Ru L2,3 XANES theoretical simulation with DFT: A test of the core-hole treatment

Density functional theory (DFT)-based relativistic calculations were performed to model the Ru L-edge X-ray absorption near edge structure (XANES) spectra of the hexaammineruthenium complex [Ru(NH₃)₆]³⁺ and “blue dimer” water oxidation catalyst, cis,cis- [(bpy)₂(H₂O)Ru^IIIORu^III(OH₂)(bpy)₂]⁴⁺ (bpy is 2,2-bipyridine). Two computational approaches were compared: simulations without the core-hole and by modeling of the core-hole within the Z+1 approximation. Good agreement between calculated and experimental XANES spectra is achieved without including the core-hole. Simulations with algorithms beyond the Z+1 approximation were only possible in a framework of the scalar relativistic treatment. Time-dependent DFT (TD-DFT) was used to compute the Ru L-edge spectrum for [Ru(NH₃)₆]³⁺ model compound. Three different core-hole treatments were compared in a real-space full multiple scattering XANES modeling within the Green function formalism (implemented in the FEFF9.5 package) for the [Ru(Mebimpy)(bpm)(H₂O)]²⁺ complex. The latter approaches worked well in cases where spin–orbit treatment of relativistic effects is not required.     

Alignment and resonances in 12C+12C inelastic scattering

Using the out-of-plane γ-ray particle coincidence method we have measured the spin alignment P_zz of excited ¹²C(2⁺) nuclei from ¹²C+¹²C inelastic scattering in the energy range 16 MeV ? E_cm ? 33 MeV.P_zz varies strongly as a function of energy and angle. The correlation of resonant structures in the cross section with maxima of the alignment is particularly clear in mutual inelastic scattering and in θ_cm = 90° single inelastic scattering.     

Photoemission of protons from4He in theΔ-resonance region

High resolution proton energy spectra from the⁴He(γ,p) reaction have been measured with tagged photons in the range E_γ = 130?525 MeV using the large Mainz NaI(T1) spectrometer atΘ _p ^lab =37.1°. Three separate reaction channels were identified, viz.⁴He(γ,p)t two-body breakup,⁴He photodisintegration via two-nucleon photon absorption processes and the quasifree pion production channel. Differential cross sections are presented for each of these channels as a function of photon energy. The sum of the two-nucleon photon absorption and the quasifree pion production differential cross sections, in the CM system, resembles that of the corresponding free-nucleon differential cross section when Fermi motion is taken into account.     

Higgs-boson pairproduction ine + e − reactions

We calculate the production cross section of Higgs-boson pairs ine ⁺ e ^? annihilation. In this reaction the lowest order contribution comes from one loop graphs. We study the behaviour of the cross section as a function of the energy, the Higgs-boson mass and the scattering angle.     

The α-<Superscript>12</Superscript>C scattering studied via the Trojan-Horse method

The Trojan-horse method has been suggested as a means to study a two-body reaction at astrophysical energies via a three-body breakup reaction. In order to test this method the ⁶Li(¹²C,α¹²C)²H reaction was studied in a kinematically complete experiment at an incident energy of 18 MeV. Coincidence spectra show the presence of the quasi-free α-¹²C scattering process. The excitation function of the three-body reaction is calculated in the plane wave impulse approximation assuming quasi-free scattering and is compared with the experimental data. Also, the excitation function of the virtual α-¹²C elastic scattering is extracted from the three-body reaction cross section at low deuteron momenta and compared with the behaviour of the free scattering cross section. Received: 4 June 1999 / Revised version: 15 November 1999     

The energy dependence of nuclear reaction cross sections

The reaction cross section σ_R^pA(E) for proton-nucleus collisions varies with energy as the total cross section σ_t^pN(E) does for proton-nucleon scattering in the energy regime 100 MeV ? E ?400 GeV. We propose several empirical relations, and test them by a χ² analysis of various data. Within the framework of Glauber theory, the parameters in the relations can be linked to the cross section for a single inelastic collision.     

