Lowenthal G., Airey P. Practical Applications of Radioactivity and Nuclear Radiations

Подождите немного. Документ загружается.

useful for applications. The low-energy KX rays (<6 keV) and the K Auger

electrons (<5 keV) from these nuclides are unlikely to interfere with the use

of the much higher energy 0.32 and 0.83 MeV g rays.

3.6.2 The internal conversion process

The de-excitation of daughter nuclides does not only proceed via g rays but

also by a competing process known as internal conversion (IC). Each

contributes a share, but the shares are commonly different (see below).

During IC, the de-excitation energy is transferred from the nucleus of the

daughter to an inner shell atomic electron, usually a K electron which is

nearest to the nucleus. The electron is ejected from its shell, dissipating the

energy received from the de-excitation, except for the part used to liberate it

from its atom (NCRP, 1985, Appendix A:1.2.4). Both EC and IC involve the

nucleus of the atom and lead to the ejection of inner shell atomic electrons.

Also, both lead to the same follow-on radiations, ¯uorescent X rays and

Auger electrons.

Internal conversion rates relative to the rate of g ray emissions are

calculated using the total internal conversion coef®cient a

. One has:

= N

, (3.10)

where N

stands for the fraction of de-excitations via conversion electrons

(between 80 and 90% are emitted from the K shell) and N

represents the

fraction proceeding via g rays. Although there are exceptions, a

is less than

0.01 when the de-excitation energy exceeds about 200 keV, but it could

3.6 Electron capture, g rays and conversion electrons 81

Figure 3.12. The ¯uorescent yields in the K shell of atoms (v

) as a function of the

Z number of the atoms (Mann et al., 1991, Section 2.4.5).

exceed a hundred when that energy is only a few kiloelectronvolts. For the

137m

Ba decay shown in Figures 3.4(c), (d), the ratio N

is approximately

equal to 0.10/0.90 & 0.11 (NCRP, 1985, Appendix A3). This is a relatively

high IC rate at 662 keV.

3.7 The role of mass energy in determining nuclear decays

3.7.1 Neutron-poor radionuclides

Radioactivity is triggered by differences in the energy equivalent of the mass

of neighbouring nuclides in appropriate circumstances. The energy is ex-

pressed in kilo- or megaelectronvolts and labelled Q. It provides for all

requirements during the decay, e.g. the kinetic energies of the emitted

radiations both primary and follow-on, as well as the energies required to

eject electrons from their atoms.

There is also the binding energy holding protons and neutrons together in

their nuclei (Figure 1.2), and the energy equivalent of the mass of each

emitted particle. This is about 3730 MeV for a particles (Table 1.2), but only

0.511 MeV for b particles, about one part in 7300 of that of a particles. It is

the low-energy equivalent of the mass of electrons which contributes to the

large number of b decays relative to a decays.

Figure 1.3 shows the stable nuclides near the middle of each row with the

neutron-poor radionuclides on the left and the neutron-rich radionuclides on

the right. Neutron-poor radionuclides have two pathways towards increased

or complete stability ± EC decay and decay by positron emissions. If EC

decays occur to the ground state of the daughter, the ¯uorescent X rays and

Auger electrons are the only emitted radiations. If the EC decay is to an

excited state de-excited by g radiations which are unconverted or nearly so,

one has g rays in addition to the X rays and Auger electrons. If IC is also

present, it reduces the g ray fraction with a corresponding increase in the

fraction of conversion electrons.

Iron-55 decays direct to the ground state of its stable daughter, manganese-

55 (Figure 3.11(c)). Because there are no emissions at higher energies, the

averagely 6 keV manganese KX rays are available, e.g. for the calibration of

low-energy photon detectors.

3.7.2 Positron decay and positron tomography

When b

or EC decays occur direct to the ground state of the respective

daughters, the Q values applying to b

decays have to provide for the mass

Properties of radiations82

and kinetic energies of the particles plus that of their anti-neutrinos and the

binding energy, but that is all. For pure EC decays, e.g. that of

Fe, they

have to provide for the neutrino energies and the binding energies needed to

dislodge the electrons. However, positron decay inevitably leads to positron±

negatron annihilation (Section 3.3.1) and so cannot compete with EC decay

unless there is suf®cient difference in nuclear mass (and so in energy) to

provide for the annihilation events which always follow positron emissions.

