## Abstract

The main difficulty of nuclear theory is that nuclei contain many (i. e. more than two) but not too many particles. Therefore, the precise equations of motion (Schrodinger equation) become practically useless, and at the same time it is impossible to apply statistical methods with confidence. The latter circumstance is graphically expressed in direct nuclear reactions. The essence of these phenomena consists in that a particle hitting the target nucleus transfers its energy and momentum either to one nuclear nucleon or to a comparatively small group of nucleons. This fact would not by itself be surprising if at the same time we did not observe a directly opposite picture corresponding to the production of a compound nucleus, i. e. the statistical distribution among all degrees of freedom of the energy transferred to the nucleus. In macroscopic physics the co-existence of. such processes is impossible since they would contradict the second law of thermodynamics. Such processes occur quite often in nuclear physics because of the inapplic- ability of the asymptotic laws of the theory of probabilities. Since statistical methods were obviously unsuited for the direct process theory, this led to the conviction that it was necessary to return to the Schrodinger
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Shapiro, I. S.

^{[1] }- Institute Of Theoretical And Experimental Physics, Moscow, USSR (Russian Federation)

## Citation Formats

Shapiro, I. S.
Dispersion Theory of Direct Nuclear Reactions.
IAEA: N. p.,
1963.
Web.

Shapiro, I. S.
Dispersion Theory of Direct Nuclear Reactions.
IAEA.

Shapiro, I. S.
1963.
"Dispersion Theory of Direct Nuclear Reactions."
IAEA.

@misc{etde_22095802,

title = {Dispersion Theory of Direct Nuclear Reactions}

author = {Shapiro, I. S.}

abstractNote = {The main difficulty of nuclear theory is that nuclei contain many (i. e. more than two) but not too many particles. Therefore, the precise equations of motion (Schrodinger equation) become practically useless, and at the same time it is impossible to apply statistical methods with confidence. The latter circumstance is graphically expressed in direct nuclear reactions. The essence of these phenomena consists in that a particle hitting the target nucleus transfers its energy and momentum either to one nuclear nucleon or to a comparatively small group of nucleons. This fact would not by itself be surprising if at the same time we did not observe a directly opposite picture corresponding to the production of a compound nucleus, i. e. the statistical distribution among all degrees of freedom of the energy transferred to the nucleus. In macroscopic physics the co-existence of. such processes is impossible since they would contradict the second law of thermodynamics. Such processes occur quite often in nuclear physics because of the inapplic- ability of the asymptotic laws of the theory of probabilities. Since statistical methods were obviously unsuited for the direct process theory, this led to the conviction that it was necessary to return to the Schrodinger equation for a system of many interacting particles. But the technique of solving such equations is still confined to perturbation theory and therefore it was the latter that was used to describe direct nuclear reactions despite the fact that the interaction between nucleons is strong and the application of perturb- ation theory to the interaction of free nucleons (to n-p or p-p scattering, for example) leads to results which strongly contradict experimental data. The results of the application of perturbation theory to direct nuclear reactions sometimes agree with experimental data and sometimes cqntradict them, but in either case they can hardly satisfy the investigator because it seems impossible to give the reasons for the agreement if it is not accidental. In short, the theory behaves like an unpredictable person. A major success in the application of perturbation theory to direct processes in the Butler theory of deuteron stripping ((d, p), (d, n)) and pick-up ((p, d), (n, d)). The Butler theory satisfactorily predicts the position of the first maximum (by the increase of the angle) in the angular distribution of reaction products as a function of the orbital momentum of the nucleon captured by the nucleus (stripping reaction) or picked up by an incident particle (pick- up reaction). This result permitted the use of stripping and pick-up reactions in nuclear spectroscopy. At the same time this led to the problem of understanding the true meaning of the Butler approximation. This problem was also essential because the Butler theory inadequately describes several other features of the stripping and pick-up reactions (such as the change of angular distribution with the energy of incident particles, the relation of intensities at the maxima of angular distributions, absolute values of. cross-sections and, sometimes, the relative probabilities for the excitation of different states of residual nuclei). A new method in direct process theory was offered not so long ago (in 1961). The method is based on fairly general properties of the reaction amplitudes and is free from the un-justified assumptions, of the form er theory, in particular the application of perturbation theory. This method makes it possible to obtain several new results and obtain a uniform description cf a great variety of processes (such as direct reactions of the conventional type at low and medium energies, the transfer of nucleons in the bombardment of nuclei by multi-charged ions and the processes of fragmentation at high energies). At the same time the new approach explains, with surprising simplicity, the causes of the form erly enigmatic success of the Butler theory and indicates the limits of its applicability. The method referred to is known as dispersion theory or dispersion method. In the form used for the description of direct processes, the dispersion theory originated and developed in the physics of the strong interactions of elementary particles. The theory has replaced the Hamiltonian formalism of quantum field thecry and contributed to a substantial advance in the solution of some problems. The possibility of applying dispersion theory to the auantitative description of direct processes stems from the very structure of this theory in which any ''compound'' particle (a nucleus, for example) which actually exists in a free state is treated exactly as an ''elementary'' particle. It is significant that certain sequences of dispersion theory are manifested in the properties of direct reactions no doubt more saliently than in the physics of the strong interactions of elementary particles. The ''dispersion nature'' of direct processes ''sticks out'' of experimental data so obviously that to grasp the essence of the dispersion approach it is worthwhile enumerating briefly the basic facts of direct nuclear reactions. (author)}

