149 research outputs found

### Incompressibility in finite nuclei and nuclear matter

The incompressibility (compression modulus) $K_{\rm 0}$ of infinite symmetric
nuclear matter at saturation density has become one of the major constraints on
mean-field models of nuclear many-body systems as well as of models of high
density matter in astrophysical objects and heavy-ion collisions. We present a
comprehensive re-analysis of recent data on GMR energies in even-even $^{\rm
112-124}$Sn and $^{\rm 106,100-116}$Cd and earlier data on 58 $\le$ A $\le$ 208
nuclei. The incompressibility of finite nuclei $K_{\rm A}$ is expressed as a
leptodermous expansion with volume, surface, isospin and Coulomb coefficients
$K_{\rm vol}$, $K_{\rm surf}$, $K_\tau$ and $K_{\rm coul}$. \textit{Assuming}
that the volume coefficient $K_{\rm vol}$ is identified with $K_{\rm 0}$, the
$K_{\rm coul}$ = -(5.2 $\pm$ 0.7) MeV and the contribution from the curvature
term K$_{\rm curv}$A$^{\rm -2/3}$ in the expansion is neglected, compelling
evidence is found for $K_{\rm 0}$ to be in the range 250 $< K_{\rm 0} <$ 315
MeV, the ratio of the surface and volume coefficients $c = K_{\rm surf}/K_{\rm
vol}$ to be between -2.4 and -1.6 and $K_{\rm \tau}$ between -840 and -350 MeV.
We show that the generally accepted value of $K_{\rm 0}$ = (240 $\pm$ 20) MeV
can be obtained from the fits provided $c \sim$ -1, as predicted by the
majority of mean-field models. However, the fits are significantly improved if
$c$ is allowed to vary, leading to a range of $K_{\rm 0}$, extended to higher
values. A self-consistent simple (toy) model has been developed, which shows
that the density dependence of the surface diffuseness of a vibrating nucleus
plays a major role in determination of the ratio K$_{\rm surf}/K_{\rm vol}$ and
yields predictions consistent with our findings.Comment: 26 pages, 13 figures; corrected minor typos in line with the proof in
Phys. Rev.

### Short range correlations in relativistic nuclear matter models

Short range correlations are introduced using unitary correlation method in a
relativistic approach to the equation of state of the infinite nuclear matter
in the framework of the Hartree-Fock approximation. It is shown that the
correlations give rise to an extra node in the ground-state wave-function in
the nucleons, contrary to what happens in non-relativistic calculations with a
hard core. The effect of the correlations in the ground state properties of the
nuclear matter and neutron matter is studied. The nucleon effective mass and
equation of state (EOS) are very sensitive to short range correlations. In
particular, if the pion contact term is neglected a softening of the EOS is
predicted. Correlations have also an important effect on the neutron matter EOS
which presents no binding but only a very shallow minimum contrary to the
Walecka model.Comment: 8pages, 4 figure

### A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time

Interval Temporal Logic (ITL) is an established temporal formalism for
reasoning about time periods. For over 25 years, it has been applied in a
number of ways and several ITL variants, axiom systems and tools have been
investigated. We solve the longstanding open problem of finding a complete
axiom system for basic quantifier-free propositional ITL (PITL) with infinite
time for analysing nonterminating computational systems. Our completeness proof
uses a reduction to completeness for PITL with finite time and conventional
propositional linear-time temporal logic. Unlike completeness proofs of equally
expressive logics with nonelementary computational complexity, our semantic
approach does not use tableaux, subformula closures or explicit deductions
involving encodings of omega automata and nontrivial techniques for
complementing them. We believe that our result also provides evidence of the
naturalness of interval-based reasoning

### Moments of Inertia of Nuclei in the Rare Earth Region: A Relativistic versus Non-Relativistic Investigation

A parameter free investigation of the moments of inertia of ground state
rotational bands in well deformed rare-earth nuclei is carried out using
Cranked Relativistic Hartree-Bogoliubov (CRHB) and non-relativistic Cranked
Hartree-Fock-Bogoliubov (CHFB) theories. In CRHB theory, the relativistic
fields are determined by the non-linear Lagrangian with the NL1 force and the
pairing interaction by the central part of finite range Gogny D1S force. In
CHFB theory, the properties in particle-hole and particle-particle channels are
defined solely by Gogny D1S forces. Using an approximate particle number
projection before variation by means of the Lipkin Nogami method improves the
agreement with the experimental data, especially in CRHB theory. The effect of
the particle number projection on the moments of inertia and pairing energies
is larger in relativistic than in non-relativistic theory.Comment: 18 pages + 2 PostScript figure

### A timeband framework for modelling real-time systems

Complex real-time systems must integrate physical processes with digital control, human operation and organisational structures. New scientific foundations are required for specifying, designing and implementing these systems. One key challenge is to cope with the wide range of time scales and dynamics inherent in such systems. To exploit the unique properties of time, with the aim of producing more dependable computer-based systems, it is desirable to explicitly identify distinct time bands in which the system is situated. Such a framework enables the temporal properties and associated dynamic behaviour of existing systems to be described and the requirements for new or modified systems to be specified. A system model based on a finite set of distinct time bands is motivated and developed in this paper

### Borromean Binding of Three or Four Bosons

We estimate the ratio $R=g_{3}/g_{2}$ of the critical coupling constants
$g_{2}$ and $g_{3}$ which are required to achieve binding of 2 or 3 bosons,
respectively, with a short-range interaction, and examine how this ratio
depends on the shape of the potential. Simple monotonous potentials give
$R\simeq 0.8$. A wide repulsive core pushes this ratio close to R=1. On the
other hand, for an attractive well protected by an external repulsive barrier,
the ratio approaches the rigorous lower bound $R=2/3$. We also present results
for N=4 bosons, sketch the extension to $N>4$, and discuss various
consequences.Comment: 12 pages, RevTeX, 5 Figures in tex include

### Improved lower bounds for the ground-state energy of many-body systems

New lower bounds for the binding energy of a quantum-mechanical system of
interacting particles are presented. The new bounds are expressed in terms of
two-particle quantities and improve the conventional bounds of the Hall-Post
type. They are constructed by considering not only the energy in the
two-particle system, but also the structure of the pair wave function. We apply
the formal results to various numerical examples, and show that in some cases
dramatic improvement over the existing bounds is reached.Comment: 29 pages, 5 figures, to be published in Phys. Rev.

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