Chiral approach to nuclear matter: role of two-pion exchange with virtual delta-isobar excitation

• Published in: Nuclear physics. A Vol. 750; no. 2; pp. 259 - 293
• Main Authors: Fritsch, S., Kaiser, N., Weise, W.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 04-04-2005
• Subjects: Nuclear matter properties; Two-pion exchange with virtual [formula omitted]-isobar excitation; 24.10.Cn; 12.38.Bx; Nuclear matter properties; 31.15.Ew; Two-pion exchange with virtual Δ -isobar excitation; 21.65.+f
• ISSN: 0375-9474
• DOI: 10.1016/j.nuclphysa.2004.12.042

We extend a recent three-loop calculation of nuclear matter by including the effects from two-pion exchange with single and double virtual
Δ
(
1232
)
-isobar excitation. Regularization dependent short-range contributions from pion-loops are encoded in a few NN-contact coupling constants. The empirical saturation point of isospin-symmetric nuclear matter,
E
¯
0
=
−
16
 MeV
,
ρ
0
=
0.16
 fm
−3
, can be well reproduced by adjusting the strength of a two-body term linear in density (and tuning an emerging three-body term quadratic in density). The nuclear matter compressibility comes out as
K
=
304
 MeV
. The real single-particle potential
U
(
p
,
k
f
0
)
is substantially improved by the inclusion of the chiral
π
N
Δ
-dynamics: it grows now monotonically with the nucleon momentum
p. The effective nucleon mass at the Fermi surface takes on a realistic value of
M
∗
(
k
f
0
)
=
0.88
M
. As a consequence of these features, the critical temperature of the liquid-gas phase transition gets lowered to the value
T
c
≃
15
 MeV
. In this work we continue the complex-valued single-particle potential
U
(
p
,
k
f
)
+
i
W
(
p
,
k
f
)
into the region above the Fermi surface
p
>
k
f
. The effects of 2
π-exchange with virtual
Δ-excitation on the nuclear energy density functional are also investigated. The effective nucleon mass associated with the kinetic energy density is
M
˜
∗
(
ρ
0
)
=
0.64
M
. Furthermore, we find that the isospin properties of nuclear matter get significantly improved by including the chiral
π
N
Δ
-dynamics. Instead of bending downward above
ρ
0
as in previous calculations, the energy per particle of pure neutron matter
E
¯
n
(
k
n
)
and the asymmetry energy
A
(
k
f
)
now grow monotonically with density. In the density regime
ρ
=
2
ρ
n
<
0.2
 fm
−3
relevant for conventional nuclear physics our results agree well with sophisticated many-body calculations and (semi)-empirical values.