be substantially improved in nuclear fusion reactors by using spin-polarized fuel.
• Improve substances with polarized nuclei of certain nuclear magnetic resonance studies, eg in medicine, the sensitivity ( see hyperpolarization (physics) ).

## Electron and positron polarization during beta decay

The emitted during beta decay particles are spin polarized along their direction of emission. Rotate Illustratively stated, for example,, viewed the electrons from beta-minus decay in their flight direction, preferably counterclockwise ( left-handed electrons). This is explained with the fact that the person responsible for the beta decay of weak interactions violate the mirror symmetry of the laws of nature maximum (see parity violation ), by generating only chiral left-handed particles and right-handed chiral antiparticles. This affects the longitudinal spin polarization of the emitted particles.

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