Positron decays are invariably accompanied by at least a small percentage

of EC decays, 0.2% for carbon-11 and nitrogen-13. However, EC percentages

can be large (e.g. 95% for zinc-65 (Figure 3.13)). As a rule, the 511 keV

annihilation g rays are more useful for applications than b

particles.

Positron decays are gaining in importance on account of their role in

computerised tomography (Section 7.2.1). Because they can be used to

provide three dimensional imaging (Section 1.4.4), tomographic techniques

3.7 The role of mass energy 83

Figure 3.13. Three decay schemes illustrating different decay modes. (a) The decay

of nitrogen-13: 99.8% b

, 0.2% EC. (b) The three-pronged decay of copper-64: 18%

, 37% b

, 45% EC. (c) The decay of zinc-65: 98.5% EC, 1.5% b

are being increasingly applied to industrial processes e.g. in the construction

industry for inspecting castings to detect cracks, or the study of ¯ow patterns

in pneumatic pipelines.

Tomographic imaging producing displays in three dimensions requires the

processing of very large amounts of data and so has to be computer assisted

(CAT). Table 3.1 lists positron emitters which could be useful for such

applications but industrial tomography is more commonly employed with

X rays (Section 7.2.3) than with the 511 keV g rays following positron

emissions.

3.7.3 Multi gamma ray emitters

The introduction and development of NaI(Tl) detectors and the associated

signal processing equipment from the mid-1940s onwards made it possible to

record multi gamma ray spectra with usefully high resolution and this almost

as a matter of routine (Crouthamel 1960, 1981, Heath 1964). Then came

another very big step forward: the advent of high-resolution semiconductor g

Properties of radiations84

Table 3.1. Positron emitters for applications.

Radionuclide Half life

Positron Data

Energy Intensity per

(MeV) decay (%)

Carbon-11 20.4 m 0.97 99.8

Nitrogen-13 9.97 m 1.20 99.8

Oxygen-15 2.04 m 1.70 99.9

Fluorine-18 109.7 m 0.64 97.0

Sodium-22 2.60 y 0.55 89.8

Aluminium-26 7.3610

y 1.17 81.8

Vanadium-48 16.0 d 0.70 50.3

Cobalt-58 70.82 d 0.48 15.0

Copper-64 12.70 h 0.65 17.9

Gallium-68 68.0 m 0.84

88.0

Note:

The g ray emissions (if any), following the decay of the positron emitters

included in this table, are unlikely to interfere with the employment of annihilation g

rays.

Positron emitters which decay with very short half lives can only be used for

applications if there is a direct access to a cyclotron and associated radiochemical

facilities.

Positron decays are invariably accompanied by EC decays and sometimes also by

negatron decays (Sect ion 3.6.1), so accounting for the less than 100% intensities.

This is the average positron energy for two branches. The other nine radionuclides

decay via a single positron branch and the stated energies are the maxima of the

spectra.

and X ray detectors beginning during the mid-1960s. High-resolution semi-

conductor g ray detectors are either crystals of lithium drifted germanium

(Ge(Li)) or high-purity germanium (HPGe) which make it possible to

routinely obtain spectra such as that of europium-152 (Figure 3.14(a)).

Europium-152 (T

1/2

= 13.51 y) undergoes a two-pronged decay (EC and

) followed by the emission of g rays with over 100 different energies

between 0.12 and 1.53 MeV, but the overall g ray emission rate is only about

1.5 g rays (of all energies) per decay of

152

Eu. The large majority of these

energies can be clearly resolved although only eleven energies are emitted

with suf®cient intensity (>3% each) to be useful for intensity calibrations. The

remaining nearly 90 energies are emitted with, on average less than 0.03%

probability each, so explaining the many very small peaks seen in Figure

3.14(a).

There are many other effects which could cause distortions in gamma ray

spectra, notably Compton backscatter. This is illustrated in Figure 3.15, with

details to come in Section 3.9.1.

Multi gamma ray emitters are of particular interest for energy and intensity

calibrations of high-resolution detectors when it is often possible to effect

calibrations over the entire energy range of interest using a single multi g ray

emitter, with europium-152 as an outstanding example. Other long-lived

multi g ray emitters frequently used for detector calibrations are europium-

154 and, for the lower energy range, barium-133 (Table 8.1). It is desirable to

use long half life radionuclides for this purpose, to justify the work involved

in the calibration. By contrast, NaI(Tl) detectors are rarely able to adequately

resolve more than a few of the peaks of multi g ray emitters (Figure 3.9(c))

except when used by specialists.

