Introduction of the one-body correlation operator in the unitary-model-operator approach

In the earlier unitary-model-operator approach (UMOA), one-body correlations have been taken into account approximately by the diagonalization of unitary-transformed Hamiltonians in the 0p0h and 1p1h space. With this prescription, the dependence of the harmonic-oscillator energy (ℏω) on calculated observables is not negligible even at larger model spaces. In the present work, we explicitly introduce the one-body correlation operator so that it optimizes the single-particle basis states and then reduces the ℏω dependence. For an actual demonstration, we calculate the energy and radius for the 4He ground state with the softened nucleon-nucleon (NN) interactions from Argonne v18 (AV18) and chiral effective field theory (χEFT) up to the next-to-next-to-next leading order (N3LO). As a result, we obtain practically ℏω-free results at sufficiently large model spaces. The present results are reasonably close to those by the other ab initio calculations with the same NN interactions. This methodological development enables more systematic analysis of calculation results in the UMOA. We also discuss qualitatively the origin of the ℏω dependence on calculated observables in a somewhat simplified way.status: publishe