Variational study of asymmetric nuclear matter and a new term in the mass formula

Masatoshi Takano, Masami Yamada

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    Asymmetric nuclear matter at zero temperature is studied using a variational method which is an extension of the methods used by the present authors previously for simpler systems. An approximate expression for the energy per nucleon in asymmetric nuclear matter is derived through a combination of two procedures, one used for symmetric nuclear matter and the other for spin-polarized liquid 3He with spin polarization replaced by isospin polarization. The approximate expression for the energy is obtained as a functional of various spin-isospin-dependent radial distribution functions, tensor distribution functions, and spin-orbit distribution functions. The Euler-Lagrange equations are derived to minimize this approximate expression for the energy; they consist of 16 coupled integrodifferential equations for various distribution functions. These equations were solved numerically for several values of the nucleon number density ρ and for many degrees of asymmetry ζ[ζ = (ρn - ρp)/ρ, where ρnp) is the neutron (proton) number density]. Unexpectedly, we find that the energies at a fixed density cannot be represented by a power series in ζ2. A new energy term, ε12 + ζ0 2)1/2i where ζ0 is a small number and ε1 is a positive coefficient, is proposed. It is shown that if the power series is supplemented with this new term, it reproduces the energies obtained by variational calculations very accurately. This new term is studied in relation to cluster formation in nuclear matter, and some mention is made of a possible similar term in the mass formula for finite nuclei.

    Original languageEnglish
    Pages (from-to)545-571
    Number of pages27
    JournalProgress of Theoretical Physics
    Volume116
    Issue number3
    DOIs
    Publication statusPublished - 2006 Sep

    Fingerprint

    distribution functions
    power series
    energy
    integrodifferential equations
    Euler-Lagrange equation
    polarization
    radial distribution
    asymmetry
    tensors
    orbits
    neutrons
    nuclei
    protons
    coefficients
    liquids
    temperature

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Variational study of asymmetric nuclear matter and a new term in the mass formula. / Takano, Masatoshi; Yamada, Masami.

    In: Progress of Theoretical Physics, Vol. 116, No. 3, 09.2006, p. 545-571.

    Research output: Contribution to journalArticle

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