radioactive decay and the origin of gamma and x-radiation · 2020-02-21 · radioactive...

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Radioactive Decay and the Origin ofGamma and X-Radiation

1.1 INTRODUCTION

In this chapter I intend to show how a basic understandingof simple decay schemes, and of the role gamma radiationplays in these, can help in identifying radioactive nuclidesand in correctly measuring quantities of such nuclides. Indoing so, I need to introduce some elementary conceptsof nuclear stability and radioactive decay. X-radiation canbe detected by using the same or similar equipment and Iwill also discuss the origin of X-rays in decay processesand the light that this knowledge sheds on characterizationprocedures.

I will show how the Karlsruhe Chart of the Nuclidescan be of help in predicting or confirming the identity ofradionuclides, being useful both for the modest amountof nuclear data it contains and for the ease with whichgeneric information as to the type of nuclide expected canbe seen.

First, I will briefly look at the nucleus and nuclearstability. I will consider a nucleus simply as an assemblyof uncharged neutrons and positively charged protons;both of these are called nucleons.

Number of neutrons = N

Number of protons = Z

Z is the atomic number, and defines the element. In theneutral atom, Z will also be the number of extranuclearelectrons in their atomic orbitals. An element has a fixedZ, but in general will be a mixture of atoms with differentmasses, depending on how many neutrons are present ineach nucleus. The total number of nucleons is called themass number.

Mass number = N +Z = A

Practical Gamma-ray Spectrometry – 2nd Edition Gordon R. Gilmore© 2008 John Wiley & Sons, Ltd

A, N and Z are all integers by definition. In practice, aneutron has a very similar mass to a proton and so there isa real physical justification for this usage. In general, anassembly of nucleons, with its associated electrons, shouldbe referred to as a nuclide. Conventionally, a nuclide ofatomic number Z, and mass number A is specified as A

ZSy,where Sy is the chemical symbol of the element. (Thisformat could be said to allow the physics to be definedbefore the symbol and leave room for chemical informa-tion to follow; for example, Co2+.) Thus, 58

27Co is a nuclidewith 27 protons and 31 neutrons. Because the chemicalsymbol uniquely identifies the element, unless there is aparticular reason for including it, the atomic number assubscript is usually omitted – as in 58Co. As it happens,this particular nuclide is radioactive and could, in orderto impart that extra item of knowledge, be referred to asa radionuclide. Unfortunately, in the world outside ofphysics and radiochemistry, the word isotope has becomesynonymous with radionuclide – something dangerousand unpleasant. In fact, isotopes are simply atoms of thesame element (i.e. same Z, different N ) – radioactive ornot. Thus 58

27Co, 5927Co and 60

27Co are isotopes of cobalt.Here 27 is the atomic number, and 58, 59 and 60 aremass numbers, equal to the total number of nucleons.59Co is stable; it is, in fact, the only stable isotope ofcobalt.

Returning to nomenclature, 58Co and 60Co are radioiso-topes, as they are unstable and undergo radioactive decay.It would be incorrect to say ‘the radioisotopes 60Co and239Pu � � � ’ as two different elements are being discussed;the correct expression would be ‘the radionuclides 60Coand 239Pu� � � ’.

If all stable nuclides are plotted as a function of Z (y-axis) and N (x-axis), then Figure 1.1 will result. This is aSegrè chart.

COPYRIG

HTED M

ATERIAL

2 Practical gamma-ray spectrometry

120 160

120

100

80

80

60

40

40

20

0

Ato

mic

num

ber,

Z

Neutron number, N

Figure 1.1 A Segrè chart. The symbols mark all known stablenuclides as a function of Z and N . At high Z, the long half-life Th and U nuclides are shown. The outer envelope enclosesknown radioactive species. The star marks the position of thelargest nuclide known to date, 277112, although its existence isstill waiting official acceptance

The Karlsruhe Chart of the Nuclides has this samebasic structure but with the addition of all known radioac-tive nuclides. The heaviest stable element is bismuth(Z = 83, N = 126). The figure also shows the location ofsome high Z unstable nuclides – the major thorium (Z =90) and uranium (Z = 92) nuclides. Theory has predictedthat there could be stable nuclides, as yet unknown, calledsuperheavy nuclides on an island of stability at aboutZ = 114, N = 184, well above the current known range.

Radioactive decay is a spontaneous change within thenucleus of an atom which results in the emission of parti-cles or electromagnetic radiation. The modes of radioac-tive decay are principally alpha and beta decay, withspontaneous fission as one of a small number of rarerprocesses. Radioactive decay is driven by mass change –the mass of the product or products is smaller than themass of the original nuclide. Decay is always exoergic;the small mass change appearing as energy in an amountdetermined by the equation introduced by Einstein:

�E = �m× c2

where the energy difference is in joules, the mass in kilo-grams and the speed of light in m s−1. On the websiterelating to this book, there is a spreadsheet to allow thereader to calculate the mass/energy differences availablefor different modes of decay.

The units of energy we use in gamma spectrometry areelectron-volts (eV), where 1 eV = 1�602 177 × 10−19 J.1

Hence, 1 eV ≡ 1�782 663×10−36 kg or 1�073 533×10−9 u(‘u’ is the unit of atomic mass, defined as 1/12th of themass of 12C). Energies in the gamma radiation range areconveniently in keV.

Gamma-ray emission is not, strictly speaking a decayprocess; it is a de-excitation of the nucleus. I will nowexplain each of these decay modes and will show, inparticular, how gamma emission frequently appears as aby-product of alpha or beta decay, being one way in whichresidual excitation energy is dissipated

1.2 BETA DECAY

Figure 1.2 shows a three-dimensional version of the low-mass end of the Segrè chart with energy/mass plotted onthe third axis, shown vertically here. We can think ofthe stable nuclides as occupying the bottom of a nuclear-stability valley that runs from hydrogen to bismuth. Thestability can be explained in terms of particular rela-tionships between Z and N . Nuclides outside this valleybottom are unstable and can be imagined as sitting onthe sides of the valley at heights that reflect their relativenuclear masses or energies.

The dominant form of radioactive decay is movementdown the hillside directly to the valley bottom. This is

0

5

1015

2025

3035

5

2015

10

Ene

rgy

(rel

ativ

e sc

ale)

Proton numberNeutro

n number

60

40

–40

–20

20

0

Figure 1.2 The beta stability valley at low Z. Adapted froma figure published by New Scientist, and reproduced withpermission

1 Values given are rounded from those recommended by the UKNational Physical Laboratory in Fundamental Physical Constantsand Energy Conversion Factors (1991).

Radioactive decay/origin of gamma and X-radiation 3

beta decay. It corresponds to transitions along an isobaror line of constant A. What is happening is that neutronsare changing to protons (�−decay), or, on the opposite sideof the valley, protons are changing to neutrons (�+ decayor electron capture). Figure 1.3 is part of the (Karlsruhe)Nuclide Chart.

N

Z

61Zn 62Zn 63Zn 64Zn 65Zn

61Cu 62Cu 63Cu 64Cu60Cu

61Ni 62Ni 63Ni60Ni59Ni

61Co 62Co60Co59Co58Co

61Fe60Fe59Fe58Fe57Fe

Figure 1.3 Part of the Chart of the Nuclides. Heavy boxesindicate the stable nuclides

26

0

2

4

6

8

27 28 29 30

A = 61

EC

Fe

β– β+

Co Ni Cu ZnZ

Mas

s di

ffere

nce

(MeV

)

Figure 1.4 The energy parabola for the isobar A = 61. 61Niis stable, while other nuclides are beta-active (EC, electroncapture)

If we consider the isobar A = 61, 61Ni is stable, and betadecay can take place along a diagonal (in this format) fromeither side. 61Ni has the smallest mass in this sequence andthe driving force is the mass difference; this appears asenergy released. These energies are shown in Figure 1.4.There are theoretical grounds, based on the liquid dropmodel of the nucleus, for thinking that these points fallon a parabola.

1.2.1 �− or negatron decay

The decay of 60Co is an example of �− or negatrondecay (negatron = negatively charged beta particle). Allnuclides unstable to �− decay are on the neutron rich sideof stability. (On the Karlsruhe chart, these are colouredblue.) The decay process addresses that instability. Anexample of �− decay is:

60Co −→ 60Ni+�− + �̄

A beta particle, �−, is an electron; in all respectsit is identical to any other electron. Following on fromSection 1.1, the sum of the masses of the 60Ni plus themass of the �−, and �̄, the anti-neutrino, are less than themass of 60Co. That mass difference drives the decay andappears as energy of the decay products. What happensduring the decay process is that a neutron is convertedto a proton within the nucleus. In that way the atomicnumber increases by one and the nuclide drops down theside of the valley to a more stable condition. A fact notoften realized is that the neutron itself is radioactive whenit is not bound within a nucleus. A free neutron has ahalf-life of only 10.2 min and decays by beta emission:

n −→ p+ +�− + �̄

That process is essentially the conversion processhappening within the nucleus.

