We investigate how the unitary correlation operator method (UCOM), developed to explicitly describe the strong short-range central and tensor correlations present in the nuclear many-body system, relates to the similarity renormalization group (SRG), a method to band-diagonalize Hamiltonians by continuous unitary transformations. We demonstrate that the structure of the UCOM transformation, originally motivated from the physically intuitive picture of correlations in coordinate space, arises naturally from the SRG flow equation. Apart from formal considerations we show that the momentum space matrix elements of the effective interactions obtained in both schemes agree extremely well.
In this work a unitary correlation operator is presented that explicitly describes the short-ranged central and tensor correlations in the nuclear many-body system. These short-ranged correlations are induced by the repulsive core and the pronounced tensor force of realistic nucleon-nucleon interactions and cannot be described by the simple many-body states of a mean-field or shell model approach. The unitary correlation operator is discussed for the Argonne V18 and the Bonn-A interactions. Applying the correlation operator onto the Hamiltonian a common effective interaction for low momenta is obtained. Calculations for 4He using the one- and two-body part of the correlated Hamiltonian compare favorably with exact many-body methods. Calculations for 16O and 40Ca which are not possible with exact methods are performed using harmonic oscillator shell model states. The observed deviation from the experimental binding energies and radii is attributed to the missing three-body forces. The correlated interaction in a basis-free representation is used in the Fermionic Molecular Dynamics model to calculate the nuclei of the p- and the sd-shell. In this model the uncorrelated many-particle state is given as a Slaterdeterminant of Gaussian wave-packets with spin and isospin degrees of freedom which allows a consistent description of spherically symmetric, intrinsically deformed and clustered nuclei.
We study symmetric nuclear matter using bare nucleon-nucleon (
NN) interactions with the finite particle-number approach within finite cubic boxes. Due to the
NN correlations originating from the bare
NN interaction, two nucleons can be excited to the high-momentum region, leading to the increase of the kinetic energy in nuclear matter. We further consider the spin excitations in the nucleon pairs, where the spins of the two nucleons are changed, and this excitation is important for the tensor correlation. The unitary correlation operator method (UCOM) is used to treat the short-range correlation. The tail correction coming from the neighboring boxes is also included. We demonstrate the contributions of various excitations of nucleon pairs as well as the tail correction to the total energy at normal density. We also discuss the effects of UCOM and correlated nucleon pairs on the density dependence of the total energy. We calculate the equations of state of symmetric nuclear matter using two kinds of the Argonne potentials and the results agree with those from other many-body theories. The density dependences of the Hamiltonian components are also shown.