Relatore
Dr.
Alejandro Kievsky
(INFN)
Descrizione
When the two-body scattering length $a$ of two identical bosons
diverges the three-boson spectrum shows the Efimov effect.
In this limit, the unitary limit, an infinite set of bound states,
$E_3^n$, appears approaching zero in a geometrical progression. In
other words, the $L=0$ sector of three identical bosons presents
a discrete scaling invariance (DSI). As the absolute value of $a$
takes finite values, the highest bound states disappear into the atom-
dimer continuum ($a>0$) or in the three-atom continuum ($a<0$).
In recent years the spectrum of the three-boson system has been
extensively studied in the $(1/a,\kappa)$ plane, with $\kappa^2=mE/\hbar^2$ [1]. When one boson is added to the system, the four-body system at the unitary limit presents two bound states, one deep ($E_4^0$) and one shallow ($E_4^1$) with the following ratios, $E_4^0/E_3^0\approx 4.6$ and $E_4^1/E_3^0\approx 1.001$, having an universal character [2]. This particular form of the spectrum has been recently studied up to six bosons [3].
In the present work I will show the spectrum of $A$ bosons for
increasing number of particles using a Leading Order description
in terms of a two-body gaussian potential plus a three-body
potential devised to describe the dimer and trimer binding energies.
The capability of this model to describe the saturation properties,
as N goes to infinite, is analysed making a direct link between the
low energy scale and the short-range correlations. We will show that
the energy per particle, $E_N/N$, can be obtained with reasonable accuracy at leading order extending the universal behaviour observed in few-boson systems close to the unitary limit to the many-body system [4].
[1] E. Braaten and H.W. Hammer, Phys. Rep. {\bf 428}, 259 (2006)
[2] A. Deltuva, R. Lazauskas and L. Platter, Few-Body Syst. {\bf 51}, 235 (2011)
[3] M. Gattobigio, A. Kievsky and M. Viviani, Phys. Rev. A {\bf 86}, 042513 (2012)
[4] A. Kievsky, A. Polls, B. Julia' Diaz and N. Timofeyuk, Phys. Rev. A (rapid communication), in press
Autore principale
Dr.
Alejandro Kievsky
(INFN)
