Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

Kelvin-Helmholtz instabilities at the magnetic cavity boundary of comet 67P/Churyumov-Gerasimenko

We investigate the plasma environment of comet 67P/Churyumov-Gerasimenko, the target of the European Space Agency's Rosetta mission. Rosetta will rendezvous with the comet in 2014 at almost 3.5 AU and follow it all the way to and past perihelion at 1.3 AU. During its journey towards the inner solar system the comet's environment will significantly change. The interaction of the solar wind with a well developed neutral coma leads to the formation of an upstream bow shock and, closer to the comet, the inner shock separating the solar wind, with cometary pick-up ions mass-loaded, from the inner cometary ions which are dragged outward through abundant collisions and charge exchange with the expanding neutral gas. As a consequence the interplanetary magnetic field is prevented from penetrating the innermost region of the comet, the so-called magnetic cavity. We use our magnetohydrodynamics model BATSRUS (Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme) to simulate the solar wind - comet interaction. The model includes photoionization, ion-electron recombination, and charge exchange. Under certain conditions our model predicts an unstable plasma flow at the inner shock. We show that the plasma shear flow around the magnetic cavity can lead to Kelvin-Helmholtz instabilities. We investigate the onset of this phenomenon with change of heliocentric distance and furthermore show that a previously stable magnetic cavity boundary can become unstable when the neutral gas is predominately released from the dayside of the comet.

Recommendations from GEC ESTRO Breast Cancer Working Group (I): Target definition and target delineation for accelerated or boost Partial Breast Irradiation using multicatheter interstitial brachytherapy after breast conserving closed cavity surgery

OBJECTIVE The aim was to develop a delineation guideline for target definition for APBI or boost by consensus of the Breast Working Group of GEC-ESTRO. PROPOSED RECOMMENDATIONS Appropriate delineation of CTV (PTV) with low inter- and intra-observer variability in clinical practice is complex and needs various steps as: (1) Detailed knowledge of primary surgical procedure, of all details of pathology, as well as of preoperative imaging. (2) Definition of tumour localization before breast conserving surgery inside the breast and translation of this information in the postoperative CT imaging data set. (3) Calculation of the size of total safety margins. The size should be at least 2 cm. (4) Definition of the target. (5) Delineation of the target according to defined rules. CONCLUSION Providing guidelines based on the consensus of a group of experts should make it possible to achieve a reproducible and consistent definition of CTV (PTV) for Accelerated Partial Breast Irradiation (APBI) or boost irradiation after breast conserving closed cavity surgery, and helps to define it after selected cases of oncoplastic surgery.

Interobserver variations of target volume delineation in multicatheter partial breast brachytherapy after open cavity surgery

PURPOSE To investigate interobserver variations of target volume delineations in accelerated partial breast irradiation with multicatheter brachytherapy (BT) and to assess the impact of guidelines on consistency of contouring. METHODS AND MATERIALS A contouring study with two phases in interstitial accelerated partial breast irradiation after open cavity surgery was conducted by the Groupe Européen de Curiethérapie-European Society for Radiotherapy and Oncology Breast Cancer Working Group. Contours of cavity and planning target volume (PTV) on preimplant and postimplant CT images were delineated. In Phase 1, nine radiation oncologists defined the target volumes of 5 patients, whereas in Phase 2, four observers draw the contours of 4 patients applying guidelines. In Phase 1, experience in breast BT after open cavity surgery was assessed. The delineations were compared between Phase 1 and Phase 2, the impact of guidelines was assessed, and cavity visualization score was related to consistency of delineations. RESULTS Significant interobserver variability in delineations of lumpectomy cavity and PTV was observed among the participants. Observers with BT experience after open cavity surgery outlined the cavity and PTV more consistently (conformity indexgen: 0.52 vs. 0.48 and 0.59 vs. 0.55 for preimplant and postimplant cavities). For all volumes, the mean Vmax/Vmin was 2.2 vs. 2.8. Having used guidelines all conformity indices increased significantly. For cavity, the increase was 14% and 11%, whereas for the PTV, 28% and 17% on the preimplant and postimplant CT images, respectively. A strong correlation was found between consistency of contours and cavity visualization score. CONCLUSIONS Simple guidelines on defining the lumpectomy cavity significantly increased the consistency of contouring. Reliable consistency of target volume definition can be expected only for good cavity visibility.

Effect of tympanic cavity evacuation and flushing on microbial isolates during total ear canal ablation with lateral bulla osteotomy in dogs.

OBJECTIVE To evaluate differences in bacterial numbers, identity, and susceptibility in samples obtained from the tympanic cavity on entry (preflush) and after evacuation and lavage (postflush) and assess perioperative and empiric antimicrobial selection in dogs that underwent total ear canal ablation (TECA) with lateral bulla osteotomy (LBO) or reoperation LBO. DESIGN Prospective clinical study. ANIMALS 34 dogs. PROCEDURE TECA with LBO or reoperation LBO was performed on 47 ears. Pre- and postflush aerobic and anaerobic samples were obtained from the tympanic cavity. Isolates and antimicrobial susceptibility patterns were compared. RESULTS Different isolates (31/44 [70%] ears) and susceptibility patterns of isolate pairs (6/44 [14%] ears) were detected in pre- and postflush samples from 84% of ears. Evacuation and lavage of the tympanic cavity decreased the number of bacterial isolates by 33%. In 26% of ears, bacteria were isolated from post-flush samples but not preflush samples. Only 26% of isolates tested were susceptible to cefazolin. At least 1 isolate from 53% of dogs that received empirically chosen antimicrobials postoperatively was resistant to the selected drugs. Anaerobic bacteria were recovered from 6 ears. CONCLUSIONS AND CLINICAL RELEVANCE Accurate microbiologic assessment of the tympanic cavity should be the basis for selection of antimicrobials in dogs undergoing TECA with LBO. Bacteria remain in the tympanic cavity after evacuation and lavage. Cefazolin was a poor choice for dogs that underwent TECA with LBO, as judged on the basis of culture and susceptibility testing results.