Elastic Scattering of Low Energy Nucleons by Complex Nuclei

Brown, G. E.; Dominicis, C T de

doi:10.1088/0370-1298/70/9/305

Cited by 20 publications

(5 citation statements)

References 7 publications

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“…In this formalism, however, one has to pay the price of shifting the boundary condition as E changes according to (4.36), thus using a different orthogonal set as E changes. For a further discussion of this point see Brown [22]. The main difference between this development and that of Section IV, B is that in the latter the energy dependence is carried by the Hamiltonian H$.…”

Section: Kapur Peierls Expansionmentioning

confidence: 88%

“…Expansions of T into an infinite resonance series have been obtained by a method suggested by Siegert [20] and investigated by Humblet [21], as well as by Kapur and Peierls [5] with improvements by Brown et al [22]. For a review of these results see Lane and Thomas [11].…”

Section: Kapur Peierls Expansionmentioning

confidence: 99%

“…These complex eigenvalues are of course independent of the energy E of the system. However it may be shown [22] that the complex eigenvalues of the Kapur Peierls expansion are close to the complex resonance energies as long as we are concerned with the complex resonance energies whose real part is near the energy E and whose imaginary part is small. This is in fact the merit of the treatment in Section IV, B since the resonance description is reserved for only these terms.…”

Section: Appendixmentioning

confidence: 99%

“…In spite of the fact that the eigenfunctions corresponding to these complex eigenvalues grow exponentially as \ : approaches infinity, they form an orthonormal set. 22 If the eigenvalues are E + and the eigenfunctions 0 + , the orthogonality and normalization conditions are The operator H operates only on 0 & . There is no difficulty in evaluating the inverse operator (E + &H) &1 for large values of \ : since here the interaction vanishes.…”

Section: Appendixmentioning

confidence: 99%

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A Unified Theory of Nuclear Reactions, II

Feshbach

2000

Annals of Physics

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The effective Hamiltonian method for nuclear reactions described in an earlier paper with the same title, part I, is generalized so as to include all possible reaction types, as well as the effects arising from the identity of particles.The principal device employed, as in part I, is the projection operator which selects the open channel components of the wave function. It is found that the formal structure of part I providing a unified description for direct and compound nuclear reactions including the coupled equation description for direct reactions remains valid in this wider context. A Kapur Peierls expansion may also be readily obtained. The concept of channel radii is not needed nor is any decomposition of the wave function for the system into angular momentum eigenstates required, so that the expressions for transition amplitudes and widths are invariant with respect to the angular momentum coupling scheme. Since the open channels can only be defined in an asymptotic sense, the corresponding projection operators are not unique. As a consequence the projection operator method has a flexibility which in the first place is consonant with the wide range of phenomena which can occur in nuclear reactions and in the second place can effectively exploit an intuitive understanding of the phenomena. Examples of projection operators are obtained including one which leads to the Wigner Eisenbud formalism, another which is appropriate for the stripping reaction, and, finally, one which takes the Pauli exclusion principle into account. Note that explicit representations of the projection operators are not required for the development of general formal results but are necessary if, eventually, quantitative calculations are made.

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Section: Kapur Peierls Expansionmentioning

confidence: 88%

Section: Kapur Peierls Expansionmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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A Unified Theory of Nuclear Reactions, II

Feshbach

2000

Annals of Physics

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“…Si maintenant nous cherchons à représenter la partie instantanée de Sa.0153 par S, c'est-à-dire la dif-(4) Pour les développements qui suivent voir C. Bloch [7], J. Bowcock [16], G. E. Brown, C. T. De Dominicis [17] et à paraître, Proc. Phys.…”

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L'interaction directe dans les réactions nucléaires

Dominicis

1958

J. Phys. Radium

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Service de Physique Mathématique. C. E. N. de Saclay.Résumé. 2014 Bref exposé d'introduction sur les insuffisances du modèle du noyau composé et ce qu'on peut attendre de processus faisant intervenir des interactions de courte durée.Abstract. 2014 Brief introductory account of the shortcomings of the compound nucleus model and what can be expected from processes involving interactions lasting a very short time.

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Nucleon-Nucleus Collisions and Intermediate Structure

Mekjian

1973

Advances in Nuclear Physics

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Elastic Scattering of Low Energy Nucleons by Complex Nuclei

Cited by 20 publications

References 7 publications

A Unified Theory of Nuclear Reactions, II

A Unified Theory of Nuclear Reactions, II

L'interaction directe dans les réactions nucléaires

Nucleon-Nucleus Collisions and Intermediate Structure

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