# ORDINARY PERTURBATION THEORY APPLIED TO NUCLEAR MATTER

## Abstract

The average binding energy and equilibrium density of nuclear matter are calculated in the self-consistent independent pair approximation. The potentials of Gammel and Thaler are used. The hard core is replaced by a pseudopotential, and the potentials are adjusted to give the same low energy scattering data. The pseudo-potential is of the Huang-Yang type, and hence one can use ordinary RayleighSchroedinger perturbation theory, which is then a joint expansion in the strength of the pseudo-potential plus the central potentials plus the tensor force. The first and second order terms in this expansion were calculated exactly, but were made self-consistent only in the effective mass approximation, the self-consistency requirement becoming the solution of a quadratic equation for the effective mass. It is found that a simple S-wave pseudopotential is not sufficient to produce saturation within a density range corresponding to k/sub F/ = 1 to 2 fm/sup -1/. A more exact treatment of the hard core gas by means of a pseudo-potential is available from the work of Martin and de Dominicis. Incorporating their results into the perturbation calculation yields saturation for nuclear matter with a binding energy per particle of about 18 Mev at a density corresponding to k/sub F/more »

- Authors:

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Tech., Cambridge

- OSTI Identifier:
- 4150506

- Report Number(s):
- TID-19097; MPI-PA-2/62

Journal ID: NUPHA; 0029-5582

- NSA Number:
- NSA-18-002878

- Resource Type:
- Journal Article

- Journal Name:
- Nuclear Physics (Netherlands) Divided into Nucl. Phys. A and Nucl. Phys. B

- Additional Journal Information:
- Journal Volume: Vol: 47; Other Information: TID-19097; MPI-PA-2/62. Orig. Receipt Date: 31-DEC-64

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

- Language:
- English

- Subject:
- PHYSICS; BINDING ENERGY; DIFFERENTIAL EQUATIONS; GAMMEL-THALER POTENTIAL; INTERACTIONS; MANY BODY PROBLEM; MASS; MATRICES; NUCLEAR MODELS; NUMERICALS; PERTURBATION THEORY; S-WAVE; SCATTERING; VECTORS

### Citation Formats

```
Schappert, G T.
```*ORDINARY PERTURBATION THEORY APPLIED TO NUCLEAR MATTER*. Country unknown/Code not available: N. p., 1963.
Web. doi:10.1016/0029-5582(63)90912-X.

```
Schappert, G T.
```*ORDINARY PERTURBATION THEORY APPLIED TO NUCLEAR MATTER*. Country unknown/Code not available. doi:10.1016/0029-5582(63)90912-X.

```
Schappert, G T. Sun .
"ORDINARY PERTURBATION THEORY APPLIED TO NUCLEAR MATTER". Country unknown/Code not available. doi:10.1016/0029-5582(63)90912-X.
```

```
@article{osti_4150506,
```

title = {ORDINARY PERTURBATION THEORY APPLIED TO NUCLEAR MATTER},

author = {Schappert, G T},

abstractNote = {The average binding energy and equilibrium density of nuclear matter are calculated in the self-consistent independent pair approximation. The potentials of Gammel and Thaler are used. The hard core is replaced by a pseudopotential, and the potentials are adjusted to give the same low energy scattering data. The pseudo-potential is of the Huang-Yang type, and hence one can use ordinary RayleighSchroedinger perturbation theory, which is then a joint expansion in the strength of the pseudo-potential plus the central potentials plus the tensor force. The first and second order terms in this expansion were calculated exactly, but were made self-consistent only in the effective mass approximation, the self-consistency requirement becoming the solution of a quadratic equation for the effective mass. It is found that a simple S-wave pseudopotential is not sufficient to produce saturation within a density range corresponding to k/sub F/ = 1 to 2 fm/sup -1/. A more exact treatment of the hard core gas by means of a pseudo-potential is available from the work of Martin and de Dominicis. Incorporating their results into the perturbation calculation yields saturation for nuclear matter with a binding energy per particle of about 18 Mev at a density corresponding to k/sub F/ = 1.4 fm/sup -1/. The main results are not so much the actual binding energy and equilibrium density of nuclear matter, but the results of the various contributions coming from second order perturbation theory, especially the interference terms between the pseudopotential and the attractive potentials, and interference terms between direct and exchange matrix elements for the attractive central and tensor forces, which were calculated exactly. (auth)},

doi = {10.1016/0029-5582(63)90912-X},

journal = {Nuclear Physics (Netherlands) Divided into Nucl. Phys. A and Nucl. Phys. B},

number = ,

volume = Vol: 47,

place = {Country unknown/Code not available},

year = {1963},

month = {9}

}