Prog. Theor. Phys. Vol. 100 No. 4 (1998) pp. 745-771
Variational Method for Infinite Nuclear Matter
Advanced Research Institute for Science and Engineering
with Noncentral Forces
Waseda University, Tokyo 169-8555, Japan
(Received April 17, 1998)
Approximate energy expressions are proposed for infinite zero-temperature
neutron matter and symmetric nuclear matter by taking into account noncentral
forces. They are explicitly expressed as functionals of spin-isospin-dependent
radial distribution functions, tensor distribution functions and spin-orbit
distribution functions, and can be used conveniently in the variational method.
The two-body noncentral cluster terms are fully included in these expressions,
while the degree of inclusion of the three-body cluster terms related to
noncentral forces is less than that of the purely central three-body terms. The
Euler-Lagrange equations are derived from these energy expressions and
numerically solved for neutron matter and symmetric nuclear matter. The
Hamada-Johnston and AV14 potentials are used as the two-body nuclear force.
The results show that the noncentral forces cause the total energy of
symmetric nuclear matter to be decreased too much with a saturation density
which is too high. Discussion is given as to the reason for this
disagreement with experiment,
and the long tails of the noncentral distribution
functions obtained in the numerical calculations are suspected to be the main reason. Then,
an effective theory is proposed by introducing a density-dependent
modification of the noncentral part of the energy expression to suppress the
long tails of the noncentral distribution functions. With a suitable choice of
the value of a parameter included in the modification, the saturation point
(both the energy and the density) of symmetric nuclear matter can be
reproduced with the Hamada-Johnston potential. Neutron stars are studied by
use of this effective theory, and reasonable results are obtained.
DOI : 10.1143/PTP.100.745
M. Takano and M. Yamada, Prog. Theor. Phys. 91 (1994), 1149[PTP].
M. Takano, Prog. Theor. Phys. 93 (1995), 745[PTP].
M. Takano and M. Yamada, Prog. Theor. Phys. 88 (1992), 1131[PTP].
M. Takano, T. Kaneko and M. Yamada, Prog. Theor. Phys. 97 (1997), 569[PTP].
T. Hamada and I. D. Johnston, Nucl. Phys. 34 (1962), 382[CrossRef].
T. Hamada, Y. Nakamura and R. Tamagaki, Prog. Theor. Phys. 33 (1965), 769[PTP].
R. B. Wiringa, R. A. Smith and T. L. Ainsworth, Phys. Rev. C29 (1984), 1207[APS].
F. Calogero and Yu. A. Simonov, Phys. Rev. Lett. 25 (1970), 881[APS].
I. E. Lagaris and V. R. Pandharipande, Nucl. Phys. A359 (1981), 331[Elsevier].
- T. Takatsuka, R. Tamagaki and T. Tatsumi, Prog. Theor. Phys. Suppl. No. 112 (1993), 67[PTP].
- T. Takatsuka and R. Tamagaki, Prog. Theor. Phys. Suppl. No. 112 (1993), 27[PTP].
R. B. Wiringa, V. Fiks and A. Fabrocini, Phys. Rev. C38 (1988), 1010[APS].
R. P. Feynman, N. Metropolis and E. Teller, Phys. Rev. 75 (1949), 1561[APS].
- G. Baym, C. Pethick and P. Sutherland, Astrophys. J. 170 (1971), 299.
- G. B. Cook, S. L. Shapiro and S. A. Teukolsky, Astrophys. J. 434 (1994), 823, and references therein.
- M. Takano and M. Yamada, Advanced Recearch Center for Science and Engineering, Waseda Univ., Technical Report No. 95-39 (1995).
- R. Malfliet, in Few Body Systems Suppl. 7, ed. B. L. G. Bakker and R. van Dantzig (Springer-Verlag, Wien, 1994), p. 380.
Citing Article(s) :
Progress of Theoretical Physics Vol. 104 No. 1 (2000) pp. 185-202
Variational Method for Infinite Nuclear Matter with the Paris Potential
Progress of Theoretical Physics Vol. 109 No. 2 (2003) pp. 213-232
Approximate Energy Expression for Spin-Polarized Fermi Liquids
Masatoshi Takano, Tomoki Endo, Ryusuke Kimura and Masami Yamada
Progress of Theoretical Physics Vol. 116 No. 3 (2006) pp. 545-571
Variational Study of Asymmetric Nuclear Matter and a New Term in the Mass Formula
Masatoshi Takano and Masami Yamada