Neutron Interactions Part I. Rebecca M. Howell, Ph.D. Radiation Physics Y2.5321

Transcription

1 Neutron Interactions Part I Rebecca M. Howell, Ph.D. Radiation Physics rhowell@mdanderson.org Y2.5321

2 Why do we as Medical Physicists care about neutrons? Neutrons in Radiation Therapy Neutron Therapy Contamination Neutrons on X-Ray Therapy Contamination Neutrons in Proton Therapy Unwanted patient dose Shielding Considerations Neutron Dose The above will be discussed in lecture #2. Today s focus will be general neutron interactions

3 Outline Neutron Interactions General properties Neutron Reaction Cross Sections Neutron Interactions

4 General Properties Neutrons are Neutral Can Not interact by coulomb forces Can travel through several cm of material without interacting. Neutrons interact with nucleus of absorbing material (do not interact with orbital electrons).

5 Reaction Cross Sections Used to describe neutron interaction probabilities.

6 Reaction Cross Sections Reaction cross sections are used to quantitatively describe the probability of interactions between neutrons and matter. Microscopic cross section, σ is defined per nucleus for each type of interaction. Units of area. Common unit for reaction neutron cross sections is the barn (10-24 cm 2 ). Energy Dependent - tabulated as a function of energy.

7 Reaction Cross Sections Macroscopic cross section, Σ, probability per unit path length that a particular type of interaction will occur. Σ = Nσ σ = microscopic cross section, cm 2 N = number of nuclei per unit volume, nuclei/cm 3 All processes can be combined to calculate Σ total, probability per unit path length that any type of interaction will occur. Σ Total = Σ scatter + Σ rad. capture +...

8 Exponential Attenuation Neutrons are removed exponentially from a collimated neutron beam by absorbing material. I o I I = I o e Σ total t σ total N where N = number of absorber atoms per cm 3 (atomic density) σ = the microscopic cross section for the absorber, cm 2 t = the absorber thickness, cm

9 Exponential Attenuation Example In an experiment designed to measure the total cross section of lead for 10 MeV neutrons, it was found that a 1 cm thick lead absorber attenuated the neutron flux to 84.5% of its initial value. The atomic weight of lead is , and its density is 11.3 g cm -3. Calculate the total cross section from these data.

10 Exponential Attenuation Example Rearrange/Solve the general attenuation equation for σ: σ = I Ln 0 I Nt = Calculate N, the atomic density of lead: g atoms 3 cm mole atoms 3 cm 1mole g = [ 1.18] log 24 2 = cm 22 atoms ( 1cm) 3 cm = 5.1 barn

11 Neutron Mean Free Path, λ Σ Total = 1 λ Slow neutrons λ is on the order of 1cm or less For fast neutrons λ may be tens of centimeters

12 Neutron Mean Free Path, λ Example Calculate the mean free path for the previous example. σ = cm 22 atoms N = cm λ = Σ 1 = 1 Total σn = = 5.95

13 A few background concepts..

14 Compound Nucleus Model Multi-step Reaction Projectile and target fuse together, then by successive nucleon-nucleon collisions within the combined system, the reaction energy becomes shared among many nucleons. Once equilibrium occurs, the compound nucleus can exist in an excited state for a long period of time ( ). Eventually deexcitation occurs, and by chance a single nucleon or group of nucleons acquires enough energy to escape

15 Resonance At higher energies x-section may have large peaks. Peaks = resonances Occur at neutron energies where reactions with nuclei are enhanced A resonance will occur if the energy of the incident neutron is close to the energy of an excited state of the compound nucleus Rinard, Fig. 12.3

16 Resonance In this example, at 250 kev, the neutron energy is such that the compound nucleus 7 Li is formed at an excitation energy which corresponds exactly to one of its higher states or natural frequencies. Energy is drawn from incident neutron into the reaction channel for the compound nucleus excited state. Cross section for 6 Li(n,α)t Peak is due to resonance in initial fusion process of the neutron with 6 Li target. Lilly, fig 1.14

17 Heavy nuclei Resonance General Trends Large and narrow resonances appear for neutron energies in ev range. For energies in kev region, resonances can be too close together to be resolved. Light nuclei Resonances appear only in MeV region and are broad and relatively small.

