Experiment ální a aplikovaná jaderná fyzika

1. Experimentální a aplikovaná jaderná fyzika Milan Krtička

2. Využití jaderných technologií • Jaderná energetika • fussion(fúze) • fission (štěpení) • Jaderné zbraně • Zdravotnictví • zobrazování, diagnostika • terapie • Jaderná magnetická rezonance • Jaderné analytické metody • Datování • Diagnostika průmyslových zařízení • Dozimetrie • Konzervace potravin • Obohacování nuklidů • Geologické průzkumy (hledání ropy,…) • …

3. Interakcečástic s látkou (stručný přehled)

4. How do we detect particles? • In order to detect a particle, it must: • interact with the material of the detector • transfer energy in some recognizable fashion (signal) – in 21st century it is something convertible to electric current • Detection of particles happens via their energy loss in the material they traverse

5. Charged particles – interaction with matter In general, two principal features characterize the passage of charged particles through matter: • a loss of energy by the particle and • a deflection of the particle from its incident direction. These effects are primarily the result of two processes: • inelastic collisions with the atomic electrons of the material • elastic scattering from nuclei. These reactions occur many times per unit path length in matter and it is their cumulative result which accounts for the two principal effects observed. Their relative importance depends on ion (mass, charge) and energy. These, however, are by no means the only reactions which can occur. Other processes include • nuclear reactions • Bremsstrahlung • emission of Cherenkov radiation / Transition radiation (high g) Typicalcrosssectionforatomicprocessesis 10-17-10-16 cm2 = 107-108 b

6. Těžké nabité částice - interakce s látkou Ionizing power described by Bethe-Bloch formula (PDG form) Max. energy transfer in a single collision z, M - incident particle Z, A - medium I- Mean excitation energy of medium d - Density correction (transv. extension of electric field)

7. Minimum ionizing particles (MIP): bg= 3-4 Saturation at large (βγ) due to densityeffect(correctionδ) (polarizationofmedium) MIP looses ~ 13 MeV/cm (r(Cu) : 8.94 g/cm3) dE/dxfalls ~ β-2; kinematicfactor … (precisedependence: ~ β-5/3) dE/dxrises ~ ln (βγ)2; relativisticrise … (rel. extension of transversal E-field)

8. 1/β2-dependence: slower particles feel electric force of atomic electron for longer time ... Relativistic rise for βγ > 4: High energy particle: transversal electric field increases due to Lorentz transform;Ey➙ γEy. Thus interaction cross section increases ... particleatrest fast moving particle Validity: 0.05 < βγ < 500M > mμ Corrections: lowenergy: shellcorrections highenergy: densitycorrections

9. Těžké nabité částice - interakce s látkou • Density correction d: electric field of the particle also tends to polarize the atoms along its path – because of the polarization, electrons far form the path of the particle will be shielded from the full electric intensity • Shell correction – velocity comparable/smaller than the orbital velocity of the bound electrons. The correction is small.

10. Těžké nabité částice - interakce s látkou • Dependence onA, Zoftargetnucleus • Minimum ionizationis typically 1-2 MeV/g.cm-2 • Dependence on z2 Validity: 0.05 < βγ < 500 For all sufficiently heavy particles (m>>me) – effectively for all from mμ

11. Těžké nabité částice - interakce s látkou • In nuclear physics we often have energies of particles at maximum about a GeV (and usually much smaller for light projectiles) • Low energies are always at the end of the track • How important are different regimes? • How important are radiation losses?

12. Těžké nabité částice - interakce s látkou • Radiation losses are very small for heavy particles at energies relevant for nuclear physics, they increase “linearly”

13. Těžké nabité částice - interakce s látkou Muon critical energy for the chemical elements, defined as the energy at which radiative and ionization energy loss rates are equal.

14. Těžké nabité částice - interakce s látkou “Standard” figure with ionization losses shows only “very high energies” from the point of view of nuclear physics Stopping power at more relevant energies (nucl. phys.)

15. Těžké nabité částice - interakce s látkou • For electronic stopping power the main qualitative features are: small energy loss per collision, and small (negligible) angular deflection. • Two main cases can be considered depending on whether the ion velocity v0 is lower or higher than the electron velocity ve in the atomic orbitals. • When v0< vethe Lindhard, Scharff and Schiott (LSS) and Firsovmodels, involving the formation of a quasi-molecule, are used. LSS model leads toSe~ Z1*.Z2.v0/ (Z12/3 + Z22/3)3/2~ E1/2up to the energy where a maximum stopping value is reached (Bragg peak). • For v0 > ve, the Bethe-Bloch models based on a pure Coulomb interaction between a fully stripped ion and e- of the target become adequate - Se~ ln(E)/E. • A complicating feature in determining S as a function of depth, is that the effective charge associated to the ion varies with velocity and it is continuously readjusting during its motion through the material.

