Inelastic scattering of a structured particle: influence of the internal degrees of freedom on the scattering cross section

We studied the 2D classical scattering of a structured particle by a Gaussian well. The structured particle is composed of three point particles, each with a different mass ($m_1=1$, $m_2=2$, $m_3=3$), forming a linear chain. The interaction between the point particles was modelled as either a harmonic or a quartic spring. We assumed that there was no other interaction between these particles. The scattering of the composite particle was evaluated numerically for 5 different elastic constant for each type of spring including a case without interaction between the point particles. We found that there is a breakdown of the differential scattering cross-section for non zero elastic constant and initial energies at the same order or smaller than the depth of well. For these low energies the structured particle may get trapped in the Gaussian well. Depending on the impact parameter the particle may escape from the well after some time or it may remain trapped. Even if the particle escapes it can leave the well at any scattering angle. Therefore for this range of impact parameters the system behaves in a chaotic way and the differential scattering cross section cannot be properly defined. This effect was more evident for small values of spring constant. In the case without interaction between the particles, however, the scattering cross section was equivalent to the case of a single particle. We found that for larger values of energy the effect of the springs was less important and the ``molecule`` behaved in a similar way to a single point particle. The results for the harmonic and quartic spring were qualitatively and quantitatively similar. Therefore the chaotic behaviour seems to be mainly due to the interaction between internal and center-of-mass degrees of freedom and not to nonlinearities in the interaction potential.