Concavity for nuclear bindings, thermodynamical functions and density functionals

Bruce R Barrett, B. G. Giraud, B. K. Jennings, N. P. Toberg

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Sequences of experimental ground-state energies for both odd and even A are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give numerical estimates of the grand potential Ω (β, μ) for a mixture of nuclei at low or moderate temperatures T = β- 1 and at many chemical potentials μ. The average nucleon number 〈 A 〉 (β, μ) then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to the drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of 〈 A 〉. Concavity, which always occurs for the free energy and is usually present for the average energy, allows easy interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. Finally we show how concavity and universality are related in the theory of the nuclear density functional.

Original languageEnglish (US)
Pages (from-to)267-282
Number of pages16
JournalNuclear Physics, Section A
Volume828
Issue number3-4
DOIs
StatePublished - Sep 15 2009

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concavity
functionals
extrapolation
binding energy
free energy
convexity
energy
lists
interpolation
nuclei
ground state
estimates
predictions
excitation
temperature

Keywords

  • Mass formula
  • Nuclear structure
  • Thermodynamic properties

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Concavity for nuclear bindings, thermodynamical functions and density functionals. / Barrett, Bruce R; Giraud, B. G.; Jennings, B. K.; Toberg, N. P.

In: Nuclear Physics, Section A, Vol. 828, No. 3-4, 15.09.2009, p. 267-282.

Research output: Contribution to journalArticle

Barrett, Bruce R ; Giraud, B. G. ; Jennings, B. K. ; Toberg, N. P. / Concavity for nuclear bindings, thermodynamical functions and density functionals. In: Nuclear Physics, Section A. 2009 ; Vol. 828, No. 3-4. pp. 267-282.
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