### Abstract

The new method of Truelove and Nicholls for obtaining reaction matrix elements for nuclear-structure calculations is discussed. In this method, the Bethe-Goldstone wave function is expanded in terms of eigenfunctions of two interacting nucleons bound in a common potential well. The Bethe-Goldstone equation, which is written in terms of an expansion over noninteracting two-particle states, is then solved iteratively. In practice, the method is most easily applied when a harmonic-oscillator basis is used; the Pauli operator Q can then be treated exactly. The convergence of the Truelove-Nicholls iteration scheme and of the above two expansions is investigated. It is shown that the original method is incorrect for nucleon-nucleon potentials with an infinite hard core. A simple way of correcting the method is presented.

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

Pages (from-to) | 1199-1204 |

Number of pages | 6 |

Journal | Physical Review C - Nuclear Physics |

Volume | 2 |

Issue number | 4 |

DOIs | |

State | Published - 1970 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review C - Nuclear Physics*,

*2*(4), 1199-1204. https://doi.org/10.1103/PhysRevC.2.1199

**Discussion of a new technique for solving the Bethe-Goldstone equation.** / Barrett, Bruce R; Hewitt, R. G L; McCarthy, R. J.

Research output: Contribution to journal › Article

*Physical Review C - Nuclear Physics*, vol. 2, no. 4, pp. 1199-1204. https://doi.org/10.1103/PhysRevC.2.1199

}

TY - JOUR

T1 - Discussion of a new technique for solving the Bethe-Goldstone equation

AU - Barrett, Bruce R

AU - Hewitt, R. G L

AU - McCarthy, R. J.

PY - 1970

Y1 - 1970

N2 - The new method of Truelove and Nicholls for obtaining reaction matrix elements for nuclear-structure calculations is discussed. In this method, the Bethe-Goldstone wave function is expanded in terms of eigenfunctions of two interacting nucleons bound in a common potential well. The Bethe-Goldstone equation, which is written in terms of an expansion over noninteracting two-particle states, is then solved iteratively. In practice, the method is most easily applied when a harmonic-oscillator basis is used; the Pauli operator Q can then be treated exactly. The convergence of the Truelove-Nicholls iteration scheme and of the above two expansions is investigated. It is shown that the original method is incorrect for nucleon-nucleon potentials with an infinite hard core. A simple way of correcting the method is presented.

AB - The new method of Truelove and Nicholls for obtaining reaction matrix elements for nuclear-structure calculations is discussed. In this method, the Bethe-Goldstone wave function is expanded in terms of eigenfunctions of two interacting nucleons bound in a common potential well. The Bethe-Goldstone equation, which is written in terms of an expansion over noninteracting two-particle states, is then solved iteratively. In practice, the method is most easily applied when a harmonic-oscillator basis is used; the Pauli operator Q can then be treated exactly. The convergence of the Truelove-Nicholls iteration scheme and of the above two expansions is investigated. It is shown that the original method is incorrect for nucleon-nucleon potentials with an infinite hard core. A simple way of correcting the method is presented.

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U2 - 10.1103/PhysRevC.2.1199

DO - 10.1103/PhysRevC.2.1199

M3 - Article

VL - 2

SP - 1199

EP - 1204

JO - Physical Review C - Nuclear Physics

JF - Physical Review C - Nuclear Physics

SN - 0556-2813

IS - 4

ER -