Constraint Molecular Dynamics and results on isotopic distributions produced in heavy ion collision — The Sn + Ni systems

The Constraint Molecular Dynamics approach is illustrated together with calculation on different heavy ion collisions. In particular the charge-mass distribution produced in the collision ¹²⁴Sn + ⁶⁴Ni and ¹¹²Sn + ⁵⁸Ni at 35 MeV/nucleon is discussed. By comparing the Y = (N ? Z)/A distributions for fragments produced in central collisions it results that this observable can be sensitive to the dynamic effects induced on the two systems by the different charge/mass ratio.     

An alternative for moduli stabilisation

The one-loop vacuum energy is explicitly computed for a class of perturbative string vacua where supersymmetry is spontaneously broken by a T-duality invariant asymmetric Scherk–Schwarz deformation. The low-lying spectrum is tachyon-free for any value of the compactification radii and thus no Hagedorn-like phase-transition takes place. Indeed, the induced effective potential is free of divergence, and has a global anti-de Sitter minimum where geometric moduli are naturally stabilised.     

Highly excited “nuclear molecules”: A way to explain the fluctuations in DBHIC excitation functions. Study of the28Si +28Si colliding system at 5.3 MeV ·A

The properties of the strong fluctuations observed in the excitation functions of Dissipative Binary Heavy Ion Collisions (DBHIC) have been studied for the system²⁸Si+²⁸Si in the energy range 150 MeV ≤E _lab ≤ 156 MeV with 150 keV step laboratory incident energy, by angular distributions and excitation functions measurements. Experimental results are compared to the the recently developed Partially Overlapping Molecular Level Model (POMLM). The parameters of the model have been determined with reasonable accuracy by describing all the quantities characterizing the fluctuations in the excitation functions i.e.: Average Angular Distributions, Energy Autocorrelation Functions, Variances, Angular Correlation Coefficients. The results of the analysis strongly support the idea of a process proceeding through the formation of an highly excited “nuclear molecule”. Experimental data collected at the most forward angles show the effects of strong excitation of a few final channels.     

Pre-equilibrium γ ray emission in different reaction mechanisms at 8 MeV/nucleon

Recent experimental results on particles-γ coincidence measurements on the systems ¹²C +⁶⁴Ni and ³⁵Cl +⁶⁴Ni at about 8 MeV/nucleon are interpreted as due to the effect of a Dipole pre-equilibrium emission produced during the damping of the proton-neutron relative collective motion in very deformed intermediate systems formed in the first instants of the collision. The pre-equilibrium effects are evaluated through semiclassic kinetic theories and through modified statistical approach to include non-stationary effects in Fusion processes, Massive Transfer reactions (in the ¹²C +⁶⁴Ni system) and in Binary Dissipative reactions (in the ³⁵Cl +⁶⁴Ni system). In particular the study performed on the dipole molecular component allows to establish a link between the above phenomenon and the charge and mass transfer process in quasi-peripheral reactions. Received: 15 April 1998 / Revised version: 8 June 1998     

Search for high energy γ-rays emission in28Si,32S+64Ni dissipative reactions at about 5 MeV/amu incident energy

Photons emitted in the²⁸ Si+⁶⁴ Ni and³² S+⁶⁴ Ni reactions at 143 MeV and 156 MeV incident energy respectively, have been detected in coincidence with the ejected charged fragments. An array of 48 BaF₂ -rays detector and 6 solid state silicon detector telescopes have been used. Photon energy spectra measured in the energy range from 2 to 20 MeV in coincidence with ejectiles coming from deep inelastic reactions, are consistent with statistical emission from the reaction products.Thanks are due to Dr.T.Noorman for the suggestions in the statistical calculations and to Mr.C.Marchetta for the preparation of high quality targets.     

Gamma-ray multiplicity measurements in the28Si+64Ni reaction at 163.8 MeV

The²⁸Si+⁶⁴Ni reaction at 163.8 MeV incident energy is studied by measuring in coincidenceγ-rays and charged particles identified from Z=2 to Z=16. The transition from quasi-elastic to more damped reactions is observed when the difference between the detected charge and the projectile one is increased. The strong influence of the particle decay on the measuredγ-ray multiplicity is evidenced with the help of the statistical model computer code CASCADE. Dissipative events are well described in the rolling limit with excitation energy equally shared between the fragments. The overall agreement is lost for the fragments with the projectile charge which show a small value of theγ-multiplicity even for dissipative events. This is probably connected with the previously observed non statistical behavior of gamma rays emitted in coincidence with projectile-like fragments. In the alpha-spectrum measured in coincidence with gamma-rays, the deexcitation of fused systems is clearly separated from in flight emission of deep inelastic fragments. The low measured gamma-ray multiplicity for fusion events is qualitatively explained taking into account the effect of alpha-emission in the statistical decay.     

Study of the excitation function fluctuations of the dissipative28Si+48Ti binary collision in the incident energy interval from 206.9 MeV to 213.8 MeV

It is shown that the Partially Overlapping Molecular Level Model (POMLM) accounts for the experimental results of the dissipative²⁸Si +⁴⁸Ti collision around 210 MeV incident energy. The general trend of the properties of the fluctuations as well as the average angular distributions are reproduced by the same set of main parameters. A general consistency is also found between the present data and the data obtained in previous work on the same colliding system performed at lower incident energy (around 123 MeV).     

Interaction times in the19F+63Cu dissipative heavy ion reaction

Coherence energies extracted from excitation functions and angular distributions for the fragments emitted in the¹⁹F+⁶³Cu reaction, measured in the range θ_lab=10° to 120° at incident energies between 100 to 108 MeV (lab.), were compared to the Kun model of dissipative collisions. An overall agreement was found for the angular distributions at forward angles. The general behavior of coherence energies was also properly described and interaction times were deduced.     

Which mathematics should we teach engineering students? An empirically grounded case for a broad notion of mathematical thinking

While many engineering educators have proposed changes to theway that mathematics is taught to engineers, the focus has oftenbeen on mathematical content knowledge. Work from the mathematicseducation community suggests that it may be beneficial to considera broader notion of mathematics: mathematical thinking. Schoenfeldidentifies five aspects of mathematical thinking: the mathematicscontent knowledge we want engineering students to learn as wellas problem-solving strategies, use of resources, attitudes andpractices. If we further consider the social and material resourcesavailable to students and the mathematical practices studentsengage in, we have a more complete understanding of the breadthof mathematics and mathematical thinking necessary for engineeringpractice. This article further discusses each of these aspectsof mathematical thinking and offers examples of mathematicalthinking practices based in the authors' previous empiricalstudies of engineering students' and practitioners' uses ofmathematics. The article also offers insights to inform theteaching of mathematics to engineering students.