How to calculate if the Isospin, angular momentum is conserved in a reaction

[jonjacson]

Homework Statement

There are a lot of similar problems so it is a general question, if you have a nuclear reaction with two particles before, and two afther the process ¿How do you calculate if the Isospin is conserved?¿or the angular momentum?.

For example(it could be any other) we have this reaction:

Pi- + proton----------->Pi0 + neutron

And the question is if it is allowed or forbidden and why.

Homework Equations

Conservation laws of nuclear quantities.

The Attempt at a Solution

Well I started searching which were the properties of these particles:

For the pions I=1, and for the p,n the I=1/2 so now ¿Should i compose the total Isospin using clebsh jordan coefficients?.Or can i consider this?:

1+1/2=1+1/2 so I is conserved.

The same for the angular momentum.

¿What do you think?

 

[vela]

You're looking to see if the total isospin and angular momentum of the final state is equal to the total isospin and angular momentum of the initial state and if the z-component of these quantities is also conserved (if you have that info). You don't really need to go to the trouble of using the actual Clebsch-Gordon coefficient, but you need to understand how angular momenta add.

For example, if the initial state consists of a spin-1 particle and spin-1/2 particle, the allowed values of total angular momentum quantum number j is 1/2 and 3/2 (neglecting any orbital angular momentum). The final state must also have this total angular momentum. So two spin-1/2 particles would be forbidden because their angular momenta would combine to give either j=0 or j=1, but a spin-3/2 particle and a spin-0 particle would be allowed.

 

[jonjacson]

You're looking to see if the total isospin and angular momentum of the final state is equal to the total isospin and angular momentum of the initial state and if the z-component of these quantities is also conserved (if you have that info). You don't really need to go to the trouble of using the actual Clebsch-Gordon coefficient, but you need to understand how angular momenta add.

For example, if the initial state consists of a spin-1 particle and spin-1/2 particle, the allowed values of total angular momentum quantum number j is 1/2 and 3/2 (neglecting any orbital angular momentum). The final state must also have this total angular momentum. So two spin-1/2 particles would be forbidden because their angular momenta would combine to give either j=0 or j=1, but a spin-3/2 particle and a spin-0 particle would be allowed.

Thanks for the answer vela, I understand what you say, so I don't need to create the states, the important quantity is the module (and that is the conserved quantity), and you only have to check if the initial values are posible in the final state.

Thank you very much