Nuclear Fragmentation Reactions from Research to Applications

NUFRA2011, Kemer, Turkey, October 2, 2011
Nuclear Fragmentation Reactions
from Research to Applications
Igor N. Mishustin
Frankfurt Institute for Advanced Studies (FIAS),
J.W. Goethe Universität, Frankfurt am Main
National Research Center “Kurchatov Institute”, Moscow
Niels Bohr Institute, University of Copenhagen

�Introduction:
Nuclear disintegration processes
�Part 1:Basic Research
Contents
Statistical description of nuclear break-up
Multifragmentation of nuclei
Nuclear L-G phase transition
�Part 2: Applications
Propagation of heavy ions through extended medium
Cancer therapy with heavy-ion beams
Transmutation of radioactive waste
�Conclusions

Centenary of Nuclear Physics
Planetary Model
In 1911, analyzing results of famous
experiment on α scattering off gold
foil (Geiger and Marsden, 1909),
Rutherford came to the conclusion
that the so-called "plum pudding
model" of J. J. Thomson was wrong,
and proposed a new planetary model
of the atom.: tiny electrons circling
around a heavy nucleus (red).
In 1913 Niels Bohr has introduced
quantum mechanics into this model
by postulating stationary electron
orbits
R(atom)~1Å=10 -10 m, ΔE~1 eV
R(nucleus)~10 fm, ΔE~1 MeV
Ernest Rutherford
(1871 – 1937)
1908 Nobel Prize in
Chemistry “for his
investigations into the
disintegration of the
elements, and the
chemistry of radioactive
substances"

Nuclear disintegration processes:
historical remarks

Anticipation of nuclear “explosions”
Nobel prize in Physics (1922) “for his services in
the investigation of the structure of atoms and of
the radiation emanating from them"
Niels Bohr (1885 – 1962)

Evaporation/fission of compound nucleus
t=0 fm/c
p A
CN
low excitation
� � �0
t>1000 fm/c
fission
Compound Nucleus (CN) is an equilibrated hot nucleus whose excitation energy
is distributed over many microscopic d.o.f. (introduced by Niels Bohr in 1936-39)
Sequential evaporation model—Weiskopf 1937,
Statistical fission model—Bohr-Wheeler 1939, Frenkel 1939

Nuclear break-up: multifragmentation
t=0 fm/c
p
pA collision
A
peripheral
AA collision
A
A ,
moderate excitation
� � P � 0
0
slow expansion
�
t>100 fm/c
equilibrated system
at freeze-out
Power-low fragment mass distribution around critical point, Y(A)~A -τ
Can be well understood within an equilibrium statistical approach
Early 80s: Randrup&Koonin, D.H.E. Gross et al, Bondorf-Mishustin-Botvina, Hahn&Stoecker;
Later: S. Das Gupta et al., Gulminelli et al, Raduta et al,...

t = 0 fm/c
Explosive disintegration of nuclei
central
AA collision
E>50 AMeV
compression+heating
fast expansion
t ≈ R/v f < 50 fm/c
collective flow
of fragments
Typically, exponential fragment mass distributions, Y(A)~exp(-bA)
The stronger is flow-the smaller are fragments-mechanical rupture
Dynamical modeling is required: QMD, IQMD, NMD, AMD, ...

We with Jakob Bondorf started our theoretical
work on multifragmentation in the NBI, inspired
by impressive photo-emulsion pictures
B. Jakobsson et al., The disintegration of nuclei in violent heavy ion interactions
at (55-110) AMeV 12 C+ArBr , Z. Phys. A307, 293 (1982).
Jakob Bondorf first discussed the possibility of multifragmentation
at the Balaton conference in 1979

Arrtistic view of multifragmenattion
W. Kandinsky “Several Circles” (1926), Guggenheim Museum, New York

Part 1.1:
Statistical description of
nuclear break-up

Statistical Multifragmentation Model (SMM)
J.P. Bondorf, R. Donangelo, I.N. Mishustin, et al., Nucl. Phys. A443 (1985) 321; A444 (1985) 460;
J.P. Bondorf, A.S. Botvina, A.S. Iljinov, I.N. Mishustin, K. Sneppen, Phys. Rep. 257 (1995) 133
α
IMF
n
HR
IMF
p
IMF
Ensemble of nucleons and fragments
in thermal equilibrium characterized by
neutron number N0 proton number Z0 ,
N0 +Z0 =A0 excitation energy E * =E0-ECN break-up volume V=(1+κ)V0 All break-up channels are enumerated by the sets of
fragment multiplicities or partitions, f={NAZ },
Total fragment multiplicity Mf = ∑AZNAZ Volume available for the translational motion, Vf (M),
grows with the fragment multiplicity, approximately
following P=const condition

