Neutron Interactions and Dosimetry I

1. Neutron Interactions and Dosimetry I Kinetic Energy Interactions Quality Factor n + ? Mixed-Field Dosimetry

2. Introduction This section is intended to provide an introduction to neutron dosimetry that is relevant to the human body, from the viewpoint of either radiation hazard or neutron-beam radiotherapy We will be primarily concerned about neutron interactions with the majority tissue elements H, O, C, and N, and the resulting absorbed dose

3. Introduction Because of the short ranges of the secondary charged particles that are produced in such interactions, CPE is usually well approximated Since no bremsstrahlung x-rays are generated, the absorbed dose can be assumed to be equal to the kerma at any point in neutron fields at least up to an energy E ? 20 MeV

4. Neutron Kinetic Energy For dosimetry purposes it is convenient to divide neutron fields into three energy categories: Thermal Neutrons Intermediate-Energy Neutrons Fast Neutrons

5. Thermal Neutrons Thermal neutrons have only the Maxwellian distribution of thermal motion that is characteristic of the temperature of the medium in which they exist Their most probable energy at 20�C is E = 0.025 eV All neutrons with energies below 0.5 eV are usually referred to as thermal because of a simple test that can be applied to a neutron field to measure how completely it has been �thermalized� by passage through a moderator

6. Cadmium Ratio A Cd filter 1 mm thick absorbs practically all incident neutrons below about 0.5 eV, but readily passes those above that energy A thermal-neutron detecting foil such as gold can be radioactivated by neutrons through the 197Au(n,?)198Au interaction Exposing two such foils in the neutron field, one foil bare and the other enclosed in 1 mm of Cd, provides two activation readings The ratio of the bare to the Cd reading is called the cadmium ratio; it is unity if no thermal neutrons are present, and rises towards infinity as the thermal-neutron component approaches 100%

7. Intermediate-Energy Neutrons Neutrons with energies above the thermal cutoff of 0.5 eV but below 10 keV are called intermediate-energy neutrons Above 10 keV, the dose in the human body is dominated by the contribution of recoil protons resulting from elastic scattering of hydrogen nuclei Below that energy the dose is mainly due to ?-rays resulting from thermal-neutron capture in hydrogen

8. Fast Neutrons These neutrons cover the energy range from 10 keV upward

9. Tissue Composition The following table gives the atomic composition, in percentage by weight, of human muscle tissue and the whole body The ICRU composition for muscle has been assumed in most cases for neutron-dose calculations, lumping the 1.1% of �other� minor elements together with oxygen to make a simple four-element (H, O, C, N) composition

11. Kerma Calculations For a single neutron energy, type of target atom, and kind of interaction, the kerma that results from a neutron fluence ? (cm-2) at a point in a medium is given by where ? is the interaction cross section in cm2/(target atom), Nt is the number of target atoms in the irradiated sample, m is the sample mass in grams, and Etr is the total kinetic energy (MeV) given to charged particles per interaction

12. Kerma Calculations K is thus given in rad (or centigrays), and its value is equal to the absorbed dose D at the same point under the usual CPE conditions The product of (1.602 ? 10-8?Ntm-1Etr) is equal to the kerma factor Fn in rad cm2/n Thus the equation reduces to

13. Kerma Calculations Fn is not generally a smooth function of Z and E, unlike the case of photon interaction coefficients Interpolation vs. Z cannot be employed to obtain values of Fn for elements for which data are not listed, and interpolation vs. E is feasible only within energy regions where resonance peaks are absent

15. Kerma Calculations For a continuous neutron spectrum with a differential fluence distribution ??(E) (n/cm2 MeV), the kerma contribution by j-type interactions with i-type target atoms is where [Etr(E)]ij is the total kinetic energy given to charged particles per type-j interaction with type-i atoms by neutrons of energy E

16. Kerma Calculations For the same units as in the first equation, Kij is given in rads or centigrays It can be summed over all i and j to obtain the kerma (or dose) due to all types of interactions and target atoms:

17. Thermal-Neutron Interactions in Tissue There are two important interactions of thermal neutrons with tissue: neutron capture by nitrogen, 14N(n,p)14C, and neutron capture by hydrogen, 1H(n,?)2H The nitrogen interaction releases a kinetic energy of Etr = 0.62 MeV that is shared by the proton (0.58 MeV) and the recoiling nucleus (0.04 MeV)

18. Thermal-Neutron Interactions in Tissue Thermal neutrons have a larger probability of capture by hydrogen atoms in muscle, because there are 41 times more H atoms than N atoms in tissue The energy given to ?-rays per unit mass and per unit fluence of thermal neutrons can be obtained from an equation similar to Eq. (1), but replacing Etr by E? = 2.2 MeV (the ?-ray energy released in each neutron capture)

19. Thermal-Neutron Interactions in Tissue This of course does not contribute directly to the kerma, since the ?-rays must interact and transfer energy to charged particles to produce kerma If the irradiated tissue mass is small enough to allow the ?-rays to escape, the kerma due to thermal neutrons is only that resulting from the nitrogen (n, p) interactions In larger masses of tissue the ?-rays are increasingly absorbed before escaping, thus contributing to the kerma

