Dependence from target’s atomic mass of the cross section
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1 A.Litvinenko 1 Dependence from target’s atomic mass of the cross section of deuterons fragmentation into cumulative and twice-cumulative pions A.Litvinenko , E. Litvinenko LHEP JINR [email protected]
description
Dependence from target’s atomic mass of the cross section of deuterons fragmentation into cumulative and twice-cumulative pions. A.Litvinenko , E . Litvinenko LHEP JINR [email protected]. 1. Outline Introduction d efinition s motivation S imulation structure - PowerPoint PPT Presentation
Transcript of Dependence from target’s atomic mass of the cross section
1A.Litvinenko 1
Dependence from target’s atomic mass of the cross section
of deuterons fragmentation into cumulative and twice-cumulative pions
A.Litvinenko , E. LitvinenkoLHEP JINR
2A.Litvinenko 2
OutlineOutlineIntroduction
definitionsmotivation
Simulationstructure contribution of the various mechanisms
Results for cumulative pionscomparison with experimental datapredictions
Simulation for twice-cumulative pions Results for twice-cumulative pions Conlusions
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Cumulative particle(с) defenition
1. subthreshold
XcAB Xcpp
2. Produced in the fragmentation region of one of the primary particles |YY||YY|
cBcA
2|YY|AB
GeV54Tb
Colliding particles are included in the definition of asymmetric!
}p,{EP ccc
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Target fragmentation
beam target
cum. part.
Beam fragmentation
beam target
cum. part.
X
X
+
+
Geometry
Colliding particles are included in the definition of asymmetric!
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Not fragmenting nucleus
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measured effect
Dependence from the atomic mass of the colliding nuclei
fragmenting nucleus
Colliding particles are included in the definition of asymmetric!
θ),f(XA~dσ cnt
V.K.Bondarev et al., JINR Rapid Comm., No.4,4, (1984) Yu.S.Anisimov at al., Nucl.Phys., 60, 1070,
(1997).
)(0πAD O-t
)(180πAp O-t
0.4tA~dσ 1.1
tA~dσ
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Experimental data
)π(0Pb)Cu,(C,AC)He,D,( Ot
4
Pb Cu, C,A ; AC pd
dσE t
nt3
L.Anderson et al., Phys.Rev.C, C28, 1224, (1983).
)p(0Pb)Cu,(C,AC)He,D,( Ot
4
E.Moeller et al., Phys.Rev.C, C28, 1246, (1983).
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hot flucton
Models of cumulative particles production
cold flucton
CC
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Simulation(structure)
INITIAL STATATEcoordinates of the nucleons
Beam nuclei
Target nuclei
PRODUCTION+
RESCATERING Of HADRONS
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INITIAL STATATEcoordinates 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
10
INITIAL STATATEcoordinates 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 STATATEcoordinates of the nucleons
Barlet R.C., Jakson D.F.Nuclea Sizes and StructureN.Y.: Oxford Univ.Press., (1997)
12A t
3/11/3- )16.11(16.1
; 54.0
)/)exp((1)(
AAR
fmd
dRr
NmrP
A
A
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Scattered particles == particles from entering the cylinder
fm 197.1 Rmb; 45 NNNN
fm 977.0R mb; 30 NN
)10/()(R mb
S.G. Mashnik et al., nucl-th/0210065v2.
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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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--probability of the deuteron scatter
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Simulation of the pion production
)0(ND Ot
)(0AD Ot
DW
-- probability of pion leave the target without scattering
)p(W
«direct» mechanism
dbb)b(W)b(Wn)NN( ~ d DNc
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Pions production
«direct» mechanism
b
L
RR
fm 3.4L
fm 4.2
fm 1
L
d
d
22 )2/(LRb
16
fm 4.4)2/L(Rb 22
fm 9.6)2/L(Rb 22
Pions production
«direct» mechanism
C
Cu
Pb
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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 «cascads»
2O
t
1t
X)0(pNp~
Xp~ND
2O
t
1t
X)0(pN~
X~ND
%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 was discussed. The simulation, based on the nucleon-nucleon scattering gives a gooddescription of the experimental data on the dependence of the cross-section from atomic mass of the target.
