171 research outputs found
Saturation properties and incompressibility of nuclear matter: A consistent determination from nuclear masses
Starting with a two-body effective nucleon-nucleon interaction, it is shown
that the infinite nuclear matter model of atomic nuclei is more appropriate
than the conventional Bethe-Weizsacker like mass formulae to extract saturation
properties of nuclear matter from nuclear masses. In particular, the saturation
density thus obtained agrees with that of electron scattering data and the
Hartree-Fock calculations. For the first time using nuclear mass formula, the
radius constant =1.138 fm and binding energy per nucleon = -16.11
MeV, corresponding to the infinite nuclear matter, are consistently obtained
from the same source. An important offshoot of this study is the determination
of nuclear matter incompressibility to be 288 28 MeV using
the same source of nuclear masses as input.Comment: 14 latex pages, five figures available on request ( to appear in Phy.
Rev. C
RPA vs. exact shell-model correlation energies
The random phase approximation (RPA) builds in correlations left out by
mean-field theory. In full 0-hbar-omega shell-model spaces we calculate the
Hartree-Fock + RPA binding energy, and compare it to exact diagonalization. We
find that in general HF+RPA gives a very good approximation to the ``exact''
ground state energy. In those cases where RPA is less satisfactory, however,
there is no obvious correlation with properties of the HF state, such as
deformation or overlap with the exact ground state wavefunction.Comment: 6 pages, 7 figures, submitted to Phys Rev
Scalar ground-state observables in the random phase approximation
We calculate the ground-state expectation value of scalar observables in the
matrix formulation of the random phase approximation (RPA). Our expression,
derived using the quasiboson approximation, is a straightforward generalization
of the RPA correlation energy. We test the reliability of our expression by
comparing against full diagonalization in 0 h-bar omega shell-model spaces. In
general the RPA values are an improvement over mean-field (Hartree-Fock)
results, but are not always consistent with shell-model results. We also
consider exact symmetries broken in the mean-field state and whether or not
they are restored in RPA.Comment: 7 pages, 3 figure
Theoretical Aspects of Science with Radioactive Nuclear Beams
Physics of radioactive nuclear beams is one of the main frontiers of nuclear
science today. Experimentally, thanks to technological developments, we are on
the verge of invading the territory of extreme N/Z ratios in an unprecedented
way. Theoretically, nuclear exotica represent a formidable challenge for the
nuclear many-body theories and their power to predict nuclear properties in
nuclear terra incognita. It is important to remember that the lesson learned by
going to the limits of the nuclear binding is also important for normal nuclei
from the neighborhood of the beta stability valley. And, of course, radioactive
nuclei are crucial astrophysically; they pave the highway along which the
nuclear material is transported up in the proton and neutron numbers during the
complicated synthesis process in stars.Comment: 26 ReVTeX pages, 11 Postscript figures, uses epsf.sty, to be
published in: Theme Issue on Science with Beams of Radioactive Nuclei,
Philosophical Transactions, ed. by W. Gelletl
Shell structure of superheavy nuclei in self-consistent mean-field models
We study the extrapolation of nuclear shell structure to the region of
superheavy nuclei in self-consistent mean-field models -- the
Skyrme-Hartree-Fock approach and the relativistic mean-field model -- using a
large number of parameterizations. Results obtained with the Folded-Yukawa
potential are shown for comparison. We focus on differences in the isospin
dependence of the spin-orbit interaction and the effective mass between the
models and their influence on single-particle spectra. While all relativistic
models give a reasonable description of spin-orbit splittings, all
non-relativistic models show a wrong trend with mass number. The spin-orbit
splitting of heavy nuclei might be overestimated by 40%-80%. Spherical
doubly-magic superheavy nuclei are found at (Z=114,N=184), (Z=120,N=172) or
(Z=126,N=184) depending on the parameterization. The Z=114 proton shell
closure, which is related to a large spin-orbit splitting of proton 2f states,
is predicted only by forces which by far overestimate the proton spin-orbit
splitting in Pb208. The Z=120 and N=172 shell closures predicted by the
relativistic models and some Skyrme interactions are found to be related to a
central depression of the nuclear density distribution. This effect cannot
appear in macroscopic-microscopic models which have a limited freedom for the
density distribution only. In summary, our findings give a strong argument for
(Z=120,N=172) to be the next spherical doubly-magic superheavy nucleus.Comment: 22 pages REVTeX, 16 eps figures, accepted for publication in Phys.
