The United States Nuclear Regulatory Commission and Duke University Present: Regulatory and Radiation Protection Issues in Radionuclide Therapy

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1 The United States Nuclear Regulatory Commission and Duke University Present: Regulatory and Radiation Protection Issues in Radionuclide Therapy Copyright 2008 Duke Radiation Safety and Duke University. All Rights Reserved.

2 Welcome! This is the Fourth of a series of training modules in Radiation Physics. These modules provide a basic introduction to Radioactivity. Sponsored by the United States Nuclear Regulatory Commission and Duke University Author: Dr. Rathnayaka Gunasingha, PhD

3 Your Instructor Dr. RathnayakaGunasinghais an Accelerator Physicist with background in High Energy physics. Dr. Gunasinghais a physicist in the Radiation Safety division and member of the Faculty of the Duke Medical Physics Graduate Program. Contact: rathnayaka.gunasingha@duke.edu

4 Goals of the Course Upon completing these instructional modules, you should be able to: understand the Basic Interaction of Radiation with Matter apply the knowledge in various calculations used in Medical and Health Physics understand the basic principles behind various instrumentation used in Medical and Health Physics

5 This Module Will Cover The processes and kinematics of 1. α, β,and γdecays 2. Electron Capture 3. Internal Conversion and, 4. Auger Electron

6 Radioactivity The spontanious disintegration or rearrangement of internal structure of an unstable nucleus by emitting particles or radiation is called "Radioactivity" Emitted particles and radiation in radioactivity are collectively called "rays" There are three kind of rays in natural occuring radioactivity. (a) α rays (b) β rays ( electrons and positrons) (c ) γ rays

7 Radioactivity α rays are helium nucleus and can be blocked by a 0.01 mm of lead. β rays are electrons or positrons and can be blocked by a 0.1 mm of lead γ rays are the most penetrating and can pass through a 100 mm thick lead.

8 Radioactivity In a radioactive dacay, Mass, energy, electric charge, linear momentum, angular momentum, and nucleon numbers should be conserved. Example: initial amount of charge = final amount of charge after decay. Initial nucleus called "parent" emits a particle and produces another particle called "daughter". Daughter may be the same nucleus, in lower energy state or an entirely new nucleus.

9 Radioactivity of α Decay α - Decay: The process of ejecting an alpha particle from a nucleus is called α- decay. Atomic number of the parent P is decreased by 2, and mass number decreased by 4, when the daughter D is produced. A Z P D + He A 4 4 Z 2 2 Example: Ra Rn + He

10 Kinematics of α Decay Let us assume, the α decay occurs in a system where the parent is at rest. P D + α From conservation of energy, M c = M c + M c + K + K p D α D α K, K Kinetic energies, M,M Masses D α D α Since K + K 0, M M + M D α p D α

11 Kinematics of α Decay The energy released is the disintegration energy and it is called Q- value. Q = K + K D α ( ) 2 Q = M M M c P D α From conservation of lenear momentum and the Q value M v = M V α D 1 1 Q = Mαv + M V D (1) (2)

12 Kinematics of α Decay Removing V from (1) and (2) 1 M + M 1 Q = M v since K = M v D α 2 α α α M D K α = M D K D = M D M DQ + M MαQ + M α α and Since M + M A K α D α A 4 = Q A

13 Decay Scheme The nuclear transformation from parent to daughter can easily be described by a decay-scheme diagram. This diagram includes the decay mode, branching ratio, and energy transitions. Conventions: 1. Arrows slanting to the left side indicate decrease in Z 2. Arrows slanting to the right side indicate the increase in Z 3. Wavy lines going straight down indicate the gamma emission from the nucleus

14 α-decay For example, Follwing figure shows the decay of 94.4%, it decays directly to ground state emitting α particles, and 5.5% of it decays to anothor lower energy state, and later to ground state by emitting gammas Ra.

15 α Decay Scheme Ra % α % α Rn 4% MeV Excited state Ground state Spectra of α-particles: discrete/mono-energetic

16 β Decay The process of in which the charge of the nucleus is changed without any change in the number of nucleons is called β -decay. There are three types of β decays. β - 1. decay - emission of β + an electron 2. decay - emission of a positron 3. electron capture In each of these decays, an additional particle called "neutrino" appears as one of the decay products.

