The Born series for $S$-wave quartet $nd$ scattering at small cutoff values

Understand

Perturbative expansions, the Born series, of the scattering length and the amplitude of $S$-wave neutron-deuteron scattering for spin quartet channel below deuteron breakup threshold are studied in pionless effective field theory at small cutoff values.

• A three-body contact interaction is introduced when the integral equation is solved using the small cutoffs.
• After renormalizing the three-body interaction by using the scattering length, we expand the integral equation as the ordinary and inverted Born series.
• We find that the scattering length and the phase shift are considerably well reproduced with a few terms of the inverted Born series at relatively large cutoff values, $\Lambda\simeq 100$ MeV.