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kylergs
kylergs
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The problem given is

"A proton of total energy 3GeV makes a head-on collision with a 5GeV electron. Calculate the available energy in the centre-of-mass system to create any new additional particles in the collision"

My attempt to solve this was to calculate $pc$ for the proton using $(E^2 - E_0^2)^{1/2}$$(E_p^2 - (m_pc^2)^2)^{1/2}$ which evaluated to $2849 MeV$. I then compared invariants in the lab frame $p^\mu = \frac{1}{c}(E_p+E_e,E_e-pc)$ and the centre of mass frame $p'^\mu = \frac{1}{c}(E,0)$, where $E$ is the Energy available for particle creation. This gave $E^2 = (E_p+E_e)^2 - (E_e-pc)^2$, where all of the terms on the right are known. However, the value for E$E$ that this expression gave was 7.71GeV$7.71 GeV$, this was different from the given value of 6.76 GeV$6.76 GeV$.

The problem given is

"A proton of total energy 3GeV makes a head-on collision with a 5GeV electron. Calculate the available energy in the centre-of-mass system to create any new additional particles in the collision"

My attempt to solve this was to calculate $pc$ for the proton using $(E^2 - E_0^2)^{1/2}$ which evaluated to $2849 MeV$. I then compared invariants in the lab frame $p^\mu = \frac{1}{c}(E_p+E_e,E_e-pc)$ and the centre of mass frame $p'^\mu = \frac{1}{c}(E,0)$. This gave $E^2 = (E_p+E_e)^2 - (E_e-pc)^2$, where all of the terms on the right are known. However, the value for E that this expression gave was 7.71GeV, this was different from the given value of 6.76 GeV.

The problem given is

"A proton of total energy 3GeV makes a head-on collision with a 5GeV electron. Calculate the available energy in the centre-of-mass system to create any new additional particles in the collision"

My attempt to solve this was to calculate $pc$ for the proton using $(E_p^2 - (m_pc^2)^2)^{1/2}$ which evaluated to $2849 MeV$. I then compared invariants in the lab frame $p^\mu = \frac{1}{c}(E_p+E_e,E_e-pc)$ and the centre of mass frame $p'^\mu = \frac{1}{c}(E,0)$, where $E$ is the Energy available for particle creation. This gave $E^2 = (E_p+E_e)^2 - (E_e-pc)^2$, where all of the terms on the right are known. However, the value for $E$ that this expression gave was $7.71 GeV$, this was different from the given value of $6.76 GeV$.

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kylergs
kylergs
  • 51
  • 6

Available energy in centre of mass system

The problem given is

"A proton of total energy 3GeV makes a head-on collision with a 5GeV electron. Calculate the available energy in the centre-of-mass system to create any new additional particles in the collision"

My attempt to solve this was to calculate $pc$ for the proton using $(E^2 - E_0^2)^{1/2}$ which evaluated to $2849 MeV$. I then compared invariants in the lab frame $p^\mu = \frac{1}{c}(E_p+E_e,E_e-pc)$ and the centre of mass frame $p'^\mu = \frac{1}{c}(E,0)$. This gave $E^2 = (E_p+E_e)^2 - (E_e-pc)^2$, where all of the terms on the right are known. However, the value for E that this expression gave was 7.71GeV, this was different from the given value of 6.76 GeV.