17 β decay Neutrino was first postulated by Pauli (1930) in order to preserve the conservation of energy and momentum of the neutron β decay. n p + e + υ e Properties of charge = 0 neutrino are : rest mass 0, spin = 1 2, electric Neutrino represents by υ and its anti particle by υ.there are three types of neutrinos and their anti pariticles. ( υ, υ, υ ) and ( υ, υ, υ ). e µ τ e µ τ

18 β Decay In β decay, nuclides with excess neutrons, convert a neutron to a proton to gain the stability. n p + e + υ and, an electron and a antineutrino are ejected. β - X(Z,A) Q β- Y(Z+1,A) A Z P A Z + 1 D e+ υ 0 e (Z,A) (Z+1,A) + e - +ν e In this process, Conservation laws (charge, lepton number and nucleon number ) should be observed. As a result, the atomic number Z of daughter is increased by 1.

19 β Decay Example : B C + e + υ 12 5 B has 7 neutrons and they are too many to be stable. one neutron is converted to a proton and created with 6 neutrons. e 12 6 C an electron and a antineutrino are ejected from the nucleus.

20 Kinematics of β Decay P D + e + A A 0 0 Z Z υ e From conservation of energy M c = M c + m c + K + K K = P D e e υ kinetic energy The Q-Value Q = K + K e v Q = ( M M m ) c p D e 2

21 β Decay Note: If masses M, M and m are given in atomic masses p D e ( ) ( ( 1) ) 2 ( p D ) Q = M p Zme M D Z + me m e c Q = M M c 2 For example, consider β decay P S + e + υ + Q Using the atomic Q = 1.71 MeV. mass differences of P S = 1.71 MeV

22 β Decay Example : Find the maximum energy of the electron of the decay of 3 3 H Solution : M c = M c + Q H Where Q = K + K e v H He + e + υ ( ) H He Q = M M c 3 1 ( ) Q = [ electron mass was neglected] MeV Q = MeV Assume the energy of neutrino is zero. Then, the maximum energy of electron is MeV.

23 ( ) β Decay When M M m decay occurs. p D e Since Q = M M the excess energy is shared by three decay particles. P D β Since nucleus is massive it receives a negligible energy. The energy is shared between electron and antineutrino. Depending of the orientation of the particles, the energy of the electron in a decay can have energy between 0 and Q. β

24 β Decay The energy spectrum of the electron in a β decay is continuous. Q The average electron energy is about. 3

25 β Decay β- per MeV interval E avg = MeV E max = 1.71 MeV The figure shows - from β decay of MeV the electron spectrum 32 P. 15 Maximum electron energy is and the average energy is MeV. 0 E (MeV) S 15 The decay scheme for P is shown in figure. Note :Since Z is increasing, arrow is slanting to the right β - E max = 1.71 MeV E avg = MeV 32 S 16

26 β + Decay Decay of a nuclides with excessive protons by β + emitting a positron is called a decay. Nuclide attempts to gain the stability, by converting a proton to a neutron, and increasing the number of neutrons. + p n + e + υ e As a result, atomic number of the daughter is 1 less than that of the parent. A Z + P D + e + υ A Z 1 example : N C + e + υ 12 7 e e

27 β + Decay Note: If masses M p,m D and m e are given in atomic masses A Z P A Z 1 D + e + + υ ( 1 m ) ( ) 2 M Zm c = M ( Z ) p e D Q = ( M M 2m ) 2 c p D e e c 2 + m c e 2 + Q When M P M D 2m, + β decay occurs.

28 β + Decay β + decay scheme 15 8 O is shown in figure at left. + and energy spectrum for e from the decay is shown at right. 64 Cu 15 O MeV 0.511MeV β MeV E max = 1.73 MeV E avg = 0.21 MeV 15 N 7 0 MeV number of positrons positron decay spectrum from βdecay of 64 Cu E (MeV) Q value of reaction = MeV

29 Electron Capture The process of capturing an atomic electron ( usually from K-shell) by the nucleus and emitting a neutrino, is called "electron capture". In an electron capture, atomic nunber of the parent is decreased by one. e + P D + υ A Z A Z 1 example: e + Be Li + υ (i.e. e + p n + υ)

30 Electron Capture Conservation of energy 2 2 ( p e K ) D = ( p + e K D ) M + m E c = M c + Q Q M m E M c 2 Where E is the binding energy of the K-shell electron K Q > 0 when M M > E p D K i.e. Electron capture is possible only when M M > E. p D K

31 Electron Capture Electron captureproducestwo particles,daughter and the neutrino,movingin oppositedirection with equalmomentum. Sincedaughter nucleusis heavy,neutrinocarriesall of kineticenergy. X(Z,A) the EC Q EC Y(Z-1,A) e- + (Z,A) (Z-1,A) + e - +ν e

32 Electron Capture Following figure shows the decay scheme diagram for Na. 10% of decay occurs through electron capture and other 90% through β decay.

