Coplanar (<Emphasis Type="Italic">e</Emphasis>, 3<Emphasis Type="Italic">e</Emphasis>) differential cross-section of He atom

We present in this paper the results of our calculation of five-fold differential cross-section (FDCS) for (e,3e) process on He atom in low momentum transfer and high electron impact energy in shake-off mechanism. The formalism has been developed in Born approximation using plane waves, Byron and Joachain as well as Le Sech and correlated BBK-type wave functions respectively for incident and scattered, bound and ejected electrons. The angular distribution of FDCS of our calculation is presented in various modes of coplanar geometry and comparison is made with the available experimental data. We observe that the present calculation is able to reproduce the trend of the experimental data. However, it differs in magnitude from the experiment. The present theory does not predict four-peak structure insummed mutual angle mode for lower excess ejected electron energies. We also discuss the importance of momentum transfer, post-collision interaction (PCI) and ion participation in the (e,3e) process in constant θ₁₂ mode     

Electron dichroism effects in the relativistic (e, 2e) process for K-shell ionization of atoms

In this communication we present theoretical demonstration of electron dichroism in the relativistic (e, 2e) process for K-shell ionization of atoms in non-coplanar asymmetric geometry. The theoretical formalism has been developed in plane wave Born approximation and in this approximation the triple differential cross-section (TDCS) has been expressed as a product of kinematical factors and atomic structure functions. The longitudinal spin asymmetry in the relativistic (e, 2e) process on K-shell of atoms has been shown to depend on the interference between the transition charge and component of the transition current in the direction perpendicular to the scattering plane. Further, the longitudinal spin asymmetry has been shown to depend on incident electron energy, atomic number of the target, azimuthal angle of the ejected electron and scattered electron angle.     

Theψ-particles in an SU4 scheme with anomalous currents

The recently discovered narrow peaks (theψ-particles) in e⁺e⁻ system at 3.105 and 3.695 GeV are interpreted as hadrons in a broken SU₄ symmetry scheme. A new additional additive quantum number, parachargeZ, is combined with the usual SU₃ quantum numbers in the group SU₄. Theψ (3.1) is assigned to a near ideally mixed15⊕1 multiplet of vector mesons (containing theρ) as theI=Y=0, charge conjugationC=−combination ofZ=±1.members. Theψ (3.7) is assigned correspondingly to another mixed15⊕1 multiplet containing theρ′ (1600). The hadronic electromagnetic interactions are modified by the addition of (non-minimal) anomalous pieces that can changeZ. The decays of theψ-particles are discussed. New enlarged SU₄ multiplets of other hadrons are proposed. Tests of our scheme are put forward. The most crucial test will be the observation of two rather broad resonances in e⁺ e⁻ collisions with masses around 4.2 GeV and 5.1 GeV. Another prediction is the presence of energetic photons in the decays of theψ-particles. Important results concerning the recently observed phenomena in the process e⁺e⁻→hadrons follow in this scheme.     

Contribution of superstring <Emphasis Type="Italic">Z</Emphasis>′ boson on the polarization effects in proton proton collisions

In this work we investigate the single- and the double-spin asymmetries at the collisions of polarized protons pp → (γ ^*, Z ⁰, Z′) + X within the scope of QCD, the electroweak interaction and superstring E ₆ theory. The helicity amplitude method is used. Analytical expressions for the single- and the double-spin asymmetries are obtained and their dependence on the transverse momentum of the lepton pair is investigated at the three different values of invariant masses of the lepton pair. The pure contribution coming from the superstring Z′ boson on the single- and double- spin asymmetries has been extracted. The results obtained allow investigation of the spin structure of the proton.     

Width effects of theZ resonance and CP-violating asymmetry ine + e − annihilation

CP-violating rate asymmetry can be generated in a process only if its amplitude possesses an absorptive part. It is pointed out that such an absorptive part can be provided ine ⁺ e ⁻ annihilation by the presence of aZ(Z′) resonance of non-zero width. The CP asymmetry in the process , wherel _i are charged leptons, is discussed in several models. In a specific two-Z model, large and observable CP asymmetry ine ⁺ e ⁻ →τ ⁺ e ⁻ (τ ⁻ e ⁺) is shown to be possible at LEP/SLC energies.     

