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.
The equation of state of symmetric nuclear matter is addressed starting both from a realistic interaction derived from nucleon-nucleon scattering processes and from a low-momentum effective potential. The approach is based on finite temperature Green’s functions. The internal energy per particle is estimated from the summation of diagrams and through the Galitskii-Koltun’s sum rule. At present, there is not a unique and reliable theory of nuclear interactions. From the study of nucleon-nucleon scattering processes different models for the basic interaction between nucleons have been developed, but difficulties arise when they are used in calculations which aim to reproduce the properties of bound nuclei. These models all reproduce the experimental N-N phase shifts up to the threshold for pion production with high accuracy, but differ in the short-wavelength region, where less experimental constraints are available. In deriving the properties of dense nuclear matter, if we start from a bare N-N potential we have to take into account the complex correlations induced
We present calculations of the energy per particle of pure neutron and symmetric nuclear matter with simplified Argonne nucleon-nucleon potentials for different many-body theories. We compare critically the Brueckner-Hartree-Fock results to other formalisms, such as the Brueckner-Bethe-Goldstone expansion up to third order, self-consistent Green's functions, auxiliary field diffusion Monte Carlo, and Fermi hypernetted chain. We evaluate the importance of spin-orbit and tensor correlations in the equation of state and find these to be important in a wide range of densities.
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.
Abstract The tensor-optimized Fermi sphere (TOFS) theory is applied first for the study of the property of nuclear matter using the Argonne V4
′NN potential. In the TOFS theory, the correlated nuclear matter wave function is taken to be a power-series type of the correlation function
F, where
F can induce central, spin–isospin, tensor, etc. correlations. This expression has been ensured by a linked cluster expansion theorem established in the TOFS theory. We take into account the contributions from all the many-body terms arising from the product of the nuclear matter Hamiltonian
H and
F. The correlation function is optimally determined in the variation of the total energy of nuclear matter. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced up to the nuclear matter density
ρ≃0.20 fm
−3 in the present numerical calculation, in comparison with other methods such as the Brueckner–Hartree–Fock approach.
Uniform neutron matter is approximated by a cubical box containing a finite number of neutrons, with periodic boundary conditions. We report variational and Green's function Monte Carlo calculations of the ground state of fourteen neutrons in a periodic box using the Argonne ${v8}^{\ensuremath{'}}$ two-nucleon interaction at densities up to one and half times the nuclear matter density. The effects of the finite box size are estimated using variational wave functions together with cluster expansion and chain summation techniques. They are small at subnuclear densities. We discuss the expansion of the energy of low-density neutron gas in powers of its Fermi momentum. This expansion is strongly modified by the large
nn scattering length, and does not begin with the Fermi-gas kinetic energy, as assumed in both Skyrme and relativistic mean field theories. The leading term of neutron gas energy is approximately half the Fermi-gas kinetic energy. The quantum Monte Carlo results are also used to calibrate the accuracy of variational calculations employing Fermi hypernetted and single operator chain summation methods to study nucleon matter over a larger density range, with more realistic Hamiltonians including three-nucleon interactions.