Dependence from target’s atomic mass of the cross section

transcript

1A.Litvinenko 1

of deuterons fragmentation into cumulative and twice-cumulative pions

A.Litvinenko , E. LitvinenkoLHEP JINR

litvin@moonhe.jinr.ru

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

3A.Litvinenko 3

Cumulative particle(с) defenition

1. subthreshold

XcAB Xcpp

2. Produced in the fragmentation region of one of the primary particles |YY||YY|

2|YY|AB

GeV54Tb

Colliding particles are included in the definition of asymmetric!

}p,{EP ccc

4A.Litvinenko 4

Target fragmentation

beam target

cum. part.

Beam fragmentation

beam target

cum. part.

Geometry

Not fragmenting nucleus

A.Litvinenko 5

measured effect

Dependence from the atomic mass of the colliding nuclei

fragmenting nucleus

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

6A.Litvinenko 6

Experimental data

)π(0Pb)Cu,(C,AC)He,D,( Ot

Pb Cu, C,A ; AC pd

dσE t

L.Anderson et al., Phys.Rev.C, C28, 1224, (1983).

)p(0Pb)Cu,(C,AC)He,D,( Ot

E.Moeller et al., Phys.Rev.C, C28, 1246, (1983).

7A.Litvinenko 7

hot flucton

Models of cumulative particles production

cold flucton

Simulation(structure)

INITIAL STATATEcoordinates of the nucleons

Beam nuclei

Target nuclei

PRODUCTION+

RESCATERING Of HADRONS

DEUTERONHulthen DWF

M.Sagavara L.Hulthen. Handb. Phys., 39, 1, (1957).

181 ,2280

b)r)-(aexp(2--2br)exp()-2arexp((

-- fm.b fm.a

baabrP

INITIAL STATATEcoordinates of the

nucleons

Barlet R.C., Jakson D.F.Nuclea Sizes and StructureN.Y.: Oxford Univ.Press., (1997)He4

)/-exp(4

Barlet R.C., Jakson D.F.Nuclea Sizes and StructureN.Y.: Oxford Univ.Press., (1997)

3/11/3- )16.11(16.1

; 54.0

)/)exp((1)(

12A.Litvinenko 12

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.

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

--probability of the deuteron scatter

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Simulation of the pion production

)0(ND Ot

)(0AD Ot

-- probability of pion leave the target without scattering

«direct» mechanism

dbb)b(W)b(Wn)NN( ~ d DNc

Pions production

fm 3.4L

fm 4.2

22 )2/(LRb

fm 4.4)2/L(Rb 22

fm 9.6)2/L(Rb 22

Pions production

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»

X)0(pNp~

X)0(pN~

%1direct

1#cascade %5.0

direct

2#cascade

- direct

- cascades (#1+#2) x 100

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

Cumulative region

Impulse approximation for pion productionin deuteron proton scattering

2intNND |pd(...)f|d

Integration over internal momentum

kp int

2intNND |pd(...)f|d

minint )p( minint )p(

Twice-cumulative region

221NN2D1D |kdkd(...)f)k()k(|d

Impulse approximation for pion productionin deuteron deuteron scattering

Non cumulative region

Cumulative region

Twice-cumulative region

minint,2 )k(

minint,1 )k(

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

short distance

high internal momentum

Simulation.Difference between production of cumulative

and twice cumulative pions

cumulative ~ density of nucleon

twice cumulative ~ density of fluctons Fn

dbb)b(W)b( Wn)NN( ~ d DNc

dbb)b(W)b( Wn)FN( ~ d DFcc

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)

A drr))r(p2)r(p(4

))r(pV)(2/)1A(A(C p

)r(pVCAp

fm 9.0r

fm 400 1 R

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).

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

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

Cumulative number (Scale variable)

)N/GeV(PB

)N/GeV(PXAc

Cm)PP()PP(

2/m)PP(X

346 March 2006 34

Cumulative number (Scale variable)

)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

Independence of the cross section behavior from cumulative particle

Independence from initial energy.

30-40 %

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

Theory

2.0pint

)c/GeV(p/2.0~.)фм(l

Non nucleon degrees of freedoms

Empirical approaches

);q6( );NN( ** );( ...);q9(

)q(F~dq

.фм1lNN

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

twice cumulative ~ density of fluctons Fn

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PbCu,C,H,A ; pd

dσE t3

)π(0Pb)Cu,C,(H,AD Ot

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)

ДУАЛИЗМ – HOW IT IS LOOKS LIKE

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Dependence from target’s atomic mass of the cross section

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