Table Of ContentUnexpected neutron/proton ratio and isospin effect in low-energy antiproton induced
reactions
∗
Zhao-Qing Feng
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People’s Republic of China
(Dated: January 24, 2017)
Theinclusivespectraofpreequilibriumnucleonsproducedinlow-energyantiproton-nucleuscolli-
sionsarethoroughlyinvestigatedwithintheframeworkoftheLanzhouquantummoleculardynamics
modelforthefirsttime. Allpossiblereactionchannelssuchaselasticscattering,annihilation,charge
exchangeandinelasticscatteringinantibaryon-baryon,baryon-baryonandmeson-baryoncollisions
have been included in the transport model. The unexpected neutron/proton ratio in comparison
to the pion and proton induced reactions is caused from the isospin effects of pion-nucleon colli-
7 sions and the density dependence of symmetry energy. It is found that the π−-neutron collisions
1 enhance the neutron emission in the antiproton annihilation in a nucleus. Different to heavy-ion
0 collisions, the isospin effects are pronounced at the low kinetic energies. A soft symmetry energy
2 withthestiffnessofγs =0.5at subsaturation densitiesisconstrained from theavailable dataof the
neutron/proton spectra.
n
a PACS number(s): 25.43.+t, 24.10.-i, 21.65.Ef
J
3
2 Since the first evidence of antiprotons was found in K etc) induced reactions and to heavy-ion collisions, in
1955 at Berkeley in collisions of protons on copper at which the particles produced in the annihilation of the
]
the energy of 6.2 GeV by Chamberlain, Segr`e, Wiegand antiproton in a nucleus are coupled to the subsequent
h
t and Ypsilantis [1], the secondary beams of antiprotons collisions with surrounding nucleons. The dynamics of
-
l were produced at many laboratories, such as CERN, antiproton-nucleus collisions is complicated, which is as-
c
BNL, KEK etc [2–5]. The stochastic cooling method sociatedwith the mean-fieldpotentials ofhadronsin nu-
u
n provides the possibility for storing the antiprotons pro- clear medium, and also coupled to a number of reaction
[ ducedinproton-nucleuscollisions. TheparticlesW±and channels,i.e.,theannihilationchannels,charge-exchange
Z0 were found for the first time with the high energy reaction, elastic and inelastic collisions. There has been
1
v protons colliding the stored antiprotons at CERN [6]. several approaches for describing the nuclear dynamics
5 On the other hand, the antiproton-nucleus collisions are induced by antiprotons, e.g., the intranuclear cascade
0 motivated to many interesting issues, i.e., charmonium model [21], kinetic approach [22], Giessen Boltzmann-
3
physics, strangeness physics, antiprotonic atom, symme- Uehling-Uhlenbecktransportmodel[23],StatisticalMul-
6
try, in-medium properties of hadrons, cold quark-gluon tifragmentation Model [24] and the Lanzhou quantum
0
plasma, highly excited nucleus etc [7, 8]. Recently, the molecular dynamics (LQMD) approach [25]. Part of ex-
.
1
antiproton-antiprotoninteractionwasinvestigatedbythe perimental data can be understood within these models.
0
STARcollaborationinrelativisticheavy-ioncollisions[9]. A more localized energy is deposited in the nucleus
7
1 In the past decades, the nuclear reactions induced by with an excitation energy of several hundreds of MeV.
: antiprotons were investigated with the facilities of the Thehotnucleusproceedstotheexplosivedecayviamul-
v
low-energy antiproton ring (LEAR) at CERN [10], the tifragmentation process or the sequential particle evap-
i
X
National Laboratory for High Energy Physics at KEK oration. On the other hand, the collisions of the an-
r [11] and Brookhaven National Laboratory Alternating tiprotonandsecondaryparticleswithsurroundingnucle-
a
GradientSynchrotron(AGS) accelerator[12]. Anumber ons lead to the pre-equilibrium particle emissions, which
ofinterestingphenomenawereobserved,e.g.,thedelayed are related to the scattering cross sections of each re-
fission from the decay of hypernuclei in antiproton anni- actionchannels,antiproton-nucleoninteraction,particle-
hilations on heavy nuclei [13], unexpected enhancement nucleonpotentials,density profile oftargetnucleus. The
ofthe Λ/K0 ratio[14], decay mode of highly excited nu- unexpectedlargeneutronyieldsproducedbystoppedan-
S
cleus etc [15, 16]. The low-energy antiprotons usually tiprotons in nuclei were reported in the LEAR experi-
annihilate atthe nucleus surfacebecauseofthe largeab- ments [26,27]. Thephenomena hasbeenpuzzling physi-
sorption cross section. The huge annihilation energy are cists several decades [28].
