Solving the Dirac Equation with Nonlocal Potential by Imaginary Time Step Method
ZHANG Ying1, LIANG Hao-Zhao1,2, MENG Jie1,3
1State Key Lab of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 1008712Institut de Physique Nucléaire, IN2P3-CNRS and Université Paris-Sud, F-91406 Orsay Cedex, France3Department of Physics, University of Stellenbosch, Stellenbosch, South Africa
Solving the Dirac Equation with Nonlocal Potential by Imaginary Time Step Method
ZHANG Ying1, LIANG Hao-Zhao1,2, MENG Jie1,3
1State Key Lab of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 1008712Institut de Physique Nucléaire, IN2P3-CNRS and Université Paris-Sud, F-91406 Orsay Cedex, France3Department of Physics, University of Stellenbosch, Stellenbosch, South Africa
摘要The imaginary time step (ITS) method is applied to solve the Dirac equation with the nonlocal potential in coordinate space by the ITS evolution for the corresponding Schrödinger-like equation for the upper component. It is demonstrated that the ITS evolution can be equivalently performed for the Schrödinger-like equation with or without localization. The latter algorithm is recommended in the application for the reason of simplicity and efficiency. The feasibility and reliability of this algorithm are also illustrated by taking the nucleus 16O as an example, where the same results as the shooting method for the Dirac equation with localized effective potentials are obtained.
Abstract：The imaginary time step (ITS) method is applied to solve the Dirac equation with the nonlocal potential in coordinate space by the ITS evolution for the corresponding Schrödinger-like equation for the upper component. It is demonstrated that the ITS evolution can be equivalently performed for the Schrödinger-like equation with or without localization. The latter algorithm is recommended in the application for the reason of simplicity and efficiency. The feasibility and reliability of this algorithm are also illustrated by taking the nucleus 16O as an example, where the same results as the shooting method for the Dirac equation with localized effective potentials are obtained.
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2009, Vol. 26 
