#### granpa

how is a penning trap used to determine the upper limit of the electron radius. google hasnt been much help.

I found this but I dont understand it at all.

http://cerncourier.com/cws/article/cern/29724

What can be learned from the more accurate electron g? The first result beyond g itself is the fine structure constant, α = e2/4πε0hbarc – the fundamental measure of the strength of the electromagnetic interaction, and also a crucial ingredient in our system of fundamental constants. A Dirac point particle has g = 2. QED predicts that vacuum fluctuations and polarization slightly increase this value.

The third use of the measured g is in probing the internal structure of the electron – limiting the electron to constituents with a mass m* > m/√(δg/2) = 130 GeV/c2, corresponding to an electron radius R <1 × 10–18 m. If this test was limited only by our experimental uncertainty in g, then we could set a limit m* > 600 GeV. This is not as stringent as the related limit set by LEP, which probes for a contact interaction at 10.3 TeV. However, the limit is obtained quite differently, and is somewhat remarkable for an experiment carried out at 100 mK.

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#### Orion1

Wikipedia cites the abstract in reference 2.
Wikipedia said:
The electron is described as a fundamental or elementary particle. It has no known substructure.[2][64] Hence, it is defined or assumed to be a point charge with no spatial extent—a point particle.[10] Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10−22 meters.[65] The classical electron radius is 2.8179 × 10−15 m. This is the radius that is inferred from the electron's electric charge, by assuming that its mass energy has exclusively electrostatic origin and using the classical theory of electrodynamics alone ignoring quantum mechanics.
QED Penning trap upper limit for the electron particle radius:
$$r_e \leq 10^{-22} \; \text{m}$$

reference 2 said:
The quantum numbers of the geonium "atom", an electron in a Penning trap, have been continuously monitored in a non-destructive way by the new "continuous" Stern-Gerlach effect. In this way the g-factors of electron and positron have been determined to unprecedented precision:
$$\frac{1}{2} g = \frac{v_s}{v_c} = 1.001 159 652 188(4)$$

Wikipedia said:
In quantum mechanics, the Stern–Gerlach experiment[1], named after Otto Stern and Walther Gerlach, is an important 1922 experiment on the deflection of particles, often used to illustrate basic principles of quantum mechanics. It can be used to demonstrate that electrons and atoms have intrinsically quantum properties, and how measurement in quantum mechanics affects the system being measured.

Reference:
http://en.wikipedia.org/wiki/Penning_trap" [Broken]
http://www.iop.org/EJ/abstract/1402-4896/1988/T22/016/"
http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment" [Broken]

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#### granpa

thank you

http://www.iop.org/EJ/abstract/1402-4896/1988/T22/016/

The classical notion of an atomic particle at rest in free space is discussed, and shown to be approximable by zero-point confinement of the particle in a laboratory trap. An important tool for cooling the particle, and in the case of an electron, for obtaining directly the difference of spin and cyclotron frequencies vs, vc, is side band excitation. The quantum numbers of the geonium "atom", an electron in a Penning trap, have been continuously monitored in a non-destructive way by the new "continuous" Stern-Gerlach effect. In this way the g-factors of electron and positron have been determined to unprecedented precision,

½g ≡ vs/vc ≡ 1.001 159 652 188(4),

providing the most severe tests of QED and of the CPT symmetry theorem, for charged elementary particles. From the close agreement of experimental and theoretical g-values a new, 10^4 × smaller, value for the electron radius, Rg < 10^-20 cm, may be extracted.

#### malawi_glenn

Homework Helper
learning more about the anomalous magnetic moments of electrons, and muons, can lead one to find corrections and contributions from non-Standard Model particles/interactions.

http://www.g-2.bnl.gov/

http://dorigo.wordpress.com/2006/09/20/muon-g-2-and-supersymmetry/
http://arxiv.org/abs/0801.4905

Similar measurements on rare decays such as pi0-> e+e- can reveal if there is contribution from non-SM particles/interactions.

#### Orion1

Geonium atom...

Wikipedia said:
A single charged particle can be trapped indefinitely in a Penning trap. Penning trap is a combination of a homogeneous magnetic field and an electrostatic quadrupole potential. A small cloud of charged particles in such a trap is like a many electron atom, with the difference that the role of the atomic nucleus is played by an adjustable external field in the trap. Such a system is called a "geonium atom" [1], since the binding is to an external apparatus residing on the Earth.

In the simplest case, the system consists of only one electron or only one ion in the trap. This is analogous to the hydrogen atom. The properties of this single bound particle can be measured and calculated with a very high precision.

Reference:
http://en.wikipedia.org/wiki/Geonium_atom" [Broken]

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