The contribution of cascade mechanisms was studied. It was shown that even for the heaviest nuclei, this contribution does not exceed one percent.
Conclusions
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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
kp int
2intNND |pd(...)f|d
minint )p( minint )p(
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Twice-cumulative region
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221NN2D1D |kdkd(...)f)k()k(|d
Impulse approximation for pion productionin deuteron deuteron scattering
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Non cumulative region
Cumulative region
Twice-cumulative region
minint,2 )k(
minint,1 )k(
minint,1 )k(
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Blokhintsev D.I., JETF (RUS), 33, 1295, (1957 ) :
«flucton – two (or greate) nucleon 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 twice cumulative pions
cumulative ~ density of nucleon
Nn
twice cumulative ~ density of fluctons Fn
221NN2D1D |kdkd(...)f)k()k(|d
dbb)b(W)b( Wn)NN( ~ d DNc
dbb)b(W)b( Wn)FN( ~ d DFcc
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for simulation one needs model needs a model of flucton
Next part of report.Volume model of flucton will be usedA.M.Baldin, PEPAN, 8(3), 429, (1977)
0
221
2ctt2
ct1
A drr))r(p2)r(p(4
))r(pV)(2/)1A(A(C p
)r(pVCAp
fm 7R
fm 9.0r
Au
c
3Au
3c
fm 400 1 R
fm 3V
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Dependence of the cross section from atomic mass of targetnuclei in cumulative and twice cumulative
(volume model of flucton )
)0(AD t
- twice cumulative
simulation
-cumulative
exp. data (cum) Yu.S.Anisimov at al., Nucl.Phys., 60, 1070, (1997).
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Dependence of the cross section from atomic mass of targetnuclei in cumulative and twice cumulative
(volume model of flucton )
)0(AD t
Pb Cu, C, A; AC pd
dσE t
nt3
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Conclusions
The reaction of the fragmentation of the incident deuterons into twice cumulative pions on targets with different atomic was discussed. The simulation, based on the nucleon-nucleon scattering shows that cross section dependence from atomic mass is sensitive to the model of flucton.
The simulation with volume model of flucton was performed. From this simulaion was obtained that dependence from target anomic mass in twice cumulative region is more stronger than in cumulative region.
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Backup Slides
3333
Cumulative number (Scale variable)
)N/GeV(PB
)N/GeV(PXAc
CP
} XP
minP2
X
2Nttb
2b
Cm)PP()PP(
2/m)PP(X
346 March 2006 34
Cumulative number (Scale variable)
3535
)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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Independence of the cross section behavior from cumulative particle
p
+π
+K
K
3737
Independence from initial energy.
30-40 %
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Independence from fragmenting nuclei
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пионы
Ю.С.Анисимов и др., ЯФ, 60, 1070, (1997).
V.K.Bondarev et al., JINR Communication,E1-93-84,Dubna, (1993). )GeV,120 p(0.5CGeV/(cN)) 5.4)(,D,B(p, O4 CHe )GeV,3 p(4.6),,,(GeV/(cN)) 5.4( O4 CHeDpC
4040
Theory
2.0pint
)c/GeV(p/2.0~.)фм(l
intNN
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 twice cumulative pions
dbb)b(W)b()Wn( ~ d DNc
dbb)b(W)b()Wn( ~ d DFc
cumulative ~ density of nucleon
Nn
twice cumulative ~ density of fluctons Fn
221NN2D1D |kdkd(...)f)k()k(|d
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PbCu,C,H,A ; pd
dσE t3
)π(0Pb)Cu,C,(H,AD Ot
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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ДУАЛИЗМ – HOW IT IS LOOKS LIKE
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