SMM: “micro-canonical” ensemble
� Baryon number and charge conservation
�∑N AZ A=A 0 , ∑�N AZ Z=Z 0
� Statistical distribution of probabilities
W f ~ exp {S f (A 0 , Z 0 , E * ,V)};
� Equipartition of energy leading to a partition temperature T f
∑�E AZ (T f )N AZ +1.5T f (M-1)+ U C f =E*
� Phenomenological description of individual fragments as
incompressible liquid drops (A>4)
� �
C
� �
� �
5/4
2 2 2 2 2 2
T T - T (A - 2Z)
2
F = -(w + )A + 4πR β + γ
AZ 0 0 2 2 1/3
ε T + T 2A
3eZ
+
5rA
0 c 0
S
f
�Ff
��
�T

Fragment mass partitions {N A }
Euler's problem: find the number of ways, P(A 0 ,M), an integer A 0
can be represented as a sum of M integers, A 0 =A 1 +A 2 +A 3 +..., ∑N A=M
PAM ( , ) � PAM ( , �1) �PA ( �MM
, )
0 0 0
Total number of partitions, P(A), can be found from the generating function
� � 1
� � � �
N � �
A
Z x = � � c x = � = �P�A�x
1�
cx
A A
N
1
, N
2
, N
A
, �=
0 A= 1 A= 1 A= 0
A
At large A 0 the result is well approximated by Hardy-Ramanujan formula
1 � 2A �
� � 0
P A = exp ,
0
�π� 48A
3
0 � �
A A
1 3A 6A
0 0
M = ln
� �
� 2 �
π 2 � bπ �
where . Total number of partitions is huge for A0 ~100
P(50)=2*105 , P(100)= 2*108 , P(200)= 4*1012 b= 0.3150
Monte Carlo sampling is required - Markov Chain +Metropolis
A.S. Botvina, A.D. Jackson, I.N. Mishustin, Phys. Rev. E62 (2000) R64

Exact formula derived by Ramanajan

Part 1.2: Multifragmentation of
nuclei

Multifragmentation of relativistic
projectile spectators
ALADIN against SMM
W. Trautmann, A.S.Botvina,
I.N. Mishustin et al., Nucl.Phys.
A584(1995)737;
H.Xi et al., Z.Phys. A359 (1997)
397
SMM gives excellent
description of data
Main conclusion:
Stat. quilibrium is
reached in these
reactions

Evolution of partitions with E *
° experiment histograms – SMM
fission
CN
- �
A , �
2
critical events?
Peripheral Au+Au collisions at 35 AMeV
M. D’Agostino et al., Nucl. Phys. A650, 329 (199)

Isoscaling and symmetry energy
ALADIN: 12 C+ 112,124 Sn A. Le Fevre et al., Phys.Rev.Lett 94, 162701 (2005)
S(N)=Y( 124 Sn)/Y( 112 Sn)=C·exp(N·α+Z·β)
S(N)
10
1
10 -1
peripheral
mid-central
central
300 MeV
0 1 2 3 4 5 6 7
Z
1
2
3
4
peripheral
mid-central
central
5 0 0.2 0.4 0.6 0.8 1
600 MeV
0 1 2 3 4 5 6 7
N
α·T ≈ -4γ (Z 1 2 /A1 2 -Z2 2 /A2 2 )
α
(MeV)
HeLi
T
(MeV)
app
γ
0.6
0.4
0.2
10
8
6
4
25
20
15
E/A (MeV)
300
600
112
Sn
124
Sn
0 0.2 0.4 0.6 0.8 1
10
0 0.2 0.4 0.6 0.8 1
1-b/b max
Most recent analysis: R. Ogul, A. Botvina, Atav, N. Buyukcizmeci et al.,
PRC 83, 023608 (2011)

Part 1.3: Nuclear liquid-gas
phase transition

Liquid-gas phase transition in
nuclear matter
B.J.Strack, Phys. Rev. C35, 691 (1987)

Gas
Multifragmentation as manifestation of
a Liquid-Gas p. t. in finite nuclei
t
3 H
e
Li
T
T c
T*
0
G
HR
L-G
C
L-G
coexistence
2d
0.5
slow expansion
1
t SI

Nuclear caloric curve
Predicted in 1985 within the SMM
Bondorf, Donangelo, Mishustin, Schulz
NPA 444 (1985) 460
Experimental discovery
Pochodzalla and ALADIN collaboration,
PRL 75 (1995) 1040

Part 2.1: Propagation of heavy ions
through extended media

Bragg discovery in 1904
�W.H. Bragg, R. Kleeman, On the ionization curves of radium,
Philosophical Magazine, S.6, 8 (1904) 726.
� W.H. Bragg, R. Kleeman, On the alpha particles of radium, and
their loss of range in passing through various atoms and molecules.
Philosophical Magazine, S.6, 10 (1905) 318.
Sir William Henry Bragg
(1862 – 1942)
1915 Nobel Prize in Physics
Experiments with 7.7 MeV α-particles in H, Al, Cu, Ag, Sn, Pt, Au and compounds
Maximum energy deposition at the end of particle’s range in the medium!
This remarkable property can be used to destroy deeply-sitting tumours.