Rev.
Cohomological tautness for Riemannian foliations
In this paper we present some new results on the tautness of Riemannian
foliations in their historical context. The first part of the paper gives a
short history of the problem. For a closed manifold, the tautness of a
Riemannian foliation can be characterized cohomologically. We extend this
cohomological characterization to a class of foliations which includes the
foliated strata of any singular Riemannian foliation of a closed manifold
Pairing Properties In Relativistic Mean Field Models Obtained From Effective Field Theory
We apply recently developed effective field theory nuclear models in mean
field approximation (parameter sets G1 and G2) to describe ground-state
properties of nuclei from the valley of -stability up to the drip lines.
For faster calculations of open-shell nuclei we employ a modified BCS approach
which takes into account quasi-bound levels owing to their centrifugal barrier,
with a constant pairing strength. We test this simple prescription by comparing
with available Hartree-plus-Bogoliubov results. Using the new effective
parameter sets we then compute separation energies, density distributions and
spin--orbit potentials in isotopic (isotonic) chains of nuclei with magic
neutron (proton) numbers. The new forces describe the experimental systematics
similarly to conventional non-linear relativistic force
parameters like NL3.Comment: 29 pages, 17 figures, accepted for publication in PR
Nuclear Ground State Observables and QCD Scaling in a Refined Relativistic Point Coupling Model
We present results obtained in the calculation of nuclear ground state
properties in relativistic Hartree approximation using a Lagrangian whose
QCD-scaled coupling constants are all natural (dimensionless and of order 1).
Our model consists of four-, six-, and eight-fermion point couplings (contact
interactions) together with derivative terms representing, respectively, two-,
three-, and four-body forces and the finite ranges of the corresponding mesonic
interactions. The coupling constants have been determined in a self-consistent
procedure that solves the model equations for representative nuclei
simultaneously in a generalized nonlinear least-squares adjustment algorithm.
The extracted coupling constants allow us to predict ground state properties of
a much larger set of even-even nuclei to good accuracy. The fact that the
extracted coupling constants are all natural leads to the conclusion that QCD
scaling and chiral symmetry apply to finite nuclei.Comment: 44 pages, 13 figures, 9 tables, REVTEX, accepted for publication in
Phys. Rev.
Modified differentials and basic cohomology for Riemannian foliations
We define a new version of the exterior derivative on the basic forms of a
Riemannian foliation to obtain a new form of basic cohomology that satisfies
Poincar\'e duality in the transversally orientable case. We use this twisted
basic cohomology to show relationships between curvature, tautness, and
vanishing of the basic Euler characteristic and basic signature.Comment: 20 pages, references added, minor corrections mad
Shell Corrections of Superheavy Nuclei in Self-Consistent Calculations
Shell corrections to the nuclear binding energy as a measure of shell effects
in superheavy nuclei are studied within the self-consistent Skyrme-Hartree-Fock
and Relativistic Mean-Field theories. Due to the presence of low-lying proton
continuum resulting in a free particle gas, special attention is paid to the
treatment of single-particle level density. To cure the pathological behavior
of shell correction around the particle threshold, the method based on the
Green's function approach has been adopted. It is demonstrated that for the
vast majority of Skyrme interactions commonly employed in nuclear structure
calculations, the strongest shell stabilization appears for Z=124, and 126, and
for N=184. On the other hand, in the relativistic approaches the strongest
spherical shell effect appears systematically for Z=120 and N=172. This
difference has probably its roots in the spin-orbit potential. We have also
shown that, in contrast to shell corrections which are fairly independent on
the force, macroscopic energies extracted from self-consistent calculations
strongly depend on the actual force parametrisation used. That is, the A and Z
dependence of mass surface when extrapolating to unknown superheavy nuclei is
prone to significant theoretical uncertainties.Comment: 14 pages REVTeX, 8 eps figures, submitted to Phys. Rev.
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