Nuclear Fragmentation Reactions from Research to Applications
Nuclear Fragmentation Reactions from Research to Applications
Nuclear Fragmentation Reactions from Research to Applications
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NUFRA2011, Kemer, Turkey, Oc<strong>to</strong>ber 2, 2011<br />
<strong>Nuclear</strong> <strong>Fragmentation</strong> <strong>Reactions</strong><br />
<strong>from</strong> <strong>Research</strong> <strong>to</strong> <strong>Applications</strong><br />
Igor N. Mishustin<br />
Frankfurt Institute for Advanced Studies (FIAS),<br />
J.W. Goethe Universität, Frankfurt am Main<br />
National <strong>Research</strong> Center “Kurcha<strong>to</strong>v Institute”, Moscow<br />
Niels Bohr Institute, University of Copenhagen
�Introduction:<br />
<strong>Nuclear</strong> disintegration processes<br />
�Part 1:Basic <strong>Research</strong><br />
Contents<br />
Statistical description of nuclear break-up<br />
Multifragmentation of nuclei<br />
<strong>Nuclear</strong> L-G phase transition<br />
�Part 2: <strong>Applications</strong><br />
Propagation of heavy ions through extended medium<br />
Cancer therapy with heavy-ion beams<br />
Transmutation of radioactive waste<br />
�Conclusions
Centenary of <strong>Nuclear</strong> Physics<br />
Planetary Model<br />
In 1911, analyzing results of famous<br />
experiment on α scattering off gold<br />
foil (Geiger and Marsden, 1909),<br />
Rutherford came <strong>to</strong> the conclusion<br />
that the so-called "plum pudding<br />
model" of J. J. Thomson was wrong,<br />
and proposed a new planetary model<br />
of the a<strong>to</strong>m.: tiny electrons circling<br />
around a heavy nucleus (red).<br />
In 1913 Niels Bohr has introduced<br />
quantum mechanics in<strong>to</strong> this model<br />
by postulating stationary electron<br />
orbits<br />
R(a<strong>to</strong>m)~1Å=10 -10 m, ΔE~1 eV<br />
R(nucleus)~10 fm, ΔE~1 MeV<br />
Ernest Rutherford<br />
(1871 – 1937)<br />
1908 Nobel Prize in<br />
Chemistry “for his<br />
investigations in<strong>to</strong> the<br />
disintegration of the<br />
elements, and the<br />
chemistry of radioactive<br />
substances"
<strong>Nuclear</strong> disintegration processes:<br />
his<strong>to</strong>rical remarks
Anticipation of nuclear “explosions”<br />
Nobel prize in Physics (1922) “for his services in<br />
the investigation of the structure of a<strong>to</strong>ms and of<br />
the radiation emanating <strong>from</strong> them"<br />
Niels Bohr (1885 – 1962)
Evaporation/fission of compound nucleus<br />
t=0 fm/c<br />
p A<br />
CN<br />
low excitation<br />
� � �0<br />
t>1000 fm/c<br />
fission<br />
Compound Nucleus (CN) is an equilibrated hot nucleus whose excitation energy<br />
is distributed over many microscopic d.o.f. (introduced by Niels Bohr in 1936-39)<br />
Sequential evaporation model—Weiskopf 1937,<br />
Statistical fission model—Bohr-Wheeler 1939, Frenkel 1939
<strong>Nuclear</strong> break-up: multifragmentation<br />
t=0 fm/c<br />
p<br />
pA collision<br />
A<br />
peripheral<br />
AA collision<br />
A<br />
A ,<br />
moderate excitation<br />
� � P � 0<br />
0<br />
slow expansion<br />
�<br />
t>100 fm/c<br />
equilibrated system<br />
at freeze-out<br />
Power-low fragment mass distribution around critical point, Y(A)~A -τ<br />
Can be well unders<strong>to</strong>od within an equilibrium statistical approach<br />
Early 80s: Randrup&Koonin, D.H.E. Gross et al, Bondorf-Mishustin-Botvina, Hahn&S<strong>to</strong>ecker;<br />
Later: S. Das Gupta et al., Gulminelli et al, Raduta et al,...
t = 0 fm/c<br />
Explosive disintegration of nuclei<br />
central<br />
AA collision<br />
E>50 AMeV<br />
compression+heating<br />
fast expansion<br />
t ≈ R/v f < 50 fm/c<br />
collective flow<br />
of fragments<br />
Typically, exponential fragment mass distributions, Y(A)~exp(-bA)<br />
The stronger is flow-the smaller are fragments-mechanical rupture<br />
Dynamical modeling is required: QMD, IQMD, NMD, AMD, ...