Calculations of inelastic cross sections for rotational excitation

Cross sections for scattering of N₂ (j=0) molecules on He atoms have been calculated for relative energies below 5 · 10^?3 eV (58 °K). The time independent scattering formalism ofArthurs andDalgarno was used together with an assumed Lennard-Jones type potential with anisotropicP ₂(cos?) terms in the attractive and repulsive parts. The resulting system of coupled differential equations was solved in the distorted wave and close coupling approximations for the differential and integral cross sections for elastic and inelastic (j=0→j=2) scattering. In the integral inelastic cross section several sharp resonances were found to contribute 40% to the cross section at energies below 40 °K. The resonance peaks are attributed to orbiting or short-lived compound states since they are also observed in the elastic cross section at energies which are lower by the excitation energy of 1.5 · 10^?3 eV. Finally, the effect of varying the potential parameters on the integral inelastic cross section was studied at 50 °K and a rough formula for the cross section as a function of the parameters is obtained. The formula shows that a certain ratio of repulsive and attractive anisotropies leads to a small inelastic cross section indicating a mutual cancellation.     

Neutron scattering in argon and <Emphasis Type="Italic">ne</Emphasis> interaction

As a preparation for the new experiment to measure the ne scattering length a_ne the total neutron cross section of gaseous argon has been obtained by the time-of-flight method at the Dubna booster IBR-30 in the energy range from ～5 eV to ～30 keV. A combined one-level analysis of the newly obtained and other known data on cross sections of Ar and ³⁶Ar has made it possible to improve some neutron parameters and calculate the scattering cross section σ_s and the scattering length a separately for ³⁶Ar and ⁴⁰Ar at any energy.     

dd → 3 Hen Reaction at Intermediate Energies

The dd → ³ Hen reaction is considered at the energies between 200 and 520?MeV. The Alt–Grassberger–Sandhas equations are iterated up to the lowest order terms over the nucleon–nucleon t-matrix. The parameterized ³ He wave function including five components is used. The angular dependence of the differential cross section and energy dependence of tensor analyzing power T ₂₀ at the zero scattering angle are presented in comparison with the experimental data.     

Partial differential cross section of inelastic magnetic neutron scattering in the paramagnetic phase of LaCoO3

The partial differential cross section of inelastic magnetic neutron scattering from the compound LaCoO₃ in the paramagnetic phase is studied theoretically. The contribution to scattering from the high-spin state of an ion in zero magnetic field and the modification of this contribution upon application of a magnetic field are calculated using the effective Hamiltonian for the ⁵ D term. The amplitude of the peak in the dependence of the scattering cross section on the energy of scattered neutrons, which corresponds to the transition from the low-spin to the intermediate-spin state, is estimated.     

Improved theoretical pion-nucleus optical potentials

An approach which makes the first order pion-nucleus optical potential theoretically sound is presented. This study should permit higher order improvements to the potential to be more meaningful and the nuclear structure information extracted from pi-nucleus scattering to be more reliable. Based on multiple scattering theory, three optical potentials are constructed and studied in momentum space. These models are the popular Kisslinger potential, the local “Laplacian” potential, and an “improved off-shell potential;” the latter one is derived from absorptive separable pion-nucleon potentials which exactly reproduce on-shell πN scattering. By working in momentum space and explicitly including πN resonances and off-shell effects in the definition of the optical potential, the approach described here is capable of handling any number of pi-nucleon partial waves, is applicable over a very wide energy region, is based on a physical model for off-shell behavior, and is extended easily to include higher order effects. The optical potentials are inserted into two different relativistic wave equations to determine the total cross section and elastic differential cross section for pi-nucleus scattering. It is found that the various models for off-shell πN scattering determine significantly different πC¹² scattering, with the improved off-shell model preferred on theoretical grounds. Also discussed is the importance of properly transforming πN scattering to the pi-nucleus c.m. system, the origin of the shift in the peak position of the π^?C total cross section, and the reason for the increased diffractive nature of the differential cross section at 180 MeV.     

Theoretical analysis of light scattering from super-fluid helium close to the λ phase transition

We calculate the contribution from order parameter fluctuations to the light scattering cross section in ⁴He near T_λ including effects from order parameter relaxation. The existence of a central dip in the critical region is discussed.     

Deuteron structure and diffractive deuteron-nucleus interaction

A nonrelativistic deuteron wave function involving the D-wave state and having a correct asymptotic behavior is constructed on the basis of the experimentally measured deuteron charge form factor G _C(q) and deuteron structure function A(q). The differential cross section for elastic deuteron-nucleus scattering is calculated by using this wave function and is found to agree with experimental data at an energy of 110 MeV. Integrated cross sections for various processes involving deuteron-nucleus interactions are also calculated. The distribution in the emission angle of the center of mass of the neutron-proton system produced in the diffractive dissociation of 110-MeV deuterons in the field of ²⁰⁸Pb nuclei is obtained.     

