Post on 03-Mar-2020
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Simulation of the reaction of deuteron fragmentation into cumulative and double
cumulative pions
A.G. Litvinenko1, 2, E.I. Litvinenko1
alitvin@jinr.ru
1. Joint Institute for Nuclear Research, Dubna, Russia,
2. Dubna University, Dubna, Russia
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Outline Introduction
definitions motivation
Simulation structure contribution of the various mechanisms
Results for cumulative pions comparison with experimental data conclusion I
Simulation for double cumulative pions results conclusion II
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Cumulative particle (с) definition
1. subthreshold
XcAB Xcpp
2. Produced in the fragmentation region of one of the primary particles
|YY||YY| cBcA
2|YY| AB N/GeV54Tb
Colliding particles are included in the definition asymmetrically!
}p,{EP ccc
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Target fragmentation
beam target
cum. part.
Beam fragmentation
beam targetcum. part.
X
X
+
+
Geometry
Colliding particles are included in the definition of asymmetric!
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Cumulative region (beam fragmentation)
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Not fragmenting nucleus
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observed effect
Dependence from the atomic mass of the colliding nuclei
fragmenting nucleus
Colliding particles are included in the definition asymmetrically
θ),f(XA~dσ c
n
t
V.K.Bondarev et al., JINR Rapid Comm., No.4,4, (1984)Yu.S.Anisimov at al., Nucl.Phys., 60, 1070, (1997).
)(0πADO-
t )(180πAp
O-
t
0.4
tA~dσ 1.1
tA~dσ
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Experimental data
)π(0Pb)Cu,(C,AC)He,D,( O
t
4
Pb Cu, C,A ; AC pd
dσE t
n
t3
L.Anderson et al., Phys.Rev.C, C28, 1224, (1983).
)p(0Pb)Cu,(C,AC)He,D,( O
t
4
E.Moeller et al., Phys.Rev.C, C28, 1246, (1983).
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PbCu,C,H,A ; pd
dσE t3
)π(0Pb)Cu,C,(H,AGeV/N) D(4.5 Ot
tA
CX
Yu.S.Anisimov at al., Nucl.Phys., 60,1070,(1997).
Experimental data
4.0tA
75.0tA
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hot flucton
Models of cumulative particles production
cold flucton
CC
A.V. Efremov, PEPAN, V.13(3), 613, (1982)
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Motivation of the simulation of cumulative particle production
“How relate the experimental data and the models with cold flucton?”
?
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Simulation(structure)
INITIAL STATEcoordinates of the nucleons
Beam nuclei Target nuclei
PRODUCTION
+
RESCATERING
OF HADRONS
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INITIAL STATEcoordinates of the nucleons
DEUTERONHulthen DWF
M.Sagavara L.Hulthen. Handb. Phys., 39, 1, (1957).
11
2
181 ,2280
)r
b)r)-(aexp(2--2br)exp()-2arexp((
)(2
)()(
-- fm.b fm.a
ba
baabrP
D
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INITIAL STATEcoordinates of the nucleons
Barlet R.C., Jakson D.F.Nuclea Sizes and StructureN.Y.: Oxford Univ.Press., (1997)He4
fmd
drd
rP
7.1
)/-exp(4
)( 22
3
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INITIAL STATEcoordinates of the nucleons
Barlet R.C., Jakson D.F.Nuclea Sizes and StructureN.Y.: Oxford Univ.Press., (1997)
12A t
3/11/3-
A
A
A)A16.11(16.1R
;fm 54.0d
)d/)Rrexp((1
N)r(P
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Scattered particles == inside of the cylinder was another particle
fm 197.1 Rmb; 45 NNNN fm 977.0R mb; 30 NN ;)10/()mb(R
S.G. Mashnik et al., nucl-th/0210065v2.
or Nor N
tN
tN
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Simulation of inelastic deuteron-nuclei cross section
A.Auce and et al., Phys.Rev.C, C53, 2919, (1996).
open circles –experimental data
closed circles – simulated data
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Simulation of the pion production
)0(ND Ot
)(0AD Ot
])z,[,b(WD
- probability that pion leave the target without scattering]),z[,b(W
«direct» mechanism
dbdzb]),z[,b(W])z,[,b(Wz)(b,n)NN( ~ d DNc
- probability deuteron reach a point with coordinates }z,b{
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Pions production
«direct» mechanism
fm 3.4L
fm 4.2
fm 1
L
d
d
22 )2/(LRb
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fm 4.4)2/L(Rb 22
fm 9.6)2/L(Rb 22
Pions production
«direct» mechanismC
Cu
Pb
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fm 1.2)2/L(Rb 22
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experiment vs theory
X)3(AC ot
V.K.Bondarev at al.,JINR Communication, E93-84, (1984)
X)0(AD ot
Yu.S.Anisimov at al., Nucl.Phys.,
60, 1070, (1997).
Simulation
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Pions production
2 «cascades»
2t
1
)0(Np~
~
X
XpND
O
t
2t
1
)0(N~
~
X
XND
O
t
%1direct
1#cascade %5.0
direct
2#cascade
- direct
- cascades (#1+#2) x 100
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The reaction of the fragmentation of the incident deuterons into cumulative pions on targets with different atomic mass was discussed. The simulation based on the hadron- hadron scattering gives a good description of the experimental data on the dependence of the cross-section from atomic mass of the target.
