Recoupling matrix elements and decay

Recoupling matrix elements are evaluated, in the harmonic oscillator approximation, for all possible angular and radial excitations in processes where quarks recombine. A diagrammatic representation is given. Their use is demonstrated in calculating the transition potential for rho to two pions in a pair creation model.Comment: 15 pages, 10 figure

Nuclear Spin Relaxation for Higher Spin

We study the relaxation of a spin I that is weakly coupled to a quantum mechanical environment. Starting from the microscopic description, we derive a system of coupled relaxation equations within the adiabatic approximation. These are valid for arbitrary I and also for a general stationary non--equilibrium state of the environment. In the case of equilibrium, the stationary solution of the equations becomes the correct Boltzmannian equilibrium distribution for given spin I. The relaxation towards the stationary solution is characterized by a set of relaxation times, the longest of which can be shorter, by a factor of up to 2I, than the relaxation time in the corresponding Bloch equations calculated in the standard perturbative way.Comment: 4 pages, Latex, 2 figure

Recurrence and differential relations for spherical spinors

We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) $\Omega_{\kappa\mu}(\mathbf{n})$ used in relativistic atomic, molecular, and solid state physics, as well as in relativistic quantum chemistry. First, we list finite expansions in the spherical spinor basis of the expressions $\mathbf{A}\cdot\mathbf{B}\,\Omega_{\kappa\mu}(\mathbf{n})$ and {$\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})\, \Omega_{\kappa\mu}(\mathbf{n})$}, where $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{C}$ are either of the following vectors or vector operators: $\mathbf{n}=\mathbf{r}/r$ (the radial unit vector), $\mathbf{e}_{0}$, $\mathbf{e}_{\pm1}$ (the spherical, or cyclic, versors), $\boldsymbol{\sigma}$ (the $2\times2$ Pauli matrix vector), $\hat{\mathbf{L}}=-i\mathbf{r}\times\boldsymbol{\nabla}I$ (the dimensionless orbital angular momentum operator; $I$ is the $2\times2$ unit matrix), $\hat{\mathbf{J}}=\hat{\mathbf{L}}+1/2\boldsymbol{\sigma}$ (the dimensionless total angular momentum operator). Then, we list finite expansions in the spherical spinor basis of the expressions $\mathbf{A}\cdot\mathbf{B}\,F(r)\Omega_{\kappa\mu}(\mathbf{n})$ and $\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})\, F(r)\Omega_{\kappa\mu}(\mathbf{n})$, where at least one of the objects $\mathbf{A}$, $\mathbf{B}$, $\mathbf{C}$ is the nabla operator $\boldsymbol{\nabla}$, while the remaining ones are chosen from the set $\mathbf{n}$, $\mathbf{e}_{0}$, $\mathbf{e}_{\pm1}$, $\boldsymbol{\sigma}$, $\hat{\mathbf{L}}$, $\hat{\mathbf{J}}$.Comment: LaTeX, 12 page

Gravitational Corrections to the Energy-Levels of a Hydrogen Atom

The first order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.Comment: 7 page

Probing the Weak Boson Sector in γe→Ze\gamma e\rightarrow Ze

We study possible deviations from the standard model in the reaction $\gamma e\rightarrow Ze$ at a 500 GeV $e^+e^-$ collider. As a photon source we use a laser backscattered photon beam. We investigate the most general $\gamma Z\gamma$ and $\gamma ZZ$ vertices including operators up to energy-dimension-six which are Lorentz invariant. These vertices require four extra parameters; two are CP-conserving, $h^\gamma_1$ and $h^Z_1$, and two are CP-violating, $h^\gamma_2$ and $h^Z_2$. We present analytical expressions of the helicity amplitudes for the process $\gamma e\rightarrow Ze$ for arbitrary values of anomalous couplings. Assuming Standard Model values are actually measured we present the allowed region in the ($h^\gamma_1,h^Z_1$) plane at the 90\% confidence level. We then show how the angular correlation of the $Z$ decay products can be used to extract detailed information on the anomalous (especially CP-violating) $\gamma Z\gamma$ and $\gamma ZZ$ couplings.Comment: Latex, 25 pages, 12 figures (not included). One compressed postscript file including all the figures available at ftp://ftp.kek.jp/kek/preprints/TH/TH-420/kekth420.ps.g

