Generalized Sum-of-Differences formula

Wojciechowski, H.

doi:10.1209/epl/i2000-00348-5

Cited by 2 publications

(7 citation statements)

References 12 publications

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“…Instead of using the analytical form of the Coulomb-scattering amplitude, we can use one of the series which, as a distribution, converges to it [1][2][3]. This series is…”

Section: Total Elastic-scattering Amplitudementioning

confidence: 99%

“…In the absence of nuclear force (S l = 1), we have the Coulomb amplitude (2). By including nuclear force, one simply modifies the low partial-wave amplitudes by complex nuclear-scattering functions S l .…”

Section: Total Elastic-scattering Amplitudementioning

confidence: 99%

“…The second term is the incomplete Coulomb-scattering amplitude of form (2), with all partial waves up to l gr removed.…”

Section: Diffractive-and Refractive-scattering Amplitudesmentioning

confidence: 99%

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Coulomb amplitude representation and nuclear diffraction and refraction

Wojciechowski

2004

Can. J. Phys.

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A new, consistent with wave-optics, method of treating diffraction and refraction in nuclear elastic scattering, is proposed and discussed. The method is based on the decomposition of the total elastic-scattering amplitude, written in a different form than usual, into the amplitude describing pure diffraction, and the rest, i.e., refraction and reflection. It is shown that nuclear diffraction is due to incompleteness of the Coulomb-scattering amplitude and is described by it. It is show that diffraction can be regarded as a kind of "background" always present, irrespective of the system being studied. PACS Nos.: 24.10.Ht, 42.25.Fx, 42.25.GyRésumé : Nous proposons et analysons une nouvelle méthode, cohérente avec l'optique ondulatoire, pour décrire la diffraction et la réfraction dans la diffusion nucléaire élastique. La méthode est basée sur la décomposition de l'amplitude de diffusion élastique totale, écrite d'une façon différente, en une amplitude décrivant la diffraction pure et une autre amplitude qui comprend la réfraction et la réflexion. Nous montrons que la diffraction nucléaire est due à l'inachèvement de l'amplitude coulombien et est décrite par elle. Nous montrons que la diffraction peut être vue comme une sorte de bruit de fond toujours présent, indépendamment du système étudié.[Traduit par la Rédaction]

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“…Instead of using the analytical form of the Coulomb-scattering amplitude, we can use one of the series which, as a distribution, converges to it [1][2][3]. This series is…”

Section: Total Elastic-scattering Amplitudementioning

confidence: 99%

Section: Total Elastic-scattering Amplitudementioning

confidence: 99%

See 1 more Smart Citation

Coulomb amplitude representation and nuclear diffraction and refraction

Wojciechowski

2004

Can. J. Phys.

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“…Replacing now the last series in relation (12) by the right hand side series of relation (15) we receive well known scattering amplitude for neutral particles of the form f el (θ) = 1 2ik lgr 0 (2l + 1)(S l − 1)P l (cos θ)…”

Section: Separation Of Diffraction and Refraction In Angular Momementioning

confidence: 99%

“…The missing flux is then the integral over the whole angular range of the difference of the above cross sections. This integral can easily be evaluated and the result is [15] 2π…”

Section: The Sum-of-differences (Sod) Formulamentioning

confidence: 99%

Quantum diffraction grating: A possible new description of nuclear elastic scattering

Wojciechowski

2016

Int. J. Mod. Phys. E

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The problem of discontinuous functions and their representations in the form of Legendre polynomial series in quantum nuclear scattering theory is presented briefly. The problem is quite old yet not adequately explained in numerous Quantum Theory textbooks and sometimes not correctly understood by physicists. Introduction of the generalized functions into the quantum scattering theory clarifies the problem and allows to propose new interpretations of nuclear elastic scattering phenomenon. The derived new forms of the full elastic scattering amplitudes and possibility of splitting them suggest existence of dynamical quantum diffraction grating around the nuclei. Particularly important fact is that this grating existing in the space around the nucleus makes considerable contribution to the experimental elastic differential cross section. All these might be quite important in analyses of nuclear elastic scattering data and so require to be stated in a more detailed and clear way.

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Generalized Sum-of-Differences formula

Cited by 2 publications

References 12 publications

Coulomb amplitude representation and nuclear diffraction and refraction

Coulomb amplitude representation and nuclear diffraction and refraction

Quantum diffraction grating: A possible new description of nuclear elastic scattering

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