Prog. Theor. Phys. Vol. 116 No. 3 (2006) pp. 545-571
Variational Study of Asymmetric Nuclear Matter and a New Term in the Mass Formula
Advanced Research Institute for Science and Engineering,
Waseda University, Tokyo 169-8555, Japan
(Received May 2, 2006)
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 + ζ20)1/2, 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
DOI : 10.1143/PTP.116.545
- J. W. Clark, Prog. Part. Nucl. Phys. 2 (1979), 89.
W. Zuo, I. Bombaci and U. Lombardo, Phys. Rev. C 60 (1999), 024605[APS].
D. Alonso and F. Sammarruca, Phys. Rev. C 67 (2003), 054301[APS].
A. Akmal, V. R. Pandharipande and D. G. Ravenhall, Phys. Rev. C 58 (1998), 1804[APS].
I. E. Lagaris and V. R. Pandharipande, Nucl. Phys. A 369 (1981), 470[CrossRef].
G. H. Bordbar and M. Modarres, Phys. Rev. C 57 (1998), 714[APS].
- M. Takano and M. Yamada, Prog. Theor. Phys. 91 (1994), 1149[PTP].
- M. Takano and M. Yamada, Prog. Theor. Phys. 100 (1998), 745[PTP].
- M. Takano, T. Endo, R. Kimura and M. Yamada, Prog. Theor. Phys. 109 (2003), 213[PTP].
- M. Takano and M. Yamada, Prog. Theor. Phys. 88 (1992), 1131[PTP].
R. A. Aziz, V. P. S. Nain, J. S. Carley, W. L. Taylor and G. T. McConville, J. Chem. Phys. 70 (1979), 4330[CrossRef].
R. B. Wiringa, V. G. J. Stoks and R. Schiavilla, Phys. Rev. C 51 (1995), 38[APS].
- F. Iwamoto and M. Yamada, Prog. Theor. Phys. 17 (1957), 543[PTP].
- M. Takano, Prog. Theor. Phys. 104 (2000), 185[PTP].
I. E. Lagaris and V. R. Pandharipande, Nucl. Phys. A 359 (1981), 349[CrossRef].
R. B. Wiringa, V. Fiks and A. Fabrocini, Phys. Rev. C 38 (1988), 1010[APS].
- M. Takano, Prog. Theor. Phys. Suppl. No. 156 (2004), 141[PTP].
- H. Koura, T. Tachibana, M. Uno and M. Yamada, Prog. Theor. Phys. 113 (2005), 305[PTP].
Citing Article(s) :
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