The decay energy is shared between the particlesin inverse ratio to their masses in order to conservemomentum. The mass of 60Ni is very large comparedto the mass of the beta particle and neutrino and, froma gamma spectrometry perspective, takes a very small,insignificant portion of the decay energy. The beta particleand the anti-neutrino share almost the whole of thedecay energy in variable proportions; each takes fromzero to 100 % in a statistically determined fashion. Forthat reason, beta particles are not mono-energetic, asone might expect from the decay scheme, and theirenergy is usually specified as E� max. The term ‘betaparticle’ is reserved for an electron that has been emittedduring a nuclear decay process. This distinguishes it from


electrons emitted as a result of other processes, whichwill usually have defined energies. The anti-neutrinoneed not concern us as it is detectable only in elabo-rate experiments. Anti-neutrinos (and neutrinos from �+

decay) are theoretically crucial in maintaining the univer-sality of the conservation laws of energy and angularmomentum.

The lowest energy state of each nuclide is called theground state, and it would be unusual for a transi-tion to be made directly from one ground state to thenext – unusual, but unfortunately far from unknown.There are a number of technologically important purebeta emitters, which are either widely used as radioac-tive tracers (3H, 14C, 35S) or have significant yields infission (90Sr/90Y, 99Tc, 147Pm). Table 1.1 lists the mostcommon.

Table 1.1 Some pure beta emittersa

Nuclide Half-lifebc Maximum betaenergy (keV)

3H 12.312 (25) year 1914C 5700 (30) year 15632P 14.284 (36) d 171135S 87.32 (16) d 16736Cl 3.01 �2�×105 year 114245Ca 162.6 1(9) db 25763Ni 98.7 (24) year 6690Sr 28.80 (7) year 54690Y 2.6684 (13) d 228299Tc 2.111 �12�×105 yearb 294147Pm 2.6234 (2) yearb 225204Tl 3.788 (15) year 763

a Data taken from DDEP (1986), with the exception ofb-latter taken from Table of Isotopes (1978, 1998).c Figures in parentheses represent the 1 uncertainties on thelast digit or digits.

The decay scheme of these will be of the form shown inFigure 1.5.

The difficulty for gamma spectrometrists is that nogamma radiation is emitted by these radionuclides andthus they cannot be measured by the techniques describedin this text. To determine pure beta emitters in a mixture ofradionuclides, a degree of chemical separation is required,followed by measurement of the beta radiation, perhapsby liquid scintillation or by using a gas-filled detector.

However, many beta transitions do not go to the groundstate of the daughter nucleus, but to an excited state.This behaviour can be seen superimposed on the isobaricenergy parabola in Figure 1.6. Excited states are shown

32S

β–

32P (14.28 d)

Figure 1.5 The decay scheme of a pure beta emitter, 32P

for both radioactive (Ag, Cd, In, Sb, Te) and stable(Sn) isobaric nuclides, and it should be noted that thesestates are approached through the preceding or parentnuclide.

47

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)

2

4

6

8

48 49 50 51

A = 117

Ag Cd In Sn Sb52Te

Z

Figure 1.6 The isobar A = 117 with individual decay schemessuperimposed. 117Sn is stable

The decay scheme for a single beta-emitting radionu-clide is part of this energy parabola with just the twocomponents of parent and daughter. Figure 1.7 shows thesimple case of 137Cs. Here, some beta decays (6.5 % ofthe total) go directly to the ground state of 137Ba; most(93.5 %) go to an excited nuclear state of 137Ba.

The gamma radiation is released as that excited statede-excites and drops to the ground state. Note that theenergy released, 661.7 keV, is actually a property of 137Ba,but is accessed from 137Cs. It is conventionally regardedas ‘the 137Cs gamma’, and is listed in data tables as such.


137Ba

661.7

(93.5 %)

(6.5 %)

0

β1

β2

γ

137Cs (30.17 year)

Figure 1.7 The decay scheme of 137Cs

However, when looking for data about energy levels inthe nucleus, as opposed to gamma-ray energies, it wouldbe necessary to look under the daughter, 137Ba.

In this particular case, 661.7 keV is the only gamma inthe decay process. More commonly, many gamma tran-sitions are involved. This is seen in Figure 1.6 and alsoin Figure 1.8, where the great majority of beta decays(those labelled �1) go to the 2505.7 keV level which fallsto the ground state in two steps. Thus, two gamma-raysappear with their energies being the difference betweenthe energies of the upper and lower levels:

1 = �2505�7−1332�5� = 1173�2 keV

2 = �1332�5−0� = 1332�5 keV

60Ni

1332.5

2505.7(0.12 %)

0

β1 (99.88 %)

β2

γ2

γ1

60Co (5.272 year)

Figure 1.8 The decay scheme of 60Co

The two gammas are said to be in cascade, and if theyappear at essentially the same time, that is, if the interme-diate level (in 60Ni at 1332.5 keV) does not delay emissionof the second gamma, then they are also said to be coin-cident. This phenomenon of two gamma-rays appearing

from the same atom at the same instant can have a signifi-cant influence on counting efficiency, as will be discussedin Chapter 8.

1.2.2 �+ or positron decay

Just as �−active nuclides are neutron rich, nuclidesunstable to �+ decay are neutron deficient. (The rednuclides on the Karlsruhe chart.) The purpose of positrondecay, again driven by mass difference, is to convert aproton into a neutron. Again, the effect is to slide down theenergy parabola in Figure 1.4, this time on the neutron-deficient side, towards stability, resulting in an atom of alower atomic number than the parent. An example is:

6429Cu −→ 64

28Ni+�+ +� �neutrino�

During this decay a positron, a positively charged elec-tron (anti-electron), is emitted, and conservation issuesare met by the appearance of a neutrino. This process isanalogous to the reverse of beta decay of the neutron.However, such a reaction would require the presence of anelectron to combine with an excess proton. Electrons arenot found within the nucleus and one must be created bythe process known as pair production, in which some ofthe decay energy is used to create an electron / positronpair – imagine decay energy condensing into two parti-cles. The electron combines with the proton and thepositron is emitted from the nucleus. Positron emission isonly possible if there is a sufficiently large energy differ-ence, that is, mass difference, between the consecutiveisobaric nuclides. The critical value is 1022 keV, whichis the combined rest mass of an electron plus positron.As with negatrons, there is a continuous energy spec-trum ranging up to a maximum value, and emission ofcomplementary neutrinos.

The positron has a short life; it is rapidly slowed inmatter until it reaches a very low, close to zero, kineticenergy. Positrons are anti-particles to electrons, and theslowed positron will inevitably find itself near an elec-tron. The couple may exist for a short time as positro-nium – then the process of annihilation occurs. Boththe positron and electron disappear and two photons areproduced, each with energy equal to the electron mass,511.00 keV (Figure 1.9). These photons are called anni-hilation radiation and the annihilation peak is a commonfeature in gamma spectra, which is much enhanced when�+ nuclides are present. To conserve momentum, thetwo 511 keV photons will be emitted in exactly oppo-site directions. I will mention here, and treat the impli-cations more fully later, that the annihilation peak inthe spectrum will be considerably broader than a peak


(b)(a)

+e+ e–

Photons

(511+ δ) keV

(511– δ) keV

Atomic electron

Positron

Figure 1.9 The annihilation process, showing how the resul-tant 511 keV photons could have a small energy shift: (a) possiblemomenta before interaction giving (b) differing photon energiesafter interaction

produced by a direct nuclear-generated gamma-ray of thesame energy. This can help in distinguishing between thetwo. The reason for such broadening is due to a Dopplereffect. At the point where the positron–electron interac-tion takes place, neither positron nor electron is likelyto be at complete rest; the positron may have a smallfraction of its initial kinetic energy, the electron – if weregard it as a particle circling the nucleus – because of itsorbital momentum. Thus, there may well be a resultantnet momentum of the particles at the moment of interac-tion, so that the conservation laws mean that one 511 keVphoton will be slightly larger in energy and the otherslightly smaller. This increases the statistical uncertaintyand widens the peak. Note that the sum of the two will stillbe (in a centre of mass system) precisely 1022.00 keV.

1.2.3 Electron capture (EC)

As described above, �+ can only occur if more than1022 keV of decay energy is available. For neutrondeficient nuclides close to stability where that energy isnot available, an alternative means of decay is available. Inthis, the electron needed to convert the proton is capturedby the nucleus from one of the extranuclear electronshells. The process is known as electron capture decay.As the K shell is closest to the nucleus (the wave functionsof the nucleus and K shell have a greater degree of overlapthan with more distant shells), then the capture of a Kelectron is most likely and indeed sometimes the processis called K-capture. The probability of capture from theless strongly bound higher shells (L, M, etc.) increases asthe decay energy decreases.

