Effect of electron exchange on atomic ionization in a strong electric field

Hartree-Fock atom in a strong electric static field is considered. It is demonstrated that exchange between outer and inner electrons, taken into account by the so-called Fock term affects strongly the long-range behavior of the inner electron wave function. As a result, it dramatically increases its probability to be ionized. A simple model is analyzed demonstrating that the decay probability, compared to the case of a local (Hartree) atomic potential, increases by many orders of magnitude. As a result of such increase, the ratio of inner to outer electrons ionization probability became not too small. It is essential that the effect of exchange upon probability of inner electron ionization by strong electric field is proportional to the square of the number of outer electrons. It signals that in clusters the inner electron ionization by strong field, the very fact of which is manifested by e.g. high energy quanta emission, has to be essentially increased as compared to this process in gaseous atomic objects.Comment: 7 pages, 1 figur

Study of a class of non-polynomial oscillator potentials

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.Comment: 16 page

Solvable simulation of a double-well problem in PT symmetric quantum mechanics

Within quantum mechanics which works with parity-pseudo-Hermitian Hamiltonians we study the tunneling in a symmetric double well formed by two delta functions with complex conjugate strengths. The model is exactly solvable and exhibits several interesting features. Besides an amazingly robust absence of any PT symmetry breaking, we observe a quasi-degeneracy of the levels which occurs all over the energy range including the high-energy domain. This pattern is interpreted as a manifestation of certain "quantum beats".Comment: 12 pages incl. 7 figure

Action Principle and Algebraic Approach to Gauge Transformations in Gauge Theories

The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to the celebrated Fock-Schwinger (FS) gauge for the abelian (QED) gauge theory without recourse to path integrals or to commutation rules and without making use of delta functionals. The interest in the FS gauge, in particular, is that it leads to Faddeev-Popov ghosts-free non-abelian gauge theories. This method is expected to be applicable to non-abelian gauge theories including supersymmetric ones.Comment: LaTeX, 12 pages, Corrected typo

Observations of quasi-periodic solar X-ray emission as a result of MHD oscillations in a system of multiple flare loops

We investigate the solar flare of 20 October 2002. The flare was accompanied by quasi-periodic pulsations (QPP) of both thermal and nonthermal hard X-ray emissions (HXR) observed by RHESSI in the 3-50 keV energy range. Analysis of the HXR time profiles in different energy channels made with the Lomb periodogram indicates two statistically significant time periods of about 16 and 36 seconds. The 36-second QPP were observed only in the nonthermal HXR emission in the impulsive phase of the flare. The 16-second QPP were more pronounced in the thermal HXR emission and were observed both in the impulsive and in the decay phases of the flare. Imaging analysis of the flare region, the determined time periods of the QPP and the estimated physical parameters of magnetic loops in the flare region allow us to interpret the observations as follows. 1) In the impulsive phase energy was released and electrons were accelerated by successive acts with the average time period of about 36 seconds in different parts of two spatially separated, but interacting loop systems of the flare region. 2) The 36-second periodicity of energy release could be caused by the action of fast MHD oscillations in the loops connecting these flaring sites. 3) During the first explosive acts of energy release the MHD oscillations (most probably the sausage mode) with time period of 16 seconds were excited in one system of the flare loops. 4) These oscillations were maintained by the subsequent explosive acts of energy release in the impulsive phase and were completely damped in the decay phase of the flare.Comment: 14 pages, 4 figure

Great Expectations: Voluntary Sports Clubs and Their Role in Delivering National Policy for English Sport

“The original publication is available at www.springerlink.com”. Copyright International Society for Third-Sector Research and The Johns Hopkins University. DOI: 10.1007/s11266-009-9095-yVoluntary sports clubs (VSCs) account for about a quarter of all volunteering in England. The volunteers work in a mutual aid, self-production, self-consumption system whose main purpose is identifying and nurturing high-level performers. But the new HMG/Sport England strategies leading to London 2012 expects volunteers to make a major contribution to sustaining and extending participation. The study utilized six focus group sessions with a total of 36 officials and members of 36 clubs across the six counties of Eastern England to assess whether and to what extent government policy objectives can be delivered through the voluntary sector. The study focused on the perceptions and attitudes of club members about being expected to serve public policy and the current pressures they and their clubs face. The results lead the authors to question the appropriateness, sensitivity, and feasibility of current sport policy, particularly the emphasis on VSCs as policy implementers.Peer reviewe

Temporal comparison of nonthermal flare emission and magnetic-flux change rates

To test the standard flare model (CSHKP-model), we measured the magnetic-flux change rate in five flare events of different GOES classes using chromospheric/photospheric observations and compared its progression with observed nonthermal flare emission. We calculated the cumulated positive and negative magnetic flux participating in the reconnection process, as well as the total reconnection flux. Finally, we investigated the relations between the total reconnection flux, the GOES class of the events, and the linear velocity of the flare-associated CMEs. Using high-cadence H-alpha and TRACE 1600 A image time-series data and MDI/SOHO magnetograms, we measured the required observables (newly brightened flare area and magnetic-field strength inside this area). RHESSI and INTEGRAL hard X-ray time profiles in nonthermal energy bands were used as observable proxies for the flare-energy release rate. We detected strong temporal correlations between the derived magnetic-flux change rate and the observed nonthermal emission of all events. The cumulated positive and negative fluxes, with flux ratios of between 0.64 and 1.35, were almost equivalent to each other. Total reconnection fluxes ranged between 1.8 x 10^21 Mx for the weakest event (GOES class B9.5) and 15.5 x 10^21 Mx for the most energetic one (GOES class X17.2). The amount of magnetic flux participating in the reconnection process was higher in more energetic events than in weaker ones. Flares with more reconnection flux were associated with faster CMEs.Comment: 12 pages, 13 figure

Leadership, the logic of sufficiency and the sustainability of education

The notion of sufficiency has not yet entered mainstream educational thinking, and it still has to make its mark upon educational leadership. However, a number of related concepts – particularly those of sustainability and complexity theory – are beginning to be noticed. This article examines these two concepts and uses them to critique the quasi-economic notion of efficiency, before arguing that the concept of sufficiency arises naturally from this discussion. This concept, originally derived from environmental thinking, has both metaphorical and practical impact for educational organizations and their leadership. An examination of three possible meanings suggests that while an embrace of an imperative concept of sufficiency seems increasingly necessary, its adoption would probably lead to a number of other problems, as it challenges some fundamental societal values and assumptions. Nevertheless, the article argues that these need to be addressed for the sake of both sustainable leadership and a sustainable planet