The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the replusive core. By formulating the correlation as a transformation of the relative distance between particle pairs, general analytic expressions for the correlated wave functions and correlated operators are given. The decomposition of correlated operators into irreducible n-body operators is discussed. The one- and two-body-irreducible parts are worked out explicitly and the contribution of three-body correlations is estimated to check convergence. Ground state energies of nuclei up to mass number A=48 are calculated with a spin-isospin-dependent potential and single Slater determinants as uncorrelated states. They show that the deduced energy- and mass-number-independent correlated two-body Hamiltonian reproduces all "exact" many-body calculations surprisingly well.
Fermionic Molecular Dynamics (FMD) models a system of fermions by means of many-body states which are composed of antisymmetrized products of single-particle states. These consist of one or several Gaussians localized in coordinate and momentum space. The parameters specifying them are the dynamical variables of the model. As the repulsive core of the nucleon-nucleon interaction induces short range correlations which cannot be accommodated by a Slater determinant, a novel approach, the unitary correlation operator method (UCOM), is applied. The unitary correlator moves two particles away from each other whenever their relative distance is within the repulsive core. The time-dependent variational principle yields the equations of motion for the variables. Energies of the stationary ground states are calculated and compared to exact many-body results for nuclei up to Ca 48. Time-dependent solutions are shown for collisions between nuclei.
Within the framework of fermionic molecular dynamics a method is developed to better account for long-range tensor correlations in nuclei when working with a single Slater determinant. Single-particle states with mixed isospin and broken parity build up an intrinsic Slater determinant, which is then charge and parity projected. By minimizing the energy of this many-body state with respect to the parameters of the single-particle states and projecting afterward on angular momentum, ground-state energies are obtained that are systematically lower than corresponding Hartree-Fock results. The realistic Argonne V18 potential is used and short-range correlations are treated with the unitary correlation operator method. Comparison with exact few-body calculations shows that in
4He about one-fifth of the correlation energy from long-range correlations are accounted for. These correlations, which extend over the whole nucleus, are visualized with the isospin and spin-isospin density of the intrinsic state. The divergence of the spin-isospin density, the source for pion fields, turns out to be of dipole nature.
In Fermionic Molecular Dynamics the occurrence of multifragmentation depends strongly on the intrinsic structure of the many-body state. Slater determinants with narrow single-particle states and a cluster substructure show multifragmentation in heavy-ion collisions while those with broad wave functions, which resemble more a shell-model picture, deexcite by particle emission. Which of the two type of states occurs as the ground state minimum or as a local minimum in the energy depends on the effective interaction. Both may equally well reproduce binding energy and radii of nuclei. This ambiguity led us to reinvestigate the derivation of the effective interaction from realistic nucleon-nucleon potentials by means of a unitary correlation operator which is much more suited for dynamical calculations than the G-matrix or the Jastrow method. First results of mixing many Slater determinants are also presented.
A general theory is proposed for the description of short-range correlations of two nucleons in nuclei in the framework of the unitary-model-operator approach. A new effective interaction is derived through the unitary transformation of the original Hamiltonian. The transformed Hamiltonian is given in a cluster expansion form, and the structure of the one- and two-body cluster terms is studied. New aspects of the present approach, compared with the G-matrix theory, are; (i) the new effective interaction is E-independent and Hermitian, (ii) it satisfies the decoupling condition between low- and high-momentum two-particle states, and (iii) it contains both of the contributions of ladder and folded diagrams. It is suggested that the properties (i)∼(iii) of the new effective interaction may offer considerable advantages in accounting manybody correlations and deriving effective interaction among valence nucleons.
The nucleon momentum distribution
nA(k) for
A=2, 3, 4, 16, and 40 nuclei is systematically analyzed in terms of wave functions resulting from advanced solutions of the nonrelativistic Schr\"odinger equation, obtained within different many-body approaches based upon different realistic bare nucleon-nucleon (
NN) interactions featuring similar short-range repulsion and tensor interactions. Particular attention is paid to the separation of the momentum distributions into the mean-field and short-range correlation (SRC) contributions. It is shown that although at high values of the momentum
k different approaches lead to some quantitative differences, these do not hinder the general conclusion that the high-momentum behavior ($k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$) of all nuclei considered are very similar, exhibiting the well-known scaling behavior with the mass number
A, independently of the used many-body approach and the details of the bare
NN interaction. To analyze and understand the frequently addressed question concerning the relationships between the nucleus,
nA(k), and the deuteron,
nD(k), momentum distributions, the spin (
S)-isospin (
T) structure of few-nucleon systems and complex nuclei is analyzed in terms of realistic
NN interactions and many-body approaches. To this end, the number of
NN pairs in a given (
ST) state, viz.,
(ST)=(10), (00), (01), and (11), and the contribution of these states to the nucleon momentum distributions are calculated. It is shown that, apart from the (00) state, which has very small effects, all other spin-isospin states contribute to the momentum distribution in a wide range of momenta. It is shown that for all nuclei considered the momentum distributions in the states
T=0 and
T=1 exhibit at $k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$ very similar behaviors, which represents strong evidence of the
A-independent character of SRCs. The ratio
nA(k)/nD(k) is analyzed in detail, stressing that in the SRC region it always increases with the momentum and the origin of such an increase is discussed and elucidated. The relationships between the one- and two-body momentum distributions, considered in a previous paper, are discussed and clarified, pointing out the relevant role played by the center-of-mass motion of a correlated pair in the (10) state. Eventually, the values of the the probability of high-momentum components in nuclei and the per nucleon probability
a2 of deuteronlike configurations in nuclei are calculated, and the relationship of the present approach with the many-body methods based upon low-momentum effective interactions is briefly discussed.