16. Těžké nabité částice - interakce s látkou • The main regimes included in the overall dependences of S = Sn + Se on ion energy E are schematically illustrated Br irradiation on LiNbO3. The plot uses E/A (MeV/amu) for scaling the ion energy. • At the low energy end the nuclear stopping dominates, whereas at the higher energies the stopping is mostly electronic. • As a rule of thumb, the max of Sn occurs ≈1 keV/amu, and the max value of Sn increases, ≈ linearly with the mass A of the projectile, reaching up to around 5 keV/nm for A ≈ 200. • On the other side, the max of Se (Bragg peak) appears ≈ 1 MeV/amu. The Se are typically >1 keV/nm and reach up to around 5 keV/nm for A ∼ 200. Much higher values can be obtained for cluster (molecular) ions, e.g. Se ∼ 46 keV/nm for fullerenes at 30 MeV impinging on Si.

17. Těžké nabité částice - interakce s látkou Energy dependences for the nuclear Sn and electronic Se stopping powers for Br ions on LiNbO3 calculated by SRIM2008 http://dx.doi.org/10.1016/j.pmatsci.2015.06.002

18. Těžké nabité částice - interakce s látkou • Charged particles have surrounding Coulomb field • Always interact with e- or nuclei of atoms in matter • In each interaction typically only a small amount of particle’s kinetic energy is lost (“continuous slowing-down approximation” – CSDA) • Typically undergo very large number of interactions, therefore can be roughly characterized by a common path length in a specific medium (range) • SortingusingImpactparameter b: • “Soft” collisions (b>>a) • Hard (“Knock-on” collisions (b~a) • Coulomb interactionswithnuclearfield (b<<a) • Nuclearinteractions by heavychargedparticles a - classical radius of atom

19. Těžké nabité částice - interakce s látkou • Hard (“Knock-on”) collisions (b~a): • Interactionwith a single atomicelectron (treated as free), whichgetsejectedwith a considerablekineticenergy • Interaction probability isdifferentfordifferentparticles • Ejectedg-raydissipatesenergyalongits track • Characteristic x-rayorAugerelectronisalsoproduced • “Soft” collisions (b>>a): • The influence oftheparticle’s Coulomb forcefieldaffectsthe atom as a whole • Atom canbeexcited to a higherenergylevel, orionized by ejectionof a valence electron • Atom receives a smallamountofenergy (~eV) • The most probable type ofinteractions

20. (Těžké) nabité částice - interakce s látkou • Coulomb interactionswithnuclearfield (b<<a) • Most importantfor e- and e+ • In all but 2-3% ofcaseselectronisdeflectedthroughalmostelasticscattering, losingalmost no energy • In 2-3% ofcaseselectronlosesalmostallofitsenergythroughinelasticradiative (bremsstrahlung) interaction • Importantforhigh Z materials, highenergies (MeV) • Forantimatteronly: in-flightannihilations – Twophotons are produced • Nuclearinteractions by heavychargedparticles • A heavychargedparticlewithkineticenergy ~ 100 MeV (> 10 MeV)and b<a mayinteractinelasticallywiththenucleus • Oneor more individualnucleonsmaybedrivenoutofthenucleus in anintranuclearcascade proces • Thehighlyexcitednucleusdecays by emissionof so-calledevaporationparticles (mostlynucleonsofrelativelylowenergy) and g-rays

21. Multiple Scattering • In addition to inelastic collisions with e’s, particles passing through matter suffer repeated elastic Coulomb scattering from nuclei although with a smaller probability. • Considering that usually nuclei have mass greater than the incoming particle, the energy transfer is negligible but each scattering centre adds a small deviation to the incoming particle’s trajectory also. Even if this deflection is small the sum of all the contribution adds a random component to the particle’s path which proceeds with a zig-zag path tracks of alpha particles from a Ra source

22. Multiple Scattering • Referring to multiple scattering, that is the most common situation, naming Θ the solid angle into which is concentrated the 98% of the beam after a thickness X of material, if we define Θ0= Θ/√2 as the projection of Θ on a plane, the angular dispersion can be calculated by the relation: • where p is the momentum and Xo is the radiation length. This last quantity is characteristic of the material and can be found tabulated by Y.S. Tsai [2] or can be used the approximated formula

