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Nuclear Physics A

Time-dependent approach to bidimensional quantum tunneling: application to the proton emission from deformed nuclei

Patrick Talou, N. Cârjan, Daniel D Strottman

Published Mar 1, 1999• 17 citations
Publisher
DOI
10.1016/s0375-9474(99)00005-6

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DYNAMICAL STUDY OF PROTON EMISSION FROM DEFORMED NUCLEI

Margarit Rizea, N. Cârjan

The most intuitive and direct way to study proton emission from unbound nuclear states is to start with a proton wave packet localized inside the well of the p-nucleus interacting potential and follow its time evolution by solving numerically the time-dependent Schrödinger equation (TDSE). Then the physical properties of the decaying system can be inferred from its solution. The most important calculable quantities are: the tunneling probability and the decay rate. In the present paper we consider bi-dimensional axially symmetric nuclear shapes, allowing the treatment of both spherical and deformed nuclei. The solution of TDSE is obtained by the Crank-Nicolson method. We discuss also the treatment of numerical boundary conditions, the preparation of the initial wave function as a quasi-stationary state and the calculation of the decay rate using the flux. In application we reveal the influence of the deformation on the decay rate.

•Jan 1, 2008•2 citations
The time evolution of single proton quasi-stationary states emitted from axially deformed nuclei is studied by solving numerically the two-dimensional time dependent Schrödinger equation. Angular distributions of emission with respect to the nuclear axis of symmetry are obtained. It is shown that the main escape paths are determined by the quantum numbers of the metastable state, rather than by the deformation of the potential. Combinations of such numerical studies of multidimensional quantum tunneling and angular distribution measurements from oriented deformed nuclei could provide invaluable nuclear structure information and imaging of Nilsson orbitals.
The most intuitive and direct way to study proton emission from unbound nuclear states is to start with a proton wave packet localized inside the well of the p-nucleus interacting potential and follow its time evolution by solving numerically the time-dependent Schrödinger equation (TDSE). Then the physical properties of the decaying system can be inferred from its solution. The most important calculable quantities are: the tunneling probability and the decay rate. In the present paper we consider bi-dimensional axially symmetric nuclear shapes, allowing the treatment of both spherical and deformed nuclei. The solution of TDSE is obtained by the Crank-Nicolson method. We discuss also the treatment of numerical boundary conditions, the preparation of the initial wave function as a quasi-stationary state and the calculation of the decay rate using the flux. In application we reveal the influence of the deformation on the decay rate.