Abstract:

Energy spectra of three particles in the universal low-energy limit of zero-range two-body interactions are considered. Besides the positive masses, also the case of one negative and two positive masses (under the condition that a sum of the masses is negative) is studied. In the sector L^P = 0⁺, energy spectrum is given by E_N = exp(2πN/|γ|) (Efimov effect), where the dependence of the parameter γ on masses is determined. For larger L, one considers two identical particles of mass m and distinct one of mass m₁. For non interacting identical particles there is a correspondence between energy spectra for the positive mass ratio m/m₁ and negative one m*/ m₁* = −1/(2 + m₁/m). The critical values of the mass ratio, which indicate different approaches to formulating the three-body problem, are presented for L = 1 − 5. The dependence of energy on the interaction strengths for the lowest total angular momenta is exemplified.