We with Jakob Bondorf started our theoretical<br />
work on multifragmentation in the NBI, inspired<br />
by impressive pho<strong>to</strong>-emulsion pictures<br />
B. Jakobsson et al., The disintegration of nuclei in violent heavy ion interactions<br />
at (55-110) AMeV 12 C+ArBr , Z. Phys. A307, 293 (1982).<br />
Jakob Bondorf first discussed the possibility of multifragmentation<br />
at the Bala<strong>to</strong>n conference in 1979
Arrtistic view of multifragmenattion<br />
W. Kandinsky “Several Circles” (1926), Guggenheim Museum, New York
Part 1.1:<br />
Statistical description of<br />
nuclear break-up
Statistical Multifragmentation Model (SMM)<br />
J.P. Bondorf, R. Donangelo, I.N. Mishustin, et al., Nucl. Phys. A443 (1985) 321; A444 (1985) 460;<br />
J.P. Bondorf, A.S. Botvina, A.S. Iljinov, I.N. Mishustin, K. Sneppen, Phys. Rep. 257 (1995) 133<br />
α<br />
IMF<br />
n<br />
HR<br />
IMF<br />
p<br />
IMF<br />
Ensemble of nucleons and fragments<br />
in thermal equilibrium characterized by<br />
neutron number N0 pro<strong>to</strong>n number Z0 ,<br />
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<br />
fragment multiplicities or partitions, f={NAZ },<br />
Total fragment multiplicity Mf = ∑AZNAZ Volume available for the translational motion, Vf (M),<br />
grows with the fragment multiplicity, approximately<br />
following P=const condition
SMM: “micro-canonical” ensemble<br />
� Baryon number and charge conservation<br />
�∑N AZ A=A 0 , ∑�N AZ Z=Z 0<br />
� Statistical distribution of probabilities<br />
W f ~ exp {S f (A 0 , Z 0 , E * ,V)};<br />
� Equipartition of energy leading <strong>to</strong> a partition temperature T f<br />
∑�E AZ (T f )N AZ +1.5T f (M-1)+ U C f =E*<br />
� Phenomenological description of individual fragments as<br />
incompressible liquid drops (A>4)<br />
� �<br />
C<br />
� �<br />
� �<br />
5/4<br />
2 2 2 2 2 2<br />
T T - T (A - 2Z)<br />
2<br />
F = -(w + )A + 4πR β + γ<br />
AZ 0 0 2 2 1/3<br />
ε T + T 2A<br />
3eZ<br />
+<br />
5rA<br />
0 c 0<br />
S<br />
f<br />
�Ff<br />
��<br />
�T
Fragment mass partitions {N A }<br />
Euler's problem: find the number of ways, P(A 0 ,M), an integer A 0<br />
can be represented as a sum of M integers, A 0 =A 1 +A 2 +A 3 +..., ∑N A=M<br />
PAM ( , ) � PAM ( , �1) �PA ( �MM<br />
, )<br />
0 0 0<br />
Total number of partitions, P(A), can be found <strong>from</strong> the generating function<br />
� � 1<br />
� � � �<br />
N � �<br />
A<br />
Z x = � � c x = � = �P�A�x<br />
1�<br />
cx<br />
A A<br />
N<br />
1<br />
, N<br />
2<br />
, N<br />
A<br />
, �=<br />
0 A= 1 A= 1 A= 0<br />
A<br />
At large A 0 the result is well approximated by Hardy-Ramanujan formula<br />
1 � 2A �<br />
� � 0<br />
P A = exp ,<br />
0<br />
�π� 48A<br />
3<br />
0 � �<br />
A A<br />
1 3A 6A<br />
0 0<br />
M = ln<br />
� �<br />
� 2 �<br />
π 2 � bπ �<br />
where . Total number of partitions is huge for A0 ~100<br />
P(50)=2*105 , P(100)= 2*108 , P(200)= 4*1012 b= 0.3150<br />
Monte Carlo sampling is required - Markov Chain +Metropolis<br />
A.S. Botvina, A.D. Jackson, I.N. Mishustin, Phys. Rev. E62 (2000) R64