availableforproducingthe 2-6pions[17,18]. Thesubse- In this letter, the preequilibrium nucleon emissions
quentprocessesarecomplicatedandalsoassociatedwith and the neutron/proton (n/p) spectra in antiproton
themultiplepion-nucleoninteraction,whichresultinthe induced nuclear reactions are investigated within the
fragmentation of target nucleus and the preequilibrium LQMD transport model. In the model, the dynam-
emissions of complex particles [19, 20]. ics of resonances with the mass below 2 GeV, hyper-
The dynamics of the antiproton-nucleus collisions is ons and mesons is coupled to the hadron-hadron colli-
more complicated in comparison to hadron (proton, π, sions, antibaryon-baryon annihilations, decays of reso-
2
nances [25, 29]. The temporal evolutions of all particles centroidof resonancemass, e.g.,1.232 GeV for ∆(1232).
are described by Hamilton’s equations of motion under Themaximumcrosssectionσ istakenfromfittingthe
max
theself-consistentlygeneratedmean-fieldpotentials. The availableexperimentaldataandsatisfiedtothesquareof
Hamiltonianofnucleonsandnucleonicresonancesiscon- Clebsch-Gordan coefficients [34], i.e., 200 mb, 133.3 mb,
structedfromtheSkyrmeenergy-densityfunctional. Dy- and 66.7 mb for π+ + p ∆++, π0 + p ∆+ and
namicsofhyperons,anti-baryonsandmesonsisdescribed π−+p ∆0, respectively.→ →
→
with the effective interactions based on the relativistic The emission of fast nucleons produced in antiproton
covariant theories. inducedreactionsissignificantobservableinunderstand-
The interaction potential of nucleonic system is eval- ingtheenergydeposition,antiproton-nucleonandmeson-
uated from the energy-density functional of Uloc = nucleon interactions in nuclear medium. Shown in Fig.
R Vloc(ρ(r))dr with 1 is the kinetic energy distributions ofneutrons andpro-
αρ2 β ρ1+γ tons produced in antiprotonannihilations on 12C, natCu
Vloc(ρ)=2 ρ0 + 1+γ ργ0 +Esloycm(ρ)ρδ2 caonmdp2a38rUedawtitthhethineciadveanitlambloemdeanttaumatothfe20L0EMAeRVf/accialintdy
+gsur( ρ)2+ gsisuor[ (ρ ρ )]2, (1) [27]. Overall,thespectracanbenicelyunderstoodwithin
n p
2ρ0 ∇ 2ρ0 ∇ − the LQMD transport model. The free nucleons in the
where the ρ , ρ and ρ = ρ + ρ are the neutron, model are constructed with a coalescence approach, in
n p n p
proton and total densities, respectively, and the δ = whichnucleonsatthe freeze-outstageinphasespaceare
(ρ ρ )/(ρ +ρ )beingtheisospinasymmetryofbary- consideredto belong to one cluster with the relative mo-
n p n p
onic−matter. Theparametersα,β andγ aretakentobe- mentum smaller than P0 and with the relative distance
226.5MeV,173.7MeVand1.309,respectively. Thesetof smaller thanR0 (here P0 = 200 MeV/c and R0 = 3 fm).
