Variation After Projection With Multi-shells And Its Calculation In The Psd Model Space

Nuclear is a quantum multi-body system,so the wave function and energy spectrum are usually obtained by solving the Schrodinger equation.The traditional shell model is based on this idea.As the research spread to heavier nuclear,the configuration space of its shell model increases dramatically,leading to a dramatic increase in shell model calculations,so it will become extremely difficult to accurately solve the eigen wave function.Therefore,people put forward various approximate methods,such as lining the Monte Carlo method,configuration space truncation,and the VAMPIR method etc,in order to get good shell model approximate results.The VAMPIR method was considered the most promising shell model approximation method.However,the computational complexity of the VAMPIR method makes it difficult to develop further in practical calculations.Firstly,there are 5-fold integral,but our research point out spin projection plays a key role in obtaining a good shell model approximation,and it makes the calculation become 3-fold integral.Secondly,the low-lying states are solved one by one in the VAMPIR,but all the low-lying states are varied together in our method.It can improve the computational efficiency.Up to now,the model space of the variation after projection method is still limited to a large shell,which makes the application range of the theoretical method very limited.In order to realize the shell model theory to push forward to the heavy nuclear,the model space must be extended to more large shells.In this paper,the model space is extended to more large shells in order to achieve a comprehensive description of the various low-lying states of the nuclear.Only by expanding the shell model space can the theoretical description of nuclear be more comprehensive and accurate.For example,in the model space of a large shell,the shell model can only give a kernel state with one parity,while in the multi-main shell space,the shell model can describe all positive and negative parity kernel states simultaneously.Therefore,the development of the variation after projection method of multi-shells is not only necessary for the study of deformed heavy nuclear,but also for the development of nuclear theory itself.For the variation after projection method of multi-shells,there are mainly two kinds of problems to deal with.One is the mixing of the parity in the wave function,so the parity projection is added in this paper.The other is the treatment of the center of mass problem,which is consistent with the standard shell model.We use the improved VAP method to calculate the low-lying energies of¹²C,¹³C,¹⁶O and ²⁰Ne in the psd model space.The results of the new VAP method developed in this paper are very close to that of the shell model,which indicates that the improved VAP method is still very effective in the psd model space.