Exact formula derived by Ramanajan
Part 1.2: Multifragmentation of<br />
nuclei
Multifragmentation of relativistic<br />
projectile specta<strong>to</strong>rs<br />
ALADIN against SMM<br />
W. Trautmann, A.S.Botvina,<br />
I.N. Mishustin et al., Nucl.Phys.<br />
A584(1995)737;<br />
H.Xi et al., Z.Phys. A359 (1997)<br />
397<br />
SMM gives excellent<br />
description of data<br />
Main conclusion:<br />
Stat. quilibrium is<br />
reached in these<br />
reactions
Evolution of partitions with E *<br />
° experiment his<strong>to</strong>grams – SMM<br />
fission<br />
CN<br />
- �<br />
A , �<br />
2<br />
critical events?<br />
Peripheral Au+Au collisions at 35 AMeV<br />
M. D’Agostino et al., Nucl. Phys. A650, 329 (199)
Isoscaling and symmetry energy<br />
ALADIN: 12 C+ 112,124 Sn A. Le Fevre et al., Phys.Rev.Lett 94, 162701 (2005)<br />
S(N)=Y( 124 Sn)/Y( 112 Sn)=C·exp(N·α+Z·β)<br />
S(N)<br />
10<br />
1<br />
10 -1<br />
peripheral<br />
mid-central<br />
central<br />
300 MeV<br />
0 1 2 3 4 5 6 7<br />
Z<br />
1<br />
2<br />
3<br />
4<br />
peripheral<br />
mid-central<br />
central<br />
5 0 0.2 0.4 0.6 0.8 1<br />
600 MeV<br />
0 1 2 3 4 5 6 7<br />
N<br />
α·T ≈ -4γ (Z 1 2 /A1 2 -Z2 2 /A2 2 )<br />
α<br />
(MeV)<br />
HeLi<br />
T<br />
(MeV)<br />
app<br />
γ<br />
0.6<br />
0.4<br />
0.2<br />
10<br />
8<br />
6<br />
4<br />
25<br />
20<br />
15<br />
E/A (MeV)<br />
300<br />
600<br />
112<br />
Sn<br />
124<br />
Sn<br />
0 0.2 0.4 0.6 0.8 1<br />
10<br />
0 0.2 0.4 0.6 0.8 1<br />
1-b/b max<br />
Most recent analysis: R. Ogul, A. Botvina, Atav, N. Buyukcizmeci et al.,<br />
PRC 83, 023608 (2011)
Part 1.3: <strong>Nuclear</strong> liquid-gas<br />
phase transition
Liquid-gas phase transition in<br />
nuclear matter<br />
B.J.Strack, Phys. Rev. C35, 691 (1987)
Gas<br />
Multifragmentation as manifestation of<br />
a Liquid-Gas p. t. in finite nuclei<br />
t<br />
3 H<br />
e<br />
Li<br />
T<br />
T c<br />
T*<br />
0<br />
G<br />
HR<br />
L-G<br />
C<br />
L-G<br />
coexistence<br />
2d<br />
0.5<br />
slow expansion<br />
1<br />
t SI
<strong>Nuclear</strong> caloric curve<br />
Predicted in 1985 within the SMM<br />
Bondorf, Donangelo, Mishustin, Schulz<br />
NPA 444 (1985) 460<br />
Experimental discovery<br />
Pochodzalla and ALADIN collaboration,<br />
PRL 75 (1995) 1040
Part 2.1: Propagation of heavy ions<br />
through extended media
Bragg discovery in 1904<br />
�W.H. Bragg, R. Kleeman, On the ionization curves of radium,<br />
Philosophical Magazine, S.6, 8 (1904) 726.<br />
� W.H. Bragg, R. Kleeman, On the alpha particles of radium, and<br />
their loss of range in passing through various a<strong>to</strong>ms and molecules.<br />
Philosophical Magazine, S.6, 10 (1905) 318.<br />
Sir William Henry Bragg<br />
(1862 – 1942)<br />
1915 Nobel Prize in Physics<br />
Experiments with 7.7 MeV α-particles in H, Al, Cu, Ag, Sn, Pt, Au and compounds<br />
Maximum energy deposition at the end of particle’s range in the medium!<br />
This remarkable property can be used <strong>to</strong> destroy deeply-sitting tumours.
