Some perturbation calculations for 1s2p, 1s 22p,and 1s 22s

The Dalgarno interchange theorem is used, together with the U function approach, to evaluate the first order perturbation corrections to <r ₁ ^-1+r ₂ ^-1> and <r ₁ + r ₂> for the two-electron states 1s2p ¹ P and 1s2p ³ P. The results for <r ₁ + r ₂> are extended by using a screening approximation, and are compared with the results of accurate variational calculations. The first order perturbation correction to spin-weighted expectation values of type <ΣV(r_j )s_zj > is given for the three-electron states 1s ²2p ² P and 1s ²2s ² S. The case V(r_j ) = r _j ^-1 is treated in detail.     

The Combined Effect of Connectivity and Dependency Links on Percolation of Networks

Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently developed mathematical framework for analyzing percolation properties of realistic scenarios of networks having links of two types, connectivity and dependency links. This formalism was applied to study Erdős-Rényi (ER) networks that include also dependency links. For an ER network with average degree [`(k)]\bar{k} that is composed of dependency clusters of size s, the fraction of nodes that belong to the giant component, P <sub>∞</sub>, is given by P<sub>￥</sub>=p<sup>s-1</sup>[1-exp(-[`(k)]pP_￥) ]^sP_{\infty}=p^{s-1}[1-\exp{(-\bar{k}pP_{\infty})} ]^{s} where 1−p is the initial fraction of randomly removed nodes. Here, we apply the formalism to the study of random-regular (RR) networks and find a formula for the size of the giant component in the percolation process: P _∞=p ^s−1(1−r ^k ) ^s where r is the solution of r=p ^s (r ^k−1−1)(1−r ^k )+1, and k is the degree of the nodes. These general results coincide, for s=1, with the known equations for percolation in ER and RR networks respectively without dependency links. In contrast to s=1, where the percolation transition is second order, for s>1 it is of first order. Comparing the percolation behavior of ER and RR networks we find a remarkable difference regarding their resilience. We show, analytically and numerically, that in ER networks with low connectivity degree or large dependency clusters, removal of even a finite number (zero fraction) of the infinite network nodes will trigger a cascade of failures that fragments the whole network. Specifically, for any given s there exists a critical degree value, [`(k)]<sub>min</sub>\bar{k}_{\min}, such that an ER network with [`(k)] ￡ [`(k)]_min\bar{k}\leq \bar{k}_{\min} is unstable and collapse when removing even a single node. This result is in contrast to RR networks where such cascades and full fragmentation can be triggered only by removal of a finite fraction of nodes in the network.     

Trinuclear Gd(III) Metal Complex with Amide Core Display Remarkable Enhancement in Relaxivity

New trinuclear gadolinium(III) complex having 2-bromoisovaleric acid pendant arm is reported. The longitudinal relaxivity (r _1p) of the complex is 23.17 mM^?1 s^?1 which correspond to a “per Gd” relaxivity of 7.72 mM^?1 s^?1. The transverse relaxivity (r _2p) of the complex is 24.79 mM^?1 s^?1 which correspond to a “per Gd” value of 8.26. The complex exhibit r _1p and r _2p values of 29.19 and 35.20, respectively, in the presence of HSA. The complex also shows pH dependant relaxivity which is an added advantage of the complex for utilization in cancer cell magnetic resonance imaging. The higher relaxivity values in water and HSA indicates a compact solution structure for the complexes and a restricted internal motion about the amide spacer.     

Charge radius change in the heavy tin isotopes until A = 132 from laser spectroscopy

Laser spectroscopy measurements have been carried out on the very neutron-rich tin isotopes with the COMPLIS experimental setup. Using the 5s ²5p ²³ P ₀ → 5s ²5p6s ³ P ₁ optical transition, hyperfine spectra of ^126-132Sn and ^{125m, 127m, 129m-131m}Sn where recorded for the first time. The variation of the mean-square charge radius ( δ〈r ²〉) between these nuclei and nuclear moments of the isomers and the odd isotopes were thus measured. An odd-even staggering which inverts at A = 130 is clearly observed. This indicates a small appearance of a plateau on the δ〈r ²〉 which has to be confirmed by measuring the isotope shift beyond A = 132. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: leblanc@ipno.in2p3.fr     