18 Classification of Neutrons by Energy November 2007 Rebecca M. Howell, Ph.D.

19 Classification of Neutrons by Energy There are three energy categories of neutrons (NCRP-38): 1. Thermal neutrons are in thermal equilibrium with the medium they are in. The average energy of thermal neutrons is typically below 1eV, depending on temperature. The most probable velocity for thermal neutrons is 2200 meters per second at o C. This velocity corresponds to an energy of eV. 2. Intermediate Energy Neutrons are classified as having intermediate energy range from above 1eV to tens of kev and typically result from elastic collisions of fast neutrons. 3. Fast Neutrons are classified as having energies above the intermediate neutrons.

20 Classification of Neutrons by Energy The classification of neutrons by energy is somewhat dependent on the reference text. Some sources may include an epithermal category while others only include fast and slow (thermal). Category Fast Intermediate Epithermal Thermal Energy Range > 500 kev 10 kev 500 kev 0.5 ev 10 kev < 0.5 ev 0.5 ev Cd-cutoff energy: sharp drop occurs in Cd absorption cross section at 0.5 ev

21 Overview of Neutron Interactions Scattering and Absorption Total Also called neutron capture Scatter Absorption Elastic Scatter (n,n) Inelastic Scatter (n,n ) Sometimes shown as (n,nγ) Nonelastic Processes (n,n 3a) (n,n 4a) (n,n etc) Electromagnetic (n,γ) Sometimes called radiative capture Charged (n,p) (n,α) (n,d) (n,etc) Neutral (n,2n) (n,3n) (n,4n) (n,xn) Sometimes called transmutation Fission (n,f) Boxes shaded in light blue follow the compound nucleus model.

22 General Neutron Interactions Scattering and Absorption Scatter When neutron is elastically or inelastically scattered by nucleus speed and direction change, but nucleus is left with same number of p + and n o as before the interaction. Elastic Scatter (n,n) Inelastic Scatter (n,n ) Nonelastic Processes Absorption When neutron is absorbed by nucleus, a wide range of radiations can be emitted or fission can be induced. Electromagnetic (n,γ) Charged (n,p) (n,α) (n,d) (n,etc) Neutral (n,2n) (n,3n) (n,4n) (n,etc) Fission (n,f)

23 Neutron Interactions are Energy Dependent

24 Neutron Interactions are Energy Dependent Fast neutrons lose energy through scatter interactions with atoms in their environment. At higher energies inelastic scatter dominates, while at lower energies elastic scatter dominates. After being slowed down to thermal or near thermal energies, they are absorbed (captured) by nuclei of the absorbing material. absorption is often followed by emission of a photon (n,γ) or another particle from the absorber nucleus e.g. (n,p), (n,α), (n,etc).

25 Scatter of Fast Neutrons Elastic Scatter Kinetic Energy AND Momentum Conserved More likely in low Z materials More likely at lower energies, < 1MeV Maximum amount of energy that can be lost is function of target nuclei mass. Larger cross sections Inelastic Scatter Reaction kinematics more complicated than for elastic scatter More likely in high Z materials More likely at higher energies E > 1MeV Can loose large amounts of energy in one collision Smaller cross sections Threshold Energy

26 Elastic Scatter of Fast Neutrons (n,n) Elastic scattering is the most likely interaction between (lower energy) fast neutrons and low Z absorbers. Billiard ball type collision Direct collision More energy transferred Indirect Collision Less Energy transferred Kinetic energy and momentum are conserved Light recoiling nucleus can cause high LET tracks

27 Kinematics of Neutron Elastic Scattering Equation demonstrates that energy given to recoil nucleus is determined by scattering angle: E R = 4A θ E ( ) ( ) n 1+ A 2 cos 2 Where A is the mass of the target nucleus E n - energy of incident neutron θ = angle of scatter of recoil nucleus Knoll, fig 15-12

28 Elastic Scatter Grazing Angle Encounter For grazing angle encounter, recoil is emitted almost perpendicular to incoming neutron (θ 90). Calculate energy of recoil nucleus : 0 4( A) E = cos 2 90 R E ( ) ( ) 2 n 1+ A For a grazing hit almost no energy goes to recoil nucleus, regardless of mass of the target nuclei.

