Higher order representation of the beam cross section deformation in large displacement finite element analysis

Most existing beam formulations assume that the cross section of the beam remains rigid regardless of the amplitude of the displacement. The absolute nodal coordinate formulation (ANCF); however, allows for the deformation of the cross section and leads to a more general beam models that capture the coupling between different modes of displacement. This paper examines the effect of the order of interpolation on the modes of deformation of the beam cross section using ANCF finite elements. To this end, a new two-dimensional shear deformable ANCF beam element is developed. The new finite element employs a higher order of interpolation, and allows for new cross section deformation modes that cannot be captured using previously developed shear deformable ANCF beam elements. The element developed in this study relaxes the assumption of planar cross section; thereby allowing for including the effect of warping as well as for different stretch values at different points on the element cross section. The displacement field of the new element is assumed to be cubic in the axial direction and quadratic in the transverse direction. Using this displacement field, more expressions for the element extension, shear and the cross section stretch can be systematically defined. The change in the cross section area is measured using Nanson’s formula. Measures of the shear angle, extension, and cross section stretch can also be systematically defined using coordinate systems defined at the element material points. Using these local coordinate systems, expressions for a nominal shear angle are obtained. The differences between the cross section deformation modes obtained using the new higher order element and those obtained using the previously developed lower order elements are highlighted. Numerical examples are presented in order to compare the results obtained using the new finite element and the results obtained using previously developed ANCF finite elements.     

Coupling to the elastic channel in electron impact spectroscopy: A simple second born model and its application to excitation of the 61P1 state of mercury and to the excitation of molecules

The matrix element in the infinite channel close coupling approximation responsible for coupling to the elastic channel in electron impact inelastic encounters is investigated. The contribution from the imaginary part of the energy denominator in the elastic coupling matrix element for dipole allowed transitions is shown to yield large angle differential cross sections in good agreement with experiment. This coupling mechanism predicts that the shape of the inelastic differential cross section will be dominated by the shape of the elastic cross section in the large angle high energy limit. In fact the coupling matrix element exhibits a dependence on incident energy, k², and momentum transfer, K, of the form 1/kK² which is in agreement with the theoretical predictions of Huo and means that in the limit of high incident energy the non-first-Born elastic coupling will dominate the angular dependence of the inelastic differential cross section at large scattering angles. In the case of molecular electron impact spectra it is shown that the analog of the Massey—Moore coherence features depending on the symmetry of the states involved in the excitation process will also occur in the coupling contribution. It is suggested that this new mechanism for producing coherent features in inelastic differential cross sections may be the explanation of the coherent features observed experimentally by Karle and Swick.It can be concluded on the basis of the results obtained here that the coupling to the elastic cross section provided by the imaginary contribution from the second Born energy denominator is sufficient to explain presently available experimental data on the large angle differential cross section and spin polarization. The simple coupling model was found to be inadequate to explain the small angle differential cross section in the range 10° < θ < 30° even at incident energies as high as 400 eV. The calculations also showed significant differences between first and second Born calculations at zero scattering angle. No conclusion can be drawn about this observation as all the omitted terms should make significant contributions in the small angle region. It is important to again emphasize that the large angle scattering even in the limit of high incident electron energy will be completely dominated by the coupling to the elastic channel^{7, 11}. On the basis of this work it appears that the coherent structure in the large angle inelastic differential cross section observed by Swick and Karle^{12, 13} at incident electron energies in the keV region may well be due to coupling to the elastic channel.     

Pion photoproduction and the “anomalous” transition 14Ng.s. → 14Cg.s.

We study the reaction ¹⁴(γ, π⁺)¹⁴Cg_g.s. near threshold. The vanishingly small Gamow-Teller matrix element allows us to probe corrections to the normally dominant σ · ε (Kroll-Ruderman) term. We find that, while the cross section for this process is strongly sensitive to nuclear structure and pion distortion inputs, the pseudoscalar terms reduce the cross section substantially from the Kroll-Ruderman value, irrespective of these uncertainties. Significant improvement is found in the comparison with experiment when the empirical nuclear wave functions, obtained from other weak and electromagnetic processes, are used, rather than the shell-model wave functions.     

Antikaon production in nucleon- nucleon reactions near threshold

The antikaon production cross section from nucleon-nucleon reactions near threshold is studied in a meson exchange model. We include both pion and kaon exchange, but neglect the interference between the amplitudes. In case of pion exchange the antikaon production cross section can be expressed in terms of the antikaon production cross section from a pion-nucleon interaction, which we take from the experimental data if available. Otherwise, a K* -resonance exchange model is introduced to relate the different reaction cross sections. In case of kaon exchange the antikaon production cross section is related to the elastic KN and K?N cross sections, which are again taken from experimental measurements. We find that the one-meson exchange model gives a satisfactory fit to the available data for the NN → NN KK? cross section at high energies. We compare our predictions for the cross section near threshold with an earlier empirical parameterization and that from phase space models.     