Comparison of different beams

Ions can deliver significant fraction of
energy to deeply-sitting tumour in brain ...
12 C beam

...while sparing healthy tissues
12 C beam
and organs at risk

Ion-beam cancer therapy short history
�Proton beams are in clinical use since 1954
�Heavy-ion beams were first tried in Berkeley (1975).
�Since 1997 12 C beams are successfully used at GSI Prof. Kraft)
�Two hospitals using HI beams are operating in Japan (Chiba
and Hyogo), one is under construction in Italy (Pavia)
�A new center in Heidelberg just started treatment with p, 3 He,
12 C and 16 O beams- about 1000 partients/year, 18 k€/patient
GSI, Darmstadt
HIMAC, Chiba
Heidelberg

12 C
12
C
Main processes to be considered:
1) Ionization energy losses, Bethe-Bloch formula
-dE/dx ~ Z 2 /� � ~1/E
Is used for unresolved electrons with mfp

Part 2.2: Cancer therapy with
heavy-ion beams

Monte Carlo for Heavy Ion Therapy (MCHIT)
GEANT4-based application created at FIAS
� Uses FIAS expertise in heavy-ion physics (UrQMD and SMM).
� Intended for validation of GEANT4 physical models with
experimental data relevant to particle therapy.
� Works with simple phantoms and beam-line elements.
� Simulations are done on event-by-event basis.
MCHIT@FIAS
FIAS group: Walter Greiner, Igor Pshenichnov, Alexander Botvina, Lucas Burigo, and INM

12 C nuclei
fragmentation
in tissue-like
media
12 C
on hydrogen
H
9 B
12 C
12 C
16 O
on oxygen
peripheral collision
16 O
central collision
15 O
�
10 C
Li
�

Violent fragmentation reactions simulated
12 C
with MCHIT
n
n
p
n
p
n
�
� p

MCHIT simulation: importance of nuclear
fragmentation reactions
100 events of 12 C @ 330 AMeV in water cube (30 cm) 3
fragments and protons in blue, electrons in red, yellow dots are interaction points
Electromagnetic interactions
only
EM interactions + hadronic elastic
scattering and fragmentation reactions

Importance of nuclear fragmentation
reactions in dose-depth distributions
only electromagnetic losses
nuclear fragmentation reactions are
responsible for a) reduction of the peak
height and b) the tail beyond the peak
insufficient to explain the
shape of the Bragg peak
including nuclear fragmentation

Secondary fragments: models at work
Evaporation
Calculations with the
Wilson abrasion model
Yields of protons are overestimated
30 to 60% of beam ions are destroyed
in nuclear fragmentation reactions
Yields of Li, Be and B are too low
data: E. Haettner et al., Rad. Prot. Dosim. 122 (2006)48, within ��

Secondary fragments: models at work
Evaporation
Fermi break-up
data: E. Haettner et al., Rad. Prot. Dosim. 122 (2006)48, within ��

Secondary neutrons in 12 C therapy
MCHIT: 330A MeV 12 C in water
100 events, only neutrons are shown
Comparison with GSI data
(D. Schardt et al.)
The total dose from neutrons is predicted at 1% of the treatment dose for
typical irradiation conditions. This was confirmed by GSI measurements,
K. Gunzert-Marx, New J. of Phys. 10 (2008) 075003)
I. Pshenichnov, I. Mishustin, W. Greiner, Neutrons from fragmentation of light nuclei in
tissue like media: a study with the GEANT4 toolkit Phys. Med. Biol. 50 (2005) 5493; Proc.
Int. Conf. on Nuclear Data for Science and Technology, Nice, France, 2007

Fragmentation reactions of 12 C leading to
positron-emitting nuclei for therapy monitoring
� e
11
C
�
e +
detector
e -
�
detector
I. Pshenichnov, A. Larionov, I. Mishustin, W. Greiner, PET monitoring of cancer therapy with
3 He and 12 C beams: a study with the GEANT4 toolkit, Phys. Med. Biol. 52 (2007) 7295
I. Pshenichnov, I. Mishustin, W. Greiner, Distributions of positron-emitting nuclei in proton
and carbon-ion therapy studied with GEANT4, Phys. Med. Biol. 51 (2006) 6099

RBE
Radiation effects on bio-molecular level
Th. Haberer
Depth in tissue cell [mm nucleus H2O] microscopic
dose
distributions
Th

Heidelberg Ion-Therapy (HIT) center
Officially in operation since December 2009. Up to1300 patients with specific
cancers of brain and prostate will be treated annually.

