Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 53

Evidence for three-particle correlations in nuclear matter†
W. Bentz∗1 and I. C. Cloët∗2
The properties of inﬁnite nuclear matter havebeen the subject of intensive investigations for many
decades, mainly because of the wide range of applications, including the properties of heavy nuclei, supernova explosions, and neutron stars. In particular, studies on three-particle correlations have a long
history, beginning with the pioneering work of Bethein 1965.1) In this paper we focus our attention on
the skewness of nuclear matter and its implications
for three-particle
correlations.
Skewness is deﬁned as
J = 27ρ3 d3 EA /dρ3 at ρ = ρ0 , where EA is the energy per nucleon in isospin symmetric nuclear matter,and ρ0 is the saturation density. Recently, empiricalvalues of J have been extracted in Ref. 2) from heavy
ion collisions and neutron star observations, and thefollowing range was deduced:−0.50 GeV < J < −0.01 GeV .

=dΩ24πM(H0 − H1 ) > 1.24M∗

(1)

(5)

tt



M − M∗
4 pF dM ∗1−× − +3+(H−H),013M
3 M ∗ dpF
(2)

t...
tt

Fig. 1. The ﬁrst two terms in the Faddeev series of thethree-particle amplitudes. Genuine three-particle correlations start with the second diagram. The circles
represent two-body t-matrices.

where K is the incompressibility, pF the Fermi momentum, M ∗ ≡ M ∗ (k = pF ) the Landau eﬀective mass∗dM ∗ (k)at the Fermi surface, dM|k=pF the slope
dpF =dkof M ∗ (k) at the Fermi surface, and the dimensionless
three-particle interaction parameters H� (� = 0, 1) aredeﬁned by
2pF M ∗h� ,ρ(3)H� =0π2References
1) H. A. Bethe, Phys. Rev. B 138, 804 (1965).
2) B. -A. Li, B. -J. Cai, L. -W. Chen, J. Xu, Prog. Part.
Nucl. Phys. 99, 29 (2018).
3) J. Negele, H. Orland, Quantum Many-particle systems(Springer, 1980).
4) C. Mahaux, P. F. Bortignon, R. A. Broglia, C. H. Dasso,Phys. Rep. 120, 1 (1985).
5) J. P. Blaizot, B. L. Friman, Nucl. Phys. A 372, 69(1981).
6) E. N. E. van Dalen, C. Fuchs, A. Faessler, Phys. Rev.
C 72, 065803 (2005).
7) Z. Zhang, L. -W. Chen, Phys. Rev. C 94, 064326 (2016).
8) J. W. Holt, N. Kaiser, T. R. Whitehead, Phys. Rev. C97, 054325 (2018).

where h� = h� (k1 = k2 = k3 = pF ) is given by the
angular average1h� (k1 , k2 , k3 )2� + 1∗2(4)The three-particle amplitudes H� satisfy a Faddeev
equation in the medium, with a 1-particle reducible
driving term (ﬁrst diagram in Fig. 1), and genuine
three-particle correlations, which start with the second diagram in Fig. 1. The driving term can be easily estimated by using eﬀective contact interactions of
the Landau-Migdal type, and give a contribution between 0.75 and 1.23 to Eq. (5). (Here we used theLandau-Migdal parameters obtained from Skyrme interactions7) ) and chiral eﬀective ﬁeld theory.8) ) This
gives us an important hint that two-particle correlations alone cannot satisfy the inequality Eq. (5), andthree-particle correlations processes are needed to explain the skewness of nuclear matter.

9p2F
J = −9K + ∗2M∗1dΩ3  ˆ ˆ �
k1 · k2 h(k1 , k2 , k3 ) .
4π

By using empirically and theoretically obtained ranges
for the incompressibility,2) the eﬀective mass M ∗ ,4)and its slope at the Fermi surface,5,6) we can deduce
the following inequality from (1) and (2):

By using the theoretical framework of the LandauMigdal theory, we will show that those empirical values
provide us with information on three-particle correlations in nuclear matter.
Extending Landau’s basic formula3) for the variationof the energy density of nuclear matter to include thethird order term, which involves the totally symmetricspin-isospin averaged three-particle forward scattering
amplitude h(k1 , k2 , k3 ), we are able to derive the following exact expression for J:†

Condensed from an article by W. Bentz and I. C. Cloët,Phys. Rev. C 100, 014303 (2019).
Department of Physics, Tokai University
Physics Division, Argonne National Laboratory- 73 -