An unified theory of direct reactions

Agodi, Antonella; Eberle, E.G.

doi:10.1007/bf02732828

Cited by 21 publications

(5 citation statements)

References 16 publications

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“…Since the publication of I, several contributions to the theory of scattering have appeared that have some overlap with the material we are going to discuss. The relevant papers are by Brenig (1959), Brenig and Haag (1959), Newton and Fonda (1960), Agodi and Eberle (1960) and also Lipperheide (1962), to which we refer the reader for further details.…”

Section: Introductionmentioning

confidence: 99%

Nuclear reactions

Lemmer

1966

Rep. Prog. Phys.

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Section: Introductionmentioning

confidence: 99%

Nuclear reactions

Lemmer

1966

Rep. Prog. Phys.

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“…5 We mention Brenig [7], Newton and Fonda [8], Agodi and Eberle [9], and most recently Lipperheide [10]. Each of these have developed material which overlaps some of our work as we shall duly note below.…”

Section: Nuclear Reactionsmentioning

confidence: 95%

“…This is discussed in Section III. 9 If P does not include all the open channels, the E in Eq. (2.8) should be replaced by…”

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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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“…In this way one can associate the "resonant state" with the eigenvectors of a non-hermitian Hamiltonian (or rather, for simplicity, of a "quasi hermitian" Hamiltonian), such eigenvectors decaying correctly in time. We shall adopt the formalism introduced by Akhiezer and Glazman [32], by Lifshitz, by Galitsky and Migdal [43], and by Agodi et al [44].…”

Section: Unstable States and Non-hermitian Hamiltonians 41 Introductionmentioning

confidence: 99%

On Non-Self-Adjoint Operators for Observables in Quantum Mechanics and Quantum Field Theory

Recami

Olkhovsky

Maydanyuk

2010

Int. J. Mod. Phys. A

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Aim of this paper is to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics. More specifically, this work starts dealing with: (i) the maximal hermitian (but not selfadjoint) Time operator in non-relativistic quantum mechanics and in quantum electrodynamics; and with: (ii) the problem of the four-position and four-momentum operators, each one with its hermitian and anti-hermitian parts, for relativistic spin-zero particles. Afterwards, other physically important applications of non-selfadjoint (and even non-hermitian) operators are discussed: In particular, (iii) we reanalyze in detail the interesting possibility of associating quasi-hermitian Hamiltonians with (decaying) unstable states in nuclear physics. Finally, we briefly mention the cases of quantum dissipation, as well as of the nuclear optical potential.

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An unified theory of direct reactions

Cited by 21 publications

References 16 publications

Nuclear reactions

Nuclear reactions

A Unified Theory of Nuclear Reactions, II

On Non-Self-Adjoint Operators for Observables in Quantum Mechanics and Quantum Field Theory

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