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Why do head-on particle collisions make more energy available for creating new particles?

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Diagram of a linear proton resonance accelerator, or linac, showing protons entering from a source, passing through a series of labeled drift tubes powered by a radio-frequency source, and exiting as a beam through a cavity. — particle accelerator The accelerator is a large-diameter tube within which an electric field oscillates at a high radio frequency. Within the accelerator tube are smaller diameter metallic drift tubes, which are carefully sized and spaced to shield the protons from decelerating oscillations of the electric field. In the spaces between the drift tubes, the electric field is oriented properly to accelerate the protons in their direction of travel.

Head-on particle collisions are more effective for creating new particles because they maximize the energy available for interaction, whereas fixed-target collisions waste a significant portion of energy on the motion of the target material.12

In a fixed-target accelerator, a beam of particles strikes a stationary target. According to the principle of conservation of momentum, the system must maintain its total momentum after the collision. Consequently, much of the beam's energy is consumed by the kinetic energy required to set the target material in motion.132

In contrast, when two beams of particles with equal mass and opposite velocity collide head-on, their net momentum is zero. Because the total momentum is zero, the products of the collision can be at rest, allowing virtually all of the combined beam energy to be converted into the energy of the interaction. This maximizes the energy available for the creation of new particles via the Einstein mass-energy relation, which states that mass and energy are equivalent and interconvertible.214