A recursive approach to determine correlation functions in multi-baryon systems

Abstract

We propose a recursive algorithm for the calculation of multi-baryon correlation functions that combines the advantages of a recursive approach with those of the recently proposed unified contraction algorithm. The independent components of the correlators are built recursively by adding the baryons one after the other in a given order. The list of nonzero independent components is also constructed in a recursive manner, significantly reducing the resources required for this step. We computed the number of operations required to calculate the correlators up to Be^8, and observed a significant speedup compared to other techniques. For the calculation of He^4 and Be^8 correlation functions in the fully relativistic case O(10^8) operations are required, whereas for non-relativistic operators this number can be reduced to e.g. O(10^4) in the case of He^4.