Supervisors:
Prof. Boguslaw Kamys ( Jagiellonian University, Krakow,
Poland)
Doc. Frank Goldenbaum ( Research Centre Jülich, Germany and
University of Wuppertal Germany)
Prof. Karl-Heinz Kampert ( University of Wuppertal, Germany)
Ph.D. Student: Sushil k. Sharma
Outline
Introduction and Motivation
Visualization of possible reaction mechanism
Physical observables
Two stages of high energy reactions
Physics Models
Properties of the INCL(4.3) Model
Observations
Current status & plans of investigations
2
Astrophysics - Reactions of cosmic rays with interstellar medium → origin of c.r.
- Nucleosynthesis in turbulence of Supernova explosions
Spallation neutron sources
- Efficient way for producing neutrons
- Shielding & aging of the constructions
ADS (Accelerator-driven system)
- Project for incinerating radioactive waste and energy production
Secondary-beam facilities
- Production of rare isotopes
Biology and medicine
Introduction & Motivation 3
What is the spallation? Why we need to
understand…….
Target Intermediate
state
projectile
(p, n, )
Spallation
Induced Fission
Fragmentation
Multi-fragmentation
Vaporization
Visualization of the possible processes 4
4 <A< fission fragments
A<4 & E* > Binding energy of the system
Physical observables
Measured in inclusive/exclusive experiments:
Yields (Total production cross-sections and their energy
dependence) of various ejectiles:
nucleons(n,p)
pions
Light charged particles(LCP)
Intermediate mass fragments(IMF)
Multiplicity of the ejectiles
Angular and energy distributions of ejectiles
Residue charge/mass and excitation energy distribution
5
Intra-nuclear
Cascade
Pre-
Equilibrium
Evaporation
Fission
Competition of
TIME
Multi-
fragmentation
Two stages of high energy reactions
First
Stage
Second
Stage
6
BERTINI
BUU(Boltzmann-Uehling-Uhlenbeck)
QMD(Quantum Molecular Dynamics)
INCL( Intranuclear cascade Liége)
ISABEL
Models for first stage of reaction mechanism
INC
MODELS 1
2
3
7
Pre-equilibrium (Exciton model,Hybrid/HMS Model)
Fission model (Fong’s Model,……)
Evaporation (EVAP (Dresner), GEM (Furihata),
ABLA (Schmidt), Gemini(Charity))
Multi- Fragmentation (SMFM(Bondorf,….)
Models for Second stage of reaction mechanism
1
2
3
4
8
Properties of INCL(4.3) Model 9
Nuclear density:
R
-V( R )
ᵨ( R )
Each nucleon is
assigned position
& momentum
Using Random
Numbers:
Saxon-Woods Density
Distribution --
--≈
45 M
eV--
-
----------------------
-------
---8a---
1 ----------------R0----------------
A. Boudard et al.,Physical Review C 66 (2002) 044615-044643
Basic–Assumptions:
De-Broglie-wavelength of cascade particles smaller than average distance of nucleons in
nucleus (d≈1.3fm) and mean free path length L in nuclear matter: <<d, <<L
Radius of strong interaction smaller than mean free path length: rint<<L
number of participating cascade particles Nc should be considerably smaller than
number of target nucleons At: Nc <<At
Rmax
R(p)
The incident proton loses part of its energy
=
cascade (~ 10–22 s ~ 30 fm/c)
First Stage
Second Stage
?!$
#?.
.
Collision criterion: dmin ≤ √ σtot / π
2 10
dmin
Relativistic Particle kinematics: Inelastic NN cross section
is treated through a Δ (3/2,3/2:1232 MeV) formation with the Δ as a resonance
decaying after some time in πN
3
Reaction/cross section:
NN NN (elastic)
NN N N N
N N (elastic)
N N
N N (charge exchange)
More channels ?
More particle species ?
Pauli Blocking: ( The only quantum mechanical effect included in INCL..) 4
N N
N N
π Δ
11
12
A
208
0.16
tstop = fstop × t0 Stopping Criterion: (fm/c) 5
J.Cugnon et al., Nucl. Phys. B8, 255(1989)
All particles (N, Δ and π) are explicitly followed in time. They are moving within
straight lines at constant speed between two interactions.