Phase-shift analysis of d-α elastic scattering between 3 and 17 MeV

Phase shifts for d-α elastic scattering have been extracted from differential cross sections and the vector and tensor analysing powers of ⁴He($\text{d}$, d)⁴He scattering in the energy range from 3 to 17 MeV. The angular momenta were restricted to L ≦ 4 and mixing parameters ε¹ and ε². Good fits could be obtained to nearly all the experimental data analysed. The total reaction cross section and polarization-transfer coefficients were predicted and compared with the measured data; satisfactory agreement was found within the experimental errors. Evidence for a new resonance was found between 11 and 15 MeV.     

Electron-hydrogen scattering just above the ionization threshold

The scattering of electrons by hydrogen atoms is studied for an incident energy of 15 eV, by means of a close coupling calculation using a pseudostate basis. Results are presented for elastic scattering and n = 2 excitation, including angular correlation parameters. The ionization cross section is extracted by an improved projection technique.     

Positron scattering from hydrocarbons

The total cross sections for positron impact on hydrocarbons have been calculated using the additivity rule in which the total cross section for a molecule is the sum of the total cross section for the constituent atoms. The energy range considered is from a few eV to several thousand eV. The total cross sections for positron impact on an atom are calculated by employing a complex spherical potential which comprises of a static, polarization and an absorption potential. We have good agreement with the experimental results for hydrocarbons for positron energy ⩾100 eV. Our results also agree with the available calculations for CH₄ and C₂H₂ which employed full molecular wavefunctions beyond 100 eV. Our absorption cross sections also agree with molecular wave-function calculations for C₂H₂ and CH₄ beyond 100 eV. We have shown the Bethe plots fore ⁺−C ande ⁺−H scattering systems and Bethe parameters have been extracted. We have fitted the cross section for positron impact on hydrocarbons in the formσ _t(C _n H _m )=naE ⁻ b+mcE ⁻ d in the energy range 300–5000 eV wherea=195.0543,b=0.7986,c=371.1757 andd=1.1379 withE in eV andσ _t in 10⁻¹⁶ cm².     

The reaction mechanism of heavy ion scattering at intermediate energies

The contribution to the real and imaginary nucleus-nucleus (N-N) optical potential from nucleon-nucleon scattering in the medium is calculated in a local density approximation from a two Fermi sphere nuclear matter picture for the N-N collision. This reaction mechanism is shown to be dominant for ¹²C + ¹²C scattering at all considered energies (160 MeV < E_lab < 2250 MeV) giving a weakly energy dependent reaction cross section of about 900 mb. Inclusion of the collective 2⁺, 3^? excitations in a coupled channel calculations gives good agreement for both the measured elastic and inelastic 2⁺ cross section at E_lab = 1016 MeV. This fully microscopic parameter free calculation indicates that the energy dependence of the reaction cross section for this system is mostly due to the decrease of the collective contribution with increasing energy contrary to current theoretical models.     

Color screening,absorption, and σ tot pp at LHC

We show that a growth of the proton-proton total cross section with energy can be entirely attributed to the purely perturbative mechanism. The infrared regularization at rather short distances R _c ? 0.3 fm allows extending the BFKL technique from deep inelastic to hadron-hadron scattering. With the inclusion of the absorption corrections our results are in agreement with the LHC data on σ _tot ^pp .     

Interactions of slow neutrons with the chromium isotopes

Neutron transmission experiments and determinations of coherent scattering lengths were performed on natural chromium and enriched samples of⁵⁰Cr,⁵²Cr,⁵³Cr and⁵⁴Cr. By means of the Christiansen-filter-technique we obtained new values for the scattering lengths of the bound atoms:b(^natCr)=3.635±0.007 fm,b(⁵⁰Cr)=?4.50±0.05 fm,b(⁵²Cr)=4.914±0.015 fm,b(53Cr)=?4.20±0.03 fm, andb(⁵⁴Cr)=4.55±0.10 fm. The transmission experiments with neutrons of 510 ΜeV, 1.26 eV and 5.19 eV energy resulted in data for the absorption cross sectionσ _a (^natCr) =3.05±0.08 b and for the scattering cross section at “zero energy”:σ ₀ (^natCr)=3.381±0.010 b. Data for incoherent and spin-state scattering and for the potential-scattering radius of the nuclei could be deduced from these results.