29 Elastic Scatter Direct Head-on Collision For direct head-on collision, recoil is emitted at almost same angle as incoming neutron (θ 0). Calculate energy of recoil nucleus : 1 4( A) E = cos 2 0 R E ( ) ( ) 2 n 1+ A 4( A) E 2 1 = E R A n ( + ) For a direct head-on collision, the energy of recoil nucleus increases with increasing mass of the target nuclei.

30 Maximum Fractional Energy Transfer in Neutron Elastic Scattering Target Nucleus E R E n = 1 H 1 4( A) ( 1 + A) 2 2 H 8/9= He 3/4= He 16/25= C 48/169= O 64/289=0.221 For direct head-on collisions: As mass of target nuclei increases: Energy of recoil nucleus. Energy of the scattered neutron. The fractional energy transfer is independent of incident neutron energy. Nuclei with lower mass are more effective on a per collision basis for slowing down neutrons!

31 Energy Distribution of Recoil Nuclei (from Elastic Neutron Scatter) In principle all scattering angles are allowed, expect a continuum between the two extremes. For most target nuclei, forward and backward scattering are somewhat favored. See ch15 on G. Knoll. Radiation Detection and Measurement

32 Inelastic Scatter of Fast Neutrons (n,n ) Compound Nucleus Model neutron is captured by target nucleus and a neutron (may not be same neutron) is reemitted along with gamma photon. 1. Neutron collides with nucleus 2. Some of the kinetic energy of the neutron excites the nucleus 3. Excitation energy is emitted as gamma photon, γ can have substantial energy. 4. Neutron (not necessarily the incoming neutron) is emitted.

33 Inelastic Scatter of Fast Neutrons Total energy of outgoing neutron and nucleus is much less than the energy of the incoming neutron. Part of original kinetic energy is used to excite compound nucleus. Can not write simple expression for energy loss because it depends on the energy levels of the target nucleus. If all excited states of compound nucleus too high, inelastic scatter is impossible.

34 Inelastic Scatter of Fast Neutrons Inelastic Scatter = Threshold Phenomenon Infinite threshold for H (inelastic can not occur) 6MeV Threshold for O 1MeV Threshold for Ur Note: Inelastic scatter with Hydrogen is impossible because Hydrogen does not have excited states. Cross section increases with increasing energy.

35 General Neutron Interactions Nonelastic Processes Nonelastic Processes Similar to inelastic scatter in that the process follows a compound nucleus model and that there is a recoil neutron. but instead of emitting γ-rays, additional secondary particles can be emitted (in addition to scattered neutron). Nucleus has different number of p+ and n o after interaction. Different from absorption because neutron is not absorbed, a scattered neutron is emitted (may not be the same one that entered rxn). Sometimes called nonelastic scatter

36 Thermal Neutron Interactions Absorption (sometimes called neutron capture) As neutrons reach thermal or near thermal energies, their likelihood of capture by an absorber nucleus increases. σ In this energy range, the absorption cross-section of many nuclei, has been found to be inversely proportional to the square root of the velocity of the neutron. 1 1 one-over-v law for slow neutron absorption E ν 1/υ region Lilly, fig 1.14

37 Thermal Neutron Interactions Absorption Thermal neutron cross sections (tabular data) are usually given for neutrons whose most probable energy is 0.025eV. If the cross section at E 0 is σ 0, then the cross section for any other neutron (within the validity of the 1/v law is given by: σ σ 0 = ν ν 0 = E 0 E