Loss of an electron from the K shell leaves a vacancythere (Figure 1.10). This is filled by an electron droppingin from a higher, less tightly bound, shell. The energyreleased in this process often appears as an X-ray, in whatis referred to as fluorescence. One X-ray may well befollowed by others (of lower energy) as electrons cascadedown from shell to shell towards greater stability.

(a)

M ML LK K

Nucleus Z Nucleus Z – 1

e–

e–

(b) + Kα X-ray

Figure 1.10 (a) Electron capture from the K shell, followed by(b) electron movement (X-ray emission) from L to K, and thenM to L, resulting in X-radiations

Sometimes, the energy released in rearranging the elec-tron structure does not appear as an X-ray. Instead, it isused to free an electron from the atom as a whole. Thisis the Auger effect, emitting Auger electrons. The prob-ability of this alternative varies with Z: at higher Z therewill be more X-rays and fewer Auger electrons; it is saidthat the fluorescence yield is greater. Auger electronsare mono-energetic, and are usually of low energy, beingemitted from an atomic orbital (L or M) where the electronbinding energies are smaller. There is a small probabilityof both Auger electrons and X-rays being emitted togetherin one decay; this is the radiative Auger effect. Note thatwhenever X-rays are emitted, they will be characteristicof the daughter, rather than the parent, as the rearrange-ment of the electron shells is occurring after the electroncapture.

For neutron deficient nuclides with a potential decayenergy somewhat above the 1022 keV threshold, bothpositron decay and electron capture decay will occur, in aproportion statistically determined by the different decayenergies of the two processes. Figure 1.11 shows the majorcomponents of the decay scheme of 22Na, where both

22Ne

1274.5

EC(9.7 %)

0

β+ (90.2 %)

22Na (2.603 year)

Figure 1.11 The decay scheme of 22Na. Note the representa-tion of positron emission, where 1022 keV is lost before emissionof the �+


positron decay and electron capture are involved. We candeduce from this that the spectrum will show a gamma-rayat 1274.5 keV, an annihilation peak at 511.0 keV (from the�+), and probably X-rays due to electron rearrangementafter the EC.

1.2.4 Multiple stable isotopes

In Figures 1.4 and 1.6, I suggested that the ground statesof the nuclides of isobaric chains lay on a parabola, andthe decay involved moving down the sides of the parabolato the stable point at the bottom. The implication must bethat there is only one stable nuclide per isobaric chain.Examination of the Karlsruhe chart shows quite clearlythat this is not true – there are many instances of two, oreven three, stable nuclides on some isobars. More carefulexamination reveals that what is true is that every odd-isobar only has one stable nuclide. It is the even numberedisobars that are the problem. If a parabola can only haveone bottom, the implication is that for even-isobars theremust be more than one stability parabola. Indeed that isso. In fact, there are two parabolas; one correspondingto even-Z/even-N (even–even) and the other to odd-Z/odd-N (odd–odd). Figure 1.12 shows this. The differencearises because pairing of nucleons give a small increasein stability – a lowering of energy. In even–even nuclidesthere are more paired nucleons than in odd–odd nuclidesand so the even–even parabola is lower in energy. Asshown in Figure 1.12 for the A = 128 isobaric chain,successive decays make the nucleus jump from odd–oddto even–even and back. There will be occasions, as here,

50

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2

4

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51 53 54 55

A = 128

Sn Sb52Te I Xe Cs

56Ba

57La

Z

Figure 1.12 The two energy parabolas for the isobar A = 128.128Te and 128Xe are stable

where a nucleus finds itself above the ultimate lowestpoint of the even–even parabola, but below the neigh-bouring odd–odd points. It will, therefore be stable. (Itis the theoretical possibility that a nuclide such as 128Tecould decay to 128Xe, which fuels the search for doublebeta decay, which I will refer to from time to time.) Inall, depending upon the particular energy levels of neigh-bouring isobaric nuclides, there could be up to three stablenuclides per even-A isobaric chain.

In the case of A = 128, there are two stable nuclides,128Te and 128Xe. 128I has a choice of destination, and93.1 % decays by �− to 128Xe and 6.98 % decays by ECto 128Te. The dominance of the 128Xe transition reflectsthe greater energy release, as indicated in Figure 1.12.This behaviour is quite common for even mass parabolasand this choice of decay mode is available for such well-known nuclides as 40K and 152Eu. Occasionally, if thedecay energy for �+ is sufficient, a nuclide will decaysometimes by �− and sometimes by EC and �+.

1.3 ALPHA DECAY

An alpha particle is an He-4 nucleus, 42He+, and the emis-

sion of this particle is commonly the preferred mode ofdecay at high atomic numbers, Z > 83. In losing an alphaparticle, the nucleus loses four units of mass and two unitsof charge:

Z −→ Z −2

A −→ A−4

Typical is the decay of the most common isotope ofradium:

22688 Ra −→ 222

86 Rn + 42He +Q

The product in this case is the most common isotope ofradon, 222Rn (usually just called ‘radon’ and which inci-dentally is responsible for the largest radiation dose from asingle nuclide to the general population). A fixed quantityof energy, Q, equal to the difference in mass between theinitial nuclide and final products, is released. This energymust be shared between the Rn and the He in a definiteratio because of the conservation of momentum. Thus,the alpha-particle is mono-energetic and alpha spectrom-etry becomes possible. In contrast to beta decay, thereare no neutrinos to take away a variable fraction of theenergy.

In many cases, especially in the lower Z range of �decay, the emission of an alpha particle takes the nucleusdirectly to the ground state of the daughter, analogousto the ‘pure-�’ emission described above. However, with


heavier nuclei, � decay can lead to excited states of thedaughter. Figure 1.13, the decay scheme of 228Th, showsgamma emission following alpha decay, but even here itwill be seen that most alpha transitions go directly to the224Ra ground state.

0

84.43

290

251

216

228Th (698.60 d )

224Ra

1

2

3

4

5

α5 0.05 % (5138 keV)

α4 0.18 % (5177 keV)

α3 0.4 % (5211 keV)

α2 26.7 % (5341 keV)

α1 72.7 % (5423 keV)

Figure 1.13 The decay scheme of 228Th

Calculation of the alpha decay energy reveals that evennuclides, such as 152Eu and the stable 151Eu, are unstabletowards alpha decay. Alpha decay of 151Eu would release1.96 MeV of energy. The reason that this, and most othernuclides, do not decay by alpha emission is the presenceof an energy barrier – it takes energy to prise an alphaparticle out of the nucleus. Unless the nucleus is excitedenough or is large enough so that the decay energy isgreater than the energy barrier, it will be stable to alphaemission. That does not preclude it from being unstableto beta decay; 151Eu is stable, 152Eu is radioactive.

1.4 SPONTANEOUS FISSION (SF)

Spontaneous fission is a natural decay process in whicha heavy nucleus spontaneously splits into two large frag-ments. An example is:

25298 Cf −→ 140

54 Xe + 10844 Ru +1

0 n +Q

The two product nuclides are only examples of what isproduced; these are fission fragments or (when in theirground states) fission products. The range of products,the energies involved (Q) and the number and energies of

neutrons emitted are all similar to those produced in morefamiliar neutron-induced fission of fissile or fissionablenuclides. 252Cf is mentioned here as it is a commerciallyavailable nuclide, which is bought either as a source offission fragments or as a source of neutrons.

Once more, the driving force for the process is therelease of energy. Q is of the order of 200 MeV, alarge quantity, indicating that the fission products havea substantially smaller joint mass than the fissioningnucleus. This is because the binding energy per nucleon issignificantly greater for nuclides in the middle of the Peri-odic Table than at the extremes. 108Ru, for example, hasa binding energy of about 8.55 MeV per nucleon, whilethe corresponding figure for 252Cf is about 7.45 MeV pernucleon. Despite the emission of neutrons in this process,fission products are overwhelmingly likely to find them-selves on the neutron rich, �−active side of the nuclearstability line. They will then undergo �− decay alongan isobar, as, for example, along the left-hand side ofFigure 1.12, until a stable nucleus is reached. During thissequence, gamma emission is almost always involved,as described earlier. The distribution of fission productmasses will be discussed in Section 1.9.

As with alpha decay, calculation of mass differencesfor notional fission outcomes suggest that even mid-rangenuclides, in terms of mass, would be unstable to fission.Fission is prevented in all but very large nuclei by thefission barrier – the energy needed to deform the nucleusfrom a sphere to a situation where two nearly sphericalfission product nuclei can split off.

