No-core shell model in an effective-field-theory framework

We present a new approach to the construction of effective interactions suitable for many-body calculations by means of the no-core shell model (NCSM). We consider an effective field theory (EFT) with only nucleon fields directly in the NCSM model spaces. In leading order, we obtain the strengths of the three contact interactions from the condition that in each model space the experimental ground-state energies of 2H, 3H and 4He be exactly reproduced. The first (0+;0)(0+;0) excited state of 4He and the ground state of 6Li are then obtained by means of NCSM calculations in several spaces and frequencies. After we remove the harmonic-oscillator frequency dependence, we predict for 4He an energy level for the first (0+;0)(0+;0) excited state in remarkable agreement with the experimental value. The corresponding 6Li binding energy is about 70% of the experimental value, consistent with the expansion parameter of the EFT.