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