23. Multiple Scattering Multiple scattering scheme where the ion beam is directed in x direction. Lateral displacement perpendicular to the beam direction is ρ(y,z),and α is the total angular deviation after the penetrated depth x Propagation of Multiple scattering angular distribution through matter. The half-width of the angular MS Distribution is α1/2 Here p, βc, and z are the momentum, velocity, and charge number of the incident particle, and x/X0 is the thickness of the scattering medium in radiation lengths

24. Energy Straggling Propagation of the Energy Straggling distribution through matter in an Al foil for protons of 19.6MeV with different distribution functions (fB:Bohr,fS:Symon,fT:Tschalar) Energy distribution of monoenergetic charged particles at various points along its path. At the end of the track distribution narrows, since the particle has less energy.

25. počet prošlých částic Těžké nabité částice

26. Těžké nabité částice - dolet An important parameter for the ion trajectory is the range R. Depending on the energy, i.e. on the stopping regime, one has different range-energy dependences. However, a useful thumb rule is: R = CEg where C and gcan be empirically determined. For high non-relativistic energies, g ~2 and it lies between 1 and 2 in most other cases.

27. Těžké nabité částice - dolet počet prošlých částic Illustration for a-particles (from RA decay) – initial energy about 5.3 MeV

28. Těžké nabité částice - dolet Comparison of model with numerical solution of the full Bethe equation (Eq. 1) and the simplified form (Eq. 6) for (a) a high energy proton and (b) a high energy Carbon ion.

29. Těžké nabité částice - dolet the obtained curve shows a 1/E dependence as predicted by the equations and the peak of the energy loss, just before it drops to 0

30. Těžké nabité částice Example proton Bragg curves in water, found using calculations of proton kinetic energy as a function of path length combined with published formulations for energy and range straggling.

31. Těžké nabité částice • Braggcurvefor 292.7 MeV/nucleonCarbonions. Rangeis 15.950 cm in HDPE. LET on entranceis 24.33 keV/mm in water. FordegraderthicknessesbeyondtheBraggPeak, 16 cm, youcanseethetailproduced by low-Z fragments. They are present as it is possible to break up the nucleus (C) as it passes through the degrader. The lighter fragments will in general have a longer range. Bragg Curve for 205 MeV p. Range in High Density PolyEthylene (HDPE, ρ = 0.97 g/cm3) is 26.100 cm (peak). The LET at the entrance point is 0.4457 keV/mm in water.

32. Těžké nabité částice When the primary ion breaks up, it results in several low-Z fragments with smaller LET. The sum total of all the energy deposited by all fragments can never add up to the energy deposited by the primary ion. This causes the Bragg Curve for fragmenting high-Z ions like Iron to drop initially. The interplay between increasing LET as the ion slows down, and decreasing LET as the ion fragments can work together to produce either a net loss or a net gain in total LET. For 1 GeV/nucleon Fe, the losses from fragmentation exceed the gains from slowing down. Bragg Curve for 962.8 MeV/nucleon Fe. Range is 24.850 cm in HDPE, for an LET in water of 151.6 keV/mm. The initial drop in LET is due to the fragmentation of Fe. The subsequent rise near 25 cm is due to the slowing down of the Iron ions. Note the substantial tail due to all the penetrating fragments out beyond the Bragg Peak.

33. Dolet částic - těžké nabité částice počet prošlých částic dolet částic v Al Braggova křivka

34. Elektrony - interakce s látkou • For electrons there are differences: • the electron has a much smaller mass than the heavy particles • the electron is identical to the particles with which it is interacting, thus giving the possibility of the exchange of identity Radiation and Ionization (Collision) losses of e- (p ionization shown for comparison) Fractional energy loss per radiation length in Pb as a function of e- or e+ energy

36. Elektrony - interakce s látkou Electron critical energy for the chemical elements (Rosi’s definition)

37. Dolet částic - elektrony počet prošlých e- v Al dolet e- v některých materiálech počet prošlých e- z b-rozpadu 185W

38. Interactions of electrons Through the interaction of electrons with matter, there are four main mechanisms by which electrons can lose energy(energies of hunderds keV or MeV): direct ionisation, delta rays from electrons ejected though ionisation, bremsstrahlung, and Cerenkov radiation. The most important of these mechanisms are direct ionisation and bremsstrahlung. For positrons there is the additional mechanism of annihilation. Ionisation (right) and scattering (left) produced by 100 keV electrons in air. The range of a 100 keV electron in air is approximately 14 cm. Ionisation (right) and scattering (left) produced by 100 keV positrons in air. Example - simulations

39. Koeficient zeslabení pro fotony

40. Pravděpodobnost vzniku párů Probability P that a photon interaction will result in conversion toan e+e− pair. Except for a few-percent contribution from photonuclear absorptionaround 10 or 20 MeV, essentially all other interactions in this energy range resultin Compton scattering off an atomic electron.