Dynamical picture of the energy dissipation
Coalescence Model (Implemented in INCL4.3 )
To form Light Charge Particles
(1H1,2H1,3H1,3He,4He)
Escaping nucleons is able to capture the nucleons placed on its way in the
nucleus and group with them might be observed as composite particle:
The necessary condition:
h0 (model parameter) =387MeV fm/c
ri,[i-1] and pi,[i-1] : Jacobian coordinates of the ith nucleon, i.e., the relative
spatial and momentum coordinates of ith nucleon with
respect to the subgroup constituted of the [i-1] nucleons
“Program checks all conditions for forming and emission of composite particles
( starts from heavier 4He) in all favorable places:
At surface i.e., R=R0+8a
At distance D along the nucleon's trajectory, outside the sphere of radius R0
Where D is the Model parameter.
13
Total reaction/absorption cross
section
Energy dependence of the total reaction cross sections in
proton induced reactions on targets ranging from 12C to
238U. The symbols present experimental data whereas
the lines show results of the parameterization of Wellisch
and Axen; Phys. Rev. C 54 (1996), 1329.1332
14
15 Experimental spectra (symbols) and results of two-step conventional
model (lines) for LCP:
Two-step model: Fast nucleons emitted from N-N collision during INC while Coalescence is responsible of high energy composite LCP.
“Two-step model reproduce qualitative properties of spectra of LCP’s produced in energy range, However, quantitative reproduction of the
data is not satisfactory and it deteriorates with increasing of the beam energy”
Conclusion: All the data at 2.5 GeV beam energy are underestimated by the model calculations whereas at lower energies the differences
are smaller. the angular dependence of the experimental spectra is different than that of the theoretical ones. experimental
cross sections decrease with the angle faster than the theoretical calculations.
“Two-step model does not take into account some significant non-equilibrium process which gives mainly
contribution to forward scattering angles and its significance increases with the beam energy”
B.Piskor-Ignatowicz., Ph.D. thesis, Jagiellonian University
(2009)
Experimental spectra (symbols) and results of two-step conventional
model (lines) for IMF:
Theoretical spectra of two-step model are much steeper than the
experimental ones for 6Li, 7Li, 7Be, and 9Be:
“theoretical cross-sections underestimate the data for large
energies of ejectiles even by 2-orders of magnitude”
The spectra of other ejectiles are also not reproduced by theoretical
model:
Conclusion:
“ These facts support the conclusion derived from the data of LCP’s.
which
Need to introduce a non-equilibrium/equilibrium mechanism of
reaction apart the mechanism of intranuclear cascade followed by
evaporation of composite particles.
Contribution of this additional mechanism increases with beam
energy and is more pronounced for forward than for backward
scattering angles”
16.1
B.Piskor-Ignatowicz., Ph.D. thesis, Jagiellonian University (2009)
B.Piskor-Ignatowicz., Ph.D. thesis, Jagiellonian University (2009)
16.2
Solutions or/ Step towards……
Nucleus break-up with fireball formation: Phenomenological model of particle
emission from moving sources
The fast proton impinging onto the target nucleus can drill the cylindrical hole in the nucleus what in turn can lead
to break-up of the nucleus in three/two different sources of particles:
Fast, hot source “Fireball” : “Responsible for large part of the cross section of LCPs emission”
Two slower sources (lower temperatures): “Participated significantly in the IMF production whereas their contribution to the LCP
emission was much smaller.”
17
Current status & plans of investigations
The main problems with description of experimental data concentrate on :
Light Charged Particles spectra in the range of their energies 100-300 MeV, especially for
small scattering angles.
High energy part of the Intermediate Mass Fragment spectra.
Solutions of this problems will be searched in following possibilities:
Microscopic description of the fireball’s emission and de-excitation
Competition of Multi-fragmentation with Evaporation processes of Intermediate Mass
Fragments
19
Thank you for your attention