Bounds on radii and kinetic energies of N-particle systems

Jan-Markus Schwindt

J. H. Sandoval, F. F. Bellotti, A. S. Jensen +1 more

We calculate root-mean-square radii for a three-body system confined to two spatial dimensions and consisting of two identical bosons ($A$) and one distinguishable particle ($B$). We use zero-range two-body interactions between each of the pairs, and focus thereby directly on universal properties. We solve the Faddeev equations in momentum space and express the mean-square radii in terms of first-order derivatives of the Fourier transforms of densities. The strengths of the interactions are adjusted for each set of masses to produce equal two-body bound-state energies between different pairs. The mass ratio, $\mathcal{A}={m}_{B}/{m}_{A}$, between particles $B$ and $A$ are varied from 0.01 to 100, providing a number of bound states decreasing from 8 to 2. Energies and mean-square radii of these states are analyzed for small $\mathcal{A}$ by use of the Born-Oppenheimer potential between the two heavy $A$ particles. For large $\mathcal{A}$ the radii of the two bound states are consistent with a slightly asymmetric three-body structure. When $\mathcal{A}$ approaches thresholds for binding of the three-body excited states, the corresponding mean-square radii diverge inversely proportional to the deviation of the three-body energy from the two-body thresholds. The structures at these three-body thresholds correspond to bound $AB$ dimers and one loosely bound $A$ particle.

Marcelo Takeshi Yamashita, D. V. Fedorov, A. S. Jensen

We compute binding energies and root-mean-square radii for weakly bound systems of $N=4$ and $5$ identical bosons. Ground and first excited states of an $N$-body system appear below the threshold for binding the system with $N\ensuremath{-}1$ particles. Their root-mean-square radii approach constants in the limit of weak binding. Their probability distributions are on average located in nonclassical regions of space which result in universal structures. Radii decrease with increasing particle number. The ground states for more than five particles are probably nonuniversal, whereas excited states may be universal.

G. M. Zhislin

Arvydas Juozapas Janavičius

The new quantum waves’ diffusion equation based on Heisenberg uncertainties and De Broglie’s frequencies of waves is presented. The free movement and quantum diffusion through a rectangular barrier are considered. We find a quantum diffusion coefficient and radii of bound systems. The obtained formula connecting radii and bound energies of simple quantum systems, such as a hydrogen atom, deuteron and mesons, consisted of quarks.