Hadron diffractive processes: the structure of soft pomeron and colour screening

On the basis of the experimental data on diffractive processes in πp, pp and pˉp collisions at intermediate, moderately high and high energies, we restore the scattering amplitude related to the t-channel exchange by vacuum quantum numbers by taking account of the diffractive s-channel rescatterings. At intermediate and moderately high energies, the t-channel exchange amplitude turns, with a good accuracy, into an effective pomeron which renders the results of the additive quark model. At superhigh energies the scattering amplitude provides a Froissart-type behaviour, with an asymptotic universality of cross sections such as σ^tot _πp/σ^tot _pp→ 1 at s→∞. The quark structure of hadrons being taken into account at the level of constituent quarks, the cross sections of pion and proton (antiproton) in the impact parameter space of quarks, σ_π(r _1⊥, r _2⊥; s) and σ_p(r _1⊥, r _2⊥, r _3⊥; s), are found as functions of s. These cross sections implicate the phenomenon of colour screening: they tend to zero at |r _i⊥−r _k⊥|→ 0. The effective colour screening radius for pion (proton) is found for different s. The predictions for the diffractive cross sections at superhigh energies are presented. Received: 15 December 1998     

Impact broadening and shift rates for the 6p2 3PJ′ → 7s 3P J o transitions of lead induced by collisions with argon and helium

The collisional broadening and shift rate coefficients of the 283.39 nm (6p ^{2 3}P₀ → 7s ³P₁ ^o ), 364.06 nm (6p ^{2 3}P₁ → 7s ³P₁ ^o ), 368.45 nm (6p ^{2 3}P₁ → 7s ³P₀ ^o ) and 405.90 nm (6p ^{2 3}P₂ → 7s ³P₁ ^o ) Pb lines by He and Ar have been measured by fitting the experimental absorption line shapes to theoretical Voigt profiles. The absorption measurements were performed in a resistively heated, Pb loaded oven with an integrated dc noble gas discharge to produce also Pb atoms in the 6p ^{2 3}P¹ and 6p ^{2 3}P² metastable states. The diffusion of the metastable atoms out of the discharge zone into the neutral noble-gas atmosphere enabled the line-shape and shift measurement of the lines involving the metastable states without the influence of the discharge plasma.     

Large-scale collisional energy transfer in laser-pumped metastable Ca atoms: Excitation of resonance states of Ca II

We report the first experimental observation of the excitation of the 4p ² P _{3/2, 1/2} resonance states of Ca II (located at 74 720.4 and 74 497.5 cm^–1 above the ground state of Ca I) following pulsed-laser pumping of the 4s ^{2 1} S _O–4s4p ³P₁ intercombination transition of Ca I (E _ex = 15 210 cm^–1). Large scale collisional transfer of energy between the laser-excited atoms is believed to be responsible for this. This is possibly because sufficient time is available (_rad of the 4s4p ³ P ₁ state is approximately 350 µs) for collisions to build such a high level of excitation. Some interesting additional features of the fluorescence spectra of the laser-pumped Ca vapor, such as temperature dependence of the fluorescence intensities and evolution in time of some selected states, are also presented.     

Structure of Sufficient Quantum Coarse-Grainings

Let H and be finite-dimensional Hilbert spaces, T: B(H) B() be a coarse-graining and D ₁, D ₂ be density matrices on H . In this Letter the consequences of the existence of a coarse-graining : B() B(H) satisfying T(D _s )=D _s are given. (This means that T is sufficient for D ₁ and D ₂.) It is shown that D _s = _p=1 ^r _s (p) SH _s ^H (p)R^H(p) (s=1,2) should hold with pairwise orthogonal summands and with commuting factors and with some probability distributions _s (p) for 1 p r (s=1,2). This decomposition allows to deduce the exact condition for equality in the strong subadditivity of the von Neumann entropy.     

On the ground state energy of a two-dimensional electron fluid

A new theory of the ground state energy of a two-dimensional electron fluid is presented. It is shown that the ring diagram contribution changes its analytical behavior atr _s =2^1/2, wherer _s is the usual density parameter defined by r_S = 1/a ₀( n)^1/2,a ₀ being the Bohr radius andn is the electron density. For smallr _s , a high density series is obtained in agreement with the previous calculation. For larger _s , a hitherto unknown low density series is obtained. In the low density region, the first order exchange energy is completely cancelled out by a term from the ring contribution so that the ground state energy decreases in proportion tor _s ^–2/3 , followed byr _s ^/–4/3 and higher order terms. The energy is found to be minimum atr _s=1.4757, the minimum value being –0.481915 Rydbergs.     

