683 research outputs found
Unveiling the origin of shape coexistence in lead isotopes
The shape coexistence in the nuclei Pb is analyzed within the
Hartree-Fock-Bogoliubov approach with the effective Gogny force. A good
agreement with the experimental energies is found for the coexisting spherical,
oblate and prolate states. Contrary to the established interpretation, it is
found that the low-lying prolate and oblate states observed in this mass
region are predominantly characterized by neutron correlations whereas the
protons behave as spectators rather than playing an active role.Comment: 5 pages, 6 postscript figure
Structural evolution in germanium and selenium nuclei within the mapped interacting boson model based on the Gogny energy density functional
The shape transitions and shape coexistence in the Ge and Se isotopes are
studied within the interacting boson model (IBM) with the microscopic input
from the self-consistent mean-field calculation based on the Gogny-D1M energy
density functional. The mean-field energy surface as a function of the
quadrupole shape variables and , obtained from the constrained
Hartree-Fock-Bogoliubov method, is mapped onto the expectation value of the IBM
Hamiltonian with configuration mixing in the boson condensate state. The
resultant Hamiltonian is used to compute excitation energies and
electromagnetic properties of the selected nuclei Ge and
Se. Our calculation suggests that many nuclei exhibit
softness. Coexistence between prolate and oblate, as well as between spherical
and -soft, shapes is also observed. The method provides a reasonable
description of the observed systematics of the excitation energy of the
low-lying energy levels and transition strengths for nuclei below the neutron
shell closure , and provides predictions on the spectroscopy of
neutron-rich Ge and Se isotopes with , where data are scarce
or not available.Comment: 16 pages, 20 figure
Spectroscopy of quadrupole and octupole states in rare-earth nuclei from a Gogny force
Collective quadrupole and octupole states are described in a series of Sm and
Gd isotopes within the framework of the interacting boson model (IBM), whose
Hamiltonian parameters are deduced from mean field calculations with the Gogny
energy density functional. The link between both frameworks is the
() potential energy surface computed within the
Hartree-Fock-Bogoliubov framework in the case of the Gogny force. The
diagonalization of the IBM Hamiltonian provides excitation energies and
transition strengths of an assorted set of states including both positive and
negative parity states. The resultant spectroscopic properties are compared
with the available experimental data and also with the results of the
configuration mixing calculations with the Gogny force within the generator
coordinate method (GCM). The structure of excited states and its
connection with double octupole phonons is also addressed. The model is shown
to describe the empirical trend of the low-energy quadrupole and octupole
collective structure fairly well, and turns out to be consistent with GCM
results obtained with the Gogny force.Comment: 17 pages, 12 figures, 4 table
Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study
Most {\em ab initio} calculations on fullerene molecules have been carried
out based on the paradigm of the H\"uckel model. This is consistent with the
restricted nature of the independent-particle model underlying such
calculations, even in single-reference-based correlated approaches. On the
other hand, previous works on some of these molecules using model Hamiltonians
have clearly indicated the importance of short-range inter-atomic spin-spin
correlations. In this work, we consider {\em ab initio} non-collinear
Hartree--Fock (HF) solutions for representative fullerene systems: the bowl,
cage, ring, and pentagon isomers of C, and the larger C,
C, C, C, and C fullerene cages. In all cases but
the ring we find that the HF minimum corresponds to a truly non-collinear
solution with a torsional spin density wave. Optimized geometries at the
generalized HF (GHF) level lead to fully symmetric structures, even in those
cases where Jahn-Teller distortions have been previously considered. The nature
of the GHF solutions is consistent with the -electron space becoming
polyradical in nature: each -orbital remains effectively singly occupied.
The spin frustration, induced by the pentagon rings in an otherwise
anti-ferromagnetic background, is minimized at the HF level by aligning the
spins in non-collinear arrangements. The long-range magnetic ordering observed
is reminiscent of the character of broken symmetry HF solutions in polyacene
systems.Comment: 16 figure
Multi-reference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model
A multi-reference configuration mixing scheme is used to describe the ground
state, characterized by well defined spin and space group symmetry quantum
numbers as well as doping fractions , of one dimensional
Hubbard lattices with nearest-neighbor hopping and periodic boundary
conditions. Within this scheme, each ground state is expanded in a given number
of nonorthogonal and variationally determined symmetry-projected
configurations. The results obtained for the ground state and correlation
energies of half-filled and doped lattices with 30, 34 and 50 sites, compare
well with the exact Lieb-Wu solutions as well as with the ones obtained with
other state-of-the-art approximations. The structure of the intrinsic
symmetry-broken determinants resulting from the variational procedure is
interpreted in terms of solitons whose translational and breathing motions can
be regarded as basic units of quantum fluctuations. It is also shown that in
the case of doped 1D lattices, a part of such fluctuations can also be
interpreted in terms of polarons. In addition to momentum distributions, both
spin-spin and density-density correlation functions are studied as functions of
doping. The spectral functions and density of states, computed with an ansatz
whose quality can be well-controlled by the number of symmetry-projected
configurations used to approximate the electron systems, display
features beyond a simple quasiparticle distribution, as well as spin-charge
separation trends.Comment: 16 pages, 11 figure
Effective shell model Hamiltonians from density functional theory: quadrupolar and pairing correlations
We describe a procedure for mapping a self-consistent mean-field theory (also
known as density functional theory) into a shell model Hamiltonian that
includes quadrupole-quadrupole and monopole pairing interactions in a truncated
space. We test our method in the deformed N=Z sd-shell nuclei Ne-20, Mg-24 and
Ar-36, starting from the Hartree-Fock plus BCS approximation of the USD shell
model interaction. A similar procedure is then followed using the SLy4 Skyrme
energy density functional in the particle-hole channel plus a zero-range
density-dependent force in the pairing channel. Using the ground-state solution
of this density functional theory at the Hartree-Fock plus BCS level, an
effective shell model Hamiltonian is constructed. We use this mapped
Hamiltonian to extract quadrupolar and pairing correlation energies beyond the
mean field approximation. The rescaling of the mass quadrupole operator in the
truncated shell model space is found to be almost independent of the coupling
strength used in the pairing channel of the underlying mean-field theory.Comment: 15 pages, 5 figure
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