Characterising current agroecological and regenerative farming research capability and infrastructure, and examining the case for a Living Lab network [Final report]

Agriculture is a major cause of greenhouse gas (GHG) emissions, biodiversity loss, and pollution. Agroecological and regenerative farming have been advocated as alternative approaches that may have fewer negative (or even net positive) environmental impacts than conventional agriculture at farm- and landscape-scales, leading to considerable interest in these approaches (Newton et al. 2020; Bohan et al. 2022; Prost et al. 2023). This report forms the third part of a Defra-funded project Evaluating the productivity, environmental sustainability and wider impacts of agroecological and regenerative farming systems compared to conventional systems. The first part of this project was a rapid evidence review of agroecological and regenerative farming systems and their impacts (Burgess et al. 2023), and the second reported interview findings to examine farmer and stakeholder perspectives on barriers and enablers in agroecological and regenerative farming (Hurley et al. 2023). This third part of the project characterised the current research capability in agroecology and regenerative farming, and explored the potential role of a new ‘living lab’ trial network. Three objectives are addressed in this report: 1) Characterise the existing agroecological and regenerative farming research capability and infrastructure in the UK. 2) Explore lessons from recent research initiatives and identify key research gaps, to inform a potential UK living labs trials network in agroecology/regenerative farming. 3) Develop recommendations for a new living lab trial or research network in agroecology/regenerative farming. Objective 1 was addressed through an online survey to gather quantitative and qualitative data on current research initiatives and networks in regenerative farming and agroecology. There were 22 respondents from 20 organisations (Section 2.2). Key findings from the survey: • The size and the timescales of research initiatives varied substantially from single sites to networks of 50-100 sites and with agroecological/regenerative practices applied from one to over 20 years. • All the survey respondents applied multiple agroecological/regenerative processes and had multiple target outcomes. • Just under 40% of respondents are not currently collecting data from their network. • Three-quarters of the survey participants not currently collecting data stated they would like to collect data, given more funding, knowledge or support. • Biodiversity was one of the most frequent target outcomes, and data collection most frequently focussed on biodiversity. • Face-to-face and email communication was most frequently used between farms in a network. Around two-thirds of respondents also held farm demonstration days as a means of knowledge exchange. • Most of the research initiatives and networks were funded by charities, NGOs or funded themselves, with a smaller number funded by UK or EU government funding. • Growing to incorporate more farms and researchers and developing knowledge exchange further were prioritised as future aspirations by survey respondents. Incorporating more researchers and applying for funding were also a focus for many research initiatives. • Targeted funding was seen as very important in achieving future aspirations by most respondents, along with improved connections with farmers and landowners and improved skills and information for knowledge exchange. Improved infrastructure and monitoring tools were emphasised less, but still considered important. The online survey results illustrate the wide range of current research initiatives in agroecology and regenerative farming, which vary from small-scale trials on a few farms to robust, repeatable data collection across a large network. To illustrate the range of approaches in more details, five case studies were described (Section 2.3) which included an ongoing living lab network, three research project and a long-term demonstration farm. Key characteristics of eight European living labs were also summarised through a network of EU agroecology living labs (the ALL-Ready project; Section 2.4). Objective 2 was addressed through an online workshop, at which participants responded to questions about research gaps and priorities, infrastructure needs, and the barriers and enablers to data sharing and access (Section 3). Participants views were gathered through online discussion boards and facilitated verbal discussion (Figure 1). Key themes and conclusions from the workshop: • Many of the impacts of agroecology and regenerative practices remain poorly understood, with biodiversity and greenhouse gas emissions highlighted. • Impacts on multiple potential benefits and trade-offs (e.g. yield vs. biodiversity vs. greenhouse gas emissions) need to be understood. The variation in responses (e.g. between soil types or regions) was seen as a priority area for