- #1

lLehner95

- 7

- 1

- Homework Statement
- In the process ##\gamma +p\rightarrow \pi _{0}+p##, in the lab frame the proton is the fixed target, and the photon has energy E_{\gamma }=144,7 MeV. Find the photon energy ##E_{\gamma }^{*}## in the center of mass frame.

- Relevant Equations
- ##E^{*}_{\gamma }=\gamma _{cm}E_{\gamma }-\beta _{cm}\gamma _{cm}p_{\gamma }##

##p_{\gamma }=\frac{E_{\gamma }}{c}##

I tried to use the Lorentz transformation:

##E^{*}_{\gamma }=\gamma _{cm}E_{\gamma }-\beta _{cm}\gamma _{cm}p_{\gamma }##

We have a photon, so it becomes:

##E^{*}_{\gamma }=\gamma _{cm}E_{\gamma }(\beta _{cm}-1)##

Unfortunately, the solutions say that the correct way is to use the inverse transormation:

##E_{\gamma }=\gamma _{cm}E^{*}_{\gamma }(\beta _{cm}+1)##

And the answer becomes:

##E^{*}_{\gamma }=\frac{E_{\gamma}}{\gamma_{cm}(1+\beta_{cm})}##

I already used the procedure to transform quantities (particles energy and momentum) from a reference to another, for example with the process ##p+\bar{p}\rightarrow \Lambda +\bar{\Lambda }##. Why it is not possible in this case?

##E^{*}_{\gamma }=\gamma _{cm}E_{\gamma }-\beta _{cm}\gamma _{cm}p_{\gamma }##

We have a photon, so it becomes:

##E^{*}_{\gamma }=\gamma _{cm}E_{\gamma }(\beta _{cm}-1)##

Unfortunately, the solutions say that the correct way is to use the inverse transormation:

##E_{\gamma }=\gamma _{cm}E^{*}_{\gamma }(\beta _{cm}+1)##

And the answer becomes:

##E^{*}_{\gamma }=\frac{E_{\gamma}}{\gamma_{cm}(1+\beta_{cm})}##

I already used the procedure to transform quantities (particles energy and momentum) from a reference to another, for example with the process ##p+\bar{p}\rightarrow \Lambda +\bar{\Lambda }##. Why it is not possible in this case?