Comparison of different beams
Ions can deliver significant fraction of<br />
energy <strong>to</strong> deeply-sitting tumour in brain ...<br />
12 C beam
...while sparing healthy tissues<br />
12 C beam<br />
and organs at risk
Ion-beam cancer therapy short his<strong>to</strong>ry<br />
�Pro<strong>to</strong>n beams are in clinical use since 1954<br />
�Heavy-ion beams were first tried in Berkeley (1975).<br />
�Since 1997 12 C beams are successfully used at GSI Prof. Kraft)<br />
�Two hospitals using HI beams are operating in Japan (Chiba<br />
and Hyogo), one is under construction in Italy (Pavia)<br />
�A new center in Heidelberg just started treatment with p, 3 He,<br />
12 C and 16 O beams- about 1000 partients/year, 18 k€/patient<br />
GSI, Darmstadt<br />
HIMAC, Chiba<br />
Heidelberg
12 C<br />
12<br />
C<br />
Main processes <strong>to</strong> be considered:<br />
1) Ionization energy losses, Bethe-Bloch formula<br />
-dE/dx ~ Z 2 /� � ~1/E<br />
Is used for unresolved electrons with mfp
Part 2.2: Cancer therapy with<br />
heavy-ion beams
Monte Carlo for Heavy Ion Therapy (MCHIT)<br />
GEANT4-based application created at FIAS<br />
� Uses FIAS expertise in heavy-ion physics (UrQMD and SMM).<br />
� Intended for validation of GEANT4 physical models with<br />
experimental data relevant <strong>to</strong> particle therapy.<br />
� Works with simple phan<strong>to</strong>ms and beam-line elements.<br />
� Simulations are done on event-by-event basis.<br />
MCHIT@FIAS<br />
FIAS group: Walter Greiner, Igor Pshenichnov, Alexander Botvina, Lucas Burigo, and INM
12 C nuclei<br />
fragmentation<br />
in tissue-like<br />
media<br />
12 C<br />
on hydrogen<br />
H<br />
9 B<br />
12 C<br />
12 C<br />
16 O<br />
on oxygen<br />
peripheral collision<br />
16 O<br />
central collision<br />
15 O<br />
�<br />
10 C<br />
Li<br />
�
Violent fragmentation reactions simulated<br />
12 C<br />
with MCHIT<br />
n<br />
n<br />
p<br />
n<br />
p<br />
n<br />
�<br />
� p
MCHIT simulation: importance of nuclear<br />
fragmentation reactions<br />
100 events of 12 C @ 330 AMeV in water cube (30 cm) 3<br />
fragments and pro<strong>to</strong>ns in blue, electrons in red, yellow dots are interaction points<br />
Electromagnetic interactions<br />
only<br />
EM interactions + hadronic elastic<br />
scattering and fragmentation reactions
Importance of nuclear fragmentation<br />
reactions in dose-depth distributions<br />
only electromagnetic losses<br />
nuclear fragmentation reactions are<br />
responsible for a) reduction of the peak<br />
height and b) the tail beyond the peak<br />
insufficient <strong>to</strong> explain the<br />
shape of the Bragg peak<br />
including nuclear fragmentation
Secondary fragments: models at work<br />
Evaporation<br />
Calculations with the<br />
Wilson abrasion model<br />
Yields of pro<strong>to</strong>ns are overestimated<br />
30 <strong>to</strong> 60% of beam ions are destroyed<br />
in nuclear fragmentation reactions<br />
Yields of Li, Be and B are <strong>to</strong>o low<br />
data: E. Haettner et al., Rad. Prot. Dosim. 122 (2006)48, within ��
Secondary fragments: models at work<br />
Evaporation<br />
Fermi break-up<br />
data: E. Haettner et al., Rad. Prot. Dosim. 122 (2006)48, within ��
Secondary neutrons in 12 C therapy<br />
MCHIT: 330A MeV 12 C in water<br />
100 events, only neutrons are shown<br />
Comparison with GSI data<br />
(D. Schardt et al.)<br />
The <strong>to</strong>tal dose <strong>from</strong> neutrons is predicted at 1% of the treatment dose for<br />
typical irradiation conditions. This was confirmed by GSI measurements,<br />
K. Gunzert-Marx, New J. of Phys. 10 (2008) 075003)<br />
I. Pshenichnov, I. Mishustin, W. Greiner, Neutrons <strong>from</strong> fragmentation of light nuclei in<br />
