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Piecewise moments method: Generalized Lanczos technique for nuclear response surfaces

Haxton, Wick C. and Nollett, Kenneth M. and Zurek, Kathryn M. (2005) Piecewise moments method: Generalized Lanczos technique for nuclear response surfaces. Physical Review C, 72 (6). Art. No. 065501. ISSN 0556-2813. doi:10.1103/physrevc.72.065501. https://resolver.caltech.edu/CaltechAUTHORS:20190611-125826233

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Abstract

For some years Lanczos moments methods have been combined with large-scale shell-model calculations in evaluations of the spectral distributions of certain operators. This technique is of great value because the alternative, a state-by-state summation over final states, is generally not feasible. The most celebrated application is to the Gamow-Teller operator, which governs β decay and neutrino reactions in the allowed limit. The Lanczos procedure determines the nuclear response along a line q = 0 in the (ω,q) plane, where ω and q are the energy and three-momentum transferred to the nucleus, respectively. However, generalizing such treatments from the allowed limit to general electroweak response functions at arbitrary momentum transfers seems considerably more difficult: The response function must be determined over the entire (ω,q) plane for an operator O(q) that is not fixed, but depends explicitly on q. Such operators arise in any semileptonic process in which the momentum transfer is comparable with (or larger than) the inverse nuclear size. Here we show, for Slater determinants built on harmonic-oscillator basis functions, that the nuclear response for any multipole operator O(q) can be determined efficiently over the full response plane by a generalization of the standard Lanczos moments method. We describe the piecewise moments method and thoroughly explore its convergence properties for the test case of electromagnetic responses in a full sd-shell calculation of ^(28)Si. We discuss possible extensions to a variety of electroweak processes, including charged- and neutral-current neutrino scattering.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physrevc.72.065501DOIArticle
https://arxiv.org/abs/nucl-th/0508034arXivDiscussion Paper
Alternate Title:The Piecewise Moments Method: A Generalized Lanczos Technique for Nuclear Response Surfaces
Additional Information:© 2005 American Physical Society. (Received 22 August 2005; published 29 December 2005) This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under contract W-31-109-ENG-38 (K. M. Nollett) and grants DE-FG02-00ER-41132 and DE-FC02-01ER-41187 (SciDAC) (W. C. Haxton and K. Zurek).
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)W-31-109-ENG-38
Department of Energy (DOE)DE-FG02-00ER-41132
Department of Energy (DOE)DE-FC02-01ER-41187
Issue or Number:6
Classification Code:PACS number(s): 25.30.−c, 21.60.Cs
DOI:10.1103/physrevc.72.065501
Record Number:CaltechAUTHORS:20190611-125826233
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190611-125826233
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96281
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:11 Jun 2019 23:20
Last Modified:16 Nov 2021 17:19

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