2. Selected Problems of Relativistic Nuclear Physics and Multiple Particle Production
A.I.Malakhov
Joint Institute for Nuclear Research, Dubna
XXXII International Symposium on
Multiparticle Dynamics,
Alushta, 7-13 September 2002

3. It is possible to obtain the record high energy particle beams by means of accelerating the heavy nuclei with large charges
January 1, 1971

5. d(d + Cu   -+ …)
(x) =
d(p + Cu   - + …)
max
x = p / p
 

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

8. Classification of Relativistic Nuclear Collisions on bik
classic nuclear physics
0.1  bik < 1
intermediate domain
bik >> 1
nuclei should be considered as
quark-gluon systems

11. The nuclear quark-parton structure function:
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) = (x > 1)
<x>   The dimension of the multi-quark system
which produces cumulative particles
The nuclear quark-parton structure function:
G(x) ~ exp (-x/<x>)

12. 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

13. Multiple Processes in Four-velocity Space

16. 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

20. In the central rapidity region (y = 0) Ф= (1/m0)[mTchY+](½ sh2Y)
Пmin  dП/dNI = 0; dП/dNII = 0
In the central rapidity region (y = 0)
(u1uI) = (u1uII)
-Y y Y
AI y = AII
NI =NII =
N = [1 + √1 + (Ф/Ф2)]Ф,
where
Ф= (1/m0)[mTchY+](½ sh2Y)
Ф= (2 - m12)(4m0 2 sh2Y)
and
Пmin = N chY

21. Asymptotics s/(2mImII)  (uIuII) = ch2Y   N  0
Пmin= (mT/2m0)[1+√1+(2-m12)/mT2
N  0

22. The analytical representation for П leads to the following conclusions:
There is the limiting value of П at high energies
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
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

23. PREDICTIONS

25. Veksler & Baldin Laboratory of High Energies
Nuclotron intensity
(particles per cycle)
Beam
have to be
(with booster)
available
JINR
p ·
d ·
d · ·1010
t ·
4He · ·1012
7Li · ·1012
12C · ·1012
24Mg · ·1011
40Ar
84Kr ·108
Veksler & Baldin Laboratory of High Energies
Dubna
NUCLOTRON

26. Experiments with relativistic nuclei Experiments with polarized beams
Nuclotron
Applied
investigations

27. Experiments with relativistic nuclei
Nucleon structure
Nuclear structure
Medium effects on particle production
Modification of nuclear matter
Hypernuclei and  nuclei

28. 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 !

29. Experiments with relativistic nuclei
Nucleon structure
STRELA project
(d/dt)dp(pp)n = 2/3(d/dt)nppn
Study of the spin-dependent component of the nucleon scattering amplitude in the charge-exchange process nppn in a deuteron beam extracted from the Nuclotron

30. Experiments with relativistic nuclei
Nuclear structure
BECQUEREL
project

31. Experiments with relativistic nuclei
Modification of nuclear matter
FAZA project L 
Hot nuclei F F
Termal mulifragmentation
Liquid-Fog Phase Transition
Tc = (20±2) MeV E

32. Experiments with relativistic nuclei
Hypernuclei
GIBS project SPHERE project
DELTA project

33. 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

34. T(np) Experiments with polarized beams
Spin structure of the np forward
scattering amplitude
DELTA-SIGMA project
is the total cross section for unpolarized particles
and
are the spin-dependent contributions
is a unit vector in the direction of the beam
momentum
and
are the beam (B) and target (T) polarizations
T(np)

35. Experiments with polarized beams
Spin deuteron structure at short distances
PIKASO project
SCAN-2 project

36. Applied research
Radiobiology and space biomedicine
The impact of nuclear beams on the
microelectronic components
The transmutation of radioactive
waste
Accelerator driven energy production

37. 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

38. REFERENCES
1. A.I.Malakhov, Research Program for the Nuclotron, Physics of Atomic Nuclei, Vol.65, No.2, 2002, pp
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)
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.