Physics Letters B 776 (2018) 447–450
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Probing proton transition momentum in neutron-rich matter
Gao-Chan Yong
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
8 July 2017
Received
in revised form 26 October 2017
Accepted
30 November 2017
Available
online 2 December 2017
Editor: W.
Haxton
Around the nuclear Fermi momentum, there is a transition of nucleon momentum distribution n(k) in
nuclear matter, i.e., from a constant to the 1/k
4
nucleon momentum distribution. While nowadays the
transition momentum of minority in asymmetric matter is rarely studied and thus undetermined. In the
framework of the IBUU transport model, proton transition momentum in nuclei is first studied. It is
found that the transition momentum of proton is sensitive to the π
−
/π
+
ratio as well as the energetic
photon production in neutron-rich nuclear reaction. This result may push the study of how the proton
momentum is distributed in neutron-rich matter forward and help us to better understand the dynamics
of both neutron-rich nuclear reactions and neutron stars.
© 2017 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
In recent two years, the study of nuclear short-range correla-
tions
attracts much attention [1–6]. It has been shown that about
20% nucleons in nuclei are correlated [7–9]. Because of the nucleon
short-range interactions [10,11], nucleons in nuclei can form pairs
with larger relative momenta and smaller center-of-mass momenta
[12,13]. The nucleon short-range correlations (SRC) in nuclei cause
a high-momentum tail (HMT) in single-nucleon momentum distri-
bution
above the Fermi-momentum [14–18]. And the HMT shape
caused by two-nucleon SRC is almost identical for all nuclei from
deuteron to very heavier nuclei [19–22], i.e., roughly exhibits a
1/k
4
tail [23–26]. And in the HMT, the number of neutron–proton
correlated pairs is about 18 times that of the proton–proton or
neutron–neutron correlated pairs [9].
Proton
transition momentum, i.e., the starting point of proton
1/k
4
momentum distribution in neutron-rich matter directly af-
fects
proton average kinetic energy in nuclear matter, thus affects
the dynamics of neutron-rich nuclear reactions and the dynamics
of neutron stars, such as the cooling of a Neutron Star, the super-
fluidity
of protons [27], etc. While for neutron-rich matter, it is not
straightforward to determine the transition momentum of proton.
One general considers that below the Fermi momentum, proton or
neutron have independent movements while above their respective
Fermi momenta, i.e., k
F
p
, k
F
n
, they respectively have 1/k
4
distri-
butions
starting from their respective Fermi momenta. This naive
opinion, however, is not consistent with the correlation picture
of neutron–proton pair [23]. The correlated neutron and proton
should have almost the same momentum whether in symmetric
E-mail address: yonggaochan@impcas.ac.cn.
or in asymmetric matter. In asymmetric matter or neutron matter,
such as the neutron stars, neutron and proton may have very dif-
ferent
Fermi momenta. If each correlated neutron and proton have
1/k
4
distributions starting from their respective Fermi momenta,
then the correlated neutron and proton would have very different
momenta. This point evidently contradicts the thought of the n–p
dominance model [23].
In
neutron-rich matter, because protons become more promi-
nent
at high momenta as their concentration decreases [28], the
starting momentum of minority 1/k
4
distribution should be not
the minority Fermi momentum. Because the minority Fermi mo-
mentum
would become very small in magnitude if proton concen-
tration
decreases sharply. Apart from its own Fermi momentum,
the left case is using the majority Fermi momentum as the start-
ing
momentum of minority 1/k
4
distribution. For very asymmetric
nuclear matter, it is hard to obtain the minority transition mo-
mentum
from microscopic theory. The ladder self-consistent Green
function approach could not get the nucleon momentum distribu-
tion
at Zero temperature [16] and the Brueckner theory with a
microscopic Three-body force gives a noncontinuous nucleon mo-
mentum
distribution [29]. That is to say, the microscopic theory
can not answer the question of minority transition momentum in
asymmetric matter, especially in the neutron matter. However, the
minority transition momentum could be checked by nuclear exper-
iments
with unequal numbers of proton and neutron.
One
way to check the starting point of proton 1/k
4
distribution,
i.e., whether the HMT starts from proton Fermi momentum or from
the correlated majority Fermi momentum, is using heavy-ion col-
lisions
with neutron-rich nuclei. In nucleus–nucleus collisions at
intermediate energies, different proton energies may cause the dif-
https://doi.org/10.1016/j.physletb.2017.11.075
0370-2693/
© 2017 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.