Effective Field Theory for Light Nuclear Systems

We have applied the general principles of Effective Field Theory for the description of light nuclear systems. The interactions between nucleons is written as a controllable expansion consisting of contact interactions with an increasing number of derivatives. The many-body dynamics is solved with the No-Core Shell model approach. The nucleons are assumed to evolve in a harmonic oscillator trap characterized by the frequency $\omega$. The presence of the trap allows for the construction of nuclear interactions within the shell-model valence space directly from the low-energy scattering physics given by the effective range expansion. Binding and excitation energies of nuclear systems in the absence of a trap are obtained by taking the limit $\omega \rightarrow 0$. Results for $^3H$ and $^4He$ at leading order and next-to-leading order will be discussed.