Determination of the neutron electric form factor from the reaction 3 He(e,e'n) at medium momentum transfer

The electric form factor of the neutron G_En has been determined in double polarized exclusive ³ He(e,e'n) scattering in quasi–elastic kinematics by measuring asymmetries A _⊥, A _∥ of the cross section with respect to helicity reversal of the electron, with the nuclear spin being oriented perpendicular to the momentum transfer q in case of A_⊥ and parallel in case of A_∥. The experiment was performed at the 855 MeV c. w. microtron MAMI at Mainz. The degree of polarization of the electron beam and of the gaseous ³ He target were each about 50%. Scattered electrons and neutrons were detected in coincidence by detector arrays covering large solid angles. Quasi–elastic scattering events were reconstructed from the measured electron scattering angles ϑ_e, φ_e and the neutron momentum vector p _n ^′ in the plane wave impulse approximation. We obtain the result <G _En>_{(0.27 < Q2c2/GeV2 < 0.5)}= 0.0334 ± 0.0033_stat± 0.0028_syst which is averaged over the indicated range of Q ², the squared momentum transfer. This G _En value is significantly smaller than measured from the D(e,e'n) reaction under similar kinematical conditions. To what extent final state interactions in ³He quench the G _En result is subject of calculations currently in progress elsewhere. Received: 29 April 1999     

Experimental studies of few-body systems at MAMI

Few-body experiments at the Mainz Microtron were focused on a number of selected topics. Double-polarization experiments to determine the neutron electric form factor G_en have been performed using both deuterium and polarized helium-3 targets. The structure of ³He has been studied in the reactions ³H e⃗ e(e⃗e,e′n) and ³H e⃗ e(e⃗e,e′p) with large (transversal) missing momenta and in quasi-elastic electron scattering. Electromagnetically induced two-nucleon knockout has been investigated in order to study the role of correlated nucleon-nucleon motion in the nucleus. Measurements of the (e,e′pn) reaction on ³He and ¹⁶O were performed for the first time. A triple-polarization experiment of type ³H e⃗ e(e⃗e,e′e⃗p⃗)d has been performed, where, in addition, the spin of the knocked out proton is analyzed. This measurement provides information on the spin-dependent momentum distribution of proton-deuteron clusters in the ³He nucleus. Hence, by tagging the outgoing deuteron spin-polarized ³He might also serve as an effective polarized proton target for electron scattering experiments. Moreover, in inclusive ^3,4He(e,e′) measurements at low momentum transfer, the effect of 3-body-forces has been studied.     

Ionization of hydrogen and helium atoms by highly charged fast ions in collisions with small momentum transfer

Ionization of hydrogen and helium atoms is studied for the case of “soft” collisions with highly charged fast ions with v≲Z≪v² and v≫v ₀, where Z is the ion charge, v is the collision velocity, and v ₀∼1 is the characteristic velocity of the electron in the ground state of the atom. Analytical expressions are derived for the singly and doubly differential cross section for ionization of a hydrogen atom accompanied by the ejection of a slow electron v _e≲v ₀, where v _e is the velocity of the ejected electron with respect to the recoil ion). The results are generalized to the case of single ionization of helium. It is shown that soft collisions provide the main contribution to the hydrogen ionization cross section and for all practical purposes determine the cross section for single ionization of helium. The asymmetry in the angular distribution of the ejected slow electrons and the properties of momentum exchange in such collisions are discussed. Finally, a formula for the cross section for single ionization of helium is proposed. Zh. éksp. Teor. Fiz. 112, 1966–1977 (December 1997)     

The exclusive reaction of pion quasi-elastic knockout from nucleon <Emphasis Type="Italic">p(e,e′ π)B</Emphasis> to various states of the final baryon-spectator <Emphasis Type="Italic">B</Emphasis> and the quark models for the pion cloud of nucleon

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N _1/2-(1535), N _1/2+(1440) are calculated in two models, the microscopic model of ³ P ₀ scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N _1/2-(1535) but are rather different for the Roper resonance N _1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).     