Part 2.3: Transmutation of radio-
active waste

Description of spallation reactions
Many people have contributed to the models which are used now
(multi)fragmentation
MCADS employs several cascade models for the fast initial stage and
Evaporation/Fermi break-up/SMM for the slow de-excitation stage

Monte Carlo model for Accelerator Driven
Systems (MCADS) developed at FIAS
Igor Pshenichnov, Igor Mishustin, Yury Malyshkin, Walter Greiner
� Based on Geant4 toolkit
(currently version 9.4 p01)
� Includes secondary
interactions of fast neutrons,
protons and fragments
� Capability to visualize target
volumes, histories of primary
protons and all secondary
particles
� Flexible scoring techniques to
calculate heat deposition and
count outgoing particles
600 MeV proton in uranium target,
white: primary proton, green: neutrons,
yellow: gammas

Simulations of the initial stage:
fragment mass distributions
Bertini cascade model
Binary cascade model
INCL/ABLA model
of Geant4
Better description of
proton-induced
fission of U reached
with INCL/ABLA
(A) (mb)
σ
(A) (mb)
σ
4
10
3
10
2
10
10
1
-1
10
-2
10
100
80
60
40
20
0
238
p (62.9 MeV) + U
MCADS/BERT_HP
MCADS/INCL_ABLA_HP
Data Isaev et al.
20 40 60 80 100 120 140 160 180 200 220 240
A
60 80 100 120 140 160 180
A

Neutron interactions in W target
all secondary
interactions
are considered
Elastic scattering only
Neutrons
per
proton
Produced
via
(p,xn)
Leaked
forward N/A 0.2
side-leaked N/A 4.4
All interactions
Neutrons
per
proton
Produced
via
(p,xn),
(n,xn)
Leaked
Forward N/A 0.1
side-leaked N/A 6.
backward N/A 2.4
backward N/A 3.5
total 8.3 7.
total 30. 9.6
In U target the number of produced neutrons is increased by a factor of 3!

Distribution of deposited heat
Probability event-by-event
10
1
-1
10
-2
10
p (600 MeV) + W
p (600 MeV) + U
MCADS/INCL_ABLA_HP
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
E /E
In case of U target fission fragments contribute significantly
beyond 1
dep
beam

Conditions in a fissile target (U)
Maps of neutron flux
Beam: E p=0.6 GeV,
I=10 mA, Ø=70 mm
Maps of heat deposition
R (cm)
R (cm)
10
9
8
7
6
5
4
3
2
1
2
n/s/cm
0
0 2 4 6 8 10 12 14 16 18 20
10
9
8
7
6
5
4
3
2
1
Z (cm)
Total power, MW:
13.751781
0
0 2 4 6 8 10 12 14 16 18 20
Z (cm)
16
10
15
10
3
kW/cm
10
10
1
2
-1
10
-2
10
-3
10

A set-up design including fissile
target and moderator
J. Galy, J. Magill, H. Van Dam, J.
Valko, NIMA 485 (2002) 739
With U target, neutron fluxes up to f=10 16 n/s/cm 2 can be reached.
This opens a possibility of transmutation of long-lived radioactive waste,
e.g. MA (Np, Am, Cm). These nuclei can be destroyed in (n,fission) process.
Better data on fission cross sections are required.

� proton accelerator of 600 MeV
(current up to 4 mA, upgrade 20mA)
● spallation target
MYRRHAproject
(Multi-purpose hybrid research reactor for high-tech application)
● multiplying core with MOX fuel,
cooled by liquid Pb-Bi.
●1 BEuro-scale European project
Spallation target

Conclusions
�Advanced basic research often leads to applications
which are not anticipated in the beginning of studies
� Nuclear fragmentation reactions play an important
role in the medical and industrial applications.
�Significant improvements in theoretical modeling and
new experimental data are still needed for better
understanding of nuclear break-up processes

Simulations of the initial stage:
fragment mass distributions
Bertini cascade model
Binary cascade model
INCL/ABLA model
of Geant4
Better description of
proton-induced
fission of U with
INCL/ABLA model

Ionenquellen
Injektor
Synchrotron
HEST+Gantry
Bestrahlung
Schematic view of HIT facility

Gantry
Heidelberg Ion-Therapy Center
Injector
Synchrotron