The Angular Momentum Projection Calculation Of The Cranked Shell Model

It was showed from the calculation for K structure in the cranked shell model that the z component of nuclear angular momentum K no longer remains a good quantum number when the rotational frequency ω≠0 .however, with increasing ω, mang components with different K values mix with each other and none of them is dominant, which implies a significant deviation of nuclear shape from axial symmetry, but the primary weakness of this model is that angular momentum is not conservative, the energy eigenvalue is only marked by K, not by I. however, the experiment value of the energy is mainly marked by I. In order to compare the energy eigenvalue with the experiment value easily, It is necessary to calculate the energy using the angular momentum projection method in the cranked shell model. because of the complexity of the calculation, few people do the work . In this text, as a example, the angular momentum projection calculation was done in a six-particle system in the single-j(j=13/2)cranked shell model, and it can be used as a scheme to calculate for actual nuclear , especially, it can provide a feasible research path for the present energy transition calculation of high K isomer.At the base of the repeated calculation of K structure in the cranked shell model ,the VBP angular momentum projection calculation is done for low-lying eigenstates of the K structure, and the result of I structure is similar to the K structure, which proves that our calculation is right. In the meantime, the calculation give us the co variation of the I structure and it's energy structure in the cranked shell model.The calculation result tells us that the system's base is band of K=0, in which I=0,2,4,6...when the rotational frequency ω = 0 ,it is similar to the base state band of the even-even nuclear, but, when the co turn out .because of the K mixing, the eigenstate of each certain co is made of various I states, and each certain I is made of various K component. So, We can only plot out the energy band structure approximately according to the proportion of K.Because this text can calculate the energy and wave function which have certain I and K , it can be use for reference in the later study of Y transition of actual nuclear.