tissue like media: a study with the GEANT4 <strong>to</strong>olkit Phys. Med. Biol. 50 (2005) 5493; Proc.<br />
Int. Conf. on <strong>Nuclear</strong> Data for Science and Technology, Nice, France, 2007
<strong>Fragmentation</strong> reactions of 12 C leading <strong>to</strong><br />
positron-emitting nuclei for therapy moni<strong>to</strong>ring<br />
� e<br />
11<br />
C<br />
�<br />
e +<br />
detec<strong>to</strong>r<br />
e -<br />
�<br />
detec<strong>to</strong>r<br />
I. Pshenichnov, A. Larionov, I. Mishustin, W. Greiner, PET moni<strong>to</strong>ring of cancer therapy with<br />
3 He and 12 C beams: a study with the GEANT4 <strong>to</strong>olkit, Phys. Med. Biol. 52 (2007) 7295<br />
I. Pshenichnov, I. Mishustin, W. Greiner, Distributions of positron-emitting nuclei in pro<strong>to</strong>n<br />
and carbon-ion therapy studied with GEANT4, Phys. Med. Biol. 51 (2006) 6099
RBE<br />
Radiation effects on bio-molecular level<br />
Th. Haberer<br />
Depth in tissue cell [mm nucleus H2O] microscopic<br />
dose<br />
distributions<br />
Th
Heidelberg Ion-Therapy (HIT) center<br />
Officially in operation since December 2009. Up <strong>to</strong>1300 patients with specific<br />
cancers of brain and prostate will be treated annually.
Part 2.3: Transmutation of radio-<br />
active waste
Description of spallation reactions<br />
Many people have contributed <strong>to</strong> the models which are used now<br />
(multi)fragmentation<br />
MCADS employs several cascade models for the fast initial stage and<br />
Evaporation/Fermi break-up/SMM for the slow de-excitation stage
Monte Carlo model for Accelera<strong>to</strong>r Driven<br />
Systems (MCADS) developed at FIAS<br />
Igor Pshenichnov, Igor Mishustin, Yury Malyshkin, Walter Greiner<br />
� Based on Geant4 <strong>to</strong>olkit<br />
(currently version 9.4 p01)<br />
� Includes secondary<br />
interactions of fast neutrons,<br />
pro<strong>to</strong>ns and fragments<br />
� Capability <strong>to</strong> visualize target<br />
volumes, his<strong>to</strong>ries of primary<br />
pro<strong>to</strong>ns and all secondary<br />
particles<br />
� Flexible scoring techniques <strong>to</strong><br />
calculate heat deposition and<br />
count outgoing particles<br />
600 MeV pro<strong>to</strong>n in uranium target,<br />
white: primary pro<strong>to</strong>n, green: neutrons,<br />
yellow: gammas
Simulations of the initial stage:<br />
fragment mass distributions<br />
Bertini cascade model<br />
Binary cascade model<br />
INCL/ABLA model<br />
of Geant4<br />
Better description of<br />
pro<strong>to</strong>n-induced<br />
fission of U reached<br />
with INCL/ABLA<br />
(A) (mb)<br />
σ<br />
(A) (mb)<br />
σ<br />
4<br />
10<br />
3<br />
10<br />
2<br />
10<br />
10<br />
1<br />
-1<br />
10<br />
-2<br />
10<br />
100<br />
80<br />
60<br />
40<br />
20<br />
0<br />
238<br />
p (62.9 MeV) + U<br />
MCADS/BERT_HP<br />
MCADS/INCL_ABLA_HP<br />
Data Isaev et al.<br />
20 40 60 80 100 120 140 160 180 200 220 240<br />
A<br />
60 80 100 120 140 160 180<br />
A
Neutron interactions in W target<br />
all secondary<br />
interactions<br />
are considered<br />
Elastic scattering only<br />
Neutrons<br />
per<br />
pro<strong>to</strong>n<br />
Produced<br />
via<br />
(p,xn)<br />
Leaked<br />
forward N/A 0.2<br />
side-leaked N/A 4.4<br />
All interactions<br />
Neutrons<br />
per<br />
pro<strong>to</strong>n<br />
Produced<br />
via<br />
(p,xn),<br />
(n,xn)<br />
Leaked<br />
Forward N/A 0.1<br />
side-leaked N/A 6.<br />
backward N/A 2.4<br />
backward N/A 3.5<br />
<strong>to</strong>tal 8.3 7.<br />
<strong>to</strong>tal 30. 9.6<br />
In U target the number of produced neutrons is increased by a fac<strong>to</strong>r of 3!
