(a) How much energy was available in the center of mass for the experiment of Segrè and Chamberlain, who used 6.4-GeV protons on a fixed proton target to produce antiprotons in the reaction given here?
p+p \rightarrow p+p+p+\bar{p}(b) How much beam energy was necessary to produce the antiprotons? (c) How much energy is available for a similar reaction with 1-TeV protons from the Tevatron on a fixed proton target?
Strategy (a) We can use Equation (14.10) to calculate the energy available in the center of mass. (b) The threshold kinetic energy can be found by using Equation (14.11). We use the Q value defined in Equation (13.7). (c) We use Equation (14.10) to determine the center-of-mass energy available for the reaction for the Tevatron.
Q=M_{x} c^{2}+M_{X} c^{2}-\left(M_{y} c^{2}+M_{Y} c^{2}\right)=K_{y}+K_{Y}-K_{x} (13.7)
E_{ cm }=\sqrt{\left(m_{1} c^{2}+m_{2} c^{2}\right)^{2}+2 m_{2} c^{2} K} (14.10)
K_{ th }=(-Q) \frac{\text { total masses involved in reaction }}{2 m_{2}} (14.11)