Discrete Scaling in Non-integer Dimensions

We explore the effect of a finite two-body energy in the discrete scale symmetry regime of two heavy bosonic impurities immersed in a light bosonic system. By means of the Born–Oppenheimer approximation in non-integer dimensions (D), we discuss the effective potential of the heavy-particles Schrodinger equation. We study how including the two-body energy in the effective potential changes the light-particles wave function and the ratio between successive Efimov states. We present the limit cycles associated with correlation between the energy of successive levels for the three and four-body systems. Our study is exemplified by considering a system composed of N-bosons, namely two Rubidium atoms interacting with N-2 Lithium ones ( \(^7\) ${}^7$ Li \(_{N-2}{-}^{87}\) ${}_{N-2}{-}^{87}$ Rb \(_2\) ${}_2$ ), which represent compounds of current experimental interest.