Hofstadter experiment

The Hofstadter experiment (after Robert Hofstadter , who described it for the first time in 1957) is a physical experiment which, in addition to Rutherford's scattering experiment, provides important information about the nature of the atomic nucleus .

Hofstadter experiment: Fast electrons create a diffraction pattern of the atomic nucleus with a diameter . The right diagram shows the radiation intensity as a function of the diffraction angle ${\displaystyle {\text{e}}^{-}}$ ${\displaystyle d}$ ${\displaystyle I}$ ${\displaystyle \theta }$

In the experiment at the linear accelerator in Stanford , electrons with an energy of over 200  MeV were shot at the atomic nucleus and the diffraction pattern was examined.

The result for the atomic nucleus radius in femtometers ( ) was: ${\displaystyle R}$ ${\displaystyle 10^{-15}\,{\text{m}}}$

${\displaystyle {\begin{alignedat}{2}R\ &=r_{0}&&\cdot {\sqrt[{3}]{A}}\\\Rightarrow R\ &\approx 1{,}2\ {\text{fm}}&&\cdot {\sqrt[{3}]{A}},\end{alignedat}}}$

where stands for the mass number . ${\displaystyle A}$

This radius is contained in the formula of the charge distribution in the nucleus according to the Wood-Saxon formula (since electrons are leptons , the nuclear force does not act on them):

${\displaystyle \rho (r)={\frac {\rho _{0}}{1+\exp {\frac {r-R}{a}}}}}$

in which

• ${\displaystyle r}$ is the distance from the center of the core;
• ${\displaystyle a}$is the edge thickness parameter , which indicates the density profile of the nuclear matter at the core edge.

literature

• Jörn Bleck-Neuhaus: Elementary Particles: Modern Physics from Atoms to the Standard Model . Springer, Berlin 2010, ISBN 978-3-540-85299-5 .

Individual evidence

1. ^ R. Hofstadter: International Congress on Nuclear Sizes and Density Distributions Held at Stanford University, December 17-19, 1957 . In: Reviews of Modern Physics . tape 30 , no. 2 , March 1, 1958, p. 412-413 , doi : 10.1103 / RevModPhys.30.412 .