Selected Problems of Relativistic

Nuclear Physics and Multiple

Particle Production

A.I.MalakhovJoint Institute for Nuclear Research, Dubna

XXXII International Symposium onMultiparticle Dynamics,

Alushta, 7-13 September 2002

It is possible to obtain the record high energy particle beams by means of accelerating the heavy nuclei with large charges

January 1, 1971

I + II 1 + ... More than one nucleon of nucleus I takes part in the interaction (A.M.Baldin)

The value NI = AI , the effective number of nucleons inside nucleus I participating in the collisions, is called the cumulative number

0 NI AI

Cumulative region NI > 1

d(d + Cu -+ …)(x) = d(p + Cu - + …)

max

x = p / p

e

Dependence of T0 parameter for pion at 180o for p-Cu collisions on the energy of incident proton Tp. Pion cross-section parameterized by the form E·d/dp3 = C·exp(-T/T0), where T is the pion laboratory kinetic energy

L.S.Schroeder et al. Phys. Rev. Lett., v.43, No.24, 1979, p.1787

I+II 1+2+3+…

bik = - (ui - uk)2

ui = pi /mi

uk = pk/mk

i, k = I, II, 1, 2, 3, …

Classification of Relativistic Nuclear Collisions on bik

bik ~ 10-2

classic nuclear physics

0.1 bik < 1

intermediate domain

bik >> 1

nuclei should be considered asquark-gluon systems

Quarks in nuclei The Problem - explanation of nuclear forces using fundamental chromodynamic forces between color quarks and gluons

New task – search for manifestation of quark degrees of freedom in nuclei (“hidden color”)

12 – quarks Experiments with relativistic nuclei in Dubna Relativistic Nuclear Physics (1971) – new domain of research in Baldin junction of Nuclear Physics and Particle Physics Study of quark-gluon structure of atomic nuclei.

The experiments show the following dependence for cross-sections of all nuclei from He up to U:

(AI AII h1 + …) = k·AIn

·AIIm(x)·exp(-x/<x>)

bI 1 > bI II >> 1

0.5 x 3.3(Cumulative effect: x > 1)

m(x) = 2/3 + x (0.5 x 1) m(x) = 1 (x > 1)

<x> 0.14 The dimension of the multi-quark system which produces cumulative particles

The nuclear quark-parton structure function:

G(x) ~ exp (-x/<x>)

The experiments in LHE (JINR):

The limit fragmentation is realized at bik ≥ 5

The detailed investigation of cumulative particle production has been carried out on more than 20 nuclei

The universal values ~ (1/AII) FII (bII 1, x1)

practically don’t depend on properties of the nucleus I

Invariant Definition of Hadron Jets

The jet is a cluster of hadrons with small relative b i k. The jet axis (a unit four-vector):

V = (ui /(ui)2)

Vo2 - V 2 = 1.

The summation is performed over all the particles belonging to the selected particle group (cluster). It is possible to determine the squared four-velocity with respect to the jet axis:

bk = - (V - uk)2.

Multiple Processes in Four-velocity Space

Distributions of - mesons оn bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL. They do not depend either on the collision energy, or on the type of fragmenting system (p, , p-, C, ... ) <bk> = 4 characterizes the average four-velocity of mesons with respect to the jet axis in the fragmentation of various quark objects The discovered UNIVERSALITY of the properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum

Correlation Depletion Principle

W W ·W b

= I , = II

I + II 1 + …

d2/dbII1dx1 FI·FII(bII1,N 1),

bII1 = (uII – u1)2

N1 – cumulative number

To study FII, we don’t need to accelerate nuclei.

Correlation Depletion Principle (CDP)

CDP was offered by Bogolyubov N.N. in statistical physics as a universal property of the probability distributions for particle location in ordinary space-time (r,t).

The principle is based on the idea that the correlation between largely spaced parts of a macroscopic system practically vanishes and the distribution is factorized.

CDP in Relativistic Nuclear Physics was suggested by Baldin A.M. in four-velocity space.

Due to complementary of rik and bik this principle is quite opposite to the Bogolyubov CDP.

The Bogolyubov CDP is valid for ri – rk2 while the Baldin CDP is fulfilled for ri – rk2 0 (or bik ) according to the asymptotic freedom.

Processes with Very High Multiplicity

The theory of these processes was developed at the Laboratory of Theoretical Physics of JINR (A. Sissakian and J.Manjavidze) in order to understand inelastic high-energy hadronic and nuclear interactions with the hadron multiplicity to be much higher than the average multiplicity

П=min[1/2(uINI +uII NII)

2]

E(d3/d3p) = (NI) (NII)

= C1.AI

. AII

. exp (- /C2)

(NI) = 1/3 + NI/3 (NII) = 1/3 + NII/3

C1 = 1,9.104 mbGeV-2c3sr-1

C2 = 0.1250.002

I + II 1 + ...

