Breakdown of universality in few-boson systems

We develop a series of resonant short-range two-boson potentials reproducing the same two-body low-energy observables and apply them in three- and four-body calculations. We demonstrate that the universal behavior predicted by effective field theory may be strongly violated and analyze the conditions for this phenomenon.

Figure 1

Evolution of the three- and four-boson binding energies with the cutoff parameter $\Lambda$.

Figure 2

Evolution of the atom-dimer and atom-trimer scattering lengths with the cutoff parameter $\Lambda$.

Figure 3

Correlation between trimer and tetramer ground-state binding energies.

Figure 4

Correlations of the trimer binding energies.

Figure 5

Correlations between the expectation values of kinetic energy and the corresponding binding energies.

Figure 6

Correlations between the mean square radii and the corresponding separation energies.

Figure 7

Configuration space $(r,r^{\prime })$ representation of the nonlocal rank-2 potentials in the form $V=r\langle r\left|v\right|r^{\prime }\rangle r^{\prime }$, obtained with $\Lambda =0.15$ Å${}^{-1}$ (top) and $\Lambda =0.27$ Å${}^{-1}$ (bottom).

Figure 8

Correlation between the atom-dimer scattering length and the trimer binding energy.

Figure 9

Correlation between the atom-trimer scattering length and the tetramer binding energy.