Born Amplitude Research Articles

On dips, structures and eikonalization

We have investigated several models of Pomeron and Odderon contributions to high energy elastic $pp$ and $\bar p p$ scattering. The questions we address concern their role in this field, the behavior of the scattering amplitude (or of the total cross-section) at high energy, and how to fit all high energy elastic data. The data are extremely well reproduced by our approach at all momenta and for sufficiently high energies. The relative virtues of Born amplitudes and of different kinds of eikonalizations are considered. An important point in this respect is that secondary structures are predicted in the differential cross-sections at increasing energies and these phenomena appear quite directly related to the procedure of eikonalizing the various Born amplitudes. We conclude that these secondary structures arise naturally within the eikonalized procedure (although their precise localization turns out to be model dependent). The fitting procedure naturally predicts the appearance of a zero at small $|t|$ in the real part of the even amplitude as anticipated by general theorems. We would like to stress, once again, how important it would be to have at LHC both $pp$ and $p \bar p$ options for many questions connected to the general properties of high energy hadronic physics and for a check of our predictions.

Electron capture into Rydberg states according to the Born approximation: Correction of an error

A general expression is derived for the Born amplitude for electron capture by bare nuclei from hydrogenic atom targets, where capture takes place into high principal, and arbitrary angular momentum, quantum numbers, n and l. Cross sections for capture into high n and $l=0,1$ are given in analytic forms. The limiting values of the ratios of the Born over the Oppenheimer-Brinkman-Kramers cross sections for $n\ensuremath{\gg}1$ and $l=0,1$ are found, and shown that they confirm the empirical law of Jackson and Schiff only approximately. For high angular momenta, it is shown that the Born cross section approaches the OBK cross section. An error in a previous publication by the author has been corrected.

Dynamic Effects in Electron Scattering in the 3d-Subshell of Lanthanum

The work reports the calculation of cross sections of inelastic electron scattering on metallic La, exciting the inner 3d-shell. The calculations are based on an atomic physics description of the triply ionized free atom. The large spin-orbit coupling constant of the 3d-hole leads to an approximate jK-coupling. The resulting excitation strength is formulated in terms of the Born amplitude including resonant contributions. The intensity is folded with a Lorentzian broadening with full width at half maximum (FWHM) parameter Γ. This parameter is considered to be dependent on the projectile electron energy so that the dynamic effects found in experimental EELS may be addressed. The systematic variation of the relative intensities of the spin-orbit doublet structures with excitation energy found in experiment is partly accounted for as Γ is varied from the experimentally measured values of 0.7 eV–0.5 eV and beyond.

Radiative corrections to the Aharonov-Bohm scattering

We consider the scattering of relativistic electrons from a thin magnetic flux tube and perturbatively calculate the order $\alpha$, radiative correction, to the first order Born approximation. We show also that the second order Born amplitude vanishes, and obtain a finite inclusive cross section for the one-body scattering which incorporates soft photon bremsstrahlung effects. Moreover, we determine the radiatively corrected Aharonov-Bohm potential and, in particular, verify that an induced magnetic field is generated outside of the flux tube.

Hadronic structure in the decayτ−→ντπ−π0π0and the sign of the tau neutrino helicity

Based on a sample corresponding to 4.3 million produced tau-pair events, we have studied hadronic dynamics in the decay tau- --> nu_tau pi- pi0 pi0 in data recorded by the CLEO II detector operating at the CESR e+e- collider. The decay is dominated by the process tau --> nu_tau a_1(1260), with the a_1 meson decaying to three pions predominantly via the lowest dimensional (mainly S-wave) a_1 --> rho pi Born amplitude. From fits to the Dalitz plot and angular observables, we find significant additional contributions from amplitudes for a_1 decay to sigma pi, f_0(1370) pi and f_2(1270) pi, as well as higher dimensional a_1 --> rho pi and rho' pi amplitudes. The squared sigma pi amplitude accounts for ~15% of the total tau- --> nu_tau pi- pi0 pi0 rate in the models considered. We have searched for additional contributions from tau --> nu_tau pi'(1300). We place 90% confidence level upper limits on the branching fraction for this channel of between 1.0*10^{-4} and 1.9*10^{-4}, depending on the pi' decay mode. The pi- pi0 pi0 mass spectrum is parametrized by a Breit-Wigner form with a mass-dependent width which is specified according to the results of the Dalitz plot fits plus a coupling to an a_1 --> K* K amplitude. From a chi^2 fit, we extract the pole mass and width of the a_1, as well as the magnitude of the K* K coupling. We have also investigated the impact of a possible contribution from the a_1'(1700) meson on this spectrum. Finally, exploiting the parity-violating angular asymmetry in a_1 --> 3pi decay, we determine the signed value of the tau neutrino helicity to be h_{\nu_\tau} = -1.02 +- 0.13(stat.) +- 0.03(syst.+model), confirming the left-handedness of the tau neutrino.