Parity violation effects in hydrogen atom in forbidden magnetic-dipole transitions

General expressions for the probability of all strongly forbidden magnetic-dipole transitions between states njl and n′jl in the hydrogen atom and light hydrogen-like ions are derived in the lowest order in the parameter (αZ) in the form W _n′jl;njl ^(Ml) = D _n′n ^lj αm _e (αZ)¹⁰ (in relativistic units), where m _e is the electron mass, α is the fine-structure constant, Z is the nuclear charge, and the constants D _n′n ^lj are presented in an analytical form. Using these expressions, the dependence of the degree of parity violation on the principal quantum numbers n and n′ of the lower and upper states in the ns _1/2-n′s _1/2 and np _1/2-n′p _1/2 M1 transitions is systematically analyzed. The results obtained can be used in designing experiments on parity violation in the hydrogen atom.     

Electron temperature (T e) measurements by Thomson scattering system

Thomson scattering technique based on high power laser has already proved its superoirity in measuring the electron temperature (T _e and density (n _e) in fusion plasma devices like tokamaks. The method is a direct and unambiguous one, widely used for the localised and simultaneous measurements of the above parameters. In Thomson scattering experiment, the light scattered by the plasma electrons is used for the measurements. The plasma electron temperature is measured from the Doppler shifted scattered spectrum and density from the total scattered intensity. A single point Thomson scattering system involving a Q-switched ruby laser and PMTs as the detector is deployed in ADITYA tokamak to give the plasma electron parameters. The system is capable of providing the parameters T _e from 30 eV to 1 keV and n _e from 5 × 10¹²cm⁻³−5 × 10¹³cm⁻³. The system is also able to give the parameter profile from the plasma center (Z=0 cm) to a vertical position of Z=+22 cm to Z=−14 cm, with a spatial resolution of 1 cm on shot to shot basis. This paper discusses the initial measurements of the plasma temperature from ADITYA.     

Universal relation between spectroscopic constants

A universal relation between the Sutherland parameter, Δ (= k _e r _e ^/2 /2D _e) and the dimensionless parameter G (= 8ω _e x _e /B _e ), has been established using 40 electronic states, which include ground as well as excited states of polar and non-polar molecules. This relation is used to predict the dissociation energy of four lowest electronic states of S ₂ molecule. The respective values for the states X ³Σ _g ^/− , a ¹Δ _g , b ¹Σ _g ^/+ and B ³Σ _u ^/− turn out to be 36557, 31431, 28247 and 13429 cm⁻¹, and are in good agreement with the experimental values. Furthermore, metastable states a ¹Δ _g and b ¹Σ _g ^/+ of S ₂ are shown to dissociate into ³ P ₁ + ³ P ₁ as against the dissociation of X ³Σ _g ^/− into ³ P ₂ + ³ P ₁. In addition, a relation between Sutherland parameter Δ and internuclear distance r _e , viz., Δ=2.2r _e has been obtained for the ground state of alkali diatomic molecules.     

Spectral-luminescent properties of chlorin <Emphasis Type="Italic">e</Emphasis><Subscript>6</Subscript> and malate dehydrogenase complexes

Spectral confirmation of the formation of stable equilibrium complexes (association constant K _as = 210⁶ M^–1) of the Krebs cycle enzyme — malate dehydrogenase (MDH) — and one of the promising photodynamic sensitizers — chlorin e ₆ — have been obtained. It is shown that the incorporation of dye molecules into the protein globule of dimeric MDH (each subunit of which contains 4 tryptophan amino acid residues, each binding one molecule of chlorin e ₆) is accompanied by quenching of the tryptophan fluorescence of the enzyme. However, despite the overlapping of the fluorescence spectra of tryptophanyls of MDH and the absorption spectrum of chlorin e ₆, the fluorescence quenching observed is not caused by singlet-singlet inductive-resonant transfer of energy from the donor to the acceptor. The conclusion has been drawn that the reason for the absence of energy transfer from tryptophanyls to the dye is the more effective intertryptophan migration of energy to one of the most longwave amino acid residues, the quenching of the luminescence of which occurs due to the reversible photoinduced transfer of an electron to chlorin e ₆ (formation of a complex with charge transfer). The formation of a complex with charge transfer between chlorin e ₆ (when it is excited) and one of the amino acid residues of the enzyme that contact with the dye at its binding site on the protein molecule is also the most noncontradictory explanation of the observed (when bound with MDH) decrease in the quantum yield of fluorescence of chlorin e ₆ upon increase in the duration of its quenching. The question of the ability of MDH to act as one of the most sensitive targets responsible for the disturbance of mitochondrial functions and initiation of the apoptosis of tumor cells in the process of photodynamic therapy is discussed.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 749–758, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Photoionization of the ground1 S e and twenty lowest excited states of the Ne-like Fe16+

