Ergodicity of the Δ3\Delta_3 statistic and purity of neutron resonance data

The $\Delta_3(L)$ statistic characterizes the fluctuations of the number of levels as a function of the length of the spectral interval. It is studied as a possible tool to indicate the regular or chaotic nature of underlying dynamics, detect missing levels and the mixing of sequences of levels of different symmetry, particularly in neutron resonance data. The relation between the ensemble average and the average over different fragments of a given realization of spectra is considered. A useful expression for the variance of $\Delta_3(L)$ which accounts for finite sample size is discussed. An analysis of neutron resonance data presents the results consistent with a maximum likelihood method applied to the level spacing distribution.Comment: 24 pages, 19 figures, 1 tabl

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding

General pairing interactions and pair truncation approximations for fermions in a single-j shell

We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.Comment: a latex text file and 2 figures, to be publishe

Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states

In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interactions is confirmed but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities.Comment: 39 pages and 8 figure

Dynamics of quantum systems

A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ matrix is derived which holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with two-body forces between the constituents or it may be a quantum billiard without any two-body forces. Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points in the complex plane. Under certain conditions, these branch points appear as double poles of the $S$ matrix. They influence the dynamics of open as well as of closed quantum systems. The dynamics of the two-level system is studied in detail analytically as well as numerically.Comment: 21 pages 7 figure

Generic Rotation in a Collective SD Nucleon-Pair Subspace

Low-lying collective states involving many nucleons interacting by a random ensemble of two-body interactions (TBRE) are investigated in a collective SD-pair subspace, with the collective pairs defined dynamically from the two-nucleon system. It is found that in this truncated pair subspace collective vibrations arise naturally for a general TBRE hamiltonian whereas collective rotations do not. A hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the hamiltonian is key to producing generic collective rotation.Comment: 11 pages, 5 figure

Quadrupole and Hexadecapole Correlations in Rotating Nuclei Studied within the Single-j Shell Model

The influence of quadrupole and hexadecapole residual interactions on rotational bands is investigated in a single-j shell model. An exact shell-model diagonalization of quadrupole-plus-hexadecapole interaction can sometimes produce a staggering of energy levels in the yrast bands.Comment: 15 pages, 9 Postscript figures, REVTEX, to be published in PR

Women’s experiences of wearing therapeutic footwear in three European countries

Background: Therapeutic footwear is recommended for those people with severe foot problems associated with rheumatoid arthritis (RA). However, it is known that many do not wear them. Although previous European studies have recommended service and footwear design improvements, it is not known if services have improved or if this footwear meets the personal needs of people with RA. As an earlier study found that this footwear has more impact on women than males, this study explores women’s experiences of the process of being provided with it and wearing it. No previous work has compared women’s experiences of this footwear in different countries, therefore this study aimed to explore the potential differences between the UK, the Netherlands and Spain. Method: Women with RA and experience of wearing therapeutic footwear were purposively recruited. Ten women with RA were interviewed in each of the three countries. An interpretive phenomenological approach (IPA) was adopted during data collection and analysis. Conversational style interviews were used to collect the data. Results: Six themes were identified: feet being visibly different because of RA; the referring practitioners’ approach to the patient; the dispensing practitioners’ approach to the patient; the footwear being visible as different to others; footwear influencing social participation; and the women’s wishes for improved footwear services. Despite their nationality, these women revealed that therapeutic footwear invokes emotions of sadness, shame and anger and that it is often the final and symbolic marker of the effects of RA on self perception and their changed lives. This results in severe restriction of important activities, particularly those involving social participation. However, where a patient focussed approach was used, particularly by the practitioners in Spain and the Netherlands, the acceptance of this footwear was much more evident and there was less wastage as a result of the footwear being prescribed and then not worn. In the UK, the women were more likely to passively accept the footwear with the only choice being to reject it once it had been provided. All the women were vocal about what would improve their experiences and this centred on the consultation with both the referring practitioner and the practitioner that provides the footwear. Conclusion: This unique study, carried out in three countries has revealed emotive and personal accounts of what it is like to have an item of clothing replaced with an ‘intervention’. The participant’s experience of their consultations with practitioners has revealed the tension between the practitioners’ requirements and the women’s ‘social’ needs. Practitioners need greater understanding of the social and emotional consequences of using therapeutic footwear as an intervention

Quadrupole Collective States in a Large Single-J Shell

We discuss the ability of the generator coordinate method (GCM) to select collective states in microscopic calculations. The model studied is a single-$j$ shell with hamiltonian containing the quadrupole-quadrupole interaction. Quadrupole collective excitations are constructed by means of the quadrupole single-particle operator. Lowest collective bands for $j$=31/2 and particle numbers $N$=4,6,8,10,12, and $14$ are found. For lower values of $j$, exact solutions are obtained and compared with the GCM results.Comment: submitted for publication in Phys. Rev. C, revtex, 28 pages, 15 PostScript figures available on request from [email protected], preprint No. IFT/17/9