On the structure of the nucleon optical potential

The structure of the nucleon generalized optical potential (GOP) is investigated in the framework of Green's function (GF) theory. First an exact relation between its imaginary part and the total reaction cross section is derived. In the second part the GOP is decomposed using a kind of projection formalism which enables to couple in the continuum in successive steps. This is achieved by splitting up the one particle GF into a discrete and a continuous part and by summing up all contributions to the GOP containing a given numbern0 continuum propagators. Three expressions are extracted corresponding to different processes involving the scattering of at most two particles in the continuum in intermediate states. The remaining terms are argued to be small. Further support for retaining only the above three terms is given by evaluating the diagonal element of their imaginary part between the exact eigenstates of the GOP. This is shown to be approximately proportional to the sum of the total inelastic, charge exchange, pick-up and knockout cross sections. The corresponding matrix element of the exact potential is proportional to the total reaction cross section.     

Threshold electrodisintegration of the deuteron caused by backward scattering of electrons

Using a new relativistic integral representation for the matrix element of electromagnetic current in terms of experimental phase shifts alone (representation of Shirokov RS) the cross section of the threshold electrodisintegration of the deuteron caused by backward scattered electrons is calculated for the S-wave deuteron in the interval of the four-momentum transfers squared 0.16 ? q² ? 5 fm^?2. Nucleon-nucleon interaction in the deuteron and the final state interaction (FSI) are taken into account in a unified manner and exactly. The effects of the meson exchange currents (MEC) and the inelastic n-p channels are neglected. The calculated cross section coincides with the experimental one.     

The photoneutron cross section of 45Sc

The photoneutron cross section of ⁴⁵Sc has been measured from threshold to 25 MeV using bremsstrahlung and direct neutron detection. The cross section is found to exhibit a large width of approximately 8 MeV and this is interpreted in terms of the Danos hydrodynamic model for the giant resonance of deformed nuclei. The integrated cross section to 25 MeV is 158 ± 24 MeV mb.     

The use of the boundary element method in solving the problems of sound scattering by an elastic noncircular cylinder

A semianalytic solution of the problem of sound scattering by an elastic cylinder with a noncircular cross section is proposed. The problem is solved by the analytic-numerical boundary element method in terms of the ideal fluid theory and the linear theory of elasticity.     

The contribution of pion absorption with two-nucleon emission to the pion-nucleus optical potential

Four terms in the pion-nucleus optical potential which arise from pion absorption with two nucleon emission are calculated using a model in which the nucleon is treated as a bound state of a pion and a nucleon. The contribution of these terms to the reaction cross section of carbon is considered. Two of the terms give rise to a negative reaction cross section, but it is shown that the sum of the four is positive definite. We find that the absorption reaction cross sections are very sensitive to the off-shell behavior of the free pion-nucleon T-matrix.     

Inclusive D production in $\gamma \gamma$ collisions: including the single-resolved contribution with massive quarks

We have calculated the next-to-leading order cross section for the inclusive production of charm quarks as a function of the transverse momentum p_T and the rapidity in two approaches using massive or massless charm quarks. For the single-resolved cross section we have derived the massless limit from the massive theory. We find that this limit differs from the genuine massless version with factorization by finite corrections. By adjusting subtraction terms we establish a massive theory with subtraction which approaches the massless theory very fast with increasing transverse momentum. With these results and including the equivalent results for the direct cross section obtained previously as well as double-resolved contributions, we calculate the inclusive cross section in collisions using realistic evolved non-perturbative fragmentation functions and compare with recent data from the LEP collaborations ALEPH, L3 and OPAL. We find good agreement. Received: 14 February 2003 / Published online: 5 May 2003     

On the direct inversion of total scattering cross sections in the glory region

The total scattering cross section as a function of velocity in the glory region can be accurately described semiclassically as the sum of an average part and an undulating part. In practice the velocity dependence of the average cross section is complicated because of contributions from different dispersion terms in the attractive part of the potential and eventually from repulsive terms as well. It is shown that the average cross section can be accurately retrieved from the data, without the assumption of a mathematical model for the potential, and that the retrieved values can be directly inverted to numerical values of the potential tail. The separated results for the undulating part yield numerical values for five of the usual glory parameters. The procedure is tested on simulated total cross section data showing several full glory oscillations, and the glory parameters and potential tail are reproduced to accuracies consistent with the graphical-numerical methods employed.     

