Dispersion relations for scattering by spin-dependent potentials

The understanding of the two- nucleon interaction is the central problem in the theory of nuclear forces. Whether specifically many -body forces turn out to be important or not, the investigation of the two -body interaction is bound to give us some insight into the mechanism responsible for the strongest binding known to man.So far, the only attempts, in theory, to go beyond pure guesswork (or phenomenology, as it is politely called) have been along two essentially different directions. The first type of computations, which were initiated by Yukawa and have since been assiduously followed up by many physicists (e.g. Taketani et al.) may be collectively classed as "meson- theoretical calculations". The main idea behind these efforts if the belief (perhaps quite true) that nuclear forces are mediated by a meson cloud and, naturally, the closer together the nucleons are, the larger the number of pions taking part. This rather loose inverse relationahip between the range of a force and the corresponding mass of the intermediate state is now widely accepted among elementary particle physicists. However, the quantitative realisation of the Taketani programme takes the form of computing one perturbation graph after another in the framework of field theory. The one pion exchange graph, of course, yielded the famous Yukawa potential which, as expected, was very successful in explaining the long range effect of the nucleon force. Higher order effects have not had the same success in the "medium" range, with the consequent flourishing of phenomenology. Apart from the increasing technical difficulty of calculating higher order graphs, it is very probable that the perturbation series is divergent in which case the whole project is essentially illusory, and any occasional agreements with experiments must be regarded as fortuitous. There have been many variations from straight expansion in the coupling strength or the number of intermediate particles. A comprehensive survey is given in the review of Y oravcsik & Noyes(16).A more hopeful approach has appeared in recent years, following Fandelstam's proposal of double dispersion relations for the scattering amplitude in a two-particles-in, two-particles-out process. It was initiated by Champ & Fubini(4), who indicated how one can obtain a useful "potential ", starting from the Mandelstam representation. But he could do it reliably only for the case of scalar particles, mainly because no one had derived a Kandelstam representation, or even a single variable dispersion relation, for two particles of spin 0.5 interacting through a general spin and velocity- dependent potential. Up to now, there have appeared only two papers on this subject and both have touched the problem only partially. Hamilton(9) has proved dispersion relations which are those (12) similar to those that Khuri obtained for central potentials, considering only an additional tensor term. The other attempt has been by Buslayev(3) who considers a particle scattered by a spin-orbit potential.The present work is intended to fill this gap; we obtain dispersion relations (in energy, for fixed momentum transfer) for two spin 2 particles interacting through a complete potential subject only to reasonable physical requirements. The relations obtained turn out to be substantially different in form from those derived or postulated as yet; and the methods used have the virtue of being generalisable to the scattering between systems of arbitrary spin, as indicated in the last chapter. The derivation of these dispersion relations is also a step forward in the fulfilment of the Charap-Fubini programme of deducing a realistic two-nucleon potential.We will now give a brief outline of this manuscript.In Chapter II, we discuss the form of the potential for a two-nucleon system, and then go on to derive some properties of the resolvent of the Hamiltonian. We also have a brief look at the spectral decomposition of the total Hamiltonian. Most of the matter contained in this chapter is of a preliminary character, and no originality is claimed.Chapter III forms the bulk of the thesis in which we obtain the analytic properties and asymptotic behaviour of the Hamiltonian Green's function in the complex energy plane. We start by deriving an integral equation for the Green's function incorporating the outgoing boundary condition. This equation does not have a bounded or square integrable kernel so that the usual methods of solution do not apply. However, it is seen that the kernel is only "weakly" singular (to use the terminology of Yikhlin(15)), and Fredholm's theorems can still be applied. This is the central point of the argument, which permits us to infer that the Green's function is analytic except on the spectrum of the Hamiltonian. We then proceed to investigate the spectrum of the total Hamiltonian, and the approach is in part borrowed from Povzner(19). The chapter concludes with a detailed investigation of the Green's function at high energy.The analyticity and asymptotics obtained in Chapter III help us in writing down an explicit form for the scattering amplitude in Chapter IV. The amplitude is treated in detail, and split into five parts with different spin-invariants, as e.g. in Goldberger, Nambu & Oehme(8) . Each coefficient separately obeys a dispersion relation which is then written down. We close the chapter with a few physical remarks of interest.Chapter V contains a generalisation of the above results to systems with arbitrarily high spins. It gives only a sketch of the arguments without going into much cumbersome detail

Understanding designer design activity; unconscious interaction between human cognition and behaviour in everyday product / Muhammad Jameel Mohamed Kamil