20. Thermal-Neutron Interactions in Tissue In the center of a 1-cm diameter sphere of tissue the kerma contributions from the (n, p) and (n, ?) processes are comparable in size In a large tissue mass (radius > 5 times the ?-ray MFP) where radiation equilibrium is approximated, the kerma due indirectly to the (n, ?) process is 26 times that of the nitrogen (n, p) interaction The human body is intermediate in size, but large enough so the 1H(n, ?)2H process dominates in kerma (and dose) production

21. Interaction by Intermediate and Fast Neutrons The following diagram summarizes the processes that contribute directly to kerma in a small mass of tissue in free space The dashed curve a is the sum of all the others It is dominated below 10-4 MeV by curve g, which represents (n,p) reactions, mostly in nitrogen Above 10-4 MeV elastic scattering of hydrogen nuclei (curve b) contributes nearly all of the kerma

23. Interaction by Intermediate and Fast Neutrons The average energy transferred by elastic scattering to a nucleus is closely approximated (i.e., assuming isotropic scattering in the center-of-mass system) by where E = neutron energy, Ma = mass of target nucleus, Mn = neutron mass

24. Interaction by Intermediate and Fast Neutrons For hydrogen recoils?Etr ? E/2 with Etr-values ranging from 0 (for protons recoiling at 90�) to Etr = E for protons recoiling straight ahead For other tissue atoms, elastic scattering gives?Etr = 0.142E for C atoms, 0.124E for N atoms, and 0.083E for O atoms

25. Neutron Sources The most widely available neutron sources are nuclear fission reactors, accelerators, and radioactive sources Fissionlike spectra have average neutron energies around 2 MeV, and are available from nuclear reactors, 252Cf radioactive (spontaneous fission) sources, critical assemblies, and other �mock� fission sources such as that produced by 12-MeV cyclotron-accelerated protons on a thick Be target

27. Neutron Sources Several types of Be(?,n) radioactive sources are in common use, employing 210Po, 239Pu, 241Am, or 226Ra as the emitter Neutron yields are on the order of 1 neutron per 104 ?-particles The following diagram exemplifies the neutron spectra emitted, which have average energies ? 4 MeV

29. Neutron Sources Low-energy neutron generators accelerate deuterium to 0.1 � 0.4 MeV and impinge them on targets containing either deuterium or tritium The output neutrons are in the range of 1.9 � 3.4 MeV for the D(d,n)3He reaction, and 12.9 � 15.6 MeV for T(d,n)4He Outputs on the order of 1011 and 1013 n/s, respectively, can be achieved in this way

32. Neutron Sources Cyclotrons can be used to produce neutron beams by accelerating protons or deuterons into various targets, most commonly Be The following diagram shows the typical bell-shaped neutron spectra that result from deuteron bombardment The neutron energies extend from zero to somewhat above the deuteron energy, and have an average of about 0.4 times that energy

34. Neutron Quality Factor For purposes of neutron radiation protection the dose equivalent H is equal to DQ, where Q is the quality factor, which depends on neutron energy according to the following curve The quality factor for all ?-rays is taken to be unity for purposes of combining neutron and ?-ray dose equivalents

36. n + ? Mixed-Field Dosimetry Neutrons and ?-rays are both indirectly ionizing radiations that are attenuated more or less exponentially in passing through matter Each is capable of generating secondary fields of the other radiation, by (n, ?) and (?, n) reactions, respectively

37. n + ? Mixed-Field Dosimetry (?, n) reactions are only significant for high-energy ?-rays (?10 MeV), but (n, ?) reactions can proceed at all neutron energies and are especially important in the case of thermal-neutron capture, as discussed for 1H(n, ?)2H As a result neutron fields are normally found to be �contaminated� by secondary ?-rays Since neutrons generally have more biological effectiveness per unit of absorbed dose than ?-rays, it is usually desirable to perform dosimetry in a way that provides separate dose accounting for ? and n components

38. n + ? Mixed-Field Dosimetry It will be convenient to discuss three general categories of dosimeters for n + ? applications: Neutron dosimeters that are relatively insensitive to ? rays ?-ray dosimeters that are relatively insensitive to neutrons Dosimeters that are comparably sensitive to both radiations

39. n + ? Mixed-Field Dosimetry It is especially important in the case of neutron dosimeters to specify the reference material to which the dose reading is supposed to refer Usually, because of the universal interest in radiation effects on the human body, kerma or absorbed dose in muscle tissue provides the reference basis for specifying dosimeter performance

40. n + ? Mixed-Field Dosimetry It should be noted that water is not as close a substitute for muscle tissue for neutrons as it is for photons Water is 1/9 hydrogen by weight; muscle is 1/10 hydrogen Water contains no nitrogen, and hence can have no 14N(n,p)14C reactions by thermal neutrons

41. Equation for n + ? Dosimeter Response The general equation for the response of a dosimeter to a mixed field of neutrons and ?-rays can be most simply written in the form or alternatively as

42. Equation for n + ? Dosimeter Response where Qn,? = total response due to the combined effects of the ?-rays and neutrons, A = response per unit of absorbed dose in tissue for ?-rays, B = response per unit of absorbed dose in tissue for neutrons, D? = ?-ray absorbed dose in tissue, and Dn = neutron absorbed dose in tissue

43. Equation for n + ? Dosimeter Response By convention the absorbed dose referred to in these terms is assumed to be that under CPE conditions in a small imaginary sphere of muscle tissue, centered at the dosimeter midpoint with the dosimeter absent Most commonly this tissue sphere is taken to be just large enough (0.52-g/cm2 radius) to produce CPE at its center in a 60Co beam