The lower energy section of spectra due to multi gamma ray sources is

invariably positioned on top of a large background due mainly to Compton

scatter. Pulses due to g rays which were Compton scattered out of the high

energy peaks build up below the lower energy part of the spectrum (Figures

3.10, 3.14(a) and 3.15). Background subtractions to obtain the net count in

full energy peaks are readily made for high-energy peaks but require

considerable care for the low-energy peaks since there are often many more

pulses in the background just below the peak than in the peak. This applies to

germanium detectors as much as to NaI(Tl) detectors.

For reasons yet to be described (Section 5.5.2), lithium drifted germanium

detectors cannot be prepared without dead layers which absorb all g rays

with energies below 30 keV (or sometimes below 40 keV) and cause signi®cant

attenuation of higher energy g rays up to about 100 keV. This is evident in

Figures 3.14(c) and 3.14(b) which respectively show the contrast between a

3.7 The role of mass energy 85

Properties of radiations86

Figure 3.14. (a) The g ray spectrum following

152

Eu decays obtained with a Ge(Li)

detector. Note the numerous small peaks due to very low-intensity g rays (Section

3.7.3). (b)

Co spectra obtained with a Ge(Li) and (c) with a HPGe detector. Note

the effect of the dead layer coating the Ge(Li) detector (Debe rtin and Helmer, 1988,

Figures 4.3, 4.26).

Co spectrum obtained with a high-purity germanium detector and the

lithium drifted type. Ge(Li) detectors are now being replaced by HPGe

detectors whenever practical (Sections 5.5.2 and 5.5.3).

The calibration and use of multi-gamma ray emitters requires specialist

equipment and skills. Readers are referred to Debertin and Helmer (1988),

Sections 3.4 and 4.1 or L'Annunziata, Ed. (1998, Ch. 3 by Fettweis and

Schwenn), for a full treatment of this subject.

3.7.4 Three-pronged decays

A few radionuclides decay via three primary branches when they provide

examples of the role of mass energy in nuclear decay. One such radionuclide

which has found many applications is copper-64. Figure 3.13 shows examples

3.7 The role of mass energy 87

Figure 3.15. A pulse height spectrum obtained with a 50 mm650 mm NaI(Tl)

detector of intensely backscattered g rays from gold-198. The 411.8 keV full energy

peak, dominant in narrow beam geometry (see ®gure 4.5), is `dwarfed' by pulses due

to Compton scatter. Two low-intensity higher energy g rays are not shown.

of a b

decay of a neutron-poor radionuclide (nitrogen-13) as well as the

three-pronged decay of copper-64 and the EC plus b

decay of zinc-65. It is

the copper-64 decay which is of interest here.

Tables of nuclear masses quoted by Mann et al. (1980, Ch. 5, see also

Wapstra and Audi, 1985), provide the following data.

Nickel-64: nuclear mass, 63 .9280 amu; Z =28

Copper-64: nuclear mass, 63.9298 amu; Z =29

Zinc-64: nuclear mass, 63.9292 amu; Z = 30.

The mass difference for the decay of copper-64 to nickel-64, 0.0018 amu has

the energy equivalent of 0.00186932 MeV = 1.68 MeV, so permitting both

EC and positron decay. Allowing for some rounding, the mass difference

copper-64 to zinc-64 is 0.0006 amu and provides for the 576 keV maximum

energy of the negatron spectrum.

Copper-64 emits 511 keV g rays with a conveniently short half life (12.7 h),

which makes it useful for tracing copper and other metals while avoiding

problems due to the disposal of longer-lived radioactive residues.

3.8 Bremsstrahlung

3.8.1 Its origin

Bremsstrahlung (from the German for braking radiation) is only indirectly

related to nuclear emissions. It is generated when b particles or other

electrons emitted from radionuclides or from other sources are slowed down

in matter.

