Nuclear fragmentation reactions: from basic research to medical applications Igor N. Mishustin
Frankfurt Institute for Advanced Studies (FIAS), J.W. Goethe Universität, Frankfurt am Main National Research Center “Kurchatov Institute”, Moscow
Part 1:
Introduction: Nuclear break-up processes
Basic Research Statistical description of nuclear break-up Multifragmentation of nuclei Nuclear Liquid-Gas phase transition
Applications Propagation of heavy ions through extended medium Cancer therapy with ion beams Transmutation of radioactive waste
Conclusions Introduction: Nuclear break-up 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 Niels Bohr (1885 – 1962) the radiation emanating from them" Evaporation/fission of compound nucleus t=0 fm/c t>1000 fm/c
p A CN
low excitation 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 t>100 fm/c p A pA collision
spectator A or B spectator A moderate excitation peripheral spectator AB collision B slow expansion 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,... Explosive disintegration of nuclei
t ≈ R/v < 50 fm/c t = 0 fm/c f
hot foreball
central AA collision compression+heating E>50 AMeV collective flow fast expansion 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 started our theoretical work on multifragmentation in the Niels Bohr Institute, inspired by impressive photo- emulsion pictures by Bo Jakobsson: B. Jakobsson et al., The disintegration of nuclei in violent heavy ion interactions at (55-110) AMeV12C+ArBr , Z. Phys. A307, 293 (1982). m
1cm≈50μm
The possibility of multifragmentation was first discussed by J. Bondorf at the Balaton conference in 1979. Our first publications on statistical model in 1983 Arrtistic view of multifragmenattion
W. Kandinsky “Several Circles” (1926), Guggenheim Museum, New York 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
Ensemble of nucleons and fragments IMF n in thermal equilibrium characterized by p neutron number N0 proton number Z , HR IMF 0 α N0+Z0=A0 * excitation energy E =E0-ECN break-up volume V=(1+κ)V IMF 0 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 A=A , N Z=Z ∑ AZ 0 ∑ AZ 0 Statistical distribution of probabilities * Wf ~ exp {Sf (A0, Z0, E ,V)};
Equipartition of energy leading to a partition temperature Tf C ∑EAZ(Tf)NAZ+1.5Tf(M-1)+ U f=E*
Phenomenological description of individual fragments as incompressible liquid drops (A>4) Fragment mass partitions {NA}
Euler's problem: find the number of ways, P(A0,M), an integer A0 can be represented as a sum of M integers, A0=A1+A2+A3+..., ∑NA=M
PAMPAMPAMM(0 , )= ( 0 , - 1) + ( 0 - , ) Total number of partitions, P(A), can be found from the generating function
¥ ¥ ¥ ¥ AAN A 1 Z( x) =å Õ( cA x) = ÕA = å P( A) x N1, N 2 , NA ,¼ = 0 A= 1 A= 1 A= 0 1- cA x
At large A0 the result is well approximated by Hardy-Ramanujan formula æ ö 1 2A0 1 3A0æ 6A 0 ö P( A0 ) =π expç ÷ M = ln 3 ç2 ÷ 48A0 è ø π2 è bπ ø
where b=0.3150 . Total number of partitions is huge for A0~100 P(50)=2*105, P(100)= 2*108, P(200)= 4*1012 Monte Carlo sampling is required - Markov Chain +Metropolis
A.S. Botvina, A.D. Jackson, I.N. Mishustin, Phys. Rev. E62 (2000) R64 Multifragmentation of nuclei: experiment vs theory 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*
histograms – SMM ° experiment
fission CN
critical events? power-law distribution Y(Z)~Z-τ with τ≈2 (Fisher, 1962)
E*/A in spectators is growing towards central collisions (smaller b)
Peripheral Au+Au collisions at 35 AMeV M. D’Agostino et al., Nucl. Phys. A650, 329 (1999) Isoscaling and symmetry energy ALADIN: 12C+ 112,124Sn (A. Le Fevre et al., Phys.Rev.Lett 94, 162701) (2005)
124 112 2 2 2 2 S(N)=Y( Sn)/Y( Sn)=C∙exp(N∙α +Z∙ β ) α·T ≈ -4γ (Z1 /A1 -Z2 /A2 )