Autoionization cross section of lithium atoms excited by electron impact

We measure the full autoionization cross section of lithium atoms excited by electrons in the energy range from the first autoionization threshold at 56.39 to 600 eV. Data are obtained by determining the total intensity of electron spectrum of autoionization states 1sn ₁ l ₁ n ₂ l ₂ detected at the “magic” observation angle of 54.7°. The cross section behavior is characterized by a sharp increase to a maximum value of 1.7 × 10⁻¹⁸ cm² in the energy interval of 56.4–60 eV and a subsequent monotonic drop to a value of 10⁻¹⁸ cm² at 600 eV. We have discovered a “thin” cross section structure that reflects the presence of strong resonances of Li⁻ ions in the near-threshold area of excitation of the lowest energy autoionization states (1s2s2)2S, (1s2s2p)⁴ P, 1s(2s2p ³ P)² P), and 1s(2s2p ¹ P)² P. We have established that the contribution of autoionization to the absolute cross section of single ionization of lithium atoms does not exceed 4%. We perform a comparative analysis of the data with analogous data for potassium and cesium atoms.     

Resonance-enhanced multiple-photon ionisation spectroscopy of excited sulphur atoms

Sulfur atoms are produced in the excited 3s ²3p ^{4 1} D ₂ and 3s ²3p ^{4 1} S ₀ levels by two-photon photodissociation of CS₂ in the gas phase in the region 285–305 nm. These excited atoms are detected by three-photon (two to resonance) ionisation at selected laser wavelengths. Many new transitions have been observed which have not been reported previously. The new dark states that have been accessed by two-photon absorption have been characterised and the energy levels with respect to the ground ³ P ₂ state have been determined. Configuration interaction between 6p ³ P ₁, 6p ⁵ P ₁, and 4p¹ P ₁ states, and also between 6p ³ P ₂, 6p ⁵ P ₂, and 4p¹ D ₂ states has been observed. It is found that intermediate states reached from the ¹ S ₀ level through two-photon absorption lie above the first ionisation potential of S⁺(⁴ S ⁰). It is proposed that autoionisation into the ⁴ S ⁰+e^– continuum is a dominant mechanism in the decay of these levels, although ionisation by a further photon absorption is not ruled out.     

Relativistic and nonrelativistic oscillator strengths in the Na isoelectronic sequence

We report the general trend of the nonrelativistic Hartree-Fock relativistic Hartree-Fock, nonrelativistic configuration-interaction, and relativistic configuration-interaction length form of the oscillator strengths for the resonance excitation 1s ²2s ²2p⁶3s ² S _J ^e 1s ²2s ²2p ⁵3s ^{2 2} P _J ^o . transition, which leads to autoionization (Auger transition), in Na, Mg¹⁺, Al²⁺, Si³⁺, P⁴⁺, S⁵⁺, Cl⁶⁺, Ar⁷⁺, K⁸⁺, Ca⁹⁺, Sc¹⁰⁺, Ti¹¹⁺, Fe¹⁵⁺, Cu¹⁸⁺, Zn¹⁹⁺, Br²⁴⁺, and Kr²⁵⁺ ions of the sodium isoelectronic sequence.     

The use of the Gáspár potential in theoretical investigations of the spectra of atoms and ions

The method of the use of theGáspár potential in theoretical investigations of the energy spectra of atoms and ions in the Hartree—Fock—Pauli approximation is described. The calculations of the energy spectra of a number of multiple-charged ions in the configurations 1s ²2s ²2p ²3s and 1s ²2s ²2p ²3d are presented as the examples and compared with the experimental data available.

     

Isotope shifts in transitions between low-lying levels of Sr I by laser-atomic-beam spectroscopy

High-resolution laser-atomic-beam spectroscopy has been used to determine isotope shifts in five transitions between low-lying states of Sr I. With these results and existing data a parametric analysis of level isotope shifts has been performed. The transition isotope shifts have been separated into field shift and mass shift contributions with a King-plot procedure using model-independent nuclear charge equivalent radiiR _k from muonic x-ray measurements. Values for the mean-square nuclear charge radiiδ〈r ₂ 〉 have been calculated from the field shifts in the optical transitions 5s ^{2 1} S ₀-5s5p ³ P ₁ and 5s5p ³ P ₀-5s6s ³ S ₁ and compared with correspondingδ〈r ² 〉 values evaluated from muonic x-ray data.     

