# NEW METHODS IN REARRANGEMENT COLLISIONS

## Abstract

Mathematical methods developed for use in elementary particle physics are applied to the problem of rearrangement collisions, in nuclear reactions in particular, to the deuteron stripping process which is a typical example of a rearrangement collision. Using the contraction rules of Lehmann, Symanzik, and Zimmermann in the Heisenberg representation, several expansions are derived for the stripping T-matrix. Some of these are equivalent to the usual Lippmann- Schwinger expansion, but others are unique, and lend themselves naturally to the application of modern dispersion theory. It is these expansions that are treated in detail. Because the analytic techniques used are new and urfamiliar in the present context, the thesis is limited to a discussion of direct nuclear reactions (which class, of course, includes stripping reactions) and processes in which compound nucleus formation or collective effects occur are not discussed. However, in principle, the methods are applicable to all reactions. In the first few sections of the thesis some of the formal and calculational difficuities associated with the traditional approach to the problem of rearrangement collisions are discussed---one very important difficulty being the lack of a formally correct perturbation scheme. It is proven that because all the potentials in the problem are capablemore »

- Authors:

- Publication Date:

- Research Org.:
- Originating Research Org. not identified

- OSTI Identifier:
- 4782923

- NSA Number:
- NSA-17-002335

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: Thesis. Orig. Receipt Date: 31-DEC-63

- Country of Publication:
- Country unknown/Code not available

- Language:
- English

- Subject:
- PHYSICS; BINDING ENERGY; BORN APPROXIMATION; COLLECTIVE MODEL; COLLISIONS; CROSS SECTIONS; DEUTERONS; DIFFERENTIAL EQUATIONS; DISPERSION THEORY; ELEMENTARY PARTICLES; ENERGY LEVELS; EXCITATION; FIELD THEORY; INTERACTIONS; LAGRANGIAN; LIPPMAN-SCHWINGER EQUATION; MATHEMATICS; MATRICES; NUCLEAR MODELS; NUCLEAR REACTIONS; NUCLEI; NUMERICALS; PERTURBATION THEORY; QUANTUM MECHANICS; SCATTERING; SECOND QUANTIZATION; STRIPPING; T-MATRIX

### Citation Formats

```
Aaron, R.
```*NEW METHODS IN REARRANGEMENT COLLISIONS*. Country unknown/Code not available: N. p., 1961.
Web.

```
Aaron, R.
```*NEW METHODS IN REARRANGEMENT COLLISIONS*. Country unknown/Code not available.

```
Aaron, R. Sun .
"NEW METHODS IN REARRANGEMENT COLLISIONS". Country unknown/Code not available.
```

```
@article{osti_4782923,
```

title = {NEW METHODS IN REARRANGEMENT COLLISIONS},

author = {Aaron, R},

abstractNote = {Mathematical methods developed for use in elementary particle physics are applied to the problem of rearrangement collisions, in nuclear reactions in particular, to the deuteron stripping process which is a typical example of a rearrangement collision. Using the contraction rules of Lehmann, Symanzik, and Zimmermann in the Heisenberg representation, several expansions are derived for the stripping T-matrix. Some of these are equivalent to the usual Lippmann- Schwinger expansion, but others are unique, and lend themselves naturally to the application of modern dispersion theory. It is these expansions that are treated in detail. Because the analytic techniques used are new and urfamiliar in the present context, the thesis is limited to a discussion of direct nuclear reactions (which class, of course, includes stripping reactions) and processes in which compound nucleus formation or collective effects occur are not discussed. However, in principle, the methods are applicable to all reactions. In the first few sections of the thesis some of the formal and calculational difficuities associated with the traditional approach to the problem of rearrangement collisions are discussed---one very important difficulty being the lack of a formally correct perturbation scheme. It is proven that because all the potentials in the problem are capable of supporting bound states, the usual Born series which is an expansion in one or more of the potentials diverges independent of the incident energy (in marked contrast to what occurs in potential scattering). Field theoretic methods are then applied in an attempt to remedy some of the above problems. In order to use the new expansions for the T- matrix discussed previously, it is found necessary to replace some to the bound states in the problem by elementary particles ---that is, in the second quartized formalism which is used, an independdent field operator which commutes with all the other opera. tors in the theory must be introduced into the Lagrangian to describe a bound state. In fact, the method of performing this replacement forms one of the central points of the thesis, and leads later to a discussion of a possible distinction between elementary particles and bound states in general. It is then shown how dispersion techniques may be used to evaluate some of the matrix elements in the problem. It is finally shown that the new methods used solve many of the formal difficulties associated with the traditional approach to the problem. Also the solutions obtained seem more amenable to approximate solution. The formalism is constructed so as to divide collision into whole physical sub-units rather than, as in the Born series, into a power series in a necessarily strong interaction. and it seems possible to pick out those contributions which are of greatest importance. Also, it is possible to relate the cross sections for reactions to elastic scattering data so that no reaction radius or similar fitting parameter need enter the theory. (Dissertation Abstr., 23: No. 3, 1962)},

doi = {},

url = {https://www.osti.gov/biblio/4782923},
journal = {},

number = ,

volume = ,

place = {Country unknown/Code not available},

year = {1961},

month = {1}

}