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.

Using PVS for Interval Temporal Logic proofs, part 1: The syntactic and semantic encoding

Interval temporal logic (ITL) is a logic that is used to specify and reason about systems. The logic has a powerful proof system but rather than doing proofs by hand, which is tedious and error prone, we want a tool that can check each proof step. Instead of developing a new tool we will use the existing prototype verification system (PVS) as a basic tool. The specification language of PVS is used to encode interval temporal logic semantically and syntactically. With this we can encode the ITL proof system within PVS. Several examples of proofs in ITL that are done per hand are checked with PVS.Funded by EPSRC Research Grant GR/K2592

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

Compositional modelling: The formal perspective

We provide a formal framework within which an Information System (IS) could be modelled, analysed, and verified in a compositional manner. Our work is based on Interval Temporal Logic (ITL) and its programming language subset, Tempura. This is achieved by considering IS, of an enterprise, as a class of reactive systems in which it is continually reacting to asynchronously occurring events within a given period of time. Such a reactive nature permits an enterprise to pursue its business activities to best compete with others in the market place. The technique is illustrated by applying it to a small case study from Public Service Systems (PSS).Funding received from the UK Engineering and Physical Sciences Research Council (EPSRC) through the Research Grant GR/M/0258

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

New features of collective motion of intrinsic degrees of freedom. Toward a possible way to classify the intrinsic states

Three exactly solvable Hamiltonians of complex structure are studied in the framework of a semi-classical approach. The quantized trajectories for intrinsic coordinates correspond to energies which may be classified in collective bands. For two of the chosen Hamiltonians the symmetry SU2xSU2 is the appropriate one to classify the eigenvalues in the laboratory frame. Connections of results presented here with the molecular spectrum and Moszkowski model are pointed out. The present approach suggests that the intrinsic states, which in standard formalisms are heading rotational bands, are forming themselves "rotational" bands, the rotations being performed in a fictious boson space.Comment: 33 pages, 9 figure