The L^2 geometry of spaces of harmonic maps S^2 -> S^2 and RP^2 -> RP^2

Harmonic maps from S^2 to S^2 are all weakly conformal, and so are represented by rational maps. This paper presents a study of the L^2 metric gamma on M_n, the space of degree n harmonic maps S^2 -> S^2, or equivalently, the space of rational maps of degree n. It is proved that gamma is Kaehler with respect to a certain natural complex structure on M_n. The case n=1 is considered in detail: explicit formulae for gamma and its holomorphic sectional, Ricci and scalar curvatures are obtained, it is shown that the space has finite volume and diameter and codimension 2 boundary at infinity, and a certain class of Hamiltonian flows on M_1 is analyzed. It is proved that \tilde{M}_n, the space of absolute degree n (an odd positive integer) harmonic maps RP^2 -> RP^2, is a totally geodesic Lagrangian submanifold of M_n, and that for all n>1, \tilde{M}_n is geodesically incomplete. Possible generalizations and the relevance of these results to theoretical physics are briefly discussed.Comment: 27 pages, 2 figure

Meson exchange currents in electromagnetic one-nucleon emission

The role of meson exchange currents (MEC) in electron- and photon-induced one-nucleon emission processes is studied in a nonrelativistic model including correlations and final state interactions. The nuclear current is the sum of a one-body and of a two-body part. The two-body current includes pion seagull, pion-in-flight and the isobar current contributions. Numerical results are presented for the exclusive 16O(e,e'p)15N and 16O(\gamma,p)15N reactions. MEC effects are in general rather small in (e,e'p), while in (\gamma,p) they are always large and important to obtain a consistent description of (e,e'p) and (\gamma,p) data, with the same spectroscopic factors. The calculated (\gamma,p) cross sections are sensitive to short-range correlations at high values of the recoil momentum, where MEC effects are larger and overwhelm the contribution of correlations.Comment: 9 pages, 6 figure

Kink fluctuation asymptotics and zero modes

In this paper we propose a refinement of the heat kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey-DeWitt heat kernel expansion.Comment: 21 pages, 8 figures, to be published in The European Physical Journal

Fractal Properties of Robust Strange Nonchaotic Attractors in Maps of Two or More Dimensions

We consider the existence of robust strange nonchaotic attractors (SNA's) in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box-counting dimension is N+1 while their information dimension is N. We also show how these properties are manifested in numerical experiments.Comment: 9 pages, 14 figure

Spectroscopic Factors in 40^{40}Ca and 208^{208}Pb from (e,e′p)(e,e'p): Fully Relativistic Analysis

We present results for spectroscopic factors of the outermost shells in $^{40}$Ca and $^{208}$Pb, which have been derived from the comparison between the available quasielastic ($e,e'p$) data from NIKHEF-K and the corresponding calculated cross-sections obtained within a fully relativistic formalism. We include exactly the effect of Coulomb distortion on the electron wave functions and discuss its role in the extraction of the spectroscopic factors from experiment. Without any adjustable parameter, we find spectroscopic factors of about 70\%, consistent with theoretical predictions. We compare our results with previous relativistic and nonrelativistic analyses of ($e,e'p$) data. In addition to Coulomb distortion effects we discuss different choices of the nucleon current operator and also analyze the effects due to the relativistic treatment of the outgoing-distorted and bound nucleon wave functions.Comment: 9 pages RevTeX, 5 figures can be obtained from the author

3s Proton Holes in the Ground State of 208-Pb

This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Assessment of the effects of ozone exposure and plant competition on the reproductive ability of three therophytic clover species from Iberian pastures

Ozone (O3) phytototoxicity has been reported on a wide range of crops and wild Central European plantspecies, however no information has been provided regarding the sensitivity of plantspecies from dehesa Mediterranean therophytic grasslands in spite of their great plantspecies richness and the high O3 levels that are recorded in this area. A study was carried out in open-top chambers (OTCs) to assess the effects of O3 and competition on the reproductiveability of threecloverspecies: Trifolium cherleri, Trifolium subterraneum and Trifolium striatum. A phytometer approach was followed, therefore plants of these species were grown in mesoscosms composed of monocultures of four plants of each species, of threeplants of each species competing against a Briza maxima individual or of a single plant of each cloverspecies competing with threeB. maximaplants. Three O3 treatments were adopted: charcoal filtered air (CFA), non-filtered air (NFA) and non-filtered air supplemented with 40 nl l−1 of O3 (NFA+). The different mesocosms were exposed to the different O3 treatments for 45 days and then they remained in the open. Ozoneexposure caused reductions in the flower biomass of the threecloverspecies assessed. In the case of T. cherleri and T. subterraneum this effect was found following their exposure to the different O3 treatments during their vegetative period. An attenuation of these effects was found when the plants remained in the open. Ozone-induced detrimental effects on the seed output of T. striatum were also observed. The flower biomass of the cloverplants grown in monocultures was greater than when competing with one or threeB. maxima individuals. An increased flower biomass was found in the CFA monoculture mesocosms of T. cherleri when compared with the remaining mesocosms, once the plants were exposed in the open for 60 days. The implications of these effects on the performance of dehesa acid grasslands and for the definition of O3 critical levels is discusse

Relativistic versus Nonrelativistic Optical Potentials in A(e,e'p)B Reactions

We investigate the role of relativistic and nonrelativistic optical potentials used in the analysis of ($e,e'p$) data. We find that the relativistic calculations produce smaller ($e,e'p$) cross sections even in the case in which both relativistic and nonrelativistic optical potentials fit equally well the elastic proton--nucleus scattering data. Compared to the nonrelativistic impulse approximation, this effect is due to a depletion in the nuclear interior of the relativistic nucleon current, which should be taken into account in the nonrelativistic treatment by a proper redefinition of the effective current operator.Comment: Added one new figure, the formalism section has been enlarged and the list of references updated. Added one appendix. This version will appear in Phys. Rev. C. Revtex 3.0, 6 figures (not included). Full postscript version of the file and figures available at http://www.nikhefk.nikhef.nl/projects/Theory/preprints

Realistic Model of the Nucleon Spectral Function in Few- and Many- Nucleon Systems

By analysing the high momentum features of the nucleon momentum distribution in light and complex nuclei, it is argued that the basic two-nucleon configurations generating the structure of the nucleon Spectral Function at high values of the nucleon momentum and removal energy, can be properly described by a factorised ansatz for the nuclear wave function, which leads to a nucleon Spectral Function in the form of a convolution integral involving the momentum distributions describing the relative and center-of-mass motion of a correlated nucleon-nucleon pair embedded in the medium. The Spectral Functions of $^3He$ and infinite nuclear matter resulting from the convolution formula and from many-body calculations are compared, and a very good agreement in a wide range of values of nucleon momentum and removal energy is found. Applications of the model to the analysis of inclusive and exclusive processes are presented, illustrating those features of the cross section which are sensitive to that part of the Spectral Function which is governed by short-range and tensor nucleon-nucleon correlations.Comment: 40 pages Latex , 16 ps figures available from the above e-mail address or from [email protected]