1.5 MINOR DECAY MODES

A number of uncommon decay modes exist which areof little direct relevance to gamma spectrometrists and Iwill content myself with just listing them: delayed neutronemission, delayed proton emission, double beta decay (thesimultaneous emission of two �− particles), two protondecay and the emission of ‘heavy ions’ or ‘clusters’, suchas 14C and 24Ne. Some detail can be found in the morerecent general texts in the Further Reading section, suchas the one by Ehmann and Vance (1991).

1.6 GAMMA EMISSION

This is not a form of decay like alpha, beta or spontaneousfission, in that there is no change in the number or typeof nucleons in the nucleus; there is no change in Z, N orA. The process is solely that of losing surplus excitationenergy, and as I have shown is usually a by-product ofalpha or beta decay. First – what is a gamma-ray?


1.6.1 The electromagnetic spectrum

Gamma radiation is electromagnetic radiation, basicallyjust like radio waves, microwaves and visible light. In theenormous range of energies in the electromagnetic spec-trum, gammas sit at the high-energy, short-wavelength,end, as shown in Figure 1.14.

Radio waves

Visible

Infrared

Microwaves

10–6

10–8

10–10

10–12

10–14

10–2

102

104

10–4

1

Wavelength(m)

LW

MW

SW

FM

Valency-electron transitions

Molecular vibrations

Molecular rotations

103

10–1

10–3

105

10

Energy(keV)

Ultraviolet Loss of valency electrons

X-rays Core-electron transitions

Gammaradiation

Nuclear transitions

Region Phenomena

Figure 1.14 The electromagnetic spectrum

Wavelength, �, or frequency, , are, in principle,equally valid as energy units for characterizing these radi-ations, and indeed are the preferred units in other partsof the electromagnetic spectrum. Relationships betweenthese quantities for all electromagnetic radiation are:

E = h× (1.1)

and

�× = c (1.2)

where h (the Planck constant) = 4�135 × 10−15 eV Hz−1

and c (the velocity of light, or any electromagneticradiation, in a vacuum) = 2�997 926 × 108 m s−1. Thus,1000 keV ≡ 1�2398×10−12 m, or 2�4180×1020 Hz. Thereis some overlap between higher-energy X-rays (the X-rays

range is from just under 1 to just over 100 keV) and lower-energy gammas (whose range we will assume here to befrom 10 to 10 000 keV). The different names used merelyindicate different origins.

The 108 eV in the figure is by no means the upper limitto energy. Astronomers detect so-called ‘cosmic gamma-rays’ (more strictly photons) at much higher energies. Ourcommon energies of around 106 eV would be their ‘soft’gammas. Above that is ‘medium energy’ to 3 × 107 eV,‘high energy’ to 1010 eV, ‘very high energy’ to 1013 eVand ‘ultra high energy’ to > 1014 eV. Measurement ofthe higher energies is via the interaction of secondaryelectrons which are produced in the atmosphere; largescale arrays of electron detectors are used.

We have already seen that gamma emissions are theresult of transitions between the excited states of nuclei.As the whole technique of gamma spectrometry rests on(a) the uniqueness of gamma energies in the characteri-zation of radioactive species, and (b) the high precisionwith which such energies can be measured, it is ofinterest to consider briefly some relevant properties ofthe excited states.

1.6.2 Some properties of nuclear transitions

It is sometimes useful to think of nucleons in a nucleusas occupying different shells in much the same way aselectrons are arranged in shells outside the nucleus. Then,exactly as quantum theory predicts that only particularelectron energies are available to extranuclear electronsgiving K, L, M shells, etc., so calculations for the nucleusonly allow the occupation of certain energy shells orenergy levels for neutrons and, independently, for protons.An excited nuclear state is when one or more nucleonshave jumped up to a higher-energy shell or shells. Ourinterest here is in movement between shells and in whatcontrols the probability of this occurring.

Nuclear energy states vary as charge and current distri-butions in the nucleus change. Charge distributions resultin electric moments; current distributions give rise tomagnetic moments (the neutron may be uncharged butit still has a magnetic moment). Consider first the elec-tric moment. Oscillating charges can be described interms of spherical harmonic vibrations, which may beexpressed in a multipole expansion. Successive terms insuch an expansion correspond to angular momenta in defi-nite quantized units. If one unit of angular momentumis involved, this is called electric dipole radiation and isindicated by E1; if two units are involved, we have elec-tric quadrupole radiation, E2, and so on. Likewise, thereis a parallel system of magnetic multipoles correspondingto changes in magnetic moments, which give rise to M1


for the magnetic dipole, M2 for the magnetic quadru-pole, etc.

As well as changes in angular momentum, there is alsothe possibility of a change in parity, �. This concept is aproperty of wave functions and is said to be either + or −(even or odd), depending on the behaviour of the wavefunction as it is mathematically reflected in the origin. So,there are three properties of a nuclear transition:

• Is it an electric or magnetic transition, E or M?• Which multiplicities are involved, or, what is the

change in angular momentum, e.g. E1, E2, E3, etc.?• Is there a change of parity?

These ideas are used in formulating selection rules forgamma transitions. This gives a sound theoretical basis tothe apparently arbitrary probability of the appearance ofparticular gamma emissions. Sometimes, decay schemeshave energy levels labelled with spin and parity, as well asenergy above the ground state. Figure 1.15 shows exam-ples of this, with the type of multipole transitions expectedaccording to the selection rules.

1/2+

3/2+

1/2–4+2+

0+

1–

0+

2+

M1

(E4)E2E2

E2E2E1

E1E1E1

Figure 1.15 Representation of some gamma decay schemes,showing spins, parities and expected multipole transitions

1.6.3 Lifetimes of nuclear energy levels

Nuclear states also have definite lifetimes, and where tran-sitions would involve a large degree of ‘forbiddenness’according to the selection rules, the levels can be appre-ciably long-lived. If the lifetime is long enough to beeasily measurable, then we have an isomeric state. Thehalf-life of the transition depends on whether it is E or M,on the multiplicity, on the energy of the transition and onthe mass number. Long half-lives are strongly favouredwhere there is high multipolarity (e.g. E4 or M4) and lowtransition energy. Most gamma transitions occur in lessthan 10−12 s. As to what is readily measurable in prac-tice is something of a moot point, but certainly millisec-onds and even microseconds give no real problems. Somewould take 1 ns as the cut-off point.

These nuclear isomers, sometimes said to be inmetastable states, are indicated by a small ‘m’ as super-script. An example is the 661.7 keV level in 137Ba (seeFigure 1.7); this has a half-life of 2.552 min and would bewritten as 137mBa (sometimes seen as 137Bam, deprecatedby this author). Note that in the measurement of 137Csthere is no indication that this hold-up in the emissionprocess exists. Only a rapid chemical separation of bariumfrom caesium, followed by a count of the barium frac-tion, would show the presence of the isomer. Normally,the 661.7 keV gamma-ray appears with the half-life of the137Cs because 137Cs and 137mBa are in secular equilibrium(See Section 1.8.3 below).

Some half-lives of isomeric states can be very long, forexample, 210mBi decays by alpha emission with a half-life of 3�0 × 106 year. Alpha decay is, however, a raremode of decay from a metastable state; gamma-ray emis-sion is much more likely. A gamma transition from anisomeric state is called an isomeric transition (IT). Onthe Karlsruhe Nuclide Chart, these are shown as whitesections within a square that is coloured (if the groundstate is radioactive) or black (if the ground state is stable).

1.6.4 Width of nuclear energy levels

A nuclear energy level is not at an infinitely preciseenergy, but has a certain finite width. This is inverselyrelated to the lifetime of the energy level throughthe Heisenberg Uncertainty Principle, which may beexpressed as:

�E ×�t ≥ h/2��= 6�582 122×10−16 eV s� (1.3)

where:

• �E is the uncertainty in the energy, which we willassume to be equivalent to an energy resolution(FWHM).

• �t is the uncertainty in time, taken as the mean life ofthe level; mean life is 1/� or 1�4427× t1/2

.• h is the Planck constant.

Thus, �E for the 661.7 keV level of 137mBa whose half-life is 2.552 min, will be about 3 × 10−18 eV – exceed-ingly small. The level involved in the decay of 60Co at1332.5 keV (see Figure 1.8) has a lifetime of 7×10−13 s;this implies an energy width of about 9 × 10−4 eV. Thisis still very small compared to the precision with whichgamma energies can be measured and to the FWHMof spectrum peaks, typically 1.9 keV at 1332.5 keV. Ingeneral, the widths of the nuclear energy levels involved


in gamma emission are not a significant factor in the prac-tical determination of gamma energies from radioactive-decay processes. This is considered further in Chapter 6.

1.6.5 Internal conversion

The emission of gamma radiation is not the only possibleprocess for de-excitation of a nuclear level. Thereare two other processes: internal conversion (IC) andpair production.