33 γ decay The process in which a nucleus initially in an excited state makes a transition to a lower energy state emitting a photon is called a gamma decay. * ( A ) ( A ) Z Z P = P + γ The charge and the atomic number do not change in the gamma decay. The energy of the emitted photon is; hυ = E E u l

34 γ decay In most cases, the excited state nucleus is the daughter nucleus following a radioactive decay ( β decay or α decay) of another nucleus. -14 Most excited nuclei have very short half lives ( 10 s). Half lives of some nuclei are measurable and seems almost stable.

35 γ decay Nucleus in the excied state appear like a separate isotope with same Z and A as the stable nucleus, with more energy. These -6 nulcleus are called "isomers" and their life times are less than 10 s. The transition to ground state of these nucleus is called the isomeric transition. The excited state is called the "metastable state" to distinguish from the ground state.

36 γ decay In the following decay scheme, 137m is a metastable state. It decays to ground state half life of 2.55 m Ba from β decay of Ba with a Cs, 137 Cs y β - ( 5.4%) e - β - ( 94.6%) (85%) 2.55 m 137m Ba Ba 56

37 Internal Conversions The process in which the energy of the excited state is transferred to an atomic electron ( K or L shell electron) and ejecting it from the atom is called "Internal Convesion". The excited state of nucleus may lose its energy by the emission of gamma ray. This gamma ray can interact with an electron in K-shell. This process perturbs the nucleus and can transist it to the ground state.

38 Internal Conversions * Energy transfer to the electron, E = E E where E is the binding energy of the K or L shell electron. B e γ B

39 Internal Conversions Figure shows β spectrum of Au with discrete electron energies of MeV and MeV lines. These electrons come from the internal conversion of MeV gamma ray in the K, L+ M shells.

40 Internal Conversions Internal conversion is schematically depicted in - the following figure. Nucleus eject a ray creating a daughter of Z + 1 protons and N -1 neutrons. If the daughter is in excited state, it can emit a gamma ray E. It can eject a electron in a K-shell with a energy E γ E γ K. This creates a hole in the daughter atom. β

41 Internal Conversions The probability of K-electron conversion is given by the internal conversion yield, α and it is defined by, α K Number of conversion electrons in K-shell = Numebr of γ -rays detected K α values range from 0 to 100 or more and increase K with incresing Z and decrease with increasing E. γ

42 Auger Electrons High speed electron or electron capture or internal conversion can create an hole in the K, L or M shell of an atom. This hole can be filled by an electron from an outer shell an emission of characteristic radiation. with In some cases, this characteristic radiation (photon) is absent and in its place, a monoenergetic electron is ejected from the atom. This ejected electron is known as the "Auger Electron"

43 Auger Electrons Assume a hole was created in the K-shell An electron from L shell can transit to fill the Amount of energy released = E E K L K-shell As an alternative to photon transmission, this energy is transfer to M electron or other ejecting it. then, T + E = E E M M K L where T = kinetic energy, E = Binding energies ( ) T = E E E M K L M x

44 Auger Electrons This process is illustrated in the follwing figure, and the electron is called the " KLM Auger electron"

45 Auger Electrons Now the atom has two vacancies, one in L -shell and other in M -shell. If two N - shell electrons move in to fill those vacancies the atom emits two more Auger electrons.assume they are from N - shell, the we would have four N - shell vacancies. T N 1 + E N = E L E N T N 1 = E L 2E N and T N 2 + E N = E M E N T N 2 = E M 2E N

46 Auger Electrons Total energy of three Auger electrons ( ) T + T + T = E E E + E 2E + E 2E M N N K L M L N M N T + T + T = E 4E M N N K N This process repeats increasing the number of electron vacancies by one for each Auger electron event, until all the vacancies located in the outer shell.

47 Auger Electrons Then, we can show, total energy carried away by all Auger electrons = (sum of binding energies of all final electron vacancies) E K For KLM Auger electrons, we have four vacancies in N-shell.

48 Auger Electrons-fluorescent The relative probability of the emission of characteristic radiation to the emission of an Auger electron is called the "fluorescent yield" Fluorescent yield ω = K Number of K-x ray photons emitted Number of K-shell vacancies

49 Credits and References Attix, F.H, Introduction to Radiological Physics and Radiation Dosimetry, Wiley- VCH(2004)

Decay Mechanisms. The laws of conservation of charge and of nucleons require that for alpha decay, He + Q 3.1

Decay Mechanisms. The laws of conservation of charge and of nucleons require that for alpha decay, He + Q 3.1 Decay Mechanisms 1. Alpha Decay An alpha particle is a helium-4 nucleus. This is a very stable entity and alpha emission was, historically, the first decay process to be studied in detail. Almost all naturally