Angular Momentum on the Lattice: The Case of Non-Zero Linear Momentum

The irreducible representations (IRs) of the double cover of the Euclidean group with parity in three dimensions are subduced to the corresponding cubic space group. The reduction of these representations gives the mapping of continuum angular momentum states to the lattice in the case of non-zero linear momentum. The continuous states correspond to lattice states with the same momentum and continuum rotational quantum numbers decompose into those of the IRs of the little group of the momentum vector on the lattice. The inverse mapping indicates degeneracies that will appear between levels of different lattice IRs in the continuum limit, recovering the continuum angular momentum multiplets. An example of this inverse mapping is given for the case of the ``moving'' isotropic harmonic oscillator.Comment: v3) Little groups for lattice momenta corrected. Includes corrections from erratum submitted to Phys. Rev. D and a more consistent labeling scheme. v2) Minor changes to little groups. (9 pages

Waterfowl Harvest and Hunter Use at Carlyle Lake During the 1973 Season

Division of Wildlife Resources Migratory Bird Section, Periodic Report No. 7Report issued on: April 15, 197

Abundance and Partitioning of OH in a High-pressure Magmatic System: Megacrysts from the Monastery Kimberlite, South Africa

Concentrations of OH, and major and trace elements were determined in a suite of mantle-derived megacrysts that represent the crystallization products of a kimberlite-like magma at ~5 GPa and ~1400–1100°C. OH concentrations, determined by single-crystal Fourier transform infrared spectroscopy, display the following ranges (ppmw H2O): olivine 54–262, orthopyroxene 215–263, garnet 15–74, clinopyroxene 195–620, and zircon 28–34. High OH concentrations in olivine imply mantle conditions of origin, with limited H loss during ascent. OH is consistently correlated with megacryst composition, exhibiting trends with Mg-number that are similar to those of other minor and trace elements and indicating a record of high-pressure magmatic evolution. H substitution is not coupled to minor elements in olivine, but may be in ortho- and clinopyroxene. The OH–Mg-number trends of garnet and clinopyroxene show inflections related to co-precipitation of ilmenite, suggesting minor element (Ti) influence on OH partitioning. During differentiation, relative OH enrichment in clinopyroxene and olivine is consistent with proportional dependence on water activity, whereas that in garnet suggests a higher power-law dependence and/or influence of temperature. Inter-mineral distribution coefficients for OH between cpx, opx, olivine and zircon are thus constant, whereas partitioning between these minerals and garnet shows a factor 4–10 variation, correlated regularly with composition (and temperature). Calculation of solid–melt partition coefficients for H at 5 GPa over a range of magmatic evolution from 1380 to 1250°C yields: ol 0·0053–0·0046, opx 0·0093–0·0059, cpx 0·016–0·013, gt 0·0014–0·0003, bulk (garnet lherzolite–melt) 0·0063–0·0051. These are consistent with experimental studies and similar to values inferred from mid-ocean ridge basalt geochemistry, confirming the moderate incompatibility of H in mantle melting

Social Work Reports to Childrens' Hearings

This thesis is concerned with the production and presentation of Social Enquiry Reports by Social Workers to the Scottish Childrens Hearings System. It seeks to provide an understanding of the perceptions of the people compiling these documents, and of the organisational constraints under which they work. It provides an analysis of Reports and suggests that a new approach is required in order to enhance the quality of reports and mobilise modern technology in pursuit of cost-effective operations. Ch. 1 provides a detailed account of methodological problems encountered and of the ways in which these were met. It shows why the classic research design was not employed, and how a two centre design came to be adopted. The kind of preliminary work which failed to evolve into a viable research project but which proved to have certain use values is given in broad outline, and the problems created by the Local Authority in respect of access arrangements is placed in practical and in theoretical contexts. The develop ment of the three main schedules is discussed with particular reference to the questions of relevance, reliability and validity. Due account is taken of the statistical methods employed and of the analysis of the data. It is shown how the work spawned a new model of Report and a general overview of the methodology is given. Ch. 2 deals with the background to the Kilbrandon Report and demonstrates that the Report was the culmination of a long process of change dating back to 1927, and that in bringing forward the concept of a new style Juvenile Justice System Kilbrandon set in train a series of changes which affected the whole range of Social Services in Scotland. Ch. 3 picks up the importance of this change and discusses the organisational settings of the Depts. and the kinds of responses which the workforce produce with reference to the core problem being addressed. It places this discussion in the context of the legal nature of the work and of the rights and responsibilities of those concerned in it. Ch. 4 is an account of observations made of the work of the Hearings in one area, with reference to the contributions made by the reporting Social Workers. Ch. 5 takes as a starting point the proposition that in order to understand the production one must first of all appreciate the perceptions of the producers. The analysis of the schedule dealing with the views and opinions of Social Workers about issues connected with the Hearings System is given in this context. Ch. 6 then turns to the analysis of 158 reports from one area and 40 from another. It is held, on the basis of the evidence that the kind and quality of the observed deficiencies are cause for concern. Doubt is cast on previous work which attempted to explain this phenomenon. Ch. 7 is the presentation of analysis of Reporter's files, in relation to certain offence characteristics. This is relatively new ground for research in this field, and there is a demonstration that it is a matter of considerable public policy importance. Ch. 8 poses the question of the influence of S. E. R. s on decision making, with particular reference to the issue as to the weight which may be placed on content as against the often strongly worded recommendations in reports. It shows that there are certain in-built problems in the internal policies of the Reporter's Dept. and that Panels seem to follow strong lines in SERs but exercise considerable discretion where these are absent. Ch. 9 argues strongly for new models and approaches to SER production and details of the work which brought about the 'Ayrshire' format. It goes beyond this in a postulation that would divorce the information provided for the Reporter from the formal SER produced for the Hearing. It suggests that this would radically cut back on time spent in this task. It also suggests that it would provide an up-to-date model capable of computerisation which would eliminate much of the uncertainty and vagueness from this area of Social Work operations. The final chapter draws together what are regarded as salient points and issues in an effort to place the problems with which the thesis has been concerned within the context of Social Assessment. In that it argues that if this is accepted then there is scope for the development of models and strategies which would effectively mobilise the strengths and skills of the Social Work profession in the production of Social Inquiry Reports of high quality and utility