Chapter 3 Discrete Scaling and Scattering Properties from Atom-Dimer Collision Lauro Tomio and M. A. Shalchi Abstract A recent proposal on a new perspective to detect the Efimov-like discrete scaling in ultra-cold binary mixtures with strong mass-imbalanced atomic species is communicated. The discrete scaling can be identified by the energy dependence of an atom-molecule elastic cross-section, when colliding a heavy atom with mass m α into a weakly-bound heavy-light (m α , m β ) dimer. In the extreme mass-imbalanced system it was verified that the s -wave elastic cross section presents zeros at several specific energies of the projectile, in which emerges a discrete behavior from the ratio between these energies. This discrete behavior is identified with the same one predicted for the trimer excited bound-states, when considering the same mass-imbalanced system in the unitary limit. 3.1 Introduction In this presentation, we are reporting some results obtained in a recent work in which it was verified that the usual Efimov scaling factor [1], obtained in the spectrum of a mass-imbalanced three-body system near the unitary limit, can also be well identified in scattering observables with a mixture of two-species strong mass-imbalanced atomic system. In order to show that, the scattering solutions for a system with two heavy and one light particles (ααβ) are obtained by considering the heaviest one (α) colliding with the dimer formed the other two particles [2]. Here, we restrict the presentation to some indicative results related to discrete scaling, which are obtained by using zero-range interactions. L. Tomio (B ) · M. A. Shalchi Instituto de Física Teórica (IFT), Universidade Estadual Paulista (UNESP), São Paulo, SP 01140-070, Brazil e-mail: lauro.tomio@unesp.br L. Tomio Instituto Tecnológico de Aeronáutica, Departamento de Ciência e Tecnologia Aeroespacial (DCTA), São José dos Campos 12228-900, Brazil © Springer Nature Switzerland AG 2020 N. A. Orr et al. (eds.), Recent Progress in Few-Body Physics, Springer Proceedings in Physics 238, https://doi.org/10.1007/978-3-030-32357-8_3 15