Jahn-Teller effects and surface interactions in multiply-charged fullerene anions and the effect on scanning tunneling microscopy images

We investigate the combined effects of Jahn-Teller (JT) coupling and interactions with a surface substrate on fullerene anions C$_{60}^{2-}$ to C$_{60}^{4-}$. JT coupling alone causes the C$_{60}$ ions to instantaneously distort from the icosahedral symmetry of the neutral molecule to a lower symmetry, with the molecule moving dynamically between a set of equivalent distortions. When adsorbed on a surface, the number of equivalent minimum-energy distortions is reduced. The implications of this on observed scanning tunneling microscopy (STM) images will be discussed, and comparisons made with existing experimental data. We show that a consistent interpretation of the images from all of the charge states of C$_{60}$ can only be obtained using a JT model in which the symmetry is further reduced by surface interactions. The comparison with experimental data also allows us to determine relationships between the quadratic Jahn-Teller coupling and surface interaction parameters

Physical and Dynamical Properties of the Atomic Spectrum and Squeezing of Information Entropy of Su(1,1) Interacting with Single Qubit

In this work, the interaction of an algebraic system of su(1,1) with qubit is investigated. Through Heisenberg’s equations of motion, the constants of motion are calculated. By solving the Schro ̈ding equation, the wave function that defines the features of the proposed system is obtained. Some statistical quantities are studied to determine the properties of the interaction of the algebraic system su(1,1) with qubit. The mathematical formula for the atomic emission spectrum is calculated and its properties are studied for many parameter values. Moreover, the periods of squeezing are defined by the entropy squeezing. The results are also compared and statistical quantities are linked together

Interplay between Coulomb and Jahn-Teller effects in icosahedral systems with triplet electronic states coupled to h-type vibrations

We will consider the role played by electron-vibration and electron-electron interactions, through Jahn-Teller (JT) and Coulomb interactions, respectively, in icosahedral systems in which triplet electronic states are coupled to hg-type vibrations. Starting from the electronic terms that arise from consideration of Coulomb interactions, we introduce JT couplings both within the terms and between nondegenerate terms. We show how the symmetry of the JT distortion can change when extra electrons are added, and give the conditions under which JT distortions can be suppressed entirely when the Coulomb interactions are sufficiently large. The relevance of our results to anions of the fullerene molecule C60 are briefly discussed, and existing experimental measurements are used to estimate values for the quadratic JT coupling constants for these anions

SARS-CoV-2 vaccination modelling for safe surgery to save lives: data from an international prospective cohort study

Background: Preoperative SARS-CoV-2 vaccination could support safer elective surgery. Vaccine numbers are limited so this study aimed to inform their prioritization by modelling. Methods: The primary outcome was the number needed to vaccinate (NNV) to prevent one COVID-19-related death in 1 year. NNVs were based on postoperative SARS-CoV-2 rates and mortality in an international cohort study (surgical patients), and community SARS-CoV-2 incidence and case fatality data (general population). NNV estimates were stratified by age (18-49, 50-69, 70 or more years) and type of surgery. Best- and worst-case scenarios were used to describe uncertainty. Results: NNVs were more favourable in surgical patients than the general population. The most favourable NNVs were in patients aged 70 years or more needing cancer surgery (351; best case 196, worst case 816) or non-cancer surgery (733; best case 407, worst case 1664). Both exceeded the NNV in the general population (1840; best case 1196, worst case 3066). NNVs for surgical patients remained favourable at a range of SARS-CoV-2 incidence rates in sensitivity analysis modelling. Globally, prioritizing preoperative vaccination of patients needing elective surgery ahead of the general population could prevent an additional 58 687 (best case 115 007, worst case 20 177) COVID-19-related deaths in 1 year. Conclusion: As global roll out of SARS-CoV-2 vaccination proceeds, patients needing elective surgery should be prioritized ahead of the general population