Asymptotic Behavior Of Wave Functions Research Articles

Continuous spectrum of three-cluster systems

For the example of the 5H = 3H + n + n nucleus, the effect of the Pauli exclusion principle on the asymptotic behavior of wave functions for the continuous spectrum of three-cluster systems is studied within a microscopic approach. It is shown that, in the asymptotic limit, the Schrodinger equation for the wave function that describes the relative motion of tritium and two neutrons reduces to the multichannel problem of valence-neutron scattering on the 4H subsystem. The single-channel approximation within which the phase shift for neutron scattering on the 4H subsystem occurring in the lowest energy state is the only feature that characterizes the continuous spectrum of the 5H nucleus is proposed and implemented.

Shell structure of weakly-bound and resonant neutrons

The systematic change of shell structure in both weakly bound and resonant neutron one-particle levels in nuclei towards the neutron drip line is exhibited, solving the coupled equations derived from the Schrödinger equation in coordinate space with the correct asymptotic behaviour of wave functions for r → ∞. The change comes from the behaviour unique in the one-particle motion with low orbital angular momenta compared with that with high orbital angular momenta. The observed deformation of very neutron-rich nuclei with N ⪆ 20 in the island of inversion is a natural result of this changed shell structure, while a possible deformation of neutron-drip-line nuclei with N ≈ 51, which are not yet observed, is suggested.

Asymptotic behaviour of wavefunctions: its applications to properties of atoms, molecules and nuclei

The asymptotic behaviour of a Schrodinger wavefunction for a bound system depends only on the separation energy of the last particle and the charges of this particle and the remaining system. An attempt is made, in terms of three simple examples, to demonstrate the importance of this behaviour in determining the properties of atoms, molecules and nuclei.

Coordinate asymptotic behavior of (3?3) wave functions for a system of three charged particles

The method set forth in the present paper enables one to find the leading terms in the asymptotic behavior of wave functions. This gives one the possibility to describe the class of functions considered in the scattering problem before one investigates the integral equations.