The contribution of the cascade mechanism was studied. It was shown that even for the heaviest nuclei this contribution does not exceed one percent.
Conclusion I
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Cumulative region
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Impulse approximation for pion productionin deuteron proton scattering
2intNND |pd(...)f|d
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Integration over internal momentum
kpint
2intNND |pd(...)f|d
minint )p( minint )p(
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Double cumulative region
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Double cumulative region
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2
21NN2D1D |kdkd(...)f)k()k(|d
Impulse approximation for pion productionin deuteron deuteron scattering
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Cumulative region
Double cumulative region
minint,2 )k(
minint,1 )k(
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minint,1 )k(
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Blokhintsev D.I., JETF (RUS), 33, 1295, (1957 ) :
«flucton – two (or more) nucleons at short distance»
c/GeV 2.0k fm; 1 l
)c/GeV(0.2/k )fm(l
intNN
intNN
short distance high internal momentum
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Simulation.Difference between production of cumulative and
double cumulative pions
cumulative ~ density of nucleonN
n
double cumulative ~ density of fluctons Fn
dbdzb]),z[,b(W])z,[,b(W )z,b(n )NN( ~ d DNc
dbdzb]),z[,b(W])z,[,b(W )z,b(n )FN( ~ d DFcd
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for simulation one needs a model of flucton
Volume model of flucton A.M.Baldin, PEPAN, 8(3), 429, (1977)
fm 7R
fm 8.0R
Au
f
3Au
3f
fm 400 1 V
fm 1.2V
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Tube model of fluconBerlad G., Dar A., and Eilam G., Phys.Rev., D13, 161, (1976)
fm 7R
fm 2 Lfm, 8.0R
Au
f
3Au
3f
fm 400 1 V
fm 0.4V
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Dependence of the cross section from atomic mass of target nuclei in cumulative and double cumulative pions (volume and tube model of fluctons )
exp. data (cum) Yu.S.Anisimov at al., Nucl.Phys.,
60, 1070, (1997).
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)0(AD t
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Dependence of the cross section from atomic mass of targetnuclei in cumulative and double cumulative
(volume model of flucton )
)0(AD t Pb Cu, C, A; AC pd
dσE t
n
t3
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Conclusion II
The reaction of the fragmentation of the incidentdeuterons into double cumulative pions on targets withdifferent atomic mass was discussed. The simulationbased on the hadron- hadron scattering shows thatcross section dependence from atomic mass is sensitive tothe model of flucton.
The simulation with volume and tube models of fluctonwas performed. From this simulation it was obtained thatdependence from the target atomic mass in the doublecumulative region is much stronger than in the cumulativeregion.
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Backup Slides
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Cumulative number (Scale variable)
)N/GeV(PB
)N/GeV(PXAc
CP
} XP
minP2
X
2Nttb
2b
Cm)PP()PP(
2/m)PP(X
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Cumulative number (Scale variable)
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)X/Xexp(~d0c
Скейлинг (Суперскейлинг? ):
Независимость от начальной энергии;
Независимость от типа детектируемой (кумулятивной) частицы;
Независимость от типа налетающей частицы;
Независимость от ядра мишени для средних и тяжелых ядер;
GeV4005EB
d,p,K,c
Налетающие частицы: лептоны, мезоны, ядра
Ядра мишени: дейтрон - свинец
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)X/Xexp(~d0c
Scaling (Superscaling ):(For brevity, it is assumed target fragmentation)
Independence from the initial energy Independence from the detected (cumulative) of the particle Independence from the incident particle Independence from the target nucleus for medium and heavy nuclei
GeV4005EB
d,p,K,c
incident particle : leptons, mesons, nuclei
targets: D - … - Pb
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Independence of the cross section behavior from cumulative particle
p
+π
+K
K
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Independence from initial energy.
30-40 %
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Independence from fragmenting nuclei
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V.K.Bondarev et al., JINR Communication,E1-93-84,Dubna, (1993).
)GeV,120 (0.5CGeV/(cN)) 5.4)(C,HeD,B(p, O4 )GeV,3 (4.6)C,He,D,p(GeV/(cN)) 5.4(C O4
Yu.S.Anisimov at al., Nucl.Phys., 60, 1070, (1997).
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Theory
2.0pint
)c/GeV(p/2.0~.)фм(lintNN
Non nucleon degrees of freedoms
Empirical approaches
);q6( );NN(**
);( ...);q9(
)q(F~dq
.фм1lNN
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Simulation.Difference between production of cumulative
and double cumulative pions
dbb)b(W)b()Wn( ~ d DNc
dbb)b(W)b()Wn( ~ d DFc
cumulative ~ density of nucleon Nn
double cumulative ~ density of fluctons Fn
2
21NN2D1D |kdkd(...)f)k()k(|d
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PbCu,C,H,A ; pd
dσE t3
)π(0Pb)Cu,C,(H,AD O
t
tA
CX
Yu.S.Anisimov at al., Nucl.Phys., 60, 1070, (1997).
A.G.Litvinenko, A.I.Malakhov,P.I.Zarubin,JINR Rapid Communication №1(58) ,27,(1993)
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X),N(N),N( t
E
pd
pd
dEtot
20)P-(P t);texp(C
pd
dE
XNN t
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duality– HOW IT IS LOOKS LIKE
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