Search results for "Amplitude"
showing 10 items of 1169 documents
Closed form for two-photon free–free transition matrix elements
2000
Abstract Two-photon free–free transitions happen in the multiphoton ionization with more than one excess photon and in bremsstralung. Up to now, the configuration space free–free transition amplitudes have not been written in closed form. We propose a modified Coulomb Green’s function (CGF) Sturmian expansion which allows one to obtain expressions for two-photon radial transition matrix elements in the closed form which are easy to continue analytically to calculate free–free transitions in H.
Photoluminescence at 1.9 eV in synthetic wet silica
2001
We report the effects of γ-irradiation on the optical activity of wet synthetic silica samples. As a function of γ-dose, the growth of a composite structure in the 4–6 eV spectral region of the absorption spectrum is observed. This structure can be resolved into two main contributions centered at 5.8 and 4.8 eV, respectively. The first component is usually attributed to an optical transition of the E′ centers. The second one is able to excite an emission band centered at 1.9 eV. The analysis of the growth kinetics, in the γ-dose range 20–1000 Mrad, of both emission at 1.9 eV and absorption at 4.8 eV shows that these two bands change in a similar way, reaching constant amplitudes, after an i…
Measurement of theE2/M1Ratio in theN→ΔTransition Using the Reactionp(γ→,p)π0[Phys. Rev. Lett. 78, 606 (1997)]
1997
The small electric quadrupole $E2$ amplitude of the predominantly magnetic dipole $M1$ $p\ensuremath{\rightarrow}\ensuremath{\Delta}(1232)$ transition has been measured using 270 to 420 MeV tagged linearly polarized photons in the $p(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}},p){\ensuremath{\pi}}^{o}$ reaction at the Mainz Microtron MAMI. Differential cross sections and photon asymmetries were determined by measuring the recoil proton in the cylindrically symmetric $4\ensuremath{\pi}$ detector DAPHNE. From the proton angular distributions the ratio $E2/M1\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}(2.5\ifmmode\pm\else\textpm\fi{}0.2\ifmmode\pm\else\textpm\…
Molecular mode-coupling theory applied to a liquid of diatomic molecules
2000
We study the molecular mode coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters ${\bf F}_{ll'}^m(q)$ and the critical amplitudes of the $\beta$ - relaxation ${\bf H}_{ll'}^m(q)$ are solved up to a cut off $l_{co}$ = 2 without any further approximations. Here $l,m$ are indices of spherical harmonics. Contrary to previous studies, where additional approximations were applied, we find in agreement with simulations, that all molecular degrees of freedom vitrify at a single temperature $T_c$. The theoretical results for the non ergodicity parameters and the critical amplitudes are compared with those from simulations. The qualitat…
NNLO QED contribution to the µe → µe elastic scattering
2020
We present the current status of the Next-to-Next-to-Leading Order QED contribution to theµescattering. Particular focus is given to the techniques involved to tackle the virtual amplitude and their automatic implementation. Renormalization of the amplitude will be also discuss in details.
Scattering amplitudes and integral equations for the collision of two charged composite particles
1980
Transition operators for the collision of two clusters composed of an arbitrary number of charged and neutral particles are represented as a sum of pure Coulomb and Coulomb-modified short-range operators. Sandwiching this relation between the corresponding channel states, correct two-fragment scattering amplitudes are obtained by adapting the conventional two-body screening and renormalization procedure. Furthermore, integral equations are derived for off-shell extensions of the full screened amplitudes and of the unscreened Coulomb-modified short-range amplitudes. For three particles, the final results coincide with those derived previously in a different approach. The proposed theory is v…
Coulomb Effects on Few-Body Scattering States
1986
Modifications of stationary momentum space scattering theory, necessitated by the presence of Coulomb forces, are described, both in the formalism which uses unscreened Coulomb potentials and in the screening and renormalization approach. Thereby, emphasis is laid on exposing the conceptual differences, as well as the different, presently achieved status of applicability. Some of the unresolved problems in both methods are enumerated.
Spherical nonlinear correlations for global invariant three-dimensional object recognition
2007
We define a nonlinear filtering based on correlations on unit spheres to obtain both rotation- and scale-invariant three-dimensional (3D) object detection. Tridimensionality is expressed in terms of range images. The phase Fourier transform (PhFT) of a range image provides information about the orientations of the 3D object surfaces. When the object is sequentially rotated, the amplitudes of the different PhFTs form a unit radius sphere. On the other hand, a scale change is equivalent to a multiplication of the amplitude of the PhFT by a constant factor. The effect of both rotation and scale changes for 3D objects means a change in the intensity of the unit radius sphere. We define a 3D fil…
JIMWLK evolution of the odderon
2016
We study the effects of a parity-odd "odderon" correlation in JIMWLK renormalization group evolution at high energy. Firstly we show that in the eikonal picture where the scattering is described by Wilson lines, one obtains a strict mathematical upper limit for the magnitude of the odderon amplitude compared to the parity even pomeron one. This limit increases with N_c, approaching infinity in the infinite N_c limit. We use a systematic extension of the Gaussian approximation including both 2- and 3-point correlations which enables us to close the system of equations even at finite N_c. In the large-N_c limit we recover an evolution equation derived earlier. By solving this equation numeric…
Coulomb Corrections in Proton-Deuteron Scattering
1976
We present the first calculations of differential cross sections for elastic proton-deuteron scattering using a three-body formalism which correctly takes into account the Coulomb repulsion between the two protons.