Gaussian Parametrization of Efimov Levels: Remnants of Discrete Scale Invariance

The Efimov window, or universal window, is a particular energy region in which few-body systems are loosely bound. Many characteristics of those systems are universal; their properties are largely independent of the particular interaction that produces the binding. This suggests the use of simple potential models characterized by few parameters to describe dynamical properties. Essentially, the potential parameters are set in order to reproduce a small number of data, and then the potential strength can be varied to explore the window. Among others, the Gaussian potential has been used to characterize the universal window. From calculations of the ground state and of the first excited state of three identical bosons using a Gaussian potential along the window, we determine what is called the gaussian-level function. This function is independent of the particular Gaussian potential used in this procedure. Moreover, it contains finite-range corrections which are of particular importance when theoretical predictions are compared to experimental data.