41. Gamma-ray detection process • A detector that is large enough such that all gamma-ray interactions are absorbed within the detector • Gamma-ray interactions with a detector of average size

42. Gamma-ray spectrum • The pulse-height spectra of an average-sized detector

43. Shape of the Compton continuum for various gamma-ray energies – shape is very similar for all energies • Unfortunately, there are several factors that complicate the spectrum even further that we must consider. These factors are: secondary electron escape, Bremsstrahlung escape, characteristic X-ray escape, secondary radiations created near the source, the effects of surrounding materials, and coincidence. • Production of bremsstrahlung photons is proportional to Z2 of the absorber

44. Effects of Surrounding Materials • Expected spectrum (dashed line) • (1) additional peak in the response function is a result of the detector absorbing the characteristic X-rays emitted from the surrounding materials. • (2) corresponds to the backscattering. This is a wider peak because of the broad range of energies a backscattered photon can have (always occurs at energies of 0.25 MeV or less). • (3) creation of annihilation photons (high Z materials must be present)

45. There are three factors that give germanium the excellent resolution that it has: • the inherent statistical spread in the number of charge carriers, • variations in the charge collection efficiency, and • contributions of electronic noise. Some of these factors will dominate over theother factors, but this is dependent on the energy of the radiation and the size and quality of the detector in use. NaIg spectrum of137Cs Ge g spectrum of a radioactive Am-Be-source

46. Neutrony • In contrast to electrons, photons and heavy charged particles, neutrons undergo extremely weak electromagnetic interactions Although the neutron has zero net charge, it may interact electromagnetically in two ways: • first, the neutron has a magnetic moment of the same order as the proton • second, it is composed of electrically charged quarks. Thus, the electromagnetic interaction is primarily important to the neutron in deep inelastic scattering and in magnetic interactions. • Neutrons therefore pass through matter largely unimpeded, only interacting with atomic nuclei (dominantly via strong interaction) • Nuclear reactions have often a low probability – but not always… … more later • In any case, the decrease in the number of not-interacting neutrons is exponential

48. Těžké nabité částice - interakce s látkou In nuclear physics we often have lower energies … (as well as at the end of the track) Stopping power of Pb for protons (theory and exp)

49. Stopping power = Energy loss per unit length of the trajectory Sn,e = (dE/dz)n,e, • Ebeing the ion energy, z referring to the ion penetration and n and e to nuclear and electronic processes, respectively. • A complicating feature when trying to determine the stopping powers as a function of depth, is that the effective charge associated to the ion varies with velocity and it is continuously readjusting during its motion through the material. A first suggestion was made by Bohr [45] proposing that electrons whose orbital velocity is lower than the ion velocity are stripped from the moving ion. Later on, different formulae have been developed to estimate the effective charge Z∗ of the moving ion as a function of its velocity. In many cases the Northcliffe formula [46], written in simplified form as,(1) • Z∗/Z=1-exp(-v/Z2/3ve)can be applied. The parameter ve in Eq. (1) stands for the Bohr velocity.

50. Stopping power = Energy loss per unit length of the trajectory Sn,e = (dE/dz)n,e, • Ebeing the ion energy, z referring to the ion penetration and n and e to nuclear and electronic processes, respectively. • A complicating feature when trying to determine the stopping powers as a function of depth, is that the effective charge associated to the ion varies with velocity and it is continuously readjusting during its motion through the material. • A first suggestion was made by Bohr proposing that electrons whose orbital velocity is lower than the ion velocity are stripped from the moving ion. Later on, different formulae have been developed to estimate the effective charge Z∗ of the moving ion as a function of its velocity. • In many cases the Northcliffeformula, written in simplified form asZ∗/Z = 1 - exp(-v/Z2/3ve) • can be applied. The parameter vestands for the Bohr velocity.