theparametersgivesthecompressionmodulusofK=230 The nucleon yields are weakly influenced by varying the
MeV for isospin symmetric nuclear matter at the satu- coalescenceparameters. The antiproton-nucleussystems
ration density (ρ0 =0.16 fm−3). The surface coefficients evolveto500fm/cforjudgingthefreenucleonformation.
g and giso are taken to be 23 MeV fm2 and -2.7 MeV It should be noticed that the neutrons are preferable to
sur sur
fm2, respectively. The third term contributes the sym- be emitted in comparison to protons. The energy de-
metry energy being of the form Esloycm = 12Csym(ρ/ρ0)γs. position in antiproton induced reactions is more explo-
The parameter C is taken as the value of 38 MeV. sive than the case in Fermi-energy heavy-ion collisions
sym
The γ could be adjusted to get the suitable case from [35, 36], which leads to the energetic nucleon emission.
s
constraining the isospin observables, e.g., the values of In the annihilation of an antiproton in a nucleus, pions
0.5, 1 and 2 being the soft, linear and hard symme- are the dominant products. For example, the multiplic-
try energy, respectively. Combined the kinetic energy ities of π− and π+ on the target of 12C are 1.5 and 0.6,
fromtheisospindifferenceofnucleonicFermimotion,the respectively. On the other hand, the larger elastic scat-
threekindscrossatthesaturationdensitywiththevalue tering cross sections in the π−n reactions (the maximal
of 31.5 MeV. The mean-field potential of antinucleon is value being 200 mb at the ∆-resonance energy (E=0.19
constructedfromthe G-paritytransformationofnucleon GeV, p=0.298 GeV/c)) in comparison to the π−p colli-
self-energieswithascalingapproach[25,30],whichleads sions (25 mb at the pion energy of 0.19 GeV), enhance
to the strength of optical potential V = 164 MeV at the π−n collision probabilities and are favorable to neu-
the normal nuclear density. N − tron emissions in the low-energy antiproton induced re-
The annihilation reactions in antibaryon-baryon col- actions even on the isospin symmetric target of 12C. For
lisions are described by a statistical model with SU(3) the neutron-rich target such as 238U, the difference of
symmetry of pseudoscalarand vectormesons [31], which neutron and proton yields is more pronounced.
considerspossible combinationswith the finalstate from The ratio spectra of the isospin particles produced in
two to six mesons [32]. Pions as the dominant products heavy-ion collisions are related to the isospin dependent
in antibaryon-baryonannihilation contribute the energy crosssectionsandinteractionpotentials[29,37,38]. The
deposition into the target nucleus via the pion-nucleon kinetic energy distributions of the n/p ratio and double
collisions,whichleadstotheemissionsofpre-equilibrium n/pratioinisotopicnuclearreactionshavebeenusedfor
particles, fission, evaporation of nucleons and light frag- constrainingthedensitydependenceofsymmetryenergy.
ments etc. The cross section of pion-nucleon scattering Theyieldratiosofneutronsandprotonsarecomplicated
is evaluated with the Breit-Wigner formula as the form in the low-energy antiproton induced reactions, which
of [33] are related to the antiproton-nucleon scattering, annihi-
lation in antinucleon-nucleoncollisions and pion-nucleon
0.25Γ2(p)
σπN→R(√s)=σmax|p0/p|20.25Γ2(p)+(√s m0)2(,2) spcioantt-earinndg.proAtlotnh-onuugchleuthsecoelxlipsieornimswenetraelnnic/eplysepxepcltarianeind
−
where the p and p are the momenta of pions at the by the intranuclear cascade model [28]. The kinetic en-
0
energies of √s and m0, respectively, and m0 being the ergy spectra of the n/p ratio in antiproton induced re-
3
10-1 12C (a) 100 natCu (b) 100 238U (c)
neutron (LEAR data) -1 -1
-2 pnreouttoron n ((LcaElA.)R data) 10 10
n10 proton (cal.)
ki
E -2 -2
10 10
d -3
N/ 10
-3 -3
d 10 10
-4
10 -4 -4
10 10
-5 -5 -5
10 10 10
0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500
E (MeV)
kin
FIG.1. (coloronline). Kineticenergyspectraofneutronsandprotonsproducedinantiprotonannihilationsoncarbon,copper
and uranium at theincident momentum of 200 MeV/c and compared with theavailable data at theLEAR facility [27].
