The isotopic spin is in the theory of elementary a Flavor - quantum number , an inner symmetry of the strong interaction describes and for classifying the hadrons is used. The designation ( iso- : “quantitatively equal”, from ancient Greek ἴσος) indicates that the system appears like a spin 1/2 particle , although it is not a spin .
The concept is used more generally (also in solid-state physics ) to describe two-state systems . The two quantum mechanical states are understood as opposing orientations of the isospin (± ). If the system is in a superposition of the two states, this is described by the two other components ( ).
In scattering processes on mirror cores it was found that the strong interaction does not differentiate between neutral neutrons and positively charged protons , i.e. This means that it acts independently of the charge. With regard to the nuclear force, the neutron and proton are identical, and their slight difference in mass is related to the electrical charge . Werner Heisenberg concluded from this in 1932 that the proton and the neutron are two different charge states of one and the same particle, the nucleon .
For a further description he “borrowed” the quantum mechanical spin formalism from the corresponding behavior of the electrons . They also have two states ( spin-up and spin-down ) which cannot be distinguished by a certain force - here the purely electrical force.
The name Isospin was coined by Eugene Wigner in 1937 and initially stood for isotopic spin . However, since this can be misinterpreted as an indication of a change in the number of neutrons (cf. isotope ), the term isobaric spin is used today. Murray Gell-Mann combined the properties of isospin and strangeness in the Eightfold Way , a direct precursor of the quark model and quantum chromodynamics .
|Quark / antiquark||u||u|
|Quark / antiquark||d||d|
Like the normal spin of the fundamental fermions (such as the electron), the quantum number of the isospin always has the value 1/2.
The canonically used third component (often also referred to as) of the isospin represents its setting and has the two possible values +1/2 and −1/2. In the quark model, these stand for the two quarks
- u ( up ): and
- d ( down , Eng .: below): .
The quarks s , c , b and t do not have an isospin. For anti quarks the sign changes from .
The number of u and d quarks and the associated antiquarks is thus given as follows :
The difference between protons and neutrons results from their composition:
- Proton p = uud
- Neutron n = udd .
This assignment is done the other way around in some books and is just a convention that doesn't matter as long as consistency is maintained.
The hypercharge is
- for up and down quark respectively:
- for anti-up and anti-down quark:
- for the nucleons ( protons p, neutron n) respectively: .
Quantum field theory
- Bogdan Povh et al .: Particles and Cores . Springer, Berlin, Heidelberg 2006, ISBN 978-3-540-36685-0