Pair production as a form of gamma decay isuncommon, and I will only touch upon it here. There areclose similarities with the process described in detail inthe section of this text on interactions of gamma radia-tion with matter, where pair production is, by contrast, ofmajor importance. It is only possible if the energy differ-ence between levels is greater than 1022 keV, when thatpart of the total energy is used to create an electron–positron pair. These two particles are ejected from thenucleus and will share the remainder of the decay energyas kinetic energy. An example of decay by pair productionis the isomeric transition of 16mO, which has a half-life of7×10−11 s, and a decay energy of 6050 keV.

Internal conversion, on the other hand, is verycommon. In this process, the energy available is trans-ferred to an extranuclear electron, which is ejected fromthe atom. This is called an internal conversion electron.It is mono-energetic, having an energy equal to the tran-sition energy less the electron binding energy and a smallnuclear recoil energy. Measurement of the distribution ofelectron energy (i.e. an electron spectrum) would revealpeaks corresponding to particular electron shells, such asK, L and M. Loss of an electron from a shell leaves avacancy and this vacancy will be filled by an electrondropping into it from a higher shell. Thus, as with elec-tron capture, an array of X-rays and Auger electrons willalso be emitted.

However, note that because IC is a mode of de-excitation and there is no change in Z, N or A, the X-radiation that is produced is characteristic of the parentisomeric state. Both ‘parent level’ and ‘daughter level’ arethe same element. This is in contrast to electron capture,where the X-rays are characteristic of the daughter. If X-ray energies are to be used as a diagnostic tool, the usermust know which decay process is occurring.

Internal conversion operates in competition withgamma-ray emission, and the ratio of the two is theinternal conversion coefficient, �:

� = number of IC electrons emitted

number of gamma-rays emitted(1.4)

This may be subdivided into �K, �L, etc., where electronsfrom the individual K and L shells are considered. Valuesof � depend on the multipolarity, transition energy andatomic number. In broad terms, � increases as the half-lifeand Z increase, and as �E decreases. At high Z, isomerictransitions with small transition energies may be 100 %converted.

A practical point arises regarding the use of informationtaken from decay scheme diagrams. It cannot be assumedthat because x % of disintegrations are feeding a certainenergy level, then the same x % of disintegrations willproduce a gamma-ray of that energy. An example of thisis the decay of 137Cs. The decay scheme (see Figure 1.7)shows that 93.5 % of decays populate the 661.7 keV levelin the daughter. However, tables of decay data state thatthe emission probability of the 661.7 keV gamma is only85.1 %. Thus, 8.4 % of the gamma decays are internallyconverted; a number which could be calculated from thecoefficient �. Another example is the decay of 228Th. Itmay be deduced from Figure 1.13 that some 27 % of the �decays feed the 224Ra level at 84.4 keV, yet the emissionprobability of the 84.4 keV gamma-ray is only 1.2 %, andinstead there are many Ra X-rays.

1.6.6 Abundance, yield and emission probability

It is common for the number of gamma-rays emitted bya nuclide to be referred to as ‘the abundance’, sometimesas the ‘yield’. Both of these terms lack precision. Histor-ically, confusion was often caused because an author ordata source would quote abundances that were effectivelybeta transition data – the 93.5 % figure quoted above. Infact, the proportion of decays that give rise to 661.7 keVgamma-rays in the example above is 85.1 % when internalconversion is taken into account. In this text, I will usethe term gamma emission probability on the basis thatit says exactly what it means – the probability that agamma-ray will be emitted, all other factors being takeninto account.

1.6.7 Ambiguity in assignment of nuclide identity

We have seen how gamma-rays are emitted with veryprecisely defined energies; these energies being charac-teristic of particular radionuclides. The majority of ambi-guities that arise in allotting nuclides to energies wouldprobably be overcome if the energy resolution of detectorsystems were improved. (In passing, it must be said thata significant improvement in the resolution of germaniumdetectors is unlikely.) However, there is a not uncommonsituation where discrimination between radionuclides bygamma energy alone is in principle not possible. This is


where isobaric nuclides are decaying to the same stableproduct from either side. The gamma radiation is the resultof transitions within energy levels in the stable nuclide;there can only be one set of energy levels and thus thegamma energies must be the same, regardless of how theenergy levels are fed.

Figure 1.16 shows the region of the (Karlsruhe) Chartof the Nuclides showing how both 51Cr and 51Ti decayto 51V. The relevant decay schemes are summarised inFigure 1.17. Data compilations give gamma energies andemission probabilities, as shown in Table 1.2. There isno way of distinguishing between the major gamma ener-gies at 320 keV as they are identical. The situation in

N

Z48Ti 49Ti 50Ti 51Ti

52V51V50V49V

50Cr 51Cr 52Cr 53Cr

β–

EC

Figure 1.16 Chart of the Nuclides, showing part of the isobarA = 51. Heavy boxes indicate the stable nuclides

051V 51V

51Cr

51Ti

320.1

928.6

EC

β –

β–

Figure 1.17 Decay schemes of 51Ti and 51Cr

Table 1.2 Gamma energies shown by two isobaricnuclides

Nuclide Gamma energy(keV)

Emissionprobability, P

51Ti 320�084 0�931608�55 0�0118928�63 0�069

51Cr 320�084 0�0987

this case is of practical interest as both 51Ti and 51Cr arethe only gamma-emitting thermal neutron activation prod-ucts of these particular elements. If there were sufficientactivity present, then the other lower emission probabilitygammas from 51Ti should be visible, so allowing discrim-ination from 51Cr, but if there is only a small peak at320 keV, these other gamma peaks may not be apparent.51Cr, as an EC nuclide, emits X-rays; these are of vana-dium, but with energies at 4.95 and 5.43 keV may well bebelow the energy range of the detector. The other nuclearparameter is half-life, and in this case the half-livesare very different, i.e. 51Ti, 5.76 min and 51Cr, 27.71 d.However, a single count does not give any half-lifeinformation.

1.7 OTHER SOURCES OF PHOTONS

1.7.1 Annihilation radiation

In Section 1.2.2, I explained how positron decay givesrise to an annihilation peak at 511.00 keV, and how thisis distinguishable by being much broader than wouldbe expected. The Doppler effect could add 2 keV toother uncertainties contributing to the width of spec-trum peaks. There are reports of very small variations inenergy (about 1 in 105) depending on the atomic massof the material; this will be of no practical significance.Some positron emitters, such as 22Na, have been usedas energy calibration standards and 22Na, in particular,has the advantage of a very simple spectrum with onlytwo widely spaced peaks. However, care must be takenif the calibration program also takes the opportunity ofmeasuring peak width or peak shape, for which purposethe 511 keV peak is quite unsuited. In general, the anni-hilation peak must be regarded as a special case needingsome thought in its interpretation. Further information isgiven later in Chapter 2, Sections 2.2.3 and 2.5.3, andChapter 6, Section 6.5.4.


1.7.2 Bremsstrahlung

Bremsstrahlung is a German word meaning ‘slowing-down radiation’. It is electromagnetic radiation producedby the interaction of fast electrons with the Coulombicfield of the nucleus. The electron energy loss appears asa continuum of photons, largely apparent in the X-rayregion, although in principle the maximum energy is thatof the beta-particle. Other energetic particles lose energyin a similar way, but bremsstrahlung is only significantwith light particles, the effect being inversely propor-tional to the square of the charged particle mass. Theeffect on a gamma spectrum is to raise the general back-ground continuum, hence making the detection of a super-imposed gamma-ray more difficult. There is an inverserelationship between the number of quanta emitted andthe photon energy, so that the bremsstrahlung backgroundlevel decreases with increasing energy.

There is a larger bremsstrahlung interaction with higheratomic number absorbers and higher electron (beta)energies. In practice, for 1000 keV betas in lead (Z = 82),there is an appreciable effect; for 1000 keV betas inaluminium (Z = 13), the effect is unimportant. It followsthat any structure near the detector, a sample jig, forexample, should be constructed of a low Z materialsuch as a rigid plastic. The use of a graded shield (seeChapter 2, Section 2.5.1) will minimize bremsstrahlungin the same way. In complete contrast, the effect isput to positive use when a source of high-intensity ‘X-radiation’ is required for photon activation analysis ormedical purposes. There are occasional reports of attemptsto reduce the bremsstrahlung effect in gamma spectra byusing an electromagnetic field near the source to divertbetas away from the detector. This is clearly a cumber-some procedure and has been found to be of limited valuein practice.

