### Abstract

A new, simple, and exact method is given for calculating the reaction matrix G in a two-particle harmonic-oscillator basis. The method makes use of an expansion of the Bethe-Goldstone wave function in terms of solutions of the Schrödinger equation for two interacting particles in a harmonic-oscillator well. Since a two-particle basis is used, the Pauli operator Q is diagonal and can be treated exactly. Reaction matrix elements based on the Hamada-Johnston potential are used in a shell-model calculation of A=18 nuclei. The results are compared with those of earlier calculations using approximate Pauli operators. The dependence of the reaction matrix on the starting energy is studied, and the relationship of this energy to the intermediate-state spectrum and to the Pauli operator Q is discussed. In this same context the difference between using a Brueckner Q and a shell-model Q is also discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 1137-1145 |

Number of pages | 9 |

Journal | Physical Review C - Nuclear Physics |

Volume | 3 |

Issue number | 3 |

DOIs | |

State | Published - 1971 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics

### Cite this

*Physical Review C - Nuclear Physics*,

*3*(3), 1137-1145. https://doi.org/10.1103/PhysRevC.3.1137

**Simple and exact method for calculating the nuclear reaction matrix.** / Barrett, Bruce R; Hewitt, R. G L; McCarthy, R. J.

Research output: Contribution to journal › Article

*Physical Review C - Nuclear Physics*, vol. 3, no. 3, pp. 1137-1145. https://doi.org/10.1103/PhysRevC.3.1137

}

TY - JOUR

T1 - Simple and exact method for calculating the nuclear reaction matrix

AU - Barrett, Bruce R

AU - Hewitt, R. G L

AU - McCarthy, R. J.

PY - 1971

Y1 - 1971

N2 - A new, simple, and exact method is given for calculating the reaction matrix G in a two-particle harmonic-oscillator basis. The method makes use of an expansion of the Bethe-Goldstone wave function in terms of solutions of the Schrödinger equation for two interacting particles in a harmonic-oscillator well. Since a two-particle basis is used, the Pauli operator Q is diagonal and can be treated exactly. Reaction matrix elements based on the Hamada-Johnston potential are used in a shell-model calculation of A=18 nuclei. The results are compared with those of earlier calculations using approximate Pauli operators. The dependence of the reaction matrix on the starting energy is studied, and the relationship of this energy to the intermediate-state spectrum and to the Pauli operator Q is discussed. In this same context the difference between using a Brueckner Q and a shell-model Q is also discussed.

AB - A new, simple, and exact method is given for calculating the reaction matrix G in a two-particle harmonic-oscillator basis. The method makes use of an expansion of the Bethe-Goldstone wave function in terms of solutions of the Schrödinger equation for two interacting particles in a harmonic-oscillator well. Since a two-particle basis is used, the Pauli operator Q is diagonal and can be treated exactly. Reaction matrix elements based on the Hamada-Johnston potential are used in a shell-model calculation of A=18 nuclei. The results are compared with those of earlier calculations using approximate Pauli operators. The dependence of the reaction matrix on the starting energy is studied, and the relationship of this energy to the intermediate-state spectrum and to the Pauli operator Q is discussed. In this same context the difference between using a Brueckner Q and a shell-model Q is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0010875782&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010875782&partnerID=8YFLogxK

U2 - 10.1103/PhysRevC.3.1137

DO - 10.1103/PhysRevC.3.1137

M3 - Article

AN - SCOPUS:0010875782

VL - 3

SP - 1137

EP - 1145

JO - Physical Review C - Nuclear Physics

JF - Physical Review C - Nuclear Physics

SN - 0556-2813

IS - 3

ER -