An unified theory of direct reactions

Journal Article · Tue Nov 01 04:00:00 EST 1960 · Nuovo Cimento

DOI:https://doi.org/10.1007/BF02732828· OSTI ID:4074247

Agodi, A.; Eberle, E.

A new dispersion theory of nuclear reactions is presented which is a generalization of the existing ones. The theory is centered around the possibility of defining a class of problems equivalent to the original scattering problem in the sense that their solutions all determine the same transition matrix elements. These equivalent problems are generated by suitably projecting the original one on a subspace of the linear space spanned by the continuum eigenstates of the total hamiltonian, containing the initial and final channel states. A derivation of the Breit-Wigner formula analogous to Feshbach's can be given in the theory, independently of any configuration space representation. The direct processes are then defined by performing the energy average on the transition matrix elements, so that the contributions from the long- lived''compound'' states are lost. In the case of nucleon-nucleus scattering, this is shown to give an alternative definition of the optical model quite analogous to the conventional ones though perhaps more accessible to a field theoretical analysis. Moreover it is shown that the well-known surface contributions to direct reactions can be isolated quite naturally in the formalism from the other direct contributions.

• Research Organization: Universita, Catania, Italy; Centro Siciliano di Fisica Nucleare, Catania, Italy
• Sponsoring Organization: USDOE
• NSA Number: NSA-15-012180
• OSTI ID: 4074247
• Journal Information: Nuovo Cimento, Journal Name: Nuovo Cimento Journal Issue: 4 Vol. 18; ISSN 0029-6341
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BREIT-WIGNER FORMULA
CONFIGURATION
CROSS SECTIONS
DIFFERENTIAL EQUATIONS
DISPERSIONS
ENERGY LEVELS
FIELD THEORY
HAMILTONIAN
INTERACTIONS
MATHEMATICS
MATRICES
NUCLEAR MODELS
NUCLEAR REACTIONS
NUCLEAR THEORY
NUCLEI
NUCLEONS
OPTICAL MODEL
RESONANCE
SCATTERING
SURFACES