Distribution of deposited heat<br />
Probability event-by-event<br />
10<br />
1<br />
-1<br />
10<br />
-2<br />
10<br />
p (600 MeV) + W<br />
p (600 MeV) + U<br />
MCADS/INCL_ABLA_HP<br />
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5<br />
E /E<br />
In case of U target fission fragments contribute significantly<br />
beyond 1<br />
dep<br />
beam
Conditions in a fissile target (U)<br />
Maps of neutron flux<br />
Beam: E p=0.6 GeV,<br />
I=10 mA, Ø=70 mm<br />
Maps of heat deposition<br />
R (cm)<br />
R (cm)<br />
10<br />
9<br />
8<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
2<br />
n/s/cm<br />
0<br />
0 2 4 6 8 10 12 14 16 18 20<br />
10<br />
9<br />
8<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
Z (cm)<br />
Total power, MW:<br />
13.751781<br />
0<br />
0 2 4 6 8 10 12 14 16 18 20<br />
Z (cm)<br />
16<br />
10<br />
15<br />
10<br />
3<br />
kW/cm<br />
10<br />
10<br />
1<br />
2<br />
-1<br />
10<br />
-2<br />
10<br />
-3<br />
10
A set-up design including fissile<br />
target and modera<strong>to</strong>r<br />
J. Galy, J. Magill, H. Van Dam, J.<br />
Valko, NIMA 485 (2002) 739<br />
With U target, neutron fluxes up <strong>to</strong> f=10 16 n/s/cm 2 can be reached.<br />
This opens a possibility of transmutation of long-lived radioactive waste,<br />
e.g. MA (Np, Am, Cm). These nuclei can be destroyed in (n,fission) process.<br />
Better data on fission cross sections are required.
� pro<strong>to</strong>n accelera<strong>to</strong>r of 600 MeV<br />
(current up <strong>to</strong> 4 mA, upgrade 20mA)<br />
● spallation target<br />
MYRRHAproject<br />
(Multi-purpose hybrid research reac<strong>to</strong>r for high-tech application)<br />
● multiplying core with MOX fuel,<br />
cooled by liquid Pb-Bi.<br />
●1 BEuro-scale European project<br />
Spallation target
Conclusions<br />
�Advanced basic research often leads <strong>to</strong> applications<br />
which are not anticipated in the beginning of studies<br />
� <strong>Nuclear</strong> fragmentation reactions play an important<br />
role in the medical and industrial applications.<br />
�Significant improvements in theoretical modeling and<br />
new experimental data are still needed for better<br />
understanding of nuclear break-up processes
Simulations of the initial stage:<br />
fragment mass distributions<br />
Bertini cascade model<br />
Binary cascade model<br />
INCL/ABLA model<br />
of Geant4<br />
Better description of<br />
pro<strong>to</strong>n-induced<br />
fission of U with<br />
INCL/ABLA model
Ionenquellen<br />
Injek<strong>to</strong>r<br />
Synchrotron<br />
HEST+Gantry<br />
Bestrahlung<br />
Schematic view of HIT facility
Gantry<br />
Heidelberg Ion-Therapy Center<br />
Injec<strong>to</strong>r<br />
Synchrotron