Systems with Weak Long Range Potentials

R.J. Lombard, Cristina Volpe A

Very weakly bound systems may manifest intriguing "universal" properties, independent of the specific interaction which keeps the system bound. An interesting example is given by relations between the size of the system and the separation energy, or scaling laws. So far, scaling laws have been investigated for short-range and long-range (repulsive) potentials. We report here on scaling laws for weakly bound two-body systems valid for a larger class of potentials, i.e. short-range potentials having a repulsive core and long-range attractive potentials. We emphasize analogies and differences between the short- and the long-range case. In particular, we show that the emergence of halos is a threshold phenomenon which can arise when the system is bound not only by short-range interactions but also by long-range ones, and this for any value of the orbital angular momentum $\ell$. These results enlarge the image of halo systems we are accustomed to.

Marc Baus

K. K. Singh

The problem of vertex renormalization at nonzero temperatures for a system of bosons interacting via a strong short-ranged repulsive potential and a weak long-ranged attractive potential is examined. It is shown that with the assumption of low temperatures and densities, one obtains expressions for the thermodynamic functions which corroborate the results of an earlier paper.

Minoru Takahashi

I. I. Zinnes

Joan Martorell, Juan Gonzalo Muga, Donald W. L. Sprung

Quantal systems are predicted to show a changeover from exponential to a slower decay rate at very long times. Asymptotically most models predict power-law decay with integer exponents. However, the postexponential decay of a trapped particle from a potential can occur with a continuous range of power-law exponents. We show that this happens when the outer part of the potential is repulsive and decreases with the inverse square of the distance. We demonstrate a simple relation between the strength of the long-range tail and the power-law exponent. We also give explicit forms for the postexponential decay laws when the outer part of the potential is weakly attractive. These systems are amenable to experimental scrutiny.