Exoplanets Bouncing Between Binary Stars

Exoplanetary systems are found not only among single stars, but also binaries of widely varying parameters. Binaries with separations of 100--1000 au are prevalent in the Solar neighborhood; at these separations planet formation around a binary member may largely proceed as if around a single star. During the early dynamical evolution of a planetary system, planet--planet scattering can eject planets from a star's grasp. In a binary, the motion of a planet ejected from one star has effectively entered a restricted three-body system consisting of itself and the two stars, and the equations of motion of the three body problem will apply as long as the ejected planet remains far from the remaining planets. Depending on its energy, escape from the binary as a whole may be impossible or delayed until the three-body approximation breaks down, and further close interactions with its planetary siblings boost its energy when it passes close to its parent star. Until then this planet may be able to transition from the space around one star to the other, and chaotically `bounce' back and forth. In this paper we directly simulate scattering planetary systems that are around one member of a circular binary, and quantify the frequency of bouncing in scattered planets. We find that a great majority (70 to 85 per cent) of ejected planets will pass at least once through the space of it's host's binary companion, and depending on the binary parameters about 45 to 75 per cent will begin bouncing. The time spent bouncing is roughly log-normally distributed with a peak at about $10^4$ years, with only a small percentage bouncing for more than a Myr. This process may perturb and possibly incite instability among existing planets around the companion star. In rare cases, the presence of multiple planets orbiting both stars may cause post-bouncing capture or planetary swapping.Comment: MNRAS in press. Animations of some orbits can be viewed at http://www.ast.cam.ac.uk/~moeckel/bouncingplanets.htm

Application of a H 2 + -like model to helium atom. Solution of the wave equation at the ground state

The wave equation of helium atom is solved based on a “H 2 + -like” model. A good agreement between the theoretical and experimental ionization energies is obtained.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43907/1/10053_2005_Article_BF01398893.pd

Screening effects on the electronic structure of the hydrogen molecular ion

ABSTRACT: We study the effect that a statically screened Coulomb potential represented by a Debye-H¨uckel-Yukawa potential has in the electronic structure of the simplest molecule H2+ within the Born-Oppenheimer approximation. The method of solution is based on a two-center partial-wave expansion expressed in confocal elliptic coordinates using B-spline polynomials. General algorithms for the computation of energies, wave functions, and dipole and nonadiabatic radial matrix elements are given in detail. As it occurs in atoms, screening in simple molecules shifts the energies of bound states upwards so that, as screening increases, every bound state eventually crosses the upper ionization threshold at a critical screening value. The loss of long-range Coulomb interactions has its effect in the structure of wave functions, and consequently in the dipole and nonadiabatic matrix elements at intermediate and long internuclear distances, which determine the dynamics in external electromagnetic fields and collisional processes. Other issues related to a practical solution of the arbitrary sign problem, as well as the assignment of angular and radial nodes to the variational eigenfunctions, and the appearance of molecular shape resonances and Borromean states inH2+ as screening increases, are also addressed in this work

Semiclassical ionization dynamics of the hydrogen molecular ion in an electric field of arbitrary orientation

Quasi-static models of barrier suppression have played a major role in our understanding of the ionization of atoms and molecules in strong laser fields. Despite their success, in the case of diatomic molecules these studies have so far been restricted to fields aligned with the molecular axis. In this paper we investigate the locations and heights of the potential barriers in the hydrogen molecular ion in an electric field of arbitrary orientation. We find that the barriers undergo bifurcations as the external field strength and direction are varied. This phenomenon represents an unexpected level of intricacy even on this most elementary level of the dynamics. We describe the dynamics of tunnelling ionization through the barriers semiclassically and use our results to shed new light on the success of a recent theory of molecular tunnelling ionization as well as earlier theories that restrict the electric field to be aligned with the molecular axis

Theoretical study of the line profiles of the hydrogen perturbed by collisions with protons

