LAUSR

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 $0\text{p}0\text{h}$ and $1\text{p}1\text{h}$ space. With this prescription, the dependence of the harmonic-oscillator energy ($\ensuremath{\hbar}\ensuremath{\omega}$) 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 $\ensuremath{\hbar}\ensuremath{\omega}$ dependence. For an actual demonstration, we calculate the energy and radius for the $^{4}\mathrm{He}$ ground state with the softened nucleon-nucleon ($NN$) interactions from Argonne v18 (AV18) and chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) up to the next-to-next-to-next leading order ($\mathrm{N}^{3}\mathrm{LO}$). As a result, we obtain practically $\ensuremath{\hbar}\ensuremath{\omega}$-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 $\ensuremath{\hbar}\ensuremath{\omega}$ dependence on calculated observables in a somewhat simplified way.