Most recent analysis: R. Ogul, A. Botvina, Atav, N. Buyukcizmeci, I. Mishustin et al., PRC 83, 023608 (2011) Nuclear liquid-gas phase transition Liquid-gas phase transition in nuclear matter Theoretical prediction, see e. g.: B.J.Strack, Phys. Rev. C35, 691 (1987)
Typical Van der Waals behaviour, like liquid-gas p. t. in water Multifragmentation is manifestation of a Liquid-Gas p. t. in finite nuclei T slow expansion tSI Li 2d HR CN t Gas L-G Liquid Nuclear caloric curve Predicted in 1985 within the SMM: Experimental confirmation: Bondorf, Donangelo, Mishustin, Schulz Pochodzalla and ALADIN collaboration, NPA 444 (1985) 460 PRL 75 (1995) 1040 Theory and experiment look similar! Propagation of heavy ions through extended media Bragg discovery in 1904 Experimental W.H. Bragg, R. Kleeman, On the ionization curves of radium, Philosophical Magazine, S.6, 8 (1904) 726. Sir William Henry Bragg W.H. Bragg, R. Kleeman, On the alpha particles of radium, and (1862 – 1942) their loss of range in passing through various atoms and molecules. 1915 Nobel Prize in Physics Philosophical Magazine, S.6, 10 (1905) 318. 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 Nuclei with enhanced biological action can be focused on the tumor volume ... 12C beam … while sparing healthy tissues and organs at risk 12C beam About 13000 patients were treated so far worldwide MainMain processesprocesses toto bebe consideredconsidered: 1) Ionization energy losses, Bethe-Bloch formula is used for unresolved electrons with mfp<0.1 mm 12C 12 2) Multiple Coulomb scattering - multiple events, smallC scattering angles 10 C 12 12 10 C 12 C C C 16O 3) Nuclear fragmentation reactions leading C to the beam particle loss 15 15 O 4) secondary reactions involving nucleons, fragments,O electrons and gammas Ion-beam cancer therapy: short history Proton beams are in clinical use since 1954. Heavy-ion beams were first tried in Berkeley (1975), but unsuccessful. Since 1997 12C beams are successfully used at GSI (Prof. Kraft) Two hospitals using HI beams are operating in Japan (Chiba and Hyogo). One hospital in Italy (Pavia) and one under construction (Trento). New center in Heidelberg provides treatment with p and 12C beams (about 750 patients/year, cost ~30 k€/patient) Heidelberg HIMAC, Chiba GSI, Darmstadt Ion-Beam Cancer Therapy worldwide ● A very advanced, but quite sophisticated method of radiation therapy which employs ion beams of intermediate energies ● Started in Berkeley in 70s, advanced in CHIBA and GSI since 90s ● Proton therapy: ~50 centers operating, ~30 under construction ● Carbon-ion therapy: 7 operating, 3 under construction ● Patient statistics (as of end 2013): over 100 000 treated with protons, about 13 000 with carbon ions Heidelbe rg Marburg Map of Carbon-ion therapy centers MARBURG, GERMANY Stated to open - 2015 750 patients per year at Hidelberg at full capacity V. Marx 2014, Nature 508 133 Heidelberg Ion-Therapy (HIT) Center Officially in operation since December 2009. Up to1000 patients with specific cancers of brain and prostate can be treated annually. Heidelberg Ion-Therapy Center Injector Synchrotron Gantry Conclusions Nuclear fragmentation reactions play an important role in basic research and in practical applications, e.g. in medicine. Reliable description of nuclear fragmentation reactions requires a combination of dynamical and statistical models, e.g. QMD+SMM Statistical approach works very well for equilibrated sources after separation of early emitted (pre-equilibrium) particles At present nuclear fragmentation reactions are well understood so that they can be reliably simulated