Shell-model treatment of nuclear reactions

A method is developed for the calculation of resonant nuclear states which preserves as many features of the shell model as possible. It is an extension of the R-matrix theory. The necessary formulas are derived and a detailed description of the computational procedure is given. The method is valid up to the two-particle emission threshold. With the assumption of consecutive decay of the nucleus, the two-particle emission process can also be described. The treatment is antisymmetrized in all particles

Damping of the giant resonance in heavy nuclei

In heavy nuclei the damping of the giant resonance is due to thermalization of the energy rather than to direct emission of particles; the latter process is strongly inhibited by the angular-momentum barrier. The thermalization proceeds via inelastic collisions leading from the particle-hole state to two-particle-two-hole states. In heavy nuclei, several hundred such states are available at the energy of the giant dipole resonance. The rather large width of the giant resonance arises from the addition of many small partial widths of channels leading to the different two-particle-two-hole states. Both the density of the two-particle-two-hole states and the mean value of the interaction matrix elements between the particle-hole and two-particle-two-hole states are evaluated in a simplified square-well shell model. In a given nucleus the energy dependence of the widths is determined mainly by the density of states; the A dependence is determined mainly by the size of the matrix elements. For A ~ 200, we find 0.5 <= Γ <=2.5 MeV. The uncertainty in this value comes mostly from the uncertainty in the strength of the interaction. Representing the energy dependence of the width by a power law we find for the exponent the value ~ 1.8

Dynamic theory of the nuclear collective model

The rotation-vibration model and the hydrodynamic dipole-oscillation model are unified. A coupling between the dipole oscillations and the quadrupole vibrations is introduced in the adiabatic approximation. The dipole oscillations act as a "driving force" for the quadrupole vibrations and stabilize the intrinsic nucleus in a nonaxially symmetric equilibrium shape. The higher dipole resonance splits into two peaks separated by about 1.5-2 MeV. On top of the several giant resonances occur bands due to rotations and vibrations of the intrinsic nucleus. The dipole operator is established in terms of the collective coordinates and the γ-absorption cross section is derived. For the most important 1- levels the relative dipole excitation is estimated. It is found that some of the dipole strength of the higher giant resonance states is shared with those states in which one surface vibration quantum is excited in addition to the giant resonance

Baryon-Rich Quark-Gluon Plasma in Nuclear Collision

The maximum achievable temperature (energy density) and minimum kinetic energy required for the formation of a baryon-rich quark-gluon plasma formed at central rapidity in small impact parameter nuclear collisions is estimated. A possible mechanism leading to the pile-up of matter is introduced. Plasma formation is expected to appear at about 15 GeV/Nucleon uranium beam energy on a stationary target or 2.7 GeV/Nucleon in colliding beams.Comment: 22 pages incl. 6 figures, to appear in proceedings of Bad Honnef meeting on "Fundamental Issues in Elementary Matter" Septmeber 25-29, 2000. This manuscript was widely circulated in November 1984 as University of Cape Town preprint UCT-TP 7/84. Its content is highly topical today. Compared to the preprint only corrections of a few equation typos seen in UCT-TP 7/84, and update of footnotes and references, were mad

Thermodynamic graph-rewriting

We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy cost function. The idea is that the generators define the qualitative dynamics, by showing which transformations are possible, while the energy patterns and cost function specify the long-term probability $\pi$ of any reachable graph. Given the generators and energy patterns, we construct a finite set of rules which (i) has the same qualitative transition system as the generators; and (ii) when equipped with suitable rates, defines a continuous-time Markov chain of which $\pi$ is the unique fixed point. The construction relies on the use of site graphs and a technique of `growth policy' for quantitative rule refinement which is of independent interest. This division of labour between the qualitative and long-term quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see the examples in S4 and S5). It also guarantees thermodynamical consistency (AKA detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications

Eigenchannel theory of nuclear reactions

A method is proposed by which the eigenstates and the eigenvalues of the S matrix, i.e., the eigenchannels, can be directly computed from the nuclear problem, for example, from the shell model. The calculation of all cross sections, viz., partial and total cross sections, is then exceedingly simple. The characteristics of the eigenchannels are described and the relation with other reaction theories is briefly discussed

Measurement in Quantum Physics

The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown, all these problems dissolve when working instead with quantum fields, which have both wave and particle character. Otherwise the predictions of quantum physics, including Bell's inequalities, coincide with those of the standard treatments. The transfer of the results of the quantum measurement to the classical realm is also discussed.Comment: 34 pages, in Latex, revised and expanded version with an extra appendix on decoherenc

Qualitative doctoral research in educational settings: reflecting on meaningful encounters

In qualitative doctoral research the methodological approach, and the research design are extremely important when ensuring the rigorousness of the work. This is particularly significant for all researchers, and even more for doctoral students who are still developing their research and analytical skills. This paper aims to support doctoral students in their research journey by highlighting some of the tensions involved in conducting qualitative research by unpicking the experiences of two doctoral students to learn from the concerns, questions and reflections on the use of qualitative methodology in their doctoral research projects. The findings reveal challenges and insights with regards to reflection, educational research and the developing identity of being a researcher. The paper discusses these reflections to support and guide doctoral students as early career researchers when planning and conducting qualitative research in educational settings