Linear Collision of a Classical Harmonic Oscillator with a Particle at High Energies

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Abstract
The collision of a harmonic oscillator with a particle is studied classically. All three particles are constrained to lie in a line. A soft exponential interaction and a rigid sphere interaction are considered and the connection between these two interactions is investigated. A relation is given between the hardness of the interaction potential, the oscillator force constant, and the collision energy. Nonmonotonicity of the energy transfer at high energies is shown to be related to multiple collisions.