Hard photon production from neutron-proton bremsstrahlung in intermediate
energy heavy-ion reactions is examined as a probe of the in-medium pn
scattering cross section within a transport model. Uncertainty of photon
production probability pn-pngamma is cancelled out by using the ratio of hard
photon spectra R_{12C+12C/p+n}(gamma) from two reactions. The in medium pn
scattering cross section is constrained by using the ratio of hard photon
production cross sections of proton-induced reactions p+12C and p+2H. A
reduction factor sigma_pn^medium/sigma_pn^free of about 0.5 ~ 0.7 around
saturation density is obtained by comparing with the existing experimental
data.Comment: 9 pages, 3 figures, accepted by PL

Baran

Bauer

Bertsch

Cassing

Chen

dʼEnterria

Fuchs

Gao-Chan Yong

Grosse

Hoefman

Horowitz

Lattimer

Martinez

Ming Ko

Nakayama

Nifenecker

Ortega

Prassa

Remington

Safkan

Schutz

Schäffer

Steiner

Stevenson

Timmermans

van Goethem

Wei Zuo

Xun-Chao Zhang

Yong

Zhang

Physics Letters B

English

arXiv

AbstractHard photon production from neutron–proton bremsstrahlung in intermediate energy heavy-ion reactions is examined as a probe of the in-medium pn scattering cross section within a transport model. Uncertainty of photon production probability pn→pnγ is cancelled out by using the ratio of hard photon spectra RC12+C12/p+n(γ) from two reactions. The in medium pn scattering cross section is constrained by using the ratio of hard photon production cross sections of proton-induced reactions p+C12 and p+H2. A reduction factor σpnmedium/σpnfree of about 0.5–0.7 around saturation density is obtained by comparing with the existing experimental data

