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I recently read in a book that a nucleon with +1/2 isospin is a proton and if the isospin is changed to -1/2, it is a neutron, so it is the same particle in different states. If a proton has a different quark configuration $uud$ than a neutron $udd$, what happens to the quark composition when the isospin changes from +1/2 to -1/2?

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Isospin is an approximate symmetry of nuclear interactions. Roughly, the "x" component of isospin consists of changing u quarks to d quarks and d quarks to u quarks. Because u quarks and d quarks are very similar - have different charges but about the same mass and reasonably precisely the same interactions with gluons and other quarks, you can quickly summarize the properties of various baryons and mesons in terms of this approximate symmetry.

The neutron and proton are not really the same particle in a different state. Rather, they are two very similar particles, which would have the same masses and other properties if there were no mass difference between the d and u quarks and there was no such thing as electromagnetic or weak interactions. If this were the case, they would be as similar (and as different) as an electron with spin "up" and an electron with spin "down", at least if you had experimental knobs (like the magnetic field for ordinary spins) that rotated the isospin of the particles. Such a knob would be (sort of) the W and Z fields.

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Like spin, isospin cannot change in isolation: an intermediate particle is required. For spin that particle is most frequently the photon: if you want to reorient a particle in a magnetic field, the correct model to use is absorption or emission of a virtual photon from the magnet.

The most important isospin-changing particle in the nuclear force is the pion, a triplet of particles with charge ±1 or 0. The $\pi^±$ are the isospin raising and lowering operators that you're interested in: the reactions $\rm p\leftrightarrow n\pi^+$ or $\rm n\leftrightarrow p\pi^-$ rotate the isospin of the nucleon but preserve quark content.

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