Application of ATMS to the 4He trimer and tetramer

Energetics and structural properties of three-dimensional bosonic clusters near threshold

“…For example, although one expects a new momentum scale µ (4) to be needed for the description of universal properties of the tetramer [14,48], there is evidence that at least some observables of the tetramer near threshold are independent of this new momentum scale [8]. In this context, a number of studies have focused on the Tjon line [4,49,50,51,52], which was first investigated in nuclear physics and refers to the approximately linear correlation between the energies of the fournucleon and the three-nucleon system [51,52]. In the following, correlations between our trimer and tetramer energies, which are calculated for realistic atom-atom interactions, are demonstrated.…”

Unitarity and Discrete Scale Invariance

“…As with the Phillips line, this correlation was discovered empirically by plotting results of phenomenological nuclear potentials. It also exists for 4 He atoms [56]. It materializes in EFT as a variation of Λ ⋆ [48,49,50] .…”

Naturalness in nuclear effective field theories

“…The EFT line lies close not only to the experimental point but also to the empirical line, meaning that the many parameters of the various phenomenological potentials amount to a single relevant parameter Λ ⋆ . Similarly, A ≥ 4 ground-state binding energies are correlated with the A = 3 ground-state energy [53,54,59] in a Tjon [66,67] and generalized Tjon [68,69] lines.…”