38 Thermal neutron cross sections Isotope Abunda nce Isotope Produced Half-life Cross section [barn atom -1 ] 23 Na 100% 24 Na 15 h P 100% 32 P 14.3 d K 6.9% 42 K 12.4 h Fe 0.33% 59 Fe 45.1 d Co 100% 60 Co 5.26 y Au 100% 198 Au 2.69 d B 19.8% 7 Li Stable 3837 B (all isotopes) Cd 12.3% 114 Cd Stable Cd (all isotopes) 2450

39 Thermal Neutron Interactions Activation (follows absorption) Nuclei are often in excited state following neutron absorption. Activated nuclei decay by normal processes. Example 14 N(n,p) 14 C 10 B(n,a) 7 Li 113 Cd(n,g) 114 C

40 General Neutron Interactions Activation Why is this important to us? Radiation Hazard after neutron beam turned off. How can we use this to our advantage? Tool for measuring neutron flux. Detection class: We will discuss neutron detection via activation foils.

41 Thermal Neutron Interactions Activation 197 Au Activation Foils 197 Au has a large thermal neutron absorption cross section (98.8 barns at 2200m/s). 198 Au atoms are formed following neutron capture. Then 198 Au decays in a β γ cascade 198 Au β T 1/2 =12ps 198 Hg γ = KeV T 1/2 2.7d Measure This!

42 Most Common Neutron Interactions in Tissue

43 Neutron Interactions with Tissue Neutrons are indirectly ionizing and but give rise to densely ionizing (high LET) particles: recoil protons, α-particles, and heavier nuclear fragments. The most common elements in the human body are Hydrogen, Carbon, Nitrogen, and Oxygen. Interactions with these elements contribute to dose in tissue.

44 Neutron Interactions are Energy Dependent Fast neutrons lose energy through scatter interactions with atoms in their environment. At higher energies inelastic scatter dominates, while at lower energies elastic scatter dominates. Fast neutrons also interact via nonelastic processes involving C and O. After being slowed to thermal or near thermal energies, absorption processes can occur.

45 Fast Neutron Interactions with Oxygen and Carbon Non-elastic processes results in recoil α- particles (high Let particles). A neutron interacts with a Carbon atom (6 protons and 6 neutrons), resulting in three α-particles. (Hall, Fig 1.10) A neutron interacts with an Oxygen atom (8 protons and 8 neutrons), resulting in four α-particles. (Hall, Fig 1.10)

46 Intermediate Neutron Interactions in Tissue Interact primarily via elastic scatter with Hydrogen For intermediate energy neutrons, the interaction between neutrons and hydrogen nuclei is the dominant process of energy transfer in soft tissues. 3 Reasons 1.Hydrogen is the most abundant atom in tissue. 2.A proton and a neutron have similar mass, 938 MeV/cm 2 versus 940 MeV/cm 2. 3.Hydrogen has a large collision cross-section for neutrons.

47 Thermal Neutron Interactions in Tissue The major component of dose from thermal neutrons is a consequence of the 14 N(n,p) 14 C MeV 0.04 MeV to recoil nucleus (local absorption) 0.58 MeV to proton (range of ~10-6 m local) Dominant energy transfer mechanism in thermal and epithermal region in body Kerma = dose Another thermal neutron interaction of some consequence is the 1 H(n,γ) 2 H MeV 2.2 MeV to gamma (nonlocal absorption) Small amount of energy to deuterium recoil (local absorption) Kerma dose (non-local absorption)

48 References J. Lilly. Nuclear Physics Principles and Applications. (2001) G. Knoll. Radiation Detection and Measurement 2 nd ed. (1989) P. Rinard. Ch-12 Neutron Interactions with Matter. Eric J. Hall. Radiobiology for the Radiologist 5 th Ed. (2000) NCRP Report 38. Protection against Neutron Radiation. (1971)