| The solution of the Schrodinger equation for a complex quantum many-bodys system such as an atomic nucleus is a long-term problem for scientists.In theory,the interaction shell model(SM)can describe the structural properties of the nucleus in a comprehensive way.With the increase of the configuration space of the model,the computation amount of the full space shell model will increase in series.Under the present computing conditions,it is very difficult to realize such large-scale calculation.Therefore,the theorists introduce the theory of mean field approximation.The mean field approximation method such as HFB has been developed.Because the calculation of the mean field method is relatively small,it can be used to calculate the whole nuclear region.However,the above mean field method can be used to calculate the whole nuclear region.The method ignores many physical effects,and its wave function is difficult to describe the structural properties of the nucleus in detail.Therefore,based on the mean field,a beyond mean field method is proposed.There are many types of surpassing mean field methods,such as configuration mixing,generating coordinate method,symmetry recovery and so on.In this paper,we use the method of projection variation after projection to restore the symmetry of mean field.In this paper,the background of VAP theory and the basic idea of interaction shell model and mean field approximation are introduced.The advantages of these two theoretical models and the difficulties encountered in their application.One of a typical example of VAP method in this paper is VAMPIR,which is a very good approximation method for shell model.In principle,this method has a good prospect of development,but the calculation of VAMPIR requires neutrons.The projection of mass number and angular momentum is a 5-fold integral,which takes a lot of time to calculate,and the progress is slow in recent years.In very recently,new advances have been made in transcendental mean field theory.A new formula for calculating the operator matrix elements between two arbitrary mean fields has been proposed.We find that the spin angular momentum projection is the key to obtain a good shell model approximation.Therefore,in the present VAP calculation,we use HF vacuum state.In VAP,we only need to do three-dimensional angular momentum projection.In HF vacuum state,we consider time inversion symmetry breaking,so we can fully describe all nuclear states of even-even nucleus,odd-A nucleus and odd-odd nucleus.We have completed the calculation program of VAP method,and carried out some calculations for light and middle kernels.In this paper,we will give the calculation data for these three kinds of kernels under the VAP method and show their convergent energies in halo states and secondary halos calculated under the VAP method.By comparing with the shell model,we also calculate several rotational halo states of even and even nuclei of zero state,and observe the approximation between the results and the calculation of shell model.Finally,this paper discusses the further development of VAP theory.We hope that we can further optimize the VAP algorithm and improve the computational efficiency.We also hope that the new VAP method can be extended to the heavy core region.If possible,we also hope to extend the VAP method to the calculation of the excited states of atomic nuclei.In this way,we can study the singularity of more nuclei and give a physical explanation. |
