# Asymmetric regularization of the ground and excited state of the helium-4 nucleus

## TL;DR

This paper uses pionless effective field theory to analyze the structure of helium-4 and related nuclei, revealing the sensitivity of nuclear states to short-distance interactions and P-wave effects.

## Contribution

It introduces an asymmetric regularization approach within Pionless EFT to predict and analyze helium-4 states, emphasizing renormalization-group invariance and sensitivity to P-wave interactions.

## Key findings

- Identifies a deeply bound helium-4 ground state and a shallow excited state.
- Demonstrates invariance of certain nuclear properties under short-distance interaction variations.
- Shows increased sensitivity of nuclei to neutron-proton P-wave interactions.

## 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 helium-4 ground state, and a shallow, unstable state at an energy 0.38(25) MeV above the triton-proton threshold which is consistent with data on the first excited state of helium-4. 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 triton-proton 1S0 phase shifts in the helium-4 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 triton-proton 1S0 phase shifts.