### Abstract

Several commonly made approximations in microscopic effective interaction calculations have been found to result in serious inaccuracies. Recent improved second-order calculations for A=18 nuclei suggested somewhat better order by order convergence in the reaction matrix G than indicated previously. A selected third-order term has been calculated to study further this possibility. The convergence of the intermediate-state summation was also investigated for this diagram. Our improved calculational technique results in a greater reduction of the third-order term than the reduction found earlier for the second-order term. The outlook for the (asymptotic) convergence of the expansion is much improved, but the prospects for a complete third-order calculation of the effective interaction are dim due to the difficulties of the calculation. [NUCLEAR STRUCTURE Effective interaction, theory; convergence of the intermediate-state sums; convergence of the diagram series through third-order in the nuclear reaction matrix; shell-model matrix elements in the sd shell.]

Original language | English (US) |
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Pages (from-to) | 777-784 |

Number of pages | 8 |

Journal | Physical Review C |

Volume | 17 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1978 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Physical Review C*,

*17*(2), 777-784. https://doi.org/10.1103/PhysRevC.17.777