Making Kraptons A little known particle physicist has proposed the existence of a new particle, with charge +2 and mass 2, which he has named the Krapton. He has calculated that this can be produced by the collision of two protons in the reaction* [latex] p^{+}+p^{+}+10 MeV \rightarrow K^{++}[/latex] Having failed to obtain funding to verify his theory, he has built his own equipment with which he accelerates protons to an energy of 16 MeV and uses them to bombard a stationary target of hydrogen. Could he succeed in making a Krapton?

Suppose a proton with kinetic energy E collides with proton at rest. Then this system has initial linear momentum [latex] (2 m E)^{1 / 2} [/latex], where m is the mass of a proton. This linear momentum is preserved by the collision so that, if a Krapton of mass 2m were produced, it would have linear momentum [latex] (2 m E)^{1 / 2} [/latex] and therefore kinetic energy E/2. Hence, only 8 MeV of the initial energy is available for Krapton building and, according to the physicist’s own calculation, this is not enough. (On the other hand, a head-on collision between two 5 MeV protons would be enough. Why?)

Question 10.4: Making Kraptons A little known particle physicist has propos...

Classical Mechanics

Making Kraptons

A little known particle physicist has proposed the existence of a new particle, with charge +2 and mass 2, which he has named the Krapton. He has calculated that this can be produced by the collision of two protons in the reaction*

$p^{+}+p^{+}+10 MeV \rightarrow K^{++}$

Having failed to obtain funding to verify his theory, he has built his own equipment with which he accelerates protons to an energy of 16 MeV and uses them to bombard a stationary target of hydrogen. Could he succeed in making a Krapton?

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Suppose a proton with kinetic energy E collides with proton at rest. Then this system has initial linear momentum $(2 m E)^{1 / 2}$ , where m is the mass of a proton. This linear momentum is preserved by the collision so that, if a Krapton of mass 2m were produced, it would have linear momentum $(2 m E)^{1 / 2}$ and therefore kinetic energy E/2. Hence, only 8 MeV of the initial energy is available for Krapton building and, according to the physicist’s own calculation, this is not enough. (On the other hand, a head-on collision between two 5 MeV protons would be enough. Why?)