1.7.3 Prompt gammas

These are gamma-rays emitted during a nuclear reaction.If we consider the thermal neutron activation of cobalt,which in the short notation is expressed as:

59Co�n� �60Co

then the gamma-ray shown is a prompt gamma releasedas the excited 60Co nucleus falls to the ground state. Thishappens quickly, in less than 10−14 s, is a product of anuclear excitation level of 60Co itself and is unrelated tothe gamma emissions of the subsequent radioactive decayof the 60Co, which as we have seen are a property of 60Ni.Any measurements of prompt gammas must necessarilybe made on-line and special equipment is needed, for

example, to extract a neutron beam from a reactor. Ener-gies are often greater than those of beta decay gammas,going up to over 10 MeV. Analytically, the method isuseful for some low Z elements which do not give activa-tion products with good decay gammas. Elements, suchas H, B, C, N, Si, P and Ca, have been determined bysuch means. I will discuss later how prompt gammas canappear from detector components if systems are operatedin neutron fields (Chapter 13), even very low naturallyoccurring neutron fields.

1.7.4 X-rays

I have described how X-radiation appears as a resultof rearrangement of the extranuclear atomic electronsafter electron capture and internal conversion. X-rays aremono-energetic, the energy being equal to the differencebetween electron energy levels (or very close to this, asconservation of energy and momentum mean that a verysmall recoil energy must be given to the whole atom, thusreducing the X-ray energy slightly).

X-ray nomenclature

X-radiation has been known from the very earliest days ofnuclear science; Röntgen named the rays in 1895, beforeBecquerel’s discovery of radioactivity, and the classi-fication of X-rays inevitably proceeded in a piecemealfashion. Hence while Figure 1.18(a) is the sort of logicalnomenclature one might pursue with today’s hindsight, inpractice this is only an approximation to the complicatedreal situation of Figure 1.18(c). Broadly, K�, K�, L� andL� fit the format more or less correctly, but the logicalsystem fails even with some of these, and does so mostdecidedly with more distant transitions.

The K-shell has only one energy level. Higher shellshave sub-shell levels; they are said to be degenerate. Thismeans that the electrons in each shell, apart from the Kshell, do not all have exactly the same energy. There isfine structure present, giving s, p, d, etc., sub-shells, and asexemplified in Figure 1.18(b), this gives rise to fine struc-ture in the X-rays; the sub-divisions are labelled K�1, K�2,L6 and so on. Not all possible transitions occur in realityas selection rules operate based on angular momentumchanges. Thus, the transition from Ll to K is very unlikelyto occur, and is said to be ‘hindered’.

X-ray energies

Present-day germanium detectors have sufficient resolu-tion to separate the energies involved in the fine structureof elements with high values of Z, where the differ-ences are marked, but would not resolve fine structure


K

(a) (b)

L

M

N

Mα

N7

N1

M5

M1

L3

L1

K

(c)

M1

M5

L3

L1

K

KγKβKα Kα1 Kα2

Kα1

Kβ 2Kα2

Kβ 1 Kβ 2′Lα1

Lα2

Lβ 1

Lβ 2

Lβ 3

Lγ 1

Lα Lβ

Figure 1.18 X-ray nomenclature: (a) how in an ideal world,the broad groups of X-rays should be named (see text); (b) anexample of fine structure; (c) how in the real world, some X-raysare named

at low Z. Because of the widespread use of lead as ashielding material, that particular set of X-rays occursvery commonly in gamma spectra. L-series and M-seriesX-radiation is much lower in energy than the K-seriesshown. A comprehensive listing of energies is given byBrowne and Firestone (1986); a few representative valuesare shown in Table 1.3.

X-rays and identification

It should be noted that X-ray measurements can give infor-mation as to the element involved, but will not identifythe isotope of the element. This is because the arrange-ment of the atomic electrons is determined only by thenumber of protons in the nucleus (Z) and not by its mass(A). I repeat the point made earlier, that in order to iden-tify a radioactive element from X-ray energies, we needto know the type of decay involved. Only in internallyconverted isomeric transitions are the X-rays character-istic of the radionuclide itself. In electron capture theyidentify the daughter; if the daughter has atomic numberZ, then that of the decaying nuclide is Z +1.

The energy widths of X-rays

We have seen how nuclear energy levels have verysmall widths that have negligible impact on the width orshape of gamma peaks in spectra. This is not always thecase with X-rays. The width of atomic electron levels isdescribed by a Lorentzian function (as are nuclear levels)and this contains a width parameter � similar to an FWHM(see Chapter 6, Section 6.1). The Lorentzian function is:

L�x� = �/2�

�x−x0�2 + ��/2�2

(1.5)

while the Gaussian is:

G�x� = 1

×√2�

exp−�x−x0�

2

22(1.6)

and FWHM = 2�355×.Figure 1.19 shows both functions, drawn so as to make

� = FWHM. Peak broadening in the detection processis described by Gaussian functions (Chapter 6). Thepulse size distribution going through the detection systemreflects both the initial Lorentzian energy distribution andthe imposed Gaussian broadening. A convolution of thesetwo, in practice usually with wildly differing ‘widths’,gives a Voight function.

Table 1.3 Some K X-rays

X-ray energy (keV)

Element Z K�1 K�2 K�1 K�2

Copper 29 8.047 8.027 8.904 8.976Germanium 32 9.885 9.854 10.981 11.10Cadmium 48 23.174 22.984 26.084 26.644Lead 82 74.969 72.805 84.784 97.306Uranium 92 98.434 94.654 111.018 114.456


Gaussian Lorentzian

G(x) L(x)

V(x)Voight

FWHM

X0 X0

Γ

Figure 1.19 The Lorentzian and Gaussian distributions, drawnwith the same x-axes and with � = FWHM. A convolution ofthese gives a Voight function

As an X-ray energy is the difference between an initialand a final state, the intrinsic width of both levels must betaken into account. With Lorentzian functions, these aresimply added directly. Table 1.4 shows the intrinsic widthof some atomic electron levels and the corresponding X-ray, and compares these to the actual X-ray energy andthe resolution of a good detector at that energy. It can beseen that:

• The intrinsic width of electron energy levels (column(b)) is many orders of magnitude greater than the widthof nuclear levels (typical examples in Section 1.6.4 are3×10−18 eV and 9×10−4 eV).

• The width of the X-ray is the sum of the widths of thetwo relevant energy levels (columns (b) and (c)).

• The widths are a strong function of Z.• Intrinsic X-ray widths are small (≤ 0.1%) compared to

X-ray energies, even at high Z (column (d)).• Intrinsic X-ray widths have a considerable influence on

the widths of their peaks in spectra at higher Z (column

(f)). The ratios in this column can be read as somemeasure of the proportions of Lorentzian and Gaussianin the mixed Voight function. More pertinently, theLorentzian function has long tails (Figure 1.19) and asignificant contribution from this intrinsic line shapewill lead to peak shapes that also have long tails. This isknown as Lorentzian broadening and may well affectcomputer analysis of peak areas. If counts in the tailsare not included, then areas of high Z X-rays will beunderestimated by up to a few percent.

1.8 THE MATHEMATICS OF DECAY ANDGROWTH OF RADIOACTIVITY

Radionuclides are, by definition, unstable and decay byone, or more, of the decay modes; alpha, beta-minus, beta-plus, electron capture or spontaneous fission. Althoughstrictly speaking a de-excitation rather than a nucleardecay process, we can include isomeric transition in thatlist from the mathematical point of view. The amount ofa radionuclide in a sample is expressed in Becquerels –numerically equal to the rate of disintegration – thenumber of disintegrations per second. We refer to thisamount as the activity of the sample. Because this amountwill change with time we must always specify at whattime the activity was measured.

From time to time we will have to take into account thefact that one radionuclide will decay into another, but forthe moment we can consider only the simple decay process.

1.8.1 The Decay equation

Radioactive decay is a first order process. The rate ofdecay is directly proportional to the number of atoms ofradionuclide present in the source, i.e. the activity, A,is directly proportional to the number of atoms, N , ofnuclide present:

A = −dN/dt = �N (1.7)

Table 1.4 The effect of the intrinsic width of atomic energy levelsa�b

Element Z (a) (b) (c) (d) (e) (f)K�2 X-rayenergy (keV)

Width of level(eV)

Width ofK�2 X-ray(eV)

width K�2

energy K�2

FWHM ofgood detector(eV)

width K�2

FWHM

K L2

Nickel 28 7�45 1�44 0�52 1�96 0�000 26 155 0�013Cadmium 48 22�98 7�28 2�62 9�9 0�000 42 200 0�049Lead 82 72�80 60�4 6�5 66�8 0�000 92 350 0�19Uranium 92 94�65 96�1 9�3 105�4 0�0011 415 0�25

a Level width data from Krause and Oliver (1979), J. Phys. Chem. Ref. Data, 8, 329.b Detector resolution assumed to vary linearly from 150 eV at 5.9 keV to 500 eV at 122 keV.