place = {IAEA}

year = {1963}

month = {Jan}

}

title = {Dispersion Theory of Direct Nuclear Reactions}

author = {Shapiro, I. S.}

abstractNote = {The main difficulty of nuclear theory is that nuclei contain many (i. e. more than two) but not too many particles. Therefore, the precise equations of motion (Schrodinger equation) become practically useless, and at the same time it is impossible to apply statistical methods with confidence. The latter circumstance is graphically expressed in direct nuclear reactions. The essence of these phenomena consists in that a particle hitting the target nucleus transfers its energy and momentum either to one nuclear nucleon or to a comparatively small group of nucleons. This fact would not by itself be surprising if at the same time we did not observe a directly opposite picture corresponding to the production of a compound nucleus, i. e. the statistical distribution among all degrees of freedom of the energy transferred to the nucleus. In macroscopic physics the co-existence of. such processes is impossible since they would contradict the second law of thermodynamics. Such processes occur quite often in nuclear physics because of the inapplic- ability of the asymptotic laws of the theory of probabilities. Since statistical methods were obviously unsuited for the direct process theory, this led to the conviction that it was necessary to return to the Schrodinger equation for a system of many interacting particles. But the technique of solving such equations is still confined to perturbation theory and therefore it was the latter that was used to describe direct nuclear reactions despite the fact that the interaction between nucleons is strong and the application of perturb- ation theory to the interaction of free nucleons (to n-p or p-p scattering, for example) leads to results which strongly contradict experimental data. The results of the application of perturbation theory to direct nuclear reactions sometimes agree with experimental data and sometimes cqntradict them, but in either case they can hardly satisfy the investigator because it seems impossible to give the reasons for the agreement if it is not accidental. In short, the theory behaves like an unpredictable person. A major success in the application of perturbation theory to direct processes in the Butler theory of deuteron stripping ((d, p), (d, n)) and pick-up ((p, d), (n, d)). The Butler theory satisfactorily predicts the position of the first maximum (by the increase of the angle) in the angular distribution of reaction products as a function of the orbital momentum of the nucleon captured by the nucleus (stripping reaction) or picked up by an incident particle (pick- up reaction). This result permitted the use of stripping and pick-up reactions in nuclear spectroscopy. At the same time this led to the problem of understanding the true meaning of the Butler approximation. This problem was also essential because the Butler theory inadequately describes several other features of the stripping and pick-up reactions (such as the change of angular distribution with the energy of incident particles, the relation of intensities at the maxima of angular distributions, absolute values of. cross-sections and, sometimes, the relative probabilities for the excitation of different states of residual nuclei). A new method in direct process theory was offered not so long ago (in 1961). The method is based on fairly general properties of the reaction amplitudes and is free from the un-justified assumptions, of the form er theory, in particular the application of perturbation theory. This method makes it possible to obtain several new results and obtain a uniform description cf a great variety of processes (such as direct reactions of the conventional type at low and medium energies, the transfer of nucleons in the bombardment of nuclei by multi-charged ions and the processes of fragmentation at high energies). At the same time the new approach explains, with surprising simplicity, the causes of the form erly enigmatic success of the Butler theory and indicates the limits of its applicability. The method referred to is known as dispersion theory or dispersion method. In the form used for the description of direct processes, the dispersion theory originated and developed in the physics of the strong interactions of elementary particles. The theory has replaced the Hamiltonian formalism of quantum field thecry and contributed to a substantial advance in the solution of some problems. The possibility of applying dispersion theory to the auantitative description of direct processes stems from the very structure of this theory in which any ''compound'' particle (a nucleus, for example) which actually exists in a free state is treated exactly as an ''elementary'' particle. It is significant that certain sequences of dispersion theory are manifested in the properties of direct reactions no doubt more saliently than in the physics of the strong interactions of elementary particles. The ''dispersion nature'' of direct processes ''sticks out'' of experimental data so obviously that to grasp the essence of the dispersion approach it is worthwhile enumerating briefly the basic facts of direct nuclear reactions. (author)}

place = {IAEA}

year = {1963}

month = {Jan}

}