research to improve the understanding of scaling-up. • Research needs to be conducted at adequate temporal and spatial scales given the timescales needed for impacts of these practices to become apparent. • There may be a bias in farmer participation in agroecological and regenerative agriculture research (those who can afford the time and money). • Understanding transitions to agroecology and regenerative farming across different types of farm business was raised as a research gap along with investigating the role of knowledge in these types of practice. This was reflected in the discussion of infrastructure and skills, with support (better guidance, input from advisors) and upskilling/improvements in education seen as priorities to support transitions. • The role of economic drivers, including subsidies and supply chain structures, is a research priority to understand why and how farmers may transition to these farming practices. • Standardised assessments and monitoring tools (including farmer apps) were highlighted to support future research, in particular standardised soil carbon assessments. Hubs to loan monitoring equipment to farmers were also suggested. • The time commitment needed was seen as an impediment to data collection by farmers, with comments that research initiatives worked better with someone external collecting data. • Data quality and formats were raised as barriers to data sharing in agroecology/regenerative farming. Formats that can be easily read across a range of software were suggested as a solution, along with more standardised approaches in data collection. • Integration and sharing of data across platforms were another solution, in particular for regulatory data (e.g. pesticide usage). • A potential tension was raised between standardising monitoring approaches and data collection, and constraining innovation by farmers. • Our understanding of how widespread agroecological and regenerative farming practices are, and which are being used / in what combinations, is constrained by lack of uptake data. Practices are being implemented with or without subsidies, and in varying combinations with more conventional approaches. Without these uptake data, larger scale research and modelling may be constrained. The online survey findings, case studies and lessons learnt from the workshop participants informed the development of recommendations for a future living labs network in the UK (Objective 3, Section 4). Four options were proposed: i) Develop a standardised methodology or protocol for each of the 12 attributes listed for assessment within the Global Farm Metric, to support consistency of farm measurements. ii) New research projects funded to collect standardised data on impacts and trade-offs across existing networks of farms applying agroecological / regenerative practices. This would maximise research synergies with existing networks. iii) New research network set up to apply agroecological / regenerative practices on commercial farms, co-designed between farmers and researchers. Standardised data collection on impacts and trade-offs. iv) Long-term living lab UK network set up, within which facilitation roles and research projects funded. These options could be applied in combination (e.g. a standardised methodology (i) developed within (iv) a long-term living lab network ). Which options are taken forward will depend on funding and factors such as the structure of available funding and timescales. Indicative costs were provided for field surveys of greenhouse gases and biodiversity, two of the impacts identified as research priorities in the workshop

Signatures of chaotic tunnelling

Recent experiments with cold atoms provide a significant step toward a better understanding of tunnelling when irregular dynamics is present at the classical level. In this paper, we lay out numerical studies which shed light on the previous experiments, help to clarify the underlying physics and have the ambition to be guidelines for future experiments.Comment: 11 pages, 9 figures, submitted to Phys. Rev. E. Figures of better quality can be found at http://www.phys.univ-tours.fr/~mouchet

Spin dynamics of wave packets evolving with the Dirac Hamiltonian in atoms with high Z

The motion of circular WP for one electron in central Coulomb field with high Z is calculated. The WP is defined in terms of solutions of the Dirac equation in order to take into account all possible relevant effects in particular the spin-orbit potential. A time scale is defined within which spin dynamics must be taken into account mainly in the atoms with high Z. Within this time scale there exists a mechanism of collapses and revivals of the spin already shown by the authors for harmonic oscillator potential and called the 'spin-orbit pendulum'. However this effect has not the exact periodicity of the simpler model, but the WP's spatial motion is nevertheless quite similar.Comment: 17 pages, 9 figures, LaTeX2e, uses IOP style files (included). Title changed, one reference adde