Asymmetric regularization of the ground and excited state of the ⁴He nucleus

Abstract.

We find the threshold structure of the two- and three-nucleon systems, with the deuteron and ³H/³He as the only bound nuclei, sufficient to predict a pair of four-nucleon states: a deeply bound state which is identified with the $\alpha$ ground state, and a shallow, unstable state at an energy $B^{\ast}_{\alpha} = [0.38\pm 0.25]$ MeV above the triton-proton threshold which is consistent with data on the first excited state of the $\alpha$ . The analysis employs the framework of Pionless EFT at leading order with a generalized regulator prescription which probes renormalization-group invariance of the two states with respect to higher-order perturbations including asymmetrical disturbances of the short-distance structure of the interaction. In addition to this invariance of the bound-state spectrum and the diagonal ³H-p ¹S₀ phase shifts in the $\alpha$ channel with respect to the short-distance structure of the nuclear interaction, our multi-channel calculations with a resonating-group method demonstrate the increasing sensitivity of nuclei to the neutron-proton P -wave interaction. We show that two-nucleon phase shifts, the triton channel, and three-nucleon negative-parity channels are less sensitive with respect to enhanced two-nucleon P -wave attraction than the four-nucleon ³H-p ¹S₀ phase shifts.