Particle Theory Approach to the Two-pion and Three-pion Systems PDF Download
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Author: L. I. SCHIFF Publisher: ISBN: Category : Languages : en Pages : 1
Book Description
The relation between the two-pion and three-pion resonances is discussed in terms of a model in which the motion of the pions is described by a partially relativistic Schrodinger-type wave equation, and the interaction between them is represented by a static potential. An attractive square-well potential that is almost strong enough to bind the di-pion gives a satisfactory account of the observed P-wave pion-pion scattering. If this potential is assumed to be additive between all pairs in the three-pion I = 0, J = 1( - ) state, it produces far too much binding to agree with observation. As an alternative to additivity, the interaction may be assumed to saturate, so that the total potential never exceeds that between any pair of pions. It is found that the model provides a qualitatively consistent explanation both of pion-pion scattering and the three-pion system if the pair interactions saturate or nearly saturate. (Author).
Author: L. I. SCHIFF Publisher: ISBN: Category : Languages : en Pages : 1
Book Description
The relation between the two-pion and three-pion resonances is discussed in terms of a model in which the motion of the pions is described by a partially relativistic Schrodinger-type wave equation, and the interaction between them is represented by a static potential. An attractive square-well potential that is almost strong enough to bind the di-pion gives a satisfactory account of the observed P-wave pion-pion scattering. If this potential is assumed to be additive between all pairs in the three-pion I = 0, J = 1( - ) state, it produces far too much binding to agree with observation. As an alternative to additivity, the interaction may be assumed to saturate, so that the total potential never exceeds that between any pair of pions. It is found that the model provides a qualitatively consistent explanation both of pion-pion scattering and the three-pion system if the pair interactions saturate or nearly saturate. (Author).
Author: A. V. Anisovich Publisher: World Scientific ISBN: 9814478814 Category : Science Languages : en Pages : 342
Book Description
The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
An attempt is made to clarify the structure of pion-nucleus scattering taking into account the fact that the pions in scattering and in nuclear forces are identical. To understand the essential points, a simple pion plus two- nucleon system is chosen. The processes considered are $pi$NN $Yields$ $pi$NN and $pi$NN reversible NN. Both relativistic and nonrelativistic approaches are adopted. In the relativistic approach Taylor's method is used, whereas in the nonrelativistic approach a Hamiltonian (Schroedinger equation) method is utilized together with a projection technique. Both approaches give a finite set of amplitude equations respectively, and the formal correspondence between these sets of equations is observed. Due to the proper consideration of pions, the problem of pion overcounting does not occur and the amplitudes are shown to satisfy at least two- and three-particle unitarity. Through the study of the scattering in the $pi$NN system, several important aspects common in general pion- nucleus scattering have been observed. For instance, this observation gives some new insight into the proper structure of pion-nucleus optical potentials. For practical applications the non-relativistic $pi$NN amplitudes are reduced in angular momentum-isospin eigenstates together with the inclusion of bound states. The reduced amplitudes are then used to study the pion absorption effect on the pion--deuteron scattering length. The result is consistent with experiment. Some possible future applications of the formulations developed are discussed. 10 tables, 2 figures, 65 references. (auth).
Author: L. I. SCHIFF
Author: L. I. SCHIFF
Author: A. V. Anisovich
Author: Defense Documentation Center (U.S.)
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