The proportionality constant, �, is called the decayconstant and has the units of reciprocal time (e.g. s−1,h−1, etc.). The reciprocal of the decay constant is themean lifetime, �, of the radionuclide, the average timewhich an atom can be expected to exist before its nucleusdecays:

� = 1/�

This time represents a decay of the source by a factor of e(i.e. 2.718). It is more convenient and meaningful to referto the half-life, t1/2

, of the radionuclide – the time duringwhich the activity decreases to half its original value:

� = ln 2/t1/2= 0�693/t1/2

For example, for 60Co:

Decay constant: 3�60×10−4 d−1

Half-life: 1925�5±0�5 d (5.27 years)Mean lifetime: 2777.9 d

The ‘year’ has alternative definitions, and there is amove towards standardizing on the ‘day’ as the unit forquoting long half-lives. Equation (1.7) leads to the morecommonly used decay equation relating number of atoms(Nt) at time (t) and half-life (t1/2

):

Nt = N0 exp ��− ln 2� �t�/t1/2� or Nt = N0 exp �−�t� (1.8)

where N0 is the number of atoms at time t = 0. In practice,it is more useful to replace number of atoms by activity,bearing in mind that activity is proportional to the numberof atoms:

At = A0 exp �−�t� (1.9)

Figure 1.20(a) illustrates the shape of the decay curve.If we take logarithms of our activity (Equation (1.9)) wetransform it into a linear relationship:

log At = log A0 −�t

So, when plotted on a logarithmic scale, the activity ofa source over a period of time would be a straight line(Figure 1.20(b)). Indeed, if a straight line is not obtainedthen one can be sure that more than one nuclide is beingmeasured. In favourable cases, it is possible to resolvecomposite decay curves to estimate the relative amounts ofthe component radionuclides and their half-lives. (Resolu-tion is easier, of course, if the half-lives are known.)

1.8.2 Growth of activity in reactors

Most radionuclides are created by nuclear reactions. Atypical example would be neutron activation within anuclear reactor. The activity at a point in time after thestart of irradiation represents a balance between the rateof creation of radioactive atoms and the rate of decay,

Act

ivity

0.001

0.01

0.1

1.0

0 2 4 6 8 10

Log

(act

ivity

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Decay time (half-lives)

Figure 1.20 The decay of a radioactive nuclide: (a) linear scale; (b) logarithmic scale (activity is plotted relative to that at the startof the decay)


which increases as the number of atoms increases. Therate of growth of activity can be expressed as:

dN/dt = NT�

where NT is the number of target atoms, � is the neutron(or, in general, the particle) flux and is the cross-sectionfor the reaction, which we might imagine in this case to bethat for thermal neutron capture, (n,), reaction. Within aparticular system all these terms are constant (or at leastthey are until a significant fraction of target atoms are‘burned up’). This means that, in the short term, the rateof growth of activity is constant.

The rate of decay is governed by Equation (1.7) and willincrease as the number of atoms of radionuclide increases.Common sense suggests that the rate of decay can neverbe greater than the rate of growth and that at some pointin time the rate of decay must become equal to the rate ofgrowth. Solving the resulting differential equation leadsto the following:

At = AS �1− exp �−�t�� (1.10)

where t is here the time of irradiation and AS is the satura-tion activity – the maximum activity that can be achievedduring an irradiation. This is illustrated in Figure 1.21.The activity rises to within 0.1 % of saturation after10 half-lives of the product. A simple practical conse-quence of the growth equation is that short-lived nuclidesreach saturation very quickly, long-lived nuclides veryslowly.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10Growth period (half-lives)

Act

ivity

rel

ativ

e to

sat

urat

ion

Figure 1.21 The growth of radioactivity in a nuclear reactor

1.8.3 Growth of activity from decay of a parent

When one radionuclide (the parent) decays into anotherradionuclide (the daughter), the rate of change of thenumber of daughter atoms must be the difference betweenthe rate of growth from the parent and the rate of decayof the daughter:

dND/dt = �PNP −�DND

= �PNP0 exp �−�Pt�−�DND

where the subscripts D and P refer to daughter and parent,respectively, and the subscript 0 indicated the number ofatoms at t = 0. Solving this linear differential equationgives:

ND = NP0�exp �–�Pt�− exp �−�Dt��P/��D −�P�

+ND0exp �−�Dt� (1.11)

Bearing in mind that A = �N , we can rewrite this in termsof activity:

AD = AP0�exp �−�Pt�− exp �−�Dt��D/��D −�P�

+AD0exp �−�Dt� (1.12)

To gain an understanding of this relationship as the ratio ofparent to daughter half-lives varies, it is useful to imaginethat we chemically separate the parent and daughter, inwhich case the second term of Equation (1.12) is zero. Wecan then follow the change in their activities in the initiallypure parent and calculate the total activity. There are threeparticular cases depending upon whether the parent half-life is greater or less than the daughter half-life.

Transient equilibrium – t1/2parent > t1/2

daughter

In a transient equilibrium, the activity of the daughternuclide is in constant ratio to that of the parent nuclideand apparently decays with the half-life of the parent. InFigure 1.22, we see the decay of the parent unaffected bythe absence or presence of daughter and the growth of thedaughter activity. (The time scale is in units of half-lifeof the daughter nuclide.) The total activity in the systemis the sum of the parent and daughter activities. Tran-sient equilibrium is established after about 10 half-lives ofthe daughter nuclide after which the daughter apparentlydecays with the half-life of the parent.

This should not be forgotten when measuring nuclidesthat are sustained by decay of a parent. For example, if95Nb is measured in a fission product mixture it is likely,


0.001

0.01

0.1

1

10

0 2 4 6 8 10 12 14 16Decay period (half-lives of daughter)

Rel

ativ

e ac

tivity

95Zr decay (64.03 d)

95Nb growth (34.98 d)

Total activity

Figure 1.22 Transient equilibrium – relative activities ofparent and daughter nuclides after separation

using the commonly available commercial gamma spec-trum analysis packages, that the normal half-life of 95Nb,34.98 d, will be extracted from the package’s nuclidelibrary and used to correct 95Nb activities. In fact, ifthe age of the fission product mixture is greater than ayear or so then the appropriate half-life is that of theparent 95Zr, i.e. 64 d. At shorter decay times, the accu-rate calculation of 95Nb activity will be beyond the capa-bilities of a standard analysis program. Fission productmixtures contain many isobaric decay chains and manysuch parent/daughter pairs of nuclides; this problem is notat all uncommon.

If we take Equation (1.12) and set t to a value muchgreater than the half-life of the daughter, we can calcu-late the relative numbers of parent and daughter atoms atequilibrium:

ND/NP = �P/��D −�P� (1.13)

and the equilibrium activity of the daughter relative tothat of the parent:

AD = AP�D/��D −�P� or, in terms of half-lives,

AD = APt1/2P/�t1/2P − t1/2D� (1.14)

where t1/2P and t1/2D are the half-lives of parent anddaughter, respectively.

Figure 1.22 also shows that, as equilibrium isapproached, the activity of the daughter nuclide becomesgreater than that of the parent. This may, at first sight,seem odd. Take the case of 140La in equilibrium withits parent 140Ba (half-lives of 1.68 and 12.74 d, respec-tively) and apply the equations above. At equilibrium, thenumber of 140La atoms in the source will be only 0.15times the number of 140Ba atoms. However, because 140Lahas a shorter half-life its activity will be 15 % greater thanthat of the parent 140Ba. The difference can be substan-tial; in an equilibrium mixture of 95Zr/95Nb the activityof the 95Nb is 64/�64−35�, i.e. 2.2 times that of the 95Zr.

Secular equilibrium – t1/2parent >> t1/2

daughter

If the half-life of the parent nuclide is very long comparedto that of the daughter, the equilibrium state is referredto as secular equilibrium. In such situations, wheret1/2D becomes negligible, Equation (1.13) becomes AD =AP, i.e. the daughter activity equals the parent activity(Figure 1.23).

0.001

0.01

0.1

1

10


Rel

ativ

e ac

tivity

234Th growth (24.1 d)

238U decay (4.47 × 109 y)

Total activity

Figure 1.23 Secular equilibrium – relative activities of parentand daughter nuclides after separation where the parent half-lifeis much greater than that of the daughter

Take, for example, the first three stages of the 238Udecay series shown in Figure 1.24. We find that in eachparent/daughter case, the half-life of the parent is very


238U

234Th

234mPa

234U

24.1 d

1.17 min

IT

2.454 × 105 years

4.468 × 109 years

234Pa 6.70 h

α

β

β

α

ββ

Figure 1.24 The first few stages of the 238U decay series (IT,isomeric transition)

much greater than the daughter and therefore there willbe a secular equilibrium established between each pair.The activity of each daughter will be equal to that ofits parent and the total activity, for this portion of thedecay chain, will be three times that of the 238U. Notethat as far as the 234Pa and the 234mPa are concerned, atequilibrium, the half-life of their parent is effectively thatof 238U. The branching of the 234Th decay means that thetotal 234Pa +234m Pa will be, at equilibrium, equal to that

0.001

0.01

0.1

1

10


Rel

ativ

e ac

tivity

210Bi decay (5.013 d)

210Po growth (138.4 d)

Total activity

Figure 1.25 Relative activities of parent and daughter nuclidesafter separation where there is no equilibrium

of the 238U. The activity will be shared between the twonuclides according to the branching ratio.

