We propose a simple algorithm to further improve the previous variation after projection(VAP)wave functions for low-lying nonyrast states.We attach a weight factor to each calculated energy;then,the sum of these weigh...We propose a simple algorithm to further improve the previous variation after projection(VAP)wave functions for low-lying nonyrast states.We attach a weight factor to each calculated energy;then,the sum of these weighted energies is minimized.It turns out that a low-lying nonyrast VAP wave function can be further optimized when the weight factor for the corresponding energy is far larger than the other ones.Based on the improved WVAP wave functions,the energy-variance extrapolation method is applied to estimate the exact shell model energies.The calculated results for nuclei in the sd and pf model spaces clearly show that the extrapolated energies for all the calculated states are very close to the exact shell model ones within 10 keV.展开更多
The variation after projection(VAP)method is expected to be an efficient way of obtaining the optimized nuclear wave functions,which can be as close as possible to the exact shell model ones.However,we found that ther...The variation after projection(VAP)method is expected to be an efficient way of obtaining the optimized nuclear wave functions,which can be as close as possible to the exact shell model ones.However,we found that there are two additional problems that may seriously affect the convergence of the VAP iteration.The first problem is the existence of irrelevant projected basis states.At a VAP iteration,the Hill-Wheeler(HW)equation is composed of all updated projected basis states.If one of these projected basis states does not mix with a calculated wave function of interest,which is obtained by solving this HW equation,it is likely that this basis state will never mix with this wave function even after the VAP iteration converges.The other problem is the poor orthonormality among the projected basis states,which seriously affects the accuracy of the calculated VAP wave function.In the present work,solutions for these two problems are proposed,and examples are presented to test the validity.With the present solutions,the most important projected basis states can be reliably obtained,and the fully optimized VAP wave functions can be accurately and efficiently calculated.展开更多
基金Supported by the National Natural Science Foundation of China(11975314)the Key Laboratory of Nuclear Data foundation(JCKY2022201C158)the Continuous Basic Scientific Research Project(WDJC-2019-13,BJ20002501)
文摘We propose a simple algorithm to further improve the previous variation after projection(VAP)wave functions for low-lying nonyrast states.We attach a weight factor to each calculated energy;then,the sum of these weighted energies is minimized.It turns out that a low-lying nonyrast VAP wave function can be further optimized when the weight factor for the corresponding energy is far larger than the other ones.Based on the improved WVAP wave functions,the energy-variance extrapolation method is applied to estimate the exact shell model energies.The calculated results for nuclei in the sd and pf model spaces clearly show that the extrapolated energies for all the calculated states are very close to the exact shell model ones within 10 keV.
基金Supported by the National Natural Science Foundation of China(11975314)the Key Laboratory of Nuclear Data foundation(JCKY2022201C158)the Continuous Basic Scientific Research Project(WDJC-2019-13,BJ2000250)
文摘The variation after projection(VAP)method is expected to be an efficient way of obtaining the optimized nuclear wave functions,which can be as close as possible to the exact shell model ones.However,we found that there are two additional problems that may seriously affect the convergence of the VAP iteration.The first problem is the existence of irrelevant projected basis states.At a VAP iteration,the Hill-Wheeler(HW)equation is composed of all updated projected basis states.If one of these projected basis states does not mix with a calculated wave function of interest,which is obtained by solving this HW equation,it is likely that this basis state will never mix with this wave function even after the VAP iteration converges.The other problem is the poor orthonormality among the projected basis states,which seriously affects the accuracy of the calculated VAP wave function.In the present work,solutions for these two problems are proposed,and examples are presented to test the validity.With the present solutions,the most important projected basis states can be reliably obtained,and the fully optimized VAP wave functions can be accurately and efficiently calculated.
