### 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 ^{3}He 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 = (ρ_{n} - ρ_{p})/ρ, where ρ_{n}(ρ_{p}) is the neutron (proton) number density]. Unexpectedly, we find that the energies at a fixed density cannot be represented by a power series in ζ^{2}. A new energy term, ε_{1} (ζ^{2} + ζ_{0}
^{2})^{1/2}i where ζ_{0} is a small number and ε_{1} 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 language | English |
---|---|

Pages (from-to) | 545-571 |

Number of pages | 27 |

Journal | Progress of Theoretical Physics |

Volume | 116 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2006 Sep |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical Physics*,

*116*(3), 545-571. https://doi.org/10.1143/PTP.116.545

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

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 116, no. 3, pp. 545-571. https://doi.org/10.1143/PTP.116.545

}

TY - JOUR

T1 - Variational study of asymmetric nuclear matter and a new term in the mass formula

AU - Takano, Masatoshi

AU - Yamada, Masami

PY - 2006/9

Y1 - 2006/9

N2 - 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 ρn(ρp) 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, ε1 (ζ2 + 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.

AB - 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 ρn(ρp) 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, ε1 (ζ2 + 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.

UR - http://www.scopus.com/inward/record.url?scp=33846289979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846289979&partnerID=8YFLogxK

U2 - 10.1143/PTP.116.545

DO - 10.1143/PTP.116.545

M3 - Article

AN - SCOPUS:33846289979

VL - 116

SP - 545

EP - 571

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 3

ER -