If we look at the complete 238U decay scheme, we find14 daughter nuclides, all of whom have much shorterhalf-lives than their ultimate parent. The total activity,assuming radioactive equilibrium is established, will be14 times the 238U activity. (A more complete discussionof gamma spectrometry of the uranium and thorium decayseries nuclides can be found in Chapter 16, Section 16.1.2)

No equilibrium – t1/2parent < t1/2

daughter

If the daughter half-life is greater than that of the parentthen, obviously, the parent will decay, leaving behind thedaughter alone. Figure 1.25 shows the growth of daughteractivity within an initially pure parent. No equilibrium isestablished; ultimately the decay curve will be that of thegrown-in daughter.

1.9 THE CHART OF THE NUCLIDES

The general layout of the Karlsruhe Chart of the Nuclideshas been described; it has been used to explain beta decayand parts have been illustrated in Figures 1.3 and 1.16.In this section, I discuss its use in diagnosis, firstly as adata source, and then as an indicator of the location ofprobable nuclides. There are other versions of this chart,but none have made it onto the walls of counting roomsas often as the Karlsruhe Chart.

1.9.1 A source of nuclear data

I would certainly not recommend printed versions of thechart as the best source of nuclear data; the numberspresented are too lacking in detail and are (probably) notup to date. There is an interactive on-line version (SeeFurther Reading and the book’s website) created by theUS National Nuclear Data Center – a very useful resourcecontaining much more up-to-date information than theprinted versions, but without nuclear cross-section data.The website does, however, have easy links to energylevel data and gamma-ray emission data. A softwareversion has been developed for PCs, which should containgood data based on the OECD Nuclear Energy Agency’sData Bank. However, access to that CD-ROM seems notto be straightforward.

The printed chart is nevertheless very useful for rapidassessment. For each element, there is the element symbol,atomic weight and thermal neutron absorption cross-section. Within the horizontal strip of isotopes, stablespecies are shown with a black background and containthe mass number, natural isotopic abundance of the


isotope in atom%, and thermal neutron absorption cross-section, , in barns (b). Where appropriate, a stable squarewill have a white section to indicate the presence of ametastable state of the stable nuclide with its half-lifeand the energy of the IT gamma decay in keV. Radioac-tive species are colour-coded: blue, �−; red, EC or �+;yellow, �; green, spontaneous fission. If two modes ofdecay occur, two colours are shown.

The 60Co square would be blue for �− and containsthe half-life, the major maximum beta energies in MeV(useful for bremsstrahlung estimation), major gammaenergy (in keV) in order of emission probability and thethermal neutron cross-section. The isomer is shown as awhite section with decay mode(s) and energies. On thisparticular chart, electron capture is shown as �, isomerictransition as I and conversion electron emission as e−,along with standard symbols.

In Figure 1.26(b), ‘ 20+17’ indicates 20 b for the (n,) cross-section to form 60mCo (t1/2

= 10�47 min) and 17 bfor the (n, ) reaction to give 60Co directly in its groundstate. For most purposes, these numbers would need tobe summed if 60Co activity was sought, as essentially allof the metastable states will end up as the ground statewithin a couple of hours.

Co Co 6010.5 mI γ 59e–..β–.. γ...σ 58 σ 2.0

γβ– 0.3

10058.9332

σ 37.2 σ 20 + 17

(a) (b) (c)

5.272 a

1.513321173

Co 59

Figure 1.26 Typical data from a chart of the nuclides: (a) theelement; (b) a stable isotope; (c) a radioisotope with a metastablestate

The chart contains sufficient information for simplecalculations as to whether the quantities of radionuclidesfound are those that might be expected. The overall acti-vation equation is:

A = NT × ×�× �1− exp�−�× tirr��× exp�−�× tdk�

(1.15)

where:

• A = induced activity (in Bq);• NT = number of target atoms;• = cross-section (probability of reaction taking

place; an area, in units of barns (b) where1 b = 10−28m2);

• � = flux of activating particle, in most cases, neutrons(units: particles per unit area per second, e.g.n cm−2s−1; note that units of area used mustbe the same as those used for the cross-section);

• tirr = irradiation time (in same units as half-life used tocalculate �);

• tdk = cooling time (decay time) from the end of theirradiation to the time of measurement (againsame units as half-life).

The shape of this expression is shown in Figure 1.27.

0Timetirr tdk Δt

0.25

0.5

0.75

1.0

Rel

ativ

e ac

tivity

, A

Figure 1.27 The quantity of radionuclide increases during irra-diation and then decreases by radioactive decay to the timeof measurement: tirr , irradiation period; tdk, decay time; �t,measurement period

The three parts of the equation correspond as follows:

• �N0 × ×�� = the saturation activity, indicated by thedashed line at A = 1�0; the maximum activity obtain-able, asymptotically approached when tirr > t1/2

.• �1 − exp �−� × tirr�� = the approach to saturation; a

useful property is that when tirr = t1/2, this factor = 0�5,

i.e. the activity is half the saturation value; at tirr =2× t1/2

, the factor is 0.75.• �exp �−�× tdk�� = normal radioactive decay from the

end of the irradiation to the time of measurement.

1.9.2 A source of generic information

The chart is helpful when tracking down unknownradionuclides detected in a measurement to know whattype of nuclear reaction may have been responsible forthe production of the activity. In most cases, this will be athermal neutron reaction resulting in activation by (n, ),or if the target material is fissile, a fission reaction (n, f).


Thermal neutron capture (n, �)

If this is the reaction, then the search for nuclides isnarrowed dramatically. From more than 2000 radionu-clides displayed on the chart, we need scan only 180or so. It is clear that as the (n, ) reaction merely addsone neutron to a stable nuclide we must look at isotopesjust one square to the right of a (black) stable one. Forexample, instead of considering all 21 radioisotopes ofarsenic, we need look at only one; the stable arsenic is75As and therefore we look at 76As. There are just twoqualifications to this simple picture:

• There is one element where there is a significant chanceof finding that two neutrons have been added – gold.

197Au +n −→198Au +n −→ 199Au

stable �− �−

� = 98�8 b� � = 25 100 b�

This is due to the very large neutron absorption cross-section of the first product, 198Au. In most cases, whilethere may be a considerable amount of activity formedby an (n, ) reaction, this will correspond to relativelyfew atoms. Thus, the amount of target material avail-able for a second reaction is small, and a large reactionprobability (as we have here with 198Au) is needed togive significant amounts of the second reaction product.

• The second complication is when the (n, ) productdoes not decay to a stable nuclide but to a radioac-tive one. Then nuclides that are an extra transforma-tion away (�− normally) need to be considered. Anexample is:

130Te �n� � 131Te −→ 131I −→ 131Xe

stable �− �25 min� �− �8�0 d� stable

or the highly significant sequence:

238U �n� � 239U −→ 239Np −→ 239Pu

‘stable’ �− �23 min� �− �2�3 d� � �2�4×104 y�

These transformations can be readily traced onthe chart.

A further point: most elements have more than onestable isotope. So, if one activation product is found,check with the chart for others that could be formed bythe same mechanism. For example, if 35.3 h 82Br is seen,formed by (n, ) from stable 81Br, look at the chart whichwill tell you that there is plenty of stable 79Br with an

adequate cross-section, so that, time scales permitting,there should be 4.4 h 80mBr present and its daughter 80Bras well.

Fast neutron reactions, (n, p) etc.

Other neutron-induced reactions will normally involveenergetic or fast neutrons, where the extra kinetic energyis needed to knock out extra particles. Common reac-tions are (n, p), (n, �) and (n, 2n), and Figure 1.28shows these transformations on the Z against N nuclidechart format. The quantity of radioactivity formed bythese reactions is often small because of relatively lowfluxes of fast neutrons and small cross-sections. However,reactor operators and persons involved in reactor decom-missioning will be aware of the significant amounts ofactivity that can be formed by certain reactions, such as,54Fe(n, p)54Mn, 58Ni(n, p)58Co and 27Al (n, �)24Na. Thelikelihood of the production of all these radionuclides canagain be followed on the nuclide chart.

N

Z

(n, p)

(n, γ)

(n, α)

(n, 2n)

Figure 1.28 Location of products of neutron reactions. Heavyboxes indicate the stable target nuclides

Fission reactions (n, f)

Figure 1.29 shows that fission products range over massesfrom about 75 to 165, which correspond to elements Ge toDy. Most probable nuclides are grouped into two distinctmass regions (the asymmetric mass distribution), as alsoshown in