On-shell transition of SRG and nuclear systems

Abstract

We make variational estimates for the binding energies of 2H, 3H, 4He, 16O, 40Ca, showing their running with the Similarity Renormalization Group (SRG) cutoff towards the infrared region and show the generalized Tjon lines that emerge from the calculations. We infer the SRG evolution of the three-body contributions for the 3H and 4He binding energies by computing the two-body contributions with a variational approach assuming that four-body forces are negligible. At any given SRG cutoff, the three-body contributions may then be inferred as being the experimental value minus the two-body contributions. The off-shell/on-shell transition at a critical SRG cutoff λc drives the behavior of all binding energies and this scale is the turning point of the generalized Tjon lines. Also, at λc the ratios between three-body and two-body contributions to the binding energies, Bλc(3)∕Bλc(2), are the same in both 3H and 4He systems and equal to 1∕4, so that Bλc(2)=4Bλc(3). All calculations are carried out with the Idaho–Salamanca N3LO potential, which is evolved with the SRG up to the infrared fixed point (λ→0) in all S, P, D, F and G partial-wave channels in order to compute the variational binding energies at several SRG cutoff scales.