PI =m0uI p1 =m1u1

PII=m0uII

(NIPI + NIIPII - p1)2=

=(NIm0 +NIIm0 + )2

is the mass of the particleproviding conservation of thebarion number, strangness andother quantum numbers

Пmin dП/dNI = 0; dП/dNII = 0In the central rapidity region (y = 0)

(u1uI) = (u1uII) -Y y +Y AI y = 0 AII

NI =NII =

N = [1 + √1 + (Ф/Ф2)]Ф,where

Ф= (1/m0)[mTchY+](½ sh2Y)Ф= (2 - m1

2)(4m0 2 sh2Y)

andПmin = N chY

Asymptotics

s/(2mImII) (uIuII) = ch2Y

Пmin= (mT/2m0)[1+√1+(2-m1

2)/mT2

N 0

The analytical representation for П leads to the following conclusions:

There is the limiting value of П at high energies

The effective number of nucleons involved in the reaction decreases with increasing collision energy

Probability of observation of antinuclei and fragments in the central rapidity region is small

Strange particles yield increases with increasing collision energy

The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising

PREDICTIONS

Beam

Nuclotron intensity (particles per cycle)

available have to be(with booster)

p 2.5·1010 1013

d 5·1010 1013

d 3·108 5·1010

t 4·105 1010

4He 8·108 2·1012

7Li 2·109 5·1012

12C 6.5·108 2·1012

24Mg 1.2·108 5·1011

40Ar 104 1010

84Kr 103 5·108

JINR

Veksler & Baldin Laboratory of High

EnergiesDubna

NUCLOTRON

Experiments with relativistic nuclei

Experimentswith polarizedbeams

Applied investigations

Nuclotron

Experiments with relativistic nuclei

• Nucleon structure

• Nuclear structure

• Medium effects on particle production

• Modification of nuclear matter

• Hypernuclei and nuclei

Experiments with relativistic nuclei• Nucleon structure NIS project

Polarized nucleon strangeness

The planned results are:

Ratio of and meson production cross sections near their thresholds in pp interaction and the comparison on the cross sections for pp and np interactions under similar kinematical conditions

SUCH EXPERIMENT IS POSSIBLE IN THE FORESEEN FUTURE ONLY AT NUCLOTRON !

Experiments with relativistic nuclei• Nucleon structure

STRELA project

Study of the spin-dependent component of the nucleon scattering amplitude in the charge-exchange process nppn in a deuteron beam extracted from the Nuclotron

(d/dt)dp(pp)n = 2/3(d/dt)nppn

Experiments with relativistic nuclei• Nuclear structure

BECQUERELproject

Experiments with relativistic nuclei

• Modification of nuclear matter

FAZA project

• Hot nuclei

• Termal mulifragmentation

• Liquid-Fog Phase Transition

Tc = (20±2) MeV

L

F

F

E

Experiments with relativistic nuclei

• Hypernuclei • nuclei

GIBS project SPHERE project DELTA project

Experiments with polarized beams

• Spin structure of the np forward scattering amplitude

• Spin deuteron structure at short distances

• Spin structure of the three nucleon systems

Experiments with polarized beams• Spin structure of the np forward

scattering amplitude

T(np)

DELTA-SIGMA project

),)(,(),( 210 kPkPPP TBtotTBtottottot

totT

tottotL

1

21

2

)(2

k

BP

TP

is a unit vector in the direction of the beam momentum

and are the beam (B) and target (T) polarizations

tot0

tot1 tot2is the total cross section for unpolarized particles

and are the spin-dependent contributions

Experiments with polarized beams

• Spin deuteron structure at short distances

SCAN-2 project

PIKASO project

Applied research

• Radiobiology and space biomedicine

• The impact of nuclear beams on the microelectronic components

• The transmutation of radioactive waste

• Accelerator driven energy production

Conclusions

The Baldin and Veksler Laboratory of High Energies of JINR has obtained unique results in Relativistic Nuclear Physics

The relevant programme of physics research will realize by international collaborations at the Nuclotron

1. A.I.Malakhov, Research Program for the Nuclotron, Physics of Atomic Nuclei, Vol.65, No.2, 2002, pp. 211-219.

2. A.M.Baldin, A.I.Malakhov, A.N.Sissakian, Selected Problems of Relativistic Nuclear Physics and Multiple Particle Production, Physics of Particles and Nuclei, Vol.32, Suppl.1 (2001) pp.4-30.

3. V.I.Sharov et al., Measurement of the np total cross section difference L at 1.59, 1.79 and 2.20 GeV, Eur.Phys.J. C 13, 255 (2000).

4. S.Afanasiev et al., Spin Effects at Fragmentation of Polarized Deuterons into Cumulative Pions, In Proceedings of the International Nuclear Physics Conference INPC 2001, Berkeley, California, 2001, Ed. By Eric Norman et al. Melville, New York, 2002, AIP Conference Proceedings, Vol.610, p.395.

5. S.P.Avdeev et al. Transition from thermal to rapid expansion in multifragmentation of gold induced by light relativistic projectiles, Physics Letters B 503 (2001) 256-262.

6. V.P.Ladygin at al., Measurment of the tensor analyzing powers in the dd 3He n and dd 3H p reactions at RIKEN, Part. And Nucl. Lett. 3[100]-2000 (2000) 74.