How Does the Bjorken x Variable Change for Bound Nucleons?

[morenopo2012]

TL;DR Summary

What is the expression used to calculate x bjorken for a given nucleon binding in a nucleus, in A number of nucleons.

Hello,

I have been looking into x bjorken variable, which is definied as $$x = \frac {Q^2} {Q^2 + W^2 - M}$$

But this expression is only validate on free nucleon, I would like to know what is the expression for binding nucleon.

Thanks.

 

[AndyW]

Hello,

Thank you for your question about the x Bjorken variable and its validity on binding nucleons. The expression for the x Bjorken variable on a bound nucleon is slightly different from the one used for free nucleons.

For a bound nucleon, the x Bjorken variable is defined as $$x = \frac{Q^2}{Q^2 + W^2 - M^2 + 2M\nu}$$
where M is the mass of the bound nucleon and $\nu$ is the energy transfer in the interaction. This expression takes into account the binding energy of the nucleon, which affects the kinematics of the interaction.

I hope this helps answer your question. If you have any further inquiries, please let me know.