Yong, Gao-Chan

Zuo, Wei

Zhang, Xun-Chao

Elsevier - Publisher Connector 

Physics Letters B 705 (2011) 240–243Contents lists available at SciVerse ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
A direct probe of the in-medium pn scattering cross section
Gao-Chan Yong ∗, Wei Zuo, Xun-Chao Zhang
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 12 August 2011
Received in revised form 11 October 2011
Accepted 11 October 2011
Available online 14 October 2011
Editor: W. Haxton
Keywords:
Neutron–proton bremsstrahlung
Hard photon production
In-medium pn scattering cross section
Hard photon production from neutron–proton bremsstrahlung in intermediate energy heavy-ion reactions
is examined as a probe of the in-medium pn scattering cross section within a transport model.
Uncertainty of photon production probability pn → pnγ is cancelled out by using the ratio of hard
photon spectra R12C+12C/p+n(γ ) from two reactions. The in medium pn scattering cross section is
constrained by using the ratio of hard photon production cross sections of proton-induced reactions
p + 12C and p + 2H. A reduction factor σmediumpn /σ freepn of about 0.5–0.7 around saturation density is
obtained by comparing with the existing experimental data.
© 2011 Elsevier B.V. All rights reserved.The in-medium nucleon–nucleon scattering cross section is
a fundamental physical quantity in nuclear physics and astro-
physics [1–3]. Besides many-body theoretical methods, in fact a lot
of literature also reported the studies of the in-medium nucleon–
nucleon scattering cross section based on transport models. Be-
cause so many uncertainties in the transport model and the com-
plexity in heavy-ion collisions in intermediate energies, till now
the in-medium nucleon–nucleon scattering cross section is still an
open question although the free nucleon–nucleon scattering cross
section is generally considered as a deterministic quantity. One of
the hot topics in today’s nuclear physics is the Equation of State
(EoS) of asymmetric nuclear matter, which is important for un-
derstanding many interesting questions in both nuclear physics
and astrophysics [1–3]. Among all the uncertainties of probing the
symmetry energy [4–8] with heavy-ion collisions, the nucleon–
nucleon scattering cross section is considered to be one of the
most important factors [4,6,9–11]. Nowadays almost all the probes
of nucleon–nucleon scattering cross section are hadronic probes.
These probes inevitably suffer from distortions due to the strong
interactions in the ﬁnal state. Ideally one expects more clean ways
to study nucleon–nucleon scattering cross section. It is noted that
the parity-violating electron scattering has been proposed to mea-
sure more precisely the size of the neutron-skin in 208Pb [12].
Similarly to electrons, photons interact with nucleons only elec-
tromagnetically. Once produced they escape almost freely from the
nuclear environment of nuclear reactions. Following the studies of
using hard photon production to probe the symmetry energy [13],
* Corresponding author.
E-mail address: yonggaochan@impcas.ac.cn (G.-C. Yong).0370-2693/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.physletb.2011.10.020in this Letter, based on the Boltzmann–Uehling–Uhlenbeck (BUU)
transport model, we report our results of using hard photons from
neutron–proton bremsstrahlung in intermediate energy heavy-ion
reactions as a direct probe of the in-medium pn scattering cross
section.
Hard photon production in heavy-ion reactions at beam en-
ergies from about 10 to 200 MeV/nucleon had been extensively
studied both experimentally and theoretically [14–16]. For in-
stance, the TAPS Collaboration carried out a series of comprehen-
sive measurements at various experimental facilities (GSI, GANIL,
KVI) studying in detail the properties of hard photons in a large
variety of nucleus–nucleus systems in the range of energies span-
ning Elab ≈ 20–200 MeV/nucleon [17]. Theoretically, it was con-
cluded that the neutron–proton bremsstrahlungs in the early stage
of the reaction are the main source of high energy γ rays. Fur-
ther, it was demonstrated clearly that the hard photons can be
used to probe the reaction dynamics leading to the formation of
dense matter [18–22]. Another favorable factor of using hard pho-
tons to probe the pn scattering cross section is that effects of the
nuclear EoS on the hard photon production was found small [23].
One of the major uncertainties of hard proton studies is the input
elementary pn → pnγ probability pγ which is still rather model
dependent [24–28,16]. The recent systematic measurements of the
pn → pnγ cross sections with neutron beams up to 700 MeV at
Los Alamos and the subsequent state-of-the-art theoretical investi-
gation may help to improve the above situation signiﬁcantly in the