150MeV.Thesymmetryenergyfurtherincreasesthen/p
ratio because of its repulsive contribution to neutrons in
theneutron-richmatter. Boththepion-nucleoncollisions
and the symmetry energy dominate the n/p spectra.
2
p) The stiffness of symmetry energy impacts the isospin
Y( dynamics in heavy-ion collisions. However, the nuclear
n)/ density of isospin particle emissions varies in the evolu-
Y(
tion of nucleus-nucleus collisions. On the other hand,
1
the rotationofcolliding systemcomplicatesthe emission
LEAR data
w/o N coll. and w/o symm. angles of isospin particles. The low-energy antiproton is
with N coll. and w/o symm. annihilatedonthesurfaceofthetargetnucleus,inwhich
full cal. the nucleons are emitted around the density of 0.1 fm−3
0 after interacting with pions. The n/p ratio directly pro-
0 100 200 300 400
vides the symmetry energy informationatsubsaturation
Ekin (MeV) densities. Shown in Fig. 3 is the kinetic energy spectra
nat
FIG. 2. (color online). Impacts of πN absorption and sym- in antiproton induced reactions on 12C, Cu, 197Au
metryenergyontheyieldratiosofneutronstoprotonsinthe and 238U with the soft (γs =0.5) and hard (γs =2) sym-
p+65Cu reaction at 200 MeV/c and the experimental data metry energies, respectively. The dashed lines represent
nat
with thestopped p on Cu [27]. the mean n/p values of target nuclei. Calculations are
performedattheantiprotonmomentumof200MeV/c. I
have checked that the spectra are insensitive to the inci-
actions can not be understood by the model. The n/p dent energy. It is obvious that the difference of the stiff-
ratio in antiproton-nucleus collisions is further investi- ness of symmetry energy is pronounced in the neutron-
gated within the LQMD transport model, in which the richnuclei. Then/pratioisenhancedwithsofteningthe
isospin effects associated with the pion and nucleon dy- symmetry energy. Overall, the available data at LEAR
namics are treated self-consistently. The yield ratios of [27] are reproduced with the soft symmetry energy. Dif-
neutrons and protons produced in the p+65Cu collisions ferentwiththeFermi-energyheavy-ioncollisions[36],the
at the incident momentum of 200 MeV/c are strongly isospin effect appears at the kinetic energies below 200
constrained by the pion-nucleon collisions and symme- MeV. The kinetic energy spectra of the n/p ratio in the
try energy as shown in Fig. 2. Here, the linear sym- antiproton induced reactions is expected to be further
metry energy with γ =1 is chosen. Pions as the domi- measuredatPANDA(AntiprotonAnnihilationatDarm-
s
nantproductsintheantiprotonannihilationinanucleus, stadt, Germany) in the near future experiments.
contribute the nucleon removal from the target nucleus Inconclusion,thekineticenergyspectraofthen/pra-
[39]. Aflatn/pspectrumappearsonceremovedthepion- tioproducedintheantiprotonannihilationinthenucleus
nucleon collisions and is close to the mean value (1.24) have been puzzling for several decades. The structure
of targetnucleus. The nπ− scattering enhances the neu- is quite different with the proton (pion) induced reac-
tron emission, in particular at the kinetic energies below tions and also with the heavy-ion collisions. The avail-
4
3
12 (a) 197 (b)
C Au
4
LEAR data
asy-soft
2 asy-hard
2
) )
p p
( 1 (
Y Y
/ /
) )
n n 0
( (
Y nat Y 238
Cu 4 U
2
2
1
0 0
0 100 200 300 400 500 0 100 200 300 400 500
E (MeV) E (MeV)
kin kin
nat
FIG. 3. (color online). The n/p ratios in antiproton induced reactions on 12C, Cu, 197Au and 238U with different stiffness
of symmetry energies and compared with theLEAR data [27].
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