Five-body calculation of $s$-wave $n$-${}^4$He scattering at next-to-leading order pionless effective field theory

We present the first five-body calculations of $s$-wave $n$-${}^4$He scattering within leading order and next-to-leading order (NLO) pionless effective field theory. Using an harmonic oscillator trap technique and pionless effective field theory fitted to just six well-established experimental parameters, we predict the $s$-wave $n$-${}^4$He phase shifts, scattering length $a_{n^4\text{He}}^{1\mathrm{/}2}(\text{NLO})=2.47(4\text{ num.})(17\text{ theor.})\mathrm{f}\mathrm{m}$, and effective range $r_{n^4\text{He}}^{1\mathrm{/}2}(\text{NLO})=1.384(3\text{ num.})(211\text{ theor.})\mathrm{f}\mathrm{m}$ in agreement with experiment. The apparent cutoff independence of our results is used to estimate the theoretical errors coming as an integral part of our final results.