TheR-matrix method is used to calculate cross-sections for the photoionization of Ne-like Fe¹⁶⁺ from ground 2s ²2p ⁶¹ S ^e and excited states belonging to 2s2p ⁶ 3l and 2s ²2p ⁵ 3l configurations. Configuration interaction wavefunctions are used to represent two target states of Fe¹⁷⁺ ion retained in theR-matrix expansion. The cross-sections are obtained as a function of kinetic energy (ε _k) of the ejected electron from 10 to 24 Ry. For low kinetic energy the cross-sections show series of Rydberg states which converge onto² S ^e threshold Fe¹⁷⁺. The calculations are carried out in the LS coupling.     

Intensity distribution in the bands of theD 1Π →X 1Σ+ system of SnO

Relative integrated intensities of the bands of theD ¹Π →X ¹Σ⁺ system of SnO have been measured by the technique of heterochromatic photographic photometry. Using the Rydberg-Klein-Rees Franck-Condon factors andr-centroids, the variation of electronic transition momentR _e with the internuclear separationr is found to beR _e (r)=const. (0.564r−1) in the range of 1.865 A≤r≤2.041A. The relative band strengths are derived. Effective vibrational temperature of the source is found to be 2559 K.     

Improved (1s)<Superscript>2</Superscript> variational model for helium

The ground-state energy of neutral helium is estimated variationally with a trial wavefunction of the form ϕ≈e ^−γ(rA/a _o)ⁿe^−γ(rB/a _o)ⁿ. This model represents a modification of traditional textbook examinations of this problem via inclusion of the power “n” as a second nonlinear variational parameter in addition to the usual effective nuclear charge γ and leads to an upper-limit on the ground state energy of −2.86107 E _h (E _h =1 hartree) in comparison with the traditional (n=1) result of −2.84766 E _h . This result represents a reduction of the percentage overestimate from the true ground-state energy (−2.90373 E _h ) of from 1.93 to 1.47. In comparison with the maximum accuracy obtainable from an uncorrelated trial wavefunction, −2.86168 E _h , the present trial wavefunction reduces the percentage overestimate from 0.49 (n=1) to 0.021. The optimum values of (n, γ) are determined to be ≈(0.897, 1.825).     

Resolved photon processes

We review high-energy scattering processes that are sensitive to the hadronic structure of the photon, describing theoretical predictions as well as recent experimental results. These processes include deep-inelastic electron-photon scattering ate ⁺ e ⁻ colliders; and the production of jets, heavy quarks and isolated photons in the collision of real photons ate ⁺ e ⁻ colliders, as well as in photon-photon collisions atep colliders. We also comment on minijet based calculations of totalγp andγγ cross-sections, and discuss the possibility that future lineare ⁺ e ⁻ colliders might produce very large photon fluxes due to the beamstrahlung phenomenon; in the most extreme cases, we predict more than one hadronicγγ event to occur at every bunch crossing.     

e + e − pair production in ultrarelativistic heavy-ion collisions at intermediate impact parameters

Using the semiclassical Green’s function in the Coulomb field, we analyze the probabilities of single and multiple e ⁺ e ⁻ pair production at a fixed impact parameter b between colliding ultrarelativistic heavy nuclei. We perform calculations in the Born approximation with respect to the parameter Z _Bα and exactly in Z _Aα, where Z _A and Z _B are the charge numbers of the corresponding nuclei. We also obtain the approximate formulas for the probabilities valid for Z _Aα, Z _Bα ≲ 1. The text was submitted by the authors in English.     

Comparison of the Seltzer Coefficient C 1 to Experimental Data

Experimental Coulomb isotope shifts δE _Coul from K _α transitions, and radius differences δ〈r ²〉 _eμ measured by electron scattering and muonic atom X-rays were used to derive ‘experimental’ coefficients C _1,exp for 54 isotope pairs of 18 elements from Mo to U. A χ²-analysis shows that these experimental coefficients are – on average – 3.5% lower than the theoretical C ₁ values calculated by Seltzer, or more precisely: C _1,exp=0.965(± 0.014)×C ₁. The need for more accurate theoretical calculations is stressed, and consequences of this deviation are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.