Gauge-invariant tree-level photoproduction amplitudes with form factors

We show how the gauge-invariance formulation given by Haberzettl is implemented in practice for photoproduction amplitudes at tree level with form factors describing composite nucleons. We demonstrate that, in contrast to Ohta's gauge-invariance prescription, this formalism allows electric current contributions to be multiplied by a form factor, i.e., it does not require that they be treated like bare currents. While different in detail, this nevertheless lends support to previous ad hoc approaches which multiply the Born amplitudes by an overall form factor. Numerical results for kaon photoproduction off the nucleon are given. They show that the gauge procedure by Haberzettl leads to much improved ${\ensuremath{\chi}}^{2}$ values compared to Ohta's prescription.

Influence of the doping element on the electron mobility in n-silicon

We present a theoretical approach to study the dependence of the electron mobility on the dopant species in n-doped silicon under low electric fields. The electron charge distribution of the impurities is calculated by the Thomas–Fermi theory using the energy functional formulation. Ionized impurity scattering has been treated within the Born approximation. Our model accounts for degenerate statistics, dispersive screening and pair scattering, which become important in heavily doped semiconductors. The dielectric function is accurately approximated by a rational function. A new expression for the second Born amplitude of a Yukawa-like charge distribution is derived, which now depends on the atomic and electron numbers of the impurity ion. Monte Carlo simulations including all important scattering mechanism have been performed in the doping concentration range from 1015 to 1021 cm−3. The agreement with experimental data is excellent. The results confirm the lower electron mobility in As-doped silicon in comparison to P-doped silicon.

Ionized-Impurity Scattering of Majority Electrons in Silicon

The Brooks–Herring approach to ionized-impurity scattering overestimates the low-field mobility of electrons in doped semiconductors. It relies on a static single-site description of the carrier-impurity interaction and on the first Born approximation. We present a consistent ionized-impurity scattering model which accounts for degenerate statistics, dispersive screening and two-ion scattering. The dielectric function is accurately approximated by a rational function. From the Schwinger scattering amplitude a correction to the first Born amplitude is derived. Plasmon scattering as another concentration dependent mechanism is included. Despite the various physical effects taken into consideration the scattering model can be used in Monte Carlo transport calculations without any significant increase in computation time. Monte Carlo calculations of majority electron mobility in silicon are discussed, and good agreement with experimental data is found in the doping range [10 14, 10 20]cm −3.

Can the magnetic moment contribution explain theAypuzzle?

We evaluate the full one-photon-exchange Born amplitude for $\mathrm{Nd}$ scattering. We include the contributions due to the magnetic moment of the proton or neutron, and the magnetic moment and quadrupole moment of the deuteron. It is found that the inclusion of the magnetic-moment interaction in the theoretical description of the $\mathrm{Nd}$ scattering observables cannot resolve the long-standing ${A}_{y}$ puzzle.

Two Coulomb waves theory for direct excitation

A theoretical model of Dewangan, in which the total scattering wave function is approximated by a distorted wave containing two Coulomb wave functions, is discussed and its relation with the Brauner-Briggs-Klar model for ionization is examined. An important feature of the theory is that it includes a second Born amplitude naturally and in addition, contains, albeit approximately, both real and imaginary parts of all higher order Born terms. The theory is applied to study the 1s→2s excitation of hydrogen by electrons in the energy range 54.4 to 400eV. The differential and integral cross sections predicted by the theory are compared with the results of other theories and experimental data at 54.4eV and a good agreement is found.

Comment on `Addition theorem for solid harmonics and the second Born amplitudes'

We draw attention to the fact that part of a recent article by Chakraborty and Dewangan has already appeared in the literature. A part of the above article published by Chakraborty and Dewangan [1] is an alternative proof of the addition theorem of regular spherical harmonics. We note, however, that this alternative proof follows a procedure also used by ourselves in proving the theorem [2]. The addition theorem of regular solid harmonics has been applied in numerous calculations over the years. The work of Deb and Sil [3] may be mentioned as one of its earlier applications.

A mesonic model of - baryon - baryon vertices

The coupling constants and form factors of the , and vertices are studied with a composite model. These form factors satisfy a set of coupled integral equations with the Born amplitudes and higher-order interactions dominated, respectively, by two-pion intermediate states and -loop corrections to the vertices. Upon solving the relevant equations self-consistently, we found that the loop corrections are unimportant for the vertex but quite significant for the and vertices. With the known values of - baryon, - baryon, and coupling constants as inputs, the model predicts a compatible with that given by the meson-exchange potentials, but a slightly weaker . The composite model also predicts soft - baryon - baryon form factors having a momentum-space range between 400 and , in agreement with other recent theoretical findings. We discuss the implications of our findings on nuclear reaction studies.

Low-energy dynamics of the γγ → ππ reaction in the NJL model

We calculate the one-quark-loop amplitude for the low energy $\gamma\gamma\to\pi\pi$ collision in the context of the Nambu and Jona-Lasinio model with scalar and pseudoscalar four quark couplings to all orders in the external momenta. We show that the NJL predictions for the $\gamma\gamma\to\pi^+\pi^-$ reaction are not far from the Born amplitude, which is close to the data, and is compatible with the chiral perturbation theory estimations. We determine the corrections given by the NJL model in leading order of $1/N_c$ to the chiral loop amplitude for $\gamma\gamma\to\pi^0\pi^0$. Numerical results for the $\gamma\gamma\rightarrow\pi\pi$ cross sections and for pion polarizabilities are given.

