1A.Litvinenko 1

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!

5

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

16

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{

18

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

22

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

33

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

34

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

386 March 2006 38

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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