near future [29,30].
Since the photon production probability is so small, i.e., only
one photon is produced in roughly a thousand nucleon–nucleon
collisions, a perturbative approach has been used in all dynam-
ical calculations of photon production in heavy-ion reactions at
G.-C. Yong et al. / Physics Letters B 705 (2011) 240–243 241Fig. 1. (Color online.) Beam energy dependence of the inclusive photon produc-
tion cross sections in 12C + 12C collisions. The photon energy is 50 MeV  εγ <
100 MeV. BUU calculations with both paγ and p
b
γ vs experimental data.
intermediate energies [14,16]. In this approach, one calculates the
photon production as a probability at each proton–neutron colli-
sion and then sum over all such collisions over the entire history
of the reaction. As discussed in detail earlier in Ref. [16], the cross
section for neutron–proton bremsstrahlung in the long-wavelength
limit separates into a product of the elastic pn scattering cross sec-
tion and a γ -production probability. The probability is often taken
from the semiclassical hard sphere collision model [14–16]. The
single differential probability reads
paγ ≡
dN
dεγ
= 1.55× 10−3 × 1
εγ
(
β2i + β2f
)
. (1)
Where εγ is energy of emitting photon, βi and β f are the initial
and ﬁnal velocities of the proton in the proton–neutron center of
mass frame. We notice that other expressions derived theoretically
involving more quantum-mechanical effects exist in the literature,
see, e.g., [24–28]. For a comparison we thus also use the prediction
of the one boson exchange model by Gan et al. [27]
pbγ ≡
dN
dεγ
= 2.1× 10−6 (1− y
2)α
y
, (2)
where y = εγ /Emax , α = 0.7319−0.5898βi , and Emax is the energy
available in the center of mass of the colliding proton–neutron
pairs. As noticed already in Ref. [27,13], the single differential
probabilities paγ and p
b
γ from the two models give quite simi-
lar but quantitatively different results especially near the kine-
matic limit where the photon production with paγ is signiﬁcantly
higher than that with pbγ . As discussed in the paper of Gan et
al. [27], compared with the result using the semiclassical expres-
sion, the quantum formula pbγ reduces proton production evidently
near the kinematic limit. While we are not aiming at reproduc-
ing any data in this exploratory work, it is necessary to ﬁrst
gauge the model by comparing with the available data. Shown
in Fig. 1 are the BUU calculations with both paγ and p
b
γ and the
experimental data for the inclusive cross sections of hard pho-
ton production in the reaction 12C + 12C [13]. It is seen that both
calculations are in reasonable agreements qualitatively with the
experimental data, especially at higher beam energies. The agree-
ment is at about the same level as previous calculations by others
in the literature [19,21,27]. It is noticed that the uncertainty in
the elementary pn → pnγ probability leads to an appreciable ef-
fect on the inclusive γ -production in heavy-ion reactions. From
Fig. 1, we can clearly see that the quantum formula pbγ seemsFig. 2. (Color online.) The ratio of hard photon spectra in the reactions of 12C+ 12C
and p + n at a beam energy of 140 MeV/nucleon with free and in-medium pn
scattering cross sections using paγ and p
b
γ , respectively.
more suitable for describing energetic photon production in in-
termediate energy heavy-ion reactions. It was noted that for nu-
clear bremsstrahlung, a strong suppression or coherence of the
bremsstrahlung cross section were observed in comparison with
predictions of transport models that include bremsstrahlung on the
basis of quasi-free nucleon–nucleon collisions [31,32]. In this study,
we use the BUU transport model [33] with an isospin-dependent
in-medium reduced nucleon–nucleon (NN) cross section [4,6] to
treat the in-medium bremsstrahlung semiclassically [34]. The en-
ergy and isospin dependent free-space NN cross sections σ freeNN are
taken from the experimental data. Another important input to the
transport model is the momentum- and isospin-dependent single
nucleon potential as given in Ref. [35]. The isoscalar part of the
single nucleon potential was shown to be in good agreement with
that of the variational many-body calculations and the results of
the Brueckner–Hartree–Fock approach including three-body forces
and the isovector potential is consistent with the experimental
Lane potential [36].
Since the energetic photons are produced in pn collisions, it is
quite obvious that pp or nn collisions do not inﬂuence the produc-
tion of photons. We can understand this way: (1) The studied hard
photon is produced via pn → pnγ , so it reﬂects pn scatterings di-
rectly. The nn or pp scatterings may affect pn scatterings, and then
affect hard photon production. But they are both secondary effects.
