# How Are Isospin Values Determined?

• jeebs
In summary, isospin values are chosen based on the number of states a particle has, such as +1/2 and -1/2 for a spin=1/2 particle. The I3 values may be arbitrary and based on conventions, such as ranking particles according to charge.
jeebs
Hi,
I'm having a little bit of trouble with isospin. What I have gathered so far is that say, for the proton and neutron, apart from their charge they are very similar, so they are considered to be different states of the same particle called the nucleon.

So, we say the nucleon has an isospin of I=1/2, and the proton has third component I3=+1/2, and the neutron has third component I3=-1/2, right? And we say the proton and neutron form the nucleon multiplet, right?

Also, there are other multiplets like the pions. the pion multiplet (which has I=1) consists of $$\pi^+$$,$$\pi^0$$ and $$\pi^-$$, which have I3=+1, 0 and -1 respectively.

What I don't get is where these numbers actually come from. How have the values for I assigned to each multiplet been worked out?

And am I right in thinking that the I3 values are arbitrary, for example, there was no reason to give protons an I3 value of +1/2 instead of -1/2, its just something that was decided on?

Thanks.

The isospin values are chosen to give the correct number of states.

Eg., "proton" and "neutron" are 2 states. We know that a spin=1/2 particle also has two states, +1/2 and -1/2. So we use I=1/2 for the isospin.

Similarly for the pion system and a spin=1 particle, which both have 3 possible states.

And am I right in thinking that the I3 values are arbitrary, for example, there was no reason to give protons an I3 value of +1/2 instead of -1/2, its just something that was decided on?
I suspect that is the case. It may be the convention to rank particles according to charge when assigning I3 values.

## What is isospin?

Isospin is a quantum number that describes the symmetry between protons and neutrons in an atomic nucleus. It is analogous to the concept of electrical charge.

## Why is isospin important in nuclear physics?

Isospin allows us to understand and predict the behavior of atomic nuclei, particularly in reactions involving protons and neutrons. It is also used to classify particles and determine their properties.

## How is isospin measured and expressed?

Isospin is measured in units of 1/2 and is typically denoted by the symbol I. It is expressed as either a positive or negative half-integer depending on the charge of the particle.

## What is the relationship between isospin and spin?

Isospin and spin are both quantum numbers that describe different properties of particles. While isospin relates to the symmetry between protons and neutrons, spin relates to the intrinsic rotational momentum of a particle.

## Can isospin be changed or manipulated?

Isospin can be changed in certain nuclear reactions, but it is a conserved quantity in most interactions. It cannot be manipulated or controlled in the same way as other physical properties, such as charge or mass.

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