We present theoretical calculations of the quasi-molecular line profiles for the Lyman (Lya, Lyb, Lyg, Lyd) and Balmer (Ha, Hb, Hg, Hd, He, H8, H9, and H10) series, perturbed by collisions with protons. In all calculations we include the dependence of the dipole moments as a function of internuclear distance during the collision. The broadening from ion collisions must be added to the normal electron Stark broadening.Comment: 13 pages, 24 figures and 7 table

Low-performing students' views on their own performance in physical education and health : A qualitative study on motivation to physical education and health

Aim The purpose of the study is to investigate and describe how low-performing students in year 9 look at their achievements in connection with teaching in sport and health. Furthermore, it is of interest to examine which motivational factors influence them to participate or not participate in the teaching.  Method The study is based on a qualitative interview study in which five pupils in year 9 between the ages of 15-16 years participated. The interview guide is based on the motivation theory Self-Determination Theory in order to be able to answer the questions of the study. The participants in the study were selected after a comfort selection and a school in the Stockholm area Results The students who participated in the study considered that the learning environment, choice of activities and how the teaching was organized affect their motivation. Additional factors that affect the students' motivation are linked to the feeling of belonging to the teacher and the students in the class. The self-esteem and experience of competence motivates the majority to participate in activities. Furthermore, the students reported that grades are considered an important factor in their desire to participate in the teaching. A couple of students also presented the inaccessibility of the dressing room as a motivational factor. Conclusions From the results and the analysis, the following factors emerged affecting the motivation of low-performing students; choice of activity, the teacher, grades, changing rooms and the feeling of competence, autonomy, and affinity. All factors are categorized as internal and external motivation factors. The conclusion for the study is that the motivational factors have a great impact on whether the students are motivated to participate in sports education.  Syfte och frågeställning  Syftet med studien är att undersöka hur lågpresterande elever i åk 9 ser på sina prestationer i samband med undervisningen i idrott och hälsa. Vidare undersöks vilka motivationsfaktorer som påverkar eleverna till att delta eller inte delta i undervisningen. ▪         Hur ser elever på sina prestationer i samband med kunskapsämnet idrott och hälsa? ▪         Vad motiverar elever till att delta eller inte delta i idrottsundervisningen? ▪         Vilka orsaker anser eleverna är bidragande till att deras betyg ligger på gränsen till godkänt i ämnet idrott och hälsa? Metod Studien baseras på en kvalitativ intervjustudie där fem elever i åk 9 mellan åldrarna 15-16 år deltog. Studiens teoretiska utgångspunkt är Self-Determination Theory. Deltagarna i studien valdes ut efter ett bekvämlighetsurval och en skola i Stockholmsområdet. Resultat Majoriteten av eleverna ansåg att prestationen är kopplad till en vilja att vilja anstränga sig och göra sitt bästa.  Vidare ses prestation vara kopplad till förmågan att ta sig an uppgiften, men också att prestationen ska visa prov på en god hanteringsförmåga samt ett gynnsamt resultat i förhållande till uppgiften. Eleverna som deltog i studien ansåg att lärandemiljön, val av aktiviteter samt hur undervisningen organiseras påverkar deras motivation. Ytterligare faktorer som påverkar elevernas motivation är kopplade till känslan av samhörighet med läraren och eleverna i klassen. Självkänslan och upplevelse av kompetens motiverar majoriteten att delta i aktiviteter. Vidare redogjorde eleverna för att betyg anses som en viktig faktor till att de vill delta i undervisningen. Ett par elever framlade även omklädningsrummets otillgänglighet som en motivationsfaktor. Slutsats Av resultat och analysen framkom följande faktorer ha inverkan på lågpresterande elevers motivation; val av aktivitet, läraren, betyg, omklädningsrum samt känslan av kompetens, autonomi och samhörighet.  Samtliga faktorer kategoriseras som inre- och yttre motivationsfaktorer. Slutsatsen för studien är att motivationsfaktorerna har en stor inverkan på huruvida eleverna motiveras att delta i idrottsundervisningen