Taking the single neutron levels of 12C in the Fermi sea as examples,the optimization of the imaginary time step(ITS) evolution with the box size and mesh size for the Dirac equation is investigated.For the weakly bou...Taking the single neutron levels of 12C in the Fermi sea as examples,the optimization of the imaginary time step(ITS) evolution with the box size and mesh size for the Dirac equation is investigated.For the weakly bound states,in order to reproduce the exact single-particle energies and wave functions,a relatively large box size is required.As long as the exact results can be reproduced,the ITS evolution with a smaller box size converges faster,while for both the weakly and deeply bound states,the ITS evolutions are less sensitive to the mesh size.Moreover,one can find a parabola relationship between the mesh size and the corresponding critical time step,i.e.,the largest time step to guarantee the convergence,which suggests that the ITS evolution with a larger mesh size allows larger critical time step,and thus can converge faster to the exact result.These conclusions are very helpful for optimizing the evolution procedure in the future self-consistent calculations.展开更多
基金supported partially by Guizhou Science and Technology Foundation (Grant No J[2010]2135)the National Basic Research Program of China (Grant No 2007CB815000)the National Natural Science Foundation of China (Grant Nos 10775004, 10947013, and 10975008)
文摘Taking the single neutron levels of 12C in the Fermi sea as examples,the optimization of the imaginary time step(ITS) evolution with the box size and mesh size for the Dirac equation is investigated.For the weakly bound states,in order to reproduce the exact single-particle energies and wave functions,a relatively large box size is required.As long as the exact results can be reproduced,the ITS evolution with a smaller box size converges faster,while for both the weakly and deeply bound states,the ITS evolutions are less sensitive to the mesh size.Moreover,one can find a parabola relationship between the mesh size and the corresponding critical time step,i.e.,the largest time step to guarantee the convergence,which suggests that the ITS evolution with a larger mesh size allows larger critical time step,and thus can converge faster to the exact result.These conclusions are very helpful for optimizing the evolution procedure in the future self-consistent calculations.
