We formulate a renormalizable pionless effective field theory (Pionless EFT) with a non-perturbative treatment of the Coulomb interaction up to next-to-leading order (NLO) for few-nucleon systems. We extract scattering observables for charged clusters by employing two-, three-, and four-body contact interactions and using the stochastic variational method with a Coulomb-corrected harmonic oscillator trap. Our NLO results yield a $pd$ spin-quartet scattering length and effective range of $a_{ pd}^{ 3/2} = 12.76(29)\,\mathrm{ fm}$ and $r_{ pd}^{ 3/2} = 1.17(7)\,\mathrm{ fm}$; for $dd$ scattering in the spin-quintet channel, we find $a_{ dd}^{ 2} = 6.26(3)\,\mathrm{ fm}$ and $r_{ dd}^{ 2} = 1.41(7)\,\mathrm{ fm}$; and for $p^3\mathrm{ He}$ scattering, the spin-singlet and spin-triplet channels are characterized by $a_{ p^3\mathrm{ He}}^0 = 11.26(4)\,\mathrm{ fm}$, $r_{ p^3\mathrm{ He}}^0 = 1.65(26)\,\mathrm{ fm}$ and $a_{ p^3\mathrm{ He}}^1 = 9.06(4)\,\mathrm{ fm}$, $r_{ p^3\mathrm{ He}}^1 = 1.36(25)\,\mathrm{ fm}$, respectively. Our predictions exhibit mild cutoff dependence and agree well with existing experimental phase shift analyses and potential model calculations. This demonstrates the predictive power of (Pionless EFT) for charged few-nucleon systems.
Categories: nucl-th