Non-perturbative study of the light pseudoscalar masses in chiral dynamics

We perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. In the calculation of the self-energies we employ the S -wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT) that include the lightest nonet of scalar resonances. Values for the bare masses of pions and kaons are obtained, as well as an estimate of the mass of the η₈ . The former are found to dominate the physical pseudoscalar masses. We also match our results with the self-energies from Chiral Perturbation Theory (CHPT) to O(p ⁴) , and resum higher orders from our calculated self-energies. A robust relation between several O(p ⁴) CHPT counterterms is then obtained. By taking into account values determined from previous chiral phenomenological studies of m _s/ and 3L ₇ + L ^r ₈(M _ρ) , we determine a tighter region of favoured values for the O(p ⁴) CHPT counterterms 2L ^r ₆(M _ρ) - L ^r ₄(M _ρ) and 2L ^r ₈(M _ρ) - L ^r ₅(M _ρ) . This determination perfectly overlaps with the recent determinations to O(p ⁶) in CHPT. We warn about a likely reduction in the value of m _s/ by higher loop diagrams and that this is not systematically accounted for by present lattice extrapolations. We also provide a favoured interval of values for m _s/ and 3L ₇ + L ^r ₈(M _ρ) .     

Invariance of the White Noise for KdV

We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space [^(b)]^s_p,￥{\widehat{b}^s_{p,\infty}} , sp < −1, contains the support of the white noise. Then, we prove local well-posedness in [^(b)]^s_{p, ￥}{\widehat{b}^s_{p, \infty}} for p = 2 + , s = -\frac12+{s = -\frac{1}{2}+} such that sp < −1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko [21].     

Computational study of collisional energy transfer and quasi-continuous population inversions in laser-pumped Ca vapor

A computational study of population inversion between several pairs of excited states viz 3d4p ³ F-4s3d ³ D, 4s5s ³ S-4s4p ³ P and 4s3d ³ D-4s4p ³ P in Ca vapor pumped on the 4s ^{2 1} S ₀-4s4p ³ P ₁ transition is presented. The main aim is to investigate the influence of various atomic processes in creating and sustaining the population inversion for long times after the excitation pulse. The delicate interplay between superelastic energy transfer to free electrons, energy pooling collisions and cascaded recombination is particulary examined. It is noted that quasi-continuous population inversion can be readily excited on the 4s3d ³ D-4s4p ³ P transitions; and under some conditions, also on the 4s5s ³ S-4s4p ³ P transitions. Furthermore, inversion on the 3d4p ³ F-4s3d ³ D transitions can also be excited for a considerable length of time. The results may be useful in designing and developing quasi-cw metal vapor lasers.     

Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: ([(?)\vec] r_p - [(?)\vec] r_n\vec \nabla \rho _p - \vec \nabla \rho _n )² G _d(r \rho) + ([(?)\vec] r_p - [(?)\vec] r_n\vec \nabla \rho _p - \vec \nabla \rho _n ·([(J)\vec]_p - [(J)\vec]_n\vec J_p - \vec J_n )G _so(r \rho) + ([(J)\vec]_p - [(J)\vec]_n\vec J_p - \vec J_n )² G _J(r \rho) pertaining to different proton and neutron densities. Our calculation treats systematically the effects from 1p \pi -exchange, iterated 1p \pi -exchange, and irreducible 2p \pi -exchange with intermediate D \Delta -isobar excitations, including Pauli-blocking corrections up to three-loop order. Using an improved density-matrix expansion, we obtain results for the strength functions G _d(r \rho) , G _so(r \rho) and G _J(r \rho) which are considerably larger than those of phenomenological Skyrme forces. These (parameter-free) predictions for the strength of the isovector surface and spin-orbit terms as provided by the long-range pion-exchange dynamics in the nuclear medium should be examined in nuclear structure calculations at large neutron excess.     

Calculation of the Hyperfinestructure and gJ-Values of the 3d 4s 4p-Configuration of Scandium

Wave functions for the 3d 4s 4p, 3d² 4p and 4s² 4p configurations of ScI are calculated, taking into account departures from SL-coupling and configuration interaction and on fitting the radial integrals to the experimental fine structure energies. Using these wave functions g J -values are derived. The intermediate coupled hfs matrix elements of the 3d 4s 4p configuration are reduced to the unknown electron coupling constants a_s, a_p and a_d and calculated on estimating these constants from the spin-orbit coupling constants and fitting them to some experimental A-values. By this way the absolute phases of the experimental A((¹P)²D)- and A((¹P)²F)-values are obtained. Good agreement between calculated and most experimental data has been achieved.