Product designers were expected to apply their hermeneutic as well as reflective design thinking skills to find a fit between technology and human behaviour interaction, including the notion of experiencecentred. However, due to dynamics of changes in technology and the way users interact with products, the past several years have witnessed a growing interest and enthusiasm for designing the product which explicitly emphasise on user behaviour and interaction. Therefore, the recent studies have been paying attention to critically understand the elements of interaction between human and product used in everyday life. Unfortunately, it has been profound that there are limited discussions were presented within a single coherent perspective of designers’ design thinking related to the Unconscious Interaction between Human Cognition and Behaviour (UIHCB) in everyday product. In other words, a little intention has been devoted on how the UIHCB in everyday product can aid designers’ design activity. Thus, the purpose of this research is to understand designer design activity towards the UIHCB in everyday product. The research objective is to determine the attributes of unconscious interaction in everyday life, what are their responses towards the UIHCB in everyday product, how their reflective practice can be described, and how does the understanding of UIHCB in everyday product helps to aid designers’ capabilities in generating product design ideations. Four research questions have been formulated to get a firm answer posed in this research. The main empirical effort for this thesis involved qualitative and quantitative research in gathering and analysed implicit and explicit designer’s knowledge

Methyl 2-[2-(2,6-dichloro-4-nitro­anilino)-3,5-dinitro­phen­yl]acetate

In the title compound, C15H10Cl2N4O8, the methyl­acetate and dichloro­anilinic groups are oriented at dihedral angles of 57.73 (8) and 62.44 (4)°, respectively to the dinitro-sustituted benzene ring. S(5) and S(7) rings are formed due to intra­molecular N—H⋯Cl and N—H⋯O hydrogen bonds, respectively. In the crystal, N—H⋯O hydrogen bonds link the mol­ecules into C(8) chains along the a axis. Further C—H⋯O and N—H⋯O hydrogen bonds link these chains in pairs, forming a polymeric network

Influence of Natural Zeolite and Paraffin Wax on Adhesion Strength Between Bitumen and Aggregate

Asphalt mixture that is used for the construction of flexible pavements is mainly composed of two constituents i.e. bitumen and aggregate. Sturdy adhesion among bitumen and aggregate is the sign of durability of asphalt pavements. Adhesion is considered as one of the most important factors for sustainable asphalt pavement. This is the motive why its miles utmost important to deeply understand the phenomenon of adhesion considering the effect of alternate in temperature, moisture conditions. In this study softer binder 80/100 was selected that has less adhesion compared to hard pen grades. Limestone aggregates which is commonly used for the construction of asphalt pavements has also been selected. Two types of modifiers (Zeolite and Paraffin Wax) were selected because of the extensive use in asphalt foaming and the polymer modified asphalt mixtures as temperature reducing agent. To investigate the strength of adhesive bond, Bitumen Bond Strength (BBS) was performed at different temperatures, in dry, and wet conditions. To quantify the effect of modifiers on penetration grade and softening point conventional testing is performed. For performance grading, the PG test was performed using Dynamic Shear Rheometer. The comparisons were developed among pull of tensile strength at dry and after 72hrs water conditioning while preserving the temperature at 25 .To check the effect of temperature BBS is performed at 15 . The results illustrate that 2% zeolite shows best results in terms of adhesion and performance grade while Paraffin wax has less adhesion and poor performance grade

Coverage of corruption scandals in the Nigerian Press : a comparative analysis of Northern and Southern Newspapers

This research is about the coverage of corruption scandals in the Nigerian press. It is a comparative study that This research is about the coverage of corruption scandals in the Nigerian press. It is a comparative study that develops an intra-national framework for the study of the Nigerian media system using corruption scandals. The scandals studied are the Petroleum Technology Development Fund (PTDF) scandal and the Former Governors Scandal. The study used both interviews and qualitative content analysis by means of critical discourse analysis. The results of the study suggest that the press in Nigeria is regionally and ethnically divided. These factors influence the way the press report issues including corruption scandals. The study also suggests that factors like clientelism, regionalism, corruption within the press, and lack of training are among the challenges faced by the Nigerian press. It is the position of this study that the press in Nigeria is active in reporting stories about corruption scandals, but has not done enough when it comes to the application of such aspects of journalistic practice like investigative journalism which contributes in the watchdog role of the media. The study concludes by suggesting areas for further research

What is in Your App? Uncovering Privacy Risks of Female Health Applications

FemTech or Female Technology, is an expanding field dedicated to providing affordable and accessible healthcare solutions for women, prominently through Female Health Applications that monitor health and reproductive data. With the leading app exceeding 1 billion downloads, these applications are gaining widespread popularity. However, amidst contemporary challenges to women's reproductive rights and privacy, there is a noticeable lack of comprehensive studies on the security and privacy aspects of these applications. This exploratory study delves into the privacy risks associated with seven popular applications. Our initial quantitative static analysis reveals varied and potentially risky permissions and numerous third-party trackers. Additionally, a preliminary examination of privacy policies indicates non-compliance with fundamental data privacy principles. These early findings highlight a critical gap in establishing robust privacy and security safeguards for FemTech apps, especially significant in a climate where women's reproductive rights face escalating threats.Comment: 9 pages, 3 table