Computing Transfer Amplitude between BCS-Pair Condensates

I propose a new algorithm that uses recursive relations to compute spectroscopic factor, pair transfer amplitude and cluster amplitude. demonstrate the it can be calculated very quickly stored within small computer memory consumption. In BCS case, particle number is always conserved time-consuming projection avoided. drive analytical expressions for expressed by asymmetry many-pair density matrix. This practically could used in all of nuclear double beta decay fields, heavy emission fields single-nucleon odd-mass isotopes.