Tensor polarized γ-deuteron Compton scattering in effective field theory

The differential cross section for γ-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams. At 90° photon scattering angle, only the pion term contributes at this order to the tensor polarized differential cross section. This provides a clean way to study the photon pion dynamics in the two nucleon sector. The effect is measurable for photon energies between 40 and 80 MeV provided the uncertainty in the measured cross sections are ≲ 7%.     

Mesonic and binding contributions to the nuclear Drell-Yan process

We have evaluated the Drell-Yan cross section in nuclei paying special attention to the meson cloud contribution from pions and ϱ-mesons, for which an accurate calculation using the meson nuclear spectral functions is used. Similarly, the nucleonic contribution is evaluated in terms of a relativistic nucleon spectral function. Fair agreement with experiment is found for different nuclei and the results show a sizeable contribution from the renormalized meson cloud. In order to reproduce the experiment a novel element is introduced, consisting of a gradual energy loss of the incoming proton in its pass through the nucleus which produces a strong A dependence at x₁ large.     

Correlation between zeroes and poles ofS matrix for complex potentials

Using several illustrative examples, the nature of resonance poles and the corresponding zeroes of the s-waveS matrix is examined for several potentials having an absorptive pocket followed by a barrier. It is shown that even though the presence of absorption practically suppresses the manifestation of resonance in the elastic scattering cross section, the effect of the resonances generated by the absorptive pocket is more clearly manifested in the absorption cross section provided the barrier width is not too large. We further find that the signature of barrier top resonances are also more clearly manifested in the absorption cross section rather than in the elastic scattering cross section. These results have been interpreted in terms of complex resonance poles and corresponding zeroes of theS matrix. This implies that in complex potential scattering like heavy ion collisions, the reaction channel cross section peak is a more reliable signature of resonance phenomenon than the variation of the elastic channel cross section with energy.     

Influence of vacuum energy on scattering

We deal with photon-electron scattering which occurs between two uncharged conducting parallel plates moving away from each other at a constant velocity. The electromagnetic vacuum field between two plates is defined by the configuration of space and also interacts with the electrons. We show the relevant operators for both the electron and photon fields and the computation of the corresponding Feynman propagator,S-matrix, and scattering cross section, taking into account the influence of the changeable vacuum field. Correction terms in the computedS-matrix and scattering cross section manifest the influence of the changeable vacuum field. We analyze an example for low-energy scattering of the influence of the changeable vacuum field upon the scattering cross section.     

Cross section calculations of randomly oriented bispheres in the small particle regime

The T-matrix is used to calculate the extinction cross section of bispherical particle systems in random orientation for a monospherical size parameter x=0.01. Differences between bispherical and monospherical (Mie) results are shown for a range of values of the refractive index. It is found that the size of the T-matrix that needs to be calculated can be large, thus preventing simple dipole approximations from being used. Once the T-matrix is computed, however, only a small number of terms is needed to obtain cross section values.     

Multichannel excitation cross sections of sodium atoms at slow collisions with hydrogen atoms

Excitation cross sections at slow collisions of hydrogen and sodium atoms are calculated based on two sets of quantum-chemical data. The results of calculations permit one to conclude that, upon the excitation of the sodium atom from the ground state in the region of near-threshold energies, the cross sections are highly sensitive to matrix nonadiabaticity elements. In addition, the matrix nonadiabaticity element was varied for the transition 3s → 3p of the sodium atom at fixed collision energy near the reaction threshold. It was found that the variation leads to a significant change in the excitation cross section 3s → 3p, and the range of the energetic dependence of this cross section was determined.     

The dependence of the photodisintegration cross section on the off-shell T-matrix

Nucleon-nucleon scattering phase shifts determine the diagonal element of the transition matrix. The off-diagonal elements are not completely arbitrary but have conditions imposed on them by the range and the tail of the potential. Electromagnetic interaction can also be used to place restrictions on the off-diagonal elements. We find that the cross section of the deuteron photodisintegration is sensitive to the off-shell transition matrix. The integrated cross section can be varied by as much as 30 % or more, and the matrix element for the El transition by a factor of 2. While the matrix element for the photodisintegration depends on the off-shell elements of the T-matrix, it cannot be used to discriminate between alternative off-shell T-matrices. We have constructed classes of different off-shell T-matrices, which produce identical photo-disintegration cross sections and other two-body scattering and bound-state properties.     

The thermal neutron induced fission cross section of 232Th

The thermal neutron induced fission cross section of ²³²Th was measured using the highly pure thermal neutron beam from the 87 m curved neutron guide at the High Flux Reactor of the ILL (Grenoble). An upper limit of 4 μb was obtained for the fission cross section, which is an order of magnitude smaller than previous results. This result is discussed in terms of the double-humped fission barrier theory.