dorsal/arxiv
View SchemaCharge-exchange reaction cross sections and the Gamow-Teller strength for double beta decay
| Authors | K. Amos, Amand Faessler, V. Rodin |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0702016 |
| URL | https://arxiv.org/abs/nucl-th/0702016 |
| DOI | 10.1103/PhysRevC.76.014604 |
| Journal | Phys.Rev.C76:014604,2007 |
Abstract
The proportionality between single charge-exchange reaction cross sections in the forward direction as found, for example from $(p,n)$ and $(^3$He,$t)$ and from $(n,p)$ and $(d,^2$He) reactions, and the Gamow-Teller (GT) strength into the same final nuclear states has been studied and/or assumed often in the past. Using the most physically justified theory we have at our disposal and for the specific example of the ${}^{76}$Ge-${}^{76}$Se system that may undergo double beta-decay, we demonstrate that the proportionality is a relative good assumption for reactions changing a neutron into a proton, i.e. ${}^{76}$Ge$(p,n){}^{76}$As. In this channel, the main contribution to the GT strengths comes from the removal of a neutron from an occupied single-particle (SP) state and putting a proton into an unoccupied SP state having either the same state quantum numbers or those of the spin-orbit partner. In contrast to this, in the second leg of the double beta decay a single proton must be taken from an occupied SP state and a neutron placed in an unoccupied one. This second process often is Pauli forbidden in medium-heavy nuclei and only can be effected if the Fermi surface is smeared out. Such is the case for ${}^{76}$Se$(n,p){}^{76}$As. Our results suggest that one may not always assume a proportionality between the forward-angle cross sections of the charge-exchange reactions and the GT strength in any such medium-heavy nuclei. The discrepancy originates from a pronounced effect of the radial dependence of the nucleon-nucleon ($NN$) interaction in connection with the Pauli principle on the cross sections in the $(n,p)$ reaction channel. Such a radial dependence is completely absent in the GT transition operator.
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"abstract": "The proportionality between single charge-exchange reaction cross sections in\nthe forward direction as found, for example from $(p,n)$ and $(^3$He,$t)$ and\nfrom $(n,p)$ and $(d,^2$He) reactions, and the Gamow-Teller (GT) strength into\nthe same final nuclear states has been studied and/or assumed often in the\npast. Using the most physically justified theory we have at our disposal and\nfor the specific example of the ${}^{76}$Ge-${}^{76}$Se system that may undergo\ndouble beta-decay, we demonstrate that the proportionality is a relative good\nassumption for reactions changing a neutron into a proton, i.e.\n${}^{76}$Ge$(p,n){}^{76}$As. In this channel, the main contribution to the GT\nstrengths comes from the removal of a neutron from an occupied single-particle\n(SP) state and putting a proton into an unoccupied SP state having either the\nsame state quantum numbers or those of the spin-orbit partner. In contrast to\nthis, in the second leg of the double beta decay a single proton must be taken\nfrom an occupied SP state and a neutron placed in an unoccupied one. This\nsecond process often is Pauli forbidden in medium-heavy nuclei and only can be\neffected if the Fermi surface is smeared out. Such is the case for\n${}^{76}$Se$(n,p){}^{76}$As. Our results suggest that one may not always assume\na proportionality between the forward-angle cross sections of the\ncharge-exchange reactions and the GT strength in any such medium-heavy nuclei.\nThe discrepancy originates from a pronounced effect of the radial dependence of\nthe nucleon-nucleon ($NN$) interaction in connection with the Pauli principle\non the cross sections in the $(n,p)$ reaction channel. Such a radial dependence\nis completely absent in the GT transition operator.",
"arxiv_id": "nucl-th/0702016",
"authors": [
"K. Amos",
"Amand Faessler",
"V. Rodin"
],
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"nucl-th"
],
"doi": "10.1103/PhysRevC.76.014604",
"journal_ref": "Phys.Rev.C76:014604,2007",
"title": "Charge-exchange reaction cross sections and the Gamow-Teller strength for double beta decay",
"url": "https://arxiv.org/abs/nucl-th/0702016"
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