(2) The increased/decreased pp or nn cross sections may also in-
crease/decrease the collision number of protons and neutrons, thus
may increase/decrease the pn collision number. But, on the con-
trary, the larger/small pp or nn cross sections may reduce/enlarge
the collision number of proton with neutron (or neutron with pro-
ton). The secondary effects are thus cancelled out each other. We
in fact checked this deduction by BUU calculations and ﬁnd that
the hard photon production is really only sensitive to pn cross sec-
tion, while not sensitive to pp or nn cross sections.
To reduce uncertainties of the input elementary pn → pnγ
probability while using hard photon to probe in-medium pn
cross section, we provide Fig. 2, the ratio of hard photon spec-
tra in the reactions 12C + 12C and p + n at a beam energy of
140 MeV/nucleon. The spectra ratio R12C+12C/p+n(γ ) reads
R12C+12C/p+n(γ ) ≡
dN
dεγ
(12C+ 12C)
dN
dεγ
(p + n) . (3)
It is seen that the R12C+12C/p+n(γ ) is quite sensitive to the pn
scattering cross section while not sensitive to theoretical formu-
242 G.-C. Yong et al. / Physics Letters B 705 (2011) 240–243Fig. 3. (Color online.) The ratio of hard photon production cross sections of p +
12C and p + 2H reactions at a beam energy of 140 MeV/nucleon with different pn
scattering cross sections. Experimental data are taken from Ref. [21].
las used. This ratio reduces the uncertainties of the theoretical
elementary pn → pnγ probability maximally. The change of the
pn scattering cross section leads to R12C+12C/p+n(γ ) a sensitiv-
ity of about 60%. Like in many experiments searching for minute
but interesting effects, ratio of observables from two reactions
can often reduce not only the systematic errors but also some
unwanted effects. At least theoretically, the uncertainty of the γ -
production probability gets almost completely cancelled out in the
ratio of photon spectra here. From our BUU calculations, the de-
ﬁned quantity R12C+12C/p+n(γ ) does not dependents on the input
γ -production probability with a high credibility of 95%. Also in this
deﬁnition we assume input γ -production probability in matter is
the same as that in vacuum since photons interact with hadrons
only electromagnetically.
The photon production in 12C + 12C is determined by pn col-
liding number and the input elementary pn → pnγ probability,
the ratio R12C+12C/p+n(γ ) thus only depends on the pn collid-
ing number in the reaction 12C + 12C at certain energies. While
the pn colliding number in a reaction depends on the pn cross
section in matter. The spectra ratio R12C+12C/p+n(γ ) is therefore
a direct probe of the in-medium pn scattering cross section essen-
tially free of the uncertainties associated with both the elementary
photon production and the nn and pp scattering cross sections.
Compared with other probes of nucleon–nucleon scattering cross
sections, such as nuclear ﬂow and nuclear stopping, hard photon
production directly affects the pn scattering cross section. Practi-
cally, besides cosmic-radiation background, one needs to consider
photons from π0 and fragment decays in the data analysis [37].
While comparing with the experimental data, we ﬁnd that
there are few existing data to use. As a rough comparison, we
did simulations of proton induced reactions on 12C and 2H tar-
gets at a beam energy of 140 MeV/nucleon as shown in Fig. 3.
Here σp+12C/σp+2H reads
σp+12C/σp+2H =
∫ bmax
0
dN
dεγ
(p + 12C)2πbdb
∫ bmax
0
dN
dεγ
(p + 2H)2πbdb
, (4)
which in fact is the ratio of Rp+12C/p+2H(γ ) with different impact
parameters. In the calculations we use simple Fermi-momentum
as nucleonic momentum in deuteron and 12C. And we ﬁnd that
photon production cross section σp+2H is not sensitive to the dis-
tribution of nucleonic momentum in deuteron [38,39,21]. We also
assumed there is no medium effect on photon production fromp + 2H. The reference reaction p + 2H thus plays roughly the
same role as pn collision. We deﬁne the reduction factor Rd =
σmediumpn /σ
free
pn . From Fig. 3 we can see that the experimental data
are roughly within the range of Rd = 0.5 and 0.7 settings of our
model. This reduction scale is somewhat larger than the Brueckner
approach calculations [40–42]. Experimentally, heavy-ion collisions
with N ∼ Z nuclei (to cancel the effect of symmetry energy) of
symmetric system and p + n collision are more suitable to give
constraints on the in-medium pn scattering cross section by using
hard photon production.
In conclusions, we did an exploratory study about effect of the
pn scattering cross section on the production of hard photons from
intermediate energy heavy-ion reactions using a perturbative ap-
proach within the BUU transport model. The ratio of hard photon
spectra R12C+12C/p+n(γ ) is not only approximately independent of