When charged particles are decelerated (braked) in the electric ®eld

surrounding the nuclei of atoms, a fraction or all of the kinetic energy of the

particles (depending on the type and thickness of the material), is converted

into electromagnetic radiation, the bremsstrahlung. Electrons are light

enough to be suf®ciently strongly decelerated to produce bremsstrahlung

photons of signi®cant intensities. The relatively very much heavier protons

and a particles (Table 1.2), are subject to proportionately smaller deceleration

when the bremsstrahlung yield can commonly be ignored unless one is

dealing with high activities.

3.8.2 Bremsstrahlung intensities

When emitted from their atoms, the energies of b particles range from near

zero to a maximum value which depends on the radionuclide (Figure 3.6(a) to

Properties of radiations88

(d)). Endpoint energies are as small as 18.6 keV (

H), but can exceed 2 MeV

(Table 8.2). Bremsstrahlung photons due to the braking of these b particles

cover the same range of energies though their average energy is nearer to

0.25E

bmax

than to the 0.33E

bmax

which applies for b particle emitters (Wilson,

1966).

The bremsstrahlung due to a high-activity b particle source is capable of

generating intense ionisations, especially so if the braking occurs in high

atomic number material (Eq. 3.11). If so, the bremsstrahlung intensity has

to be monitored to ensure adequate protection for experimenters or to

avoid errors when radioactivity measurements make use of ionisation

processes.

If b particles or other electrons move a small distance dx in a material of

atomic number Z they lose kinetic energy 7dE through collisions causing

excitations and ionisations of atomic electrons (7dE/dx)

coll

and through the

conversion of kinetic energy into bremsstrahlung (7dE/dx)

rad

. From com-

ments in NCRP 1985 (Appendix A1.2.9), one has approximately:

(7dE/dx)

rad

/(7dE/dx)

coll

& E

bav

6 Z / 700, (3.11)

where E

bav

stands for the average energy of the b particle spectrum expressed

in megaelectronvolts. If

P particles (E

bav

= 0.70 MeV) are absorbed in

copper (Z = 29), the fraction of the initial kinetic energy of the b particles

converted to bremsstrahlung is 0.70629/700 = 0.03 or about 3%.

The X rays discovered by Ro

ntgen were bremsstrahlung photons produced

when electrons emitted from a hot cathode in an evacuated glass tube and

subsequently accelerated by an electric ®eld were stopped in metal parts and

in the glass envelope of the vacuum tube. The high-energy, high-intensity

X rays required for modern medical and industrial purposes (well up in the

megaelectronvolt range) are produced by accelerating electrons in high-

voltage machines and decelerating them in the ®rst few millimetres of high Z

number water-cooled targets, commonly tungsten targets (Z = 74).

3.9 Fluorescent radiations

3.9.1 Fluorescent X rays

Fluorescent X rays and Auger electrons (Section 3.9.3) are emitted as a

consequence of the transfer of electrons from outer to inner shells of their

atoms (Sections 3.6.1 and 3.6.2). These radiations carry away the energy that

is liberated during the transfer. The measurement of ¯uorescent X ray

energies is a long practised technique for chemical analysis because these

3.9 Fluorescent radiations 89

energies are functions of the Z number of the element from which they were

emitted (see e.g. Mann et al., 1991, Section 2.4.5).

As explained in physics texts (see e.g. Mann et al., 1980, p. 60), electrons

are held in their shells by accurately measurable binding energies which

decrease from inner to outer shells (Figure 3.16(a)). If a vacancy occurs in the

K shell it is promptly ®lled by electrons from an outer shell, when the

difference in the binding energies is liberated as ¯uorescent X rays or Auger

electrons. The X rays are labelled ¯uorescent since they persist no longer than

the excitations (10

712

s).

Quantum theory demands that the K shell of atoms can only accept atomic

electrons for the ®rst two elements: hydrogen and helium (Figure 1.1). When

Z > 2, the ®lling of the K shell is followed by that of the L shell, then M, N,

etc, with the order in which electrons are added to the shells depending on

rules derived from quantum theory. The shell and subshell structure shown in

Figure 3.16(a) applies to nickel (Z = 28).

Properties of radiations90

Figure 3.16. (a) A typical series of de-excitations in atoms of nickel (Z = 28),

showing the energies of the K. L, M electronic shells. (b) The energies of K, L, M

X rays as functions of the atomic number of the emitting atoms (Debertin and

Helmer, 1988, Figures 1.4 and 1.7).