Constant-cutoff approach to pion-nucleon scattering

Pion-nucleon scattering amplitudes as well as Born amplitudes are calculated in a constant-cutoff approach to the canonical quantization of skyrmions, with the subsidiary conditions imposed on the quantum fields and their conjugate momenta such that all infrared singularities from the zero-frequency modes are eliminated. It is shown that the Born terms with recoil corrections are reproduced by the pion-nucleon linear and quadratic interactions.

CP violation in heavy neutrino mediated e−e− → W−W−

We consider the reaction e − e − → W − W − mediated by possible heavy neutrino exchange at future LINAC energies of s ⪢ 2 m w . This reaction is sensitive to CP phases of the neutrino mixing matrices, even at the level of Born amplitudes. Certain integrated cross-sections are shown to have the power to resolve the CP phases when the experimental configurations are varied. Asymmetries sensitive to CP violation (involving initial QED phases) for e − e − and e + e + reactions are constructed and their consequences considered.

Multilevel effects on the balance of dipole-allowed to dipole-forbidden transitions in Rydberg atoms induced by a dipole interaction with slow charged projectiles.

In collisions of Rydberg atoms with charged projectiles at velocities approximately matching the speed of the Rydberg electron {ital v}{sub {ital n}} (matching velocity), {ital n} being the principal quantum number of the Rydberg level, the dipole-forbidden transitions with large angular-momentum transfer {Delta}{ital l}{gt}1 substantially dominate over dipole-allowed transitions {Delta}{ital l}=1, although both are induced by the dipole interaction. Here it is shown that as the projectile velocity decreases the adiabatic character of the depopulation depends on the energy distribution of states in the vicinity of the initial level. If the spectrum is close to degeneracy (as for high-{ital l} levels) the dipole-forbidden depopulation prevails practically over the entire low-velocity region, down to velocities {approximately}{ital n}{sup 3}[{Delta}{ital E}/Ry]{ital v}{sub {ital n}}, where {Delta}{ital E} is the energy spacing adjoining to the level due to either a quantum defect or the relevant level width or splitting, whichever is greater. If the energy gaps are substantial (as for strongly nonhydrogenic {ital s} and {ital p} levels in alkali-metal atoms), then the fraction of dipole transitions in the total depopulation reaches a flat minimum just below the matching velocity and then grows again, making the progressively increasing contribution to the low-velocity depopulation. Themore » analytic models based on the first-order Born amplitudes (rather than the two-level adiabatic approximation) furnish reasonable estimates of the fractional dipole-allowed and dipole-forbidden depopulations. {copyright} {ital 1996 The American Physical Society.}« less

Electromagnetic meson exchange currents and the sachs nucleon form factors

Abstract The operator of the nuclear electromagnetic isovector π-meson exchange current is constructed starting from the one-nucleon current in the Sachs parametrization and the two-nucleon π-exchange Born amplitude primarily in pseudoscalar πN-coupling but mixtures of pseudoscalar-pseudovector coupling have been considered in a nuclear potential, too. The current satisfies the continuity equation up to the considered order O( 1 M 3 ) . In addition, an extension of this model is presented to a current independent of the ps-pv mixing.

Effects of meson-decay diagrams in proton-proton bremsstrahlung.

We investigate the effect of meson-decay diagrams on the proton-proton bremsstrahlung process. We explicitly include short-range correlations by calculating single- and double-scattering diagrams using an NN T-matrix interaction. We find that in general these diagrams interfere destructively with the corresponding Born amplitudes so that the net effect of the meson-decay process on proton-proton bremsstrahlung reactions is considerably smaller than that of the Born amplitude alone.

Coherent pion photoproduction on the deuteron in the Δ resonance region

Abstract Coherent pion photoproduction on the deuteron in the Δ resonance region is calculated adopting a nonrelativistic model based on time-ordered perturbation theory without rescattering. Results for cross sections and polarization observables corresponding to the polarized photon beam and/or the deuteron target are presented for which the influence of the nonresonant Born amplitudes and the sensitivity to several multipoles of the elementary photoproduction on the nucleon are studied in detail. Furthermore, the role of a two-body mechanism where photon absorption and pion emission take place at different nucleons is discussed.

Gauge invariant effective action for high energy processes in QCD

The Born amplitudes for quasi-multi-Regge kinematics of produced gluons are constructed in accordance with the Feynman rules including, apart from the usual Yang-Mills vertices, also an infinite number of induced vertices. The new vertices describe the interaction of physical gluons produced in direct channels with the reggeized gluons propagating in crossing channels. The non-linear gauge invariant effective action generating these Feynman rules is constructed with the use of the Wilson contour integrals. By integrating over the physical degrees of freedom the reggeon action is derived.