the uncertainties of nn, pp cross sections and the theoretical ele-
mentary pn → pnγ probability, but also quite sensitive to the pn
scattering cross section. Compared with other probes of nucleon–
nucleon scattering cross sections, hard photons are completely free
of ﬁnal state strong interactions, directly reﬂect the magnitude pn
scattering cross section and are quite sensitive to the pn scattering
cross section. Through comparing with existing experimental data,
we obtain a reduction factor σmediumpn /σ
free
pn of about 0.5–0.7 around
saturation density. Heavy-ion collisions with N ∼ Z nuclei of sym-
metric system and p + n collision are needed to further constrain
the in-medium pn scattering cross section at different densities
and nucleonic momenta.
Acknowledgements
The author Gao-Chan Yong acknowledges Bao-An Li and Lie-
Wen Chen for the comments on the manuscript. The work is
supported by the National Natural Science Foundation of China
(10875151, 11175219, 10740420550), the Knowledge Innovation
Project (KJCX2-EW-N01) of Chinese Academy of Sciences, the Ma-
jor State Basic Research Developing Program of China under No.
2007CB815004, the CAS/SAFEA International Partnership Program
for Creative Research Teams (CXTD-J2005-1), and the National Nat-
ural Science Foundation of China under Grant Nos. 10975064,
11175074 and 11105035, the Zhejiang Provincial Natural Science
Foundation (Y6110644)
References
[1] J.M. Lattimer, M. Prakash, Science 304 (2004) 536.
[2] A.W. Steiner, M. Prakash, J.M. Lattimer, P.J. Ellis, Phys. Rep. 411 (2005) 325.
[3] B.A. Li, L.W. Chen, C.M. Ko, Phys. Rep. 464 (2008) 113;
V. Baran, M. Colonna, V. Greco, M. Di Toro, Phys. Rep. 410 (2005) 335.
[4] B.A. Li, L.W. Chen, Phys. Rev. C 72 (2005) 064611.
[5] G.C. Yong, Phys. Rev. C 81 (2010) 054603.
[6] G.C. Yong, Eur. Phys. J. A 46 (2010) 399.
[7] Y. Gao, L. Zhang, H.F. Zhang, X.M. Chen, G.C. Yong, Phys. Rev. C 83 (2011)
047602.
[8] G.C. Yong, Y. Gao, W. Zuo, X.C. Zhang, Phys. Rev. C 84 (2011) 034609.
[9] Q.F. Li, Z.X. Li, G.J. Mao, Phys. Rev. C 62 (2000) 014606.
[10] V. Prassa, G. Ferini, T. Gaitanos, H.H. Wolter, G.A. Lalazissis, M. Di Toro, Nucl.
Phys. A 789 (2007) 311.
[11] Y. Zhang, Z.X. Li, P. Danielewicz, Phys. Rev. C 75 (2007) 034615.
[12] C.J. Horowitz, J. Piekarewicz, Phys. Rev. Lett. 86 (2001) 5647;
C.J. Horowitz, J. Piekarewicz, Phys. Rev. C 66 (2002) 055803.
[13] G.C. Yong, B.A. Li, L.W. Chen, Phys. Lett. B 661 (2008) 82.
[14] G.F. Bertsch, S. Das Gupta, Phys. Rep. 160 (1988) 189.
[15] H. Nifenecker, J.A. Pinston, Annu. Rev. Nucl. Part. Sci. 40 (1990) 113.
[16] W. Cassing, V. Metag, U. Mosel, K. Niita, Phys. Rep. 188 (1990) 363.
[17] Y. Schutz, et al., TAPS Collaboration, Nucl. Phys. A 622 (1997) 404;
G. Martinez, et al., Phys. Lett. B 461 (1999) 28;
David d’Enterria, et al., Phys. Lett. B 538 (2002) 27;
R. Ortega, et al., Eur. Phys. J. A 28 (2006) 161.
[18] B.A. Remington, M. Blann, G.F. Bertsch, Phys. Rev. Lett. 57 (1986) 2909.
G.-C. Yong et al. / Physics Letters B 705 (2011) 240–243 243[19] Che Ming Ko, G.F. Bertsch, J. Aichelin, Phys. Rev. C 31 (1985) 2324(R).
[20] W. Cassing, T. Biro, U. Mosel, M. Tohyama, W. Bauer, Phys. Lett. B 181 (1986)
217.
[21] W. Bauer, G.F. Bertsch, W. Cassing, U. Mosel, Phys. Rev. C 34 (1986) 2127.
[22] J. Stevenson, et al., Phys. Rev. Lett. 57 (1986) 555.
[23] C.M. Ko, J. Aichelin, Phys. Rev. C 35 (1987) 1976.
[24] H. Nifenecker, J.P. Bondorf, Nucl. Phys. A 442 (1985) 478.
[25] K. Nakayama, G.F. Bertsch, Phys. Rev. C 34 (1986) 2190.
[26] M. Schäffer, T.S. Biro, W. Cassing, U. Mosel, H. Nifenecker, J.A. Pinstan, Z. Phys.
A 339 (1991) 391.
[27] N. Gan, et al., Phys. Rev. C 49 (1994) 298.
[28] R.G.E. Timmermans, T.D. Penninga, B.F. Gibson, M.K. Liou, Phys. Rev. C 73 (2006)
034006.
[29] Y. Safkan, et al., Phys. Rev. C 75 (2007) 031001(R).
[30] Y. Li, et al., Phys. Rev. C 77 (2008) 044001.[31] M.J. van Goethem, et al., Phys. Rev. Lett. 88 (2002) 122302.
[32] M. Hoefman, et al., Phys. Rev. Lett. 85 (2000) 1404.
[33] B.A. Li, C.B. Das, S. Das Gupta, C. Gale, Phys. Rev. C 69 (2004) 011603(R);
B.A. Li, C.B. Das, S. Das Gupta, C. Gale, Nucl. Phys. A 735 (2004) 563.
[34] T. Alm, et al., Phys. Rev. C 52 (1995) 1972.
[35] C.B. Das, S. Das Gupta, C. Gale, B.A. Li, Phys. Rev. C 67 (2003) 034611.
[36] G.C. Yong, Phys. Lett. B 700 (2011) 249.
[37] E. Grosse, et al., Eur. Phys. Lett. 2 (1986) 9.
[38] Xiangdong Ji, J. Engel, Phys. Rev. C 40 (1989) 497.
[39] Lie-Wen Chen, C.M. Ko, Bao-An Li, Nucl. Phys. A 729 (2003) 809.
[40] G.Q. Li, R. Machleidt, Phys. Rev. C 48 (1993) 1702.
[41] C. Fuchs, A. Faessler, M. El-Shabshiry, Phys. Rev. C 64 (2001) 024003.
[42] H.F. Zhang, Z.H. Li, U. Lombardo, P.Y. Luo, F. Sammarruca, W. Zuo, Phys. Rev.
C 76 (2007) 054001;
H.F. Zhang, U. Lombardo, W. Zuo, Phys. Rev. C 82 (2010) 015805.


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