The scaling of respiratory metabolism with body mass is one of the most pervasive phenomena in biology. Using a single allometric equation to characterize empirical scaling relationships and to evaluate alternative hypotheses about mechanisms has been controversial. We developed a method to directly measure respiration of 271 whole plants, spanning nine orders of magnitude in body mass, from small seedlings to large trees, and from tropical to boreal ecosystems. Our measurements include the roots, which have often been ignored. Rather than a single power-law relationship, our data are fit by a biphasic, mixed-power function. The allometric exponent varies continuously from 1 in the smallest plants to 3/4 in larger saplings and trees. The transition from linear to 3/4-power scaling may indicate fundamental physical and physiological constraints on the allocation of plant biomass between photosynthetic and nonphotosynthetic organs over the course of ontogenetic plant growth.allometry | metabolic scaling | mixed-power function | whole-plant respiration | simple-power function F rom the smallest seedlings to giant trees, the masses of vascular plants span 12 orders of magnitude in mass (1). The growth rates of most plants, which are generally presented in terms of net assimilation rates of CO 2 , are believed to be controlled by respiration (2, 3). Furthermore, many of the CO 2 -budget models of plant growth and carbon dynamics in terrestrial ecosystems are based on whole-plant respiration rates in relation to plant size (2, 4-7). Thus far, however, there have been few studies of wholeplant respiration over the entire range of plant size from tiny seedlings to large trees. The purpose of the present study was to quantify the allometric scaling of metabolism by directly measuring whole-plant respiration over a representative range of sizes.For the past century, the scaling of metabolic rate with body size has usually been described using an allometric equation, or simple power function, for the form (8-17)where Y is the respiratory metabolic rate (μmol s −1 ), F is a constant (μmol s −1 kg -f ), M is the body mass (kg), and f is the scaling exponent. The exponent f has been controversial, and various values have been reported based on studies of both animals and plants (15). Recently, it was suggested that f = 1 for relatively small plants, based on data for a 10 6 -fold range of body mass (16), including measurements using a whole-plant chamber (18,19). If f = 1, this means that whole-plant respiration scales isometrically with body mass, which may be reasonable in the case of herbaceous plants and small trees because nearly all of their cells, even those in the stems, should be active in respiration. However, it was suggested that f = 3/4 based originally on empirical studies of animal metabolism (8). This idea is consistent with the mechanistic models of resource distribution in vascular systems (10, 11), including the pipe model (20, 21) and models based on space-filling, hierarchical, fractal-like networks of br...

The angular and energy dependence of circular dichroism in photo-double-ionization of helium at a photon energy of 99 eV is investigated. Using cold target recoil ion momentum spectroscopy the absolute fivefold differential cross section has been obtained by a coincident measurement of the vector momenta of one electron and the recoiling He 21 ion covering all relative azimuthal and polar angles. The experimental results are contrasted with numerical calculations using different helium ground state wave functions and forms of the dipole operator. [S0031-9007(98)06337-6] PACS numbers: 32.80.Fb, 33.55.AdHelicity adds a new twist to photo-double-ionization of helium: How is the handedness of a circularly polarized photon, absorbed by the spherical symmetric He 1S ground state, transferred to the three-body Coulomb continuum? The handedness leads to a symmetry break in the phase space of the diverging two electrons and the target nucleus. This additional aspect provides a novel tool for the investigation of the photon-induced fragmentation of helium, which is one of the simplest and hence most fundamental manifestations of electron-electron correlation. Helicity dependence can also be used to prove symmetry principles of the three-body Coulomb problem as parity conservation and time reversal invariance.Helicity dependence in photoionization is termed circular dichroism (CD). CD is well known in magnetic solids and chiral or aligned molecules (for a recent review see [1]). However, Berakdar and Klar [2] have theoretically shown that CD does not require a chiral or aligned initial state. They predicted that CD may also be observable in a coincidence measurement (e.g., of the two electrons) in photo-double-ionization of helium from its ground state. In general an appropriate experimental approach to investigate a many body system is to measure the fully differential cross section for the fragmentation of the system by a coincident determination of the vector momenta of all outgoing particles. In their pioneering coincidence experiment Schwarzkopf et al.[3] reported the first fivefold differential cross sections (5DCS) [4] for photo-double-ionization of helium using linearly polarized light. Also the technique of cold target recoil ion momentum spectroscopy (COLTRIMS) has already been used to perform fully differential experiments on photo-double-ionization of helium with linearly polarized light [5]. In 1996 Viefhaus et al. [6] reported the first experimental evidence for CD in the helical photo-double-ionization of helium. They obtained the relative 5DCS for five electron energies each at three fixed angles.In the present experiment we have used COLTRIMS [7-9] to investigate the helical photo-double-ionization of helium at an energy of 20 eV above the double ionization threshold. We have measured the 5DCS for all relative polar and azimuthal angles in the electron energy range of 11.5 through 20 eV. A coincidence solid angle of 10% has been achieved, which is an increase of nearly 3 orders of magnitude compared to t...

The Kα satellite spectra arising from the correlative multielectron processes accompanying K-shell photoionization of Ca, Ti and V were measured using a broad range crystal spectrometer. Multiconfiguration Dirac–Fock calculations were performed to interpret the observed x-ray energies and the spectral line shape. The calculations agree fairly well with the experimental results. The variation of the Kα L1 satellite and the Kα1,2h hypersatellite intensities was measured as a function of excitation energy in the range of 8–35 keV. The Kα L1/Kα1,2 intensity ratio for each element is already saturated in our energy range, and the asymptotic values of 1.58 ± 0.08, 1.26 ± 0.06 and 0.97 ± 0.05 % for Ca, Ti and V were determined. By combining the present results and the previously measured values for various elements, we have found a Z−3.5 scaling law for the Kα L1/Kα1,2 intensity ratio. The measured Kα1,2h/Kα1,2 intensity ratio, for each element, is found to increase smoothly from its onset and shows a long saturation range extending up to at least 25 keV above the threshold for Ti. The evolution of the Kα1,2h/Kα1,2 intensity ratio is compared with the analytic Thomas model and with the theoretical calculation based on the screened hydrogenic model.

Using a photon-ion merged-beam technique, we measured the relative yield spectra of Xe 2+ and Xe 3+ ions created by photoionization of Xe + ions as a function of the photon energy in the 4d ionization region. The Xe 3+ ion production, i.e. the double-electron ionization process is found to be dominant throughout the energy range investigated. A broad structure of 4d excitation ionization around 100 eV photon energy was observed in the Xe 3+ yield spectrum. A spectral shoulder was observed for Xe 3+ at around 85 eV, which was absent in the photoionization of neutral Xe. Some discrete lines were observed for both the Xe 2+ -and Xe 3+yield spectra below 75 eV. The experimental spectra were analysed by a multiconfiguration Dirac-Fock calculation. The largest structure at around 100 eV is attributable to 4d 10 5s 2 5p 5 → 4d 9 4f5s 2 5p 4 np (n = 6, 7) two-electron transitions. The discrete lines were found to be due to 4d → np, nf transitions. A serious 4f-orbital collapse is suspected in the 4fnp two-electron excited states, whereas the collapse is moderate in the singly excited 4f-orbitals.

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