Eur. Phys. J. A (2018) 54: 137
https://doi.org/10.1140/epja/i2018-12573-7

Regular Article - Theoretical Physics

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

¹ Department of Physics, The City College of New York, 10031, New York, NY, USA
² Kavli Institute for Theoretical Physics, University of California, 93106, Santa Barbara, CA, USA
³ Institute for Nuclear Studies, Department of Physics, George Washington University, 20052, Washington DC, USA

^* e-mail: kirschjs@web.de

Received: 29 March 2018
Accepted: 26 July 2018
Published online: 23 August 2018

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 ground state, and a shallow, unstable state at an energy MeV above the triton-proton threshold which is consistent with data on the first excited state of the . 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 ¹ S ₀ phase shifts in the 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 ¹ S ₀ phase shifts.