{
  "id": "0907.2413",
  "version": "v1",
  "published": "2009-07-14T17:19:51.000Z",
  "updated": "2009-07-14T17:19:51.000Z",
  "title": "Collapse of the random phase approximation: examples and counter-examples from the shell model",
  "authors": [
    "Calvin W. Johnson",
    "Ionel Stetcu"
  ],
  "comment": "8 pages, 7 figures",
  "journal": "Phys.Rev.C80:024320,2009",
  "doi": "10.1103/PhysRevC.80.024320",
  "categories": [
    "nucl-th"
  ],
  "abstract": "The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a symmetry-conserving state (also referred to as a ``phase transition'' in the literature). The order of the transition is important when one applies the random phase approximation (RPA) to the of the Hartree-Fock wavefunction: if first order, RPA is stable through the transition, but if second-order, then the RPA amplitudes become large and lead to unphysical results. The latter is known as ``collapse'' of the RPA. While the difference between first- and second-order transitions in the RPA was first pointed out by Thouless, we present for the first time non-trivial examples of both first- and second-order transitions in a uniform model, the interacting shell-model, where we can compare to exact numerical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-14T17:19:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "21.60.Cs",
      "21.60.Jz"
    ],
    "keywords": [
      "random phase approximation",
      "shell model",
      "first time non-trivial examples",
      "second-order transitions",
      "counter-examples"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review C",
      "year": 2009,
      "month": "Aug",
      "volume": 80,
      "number": 2,
      "pages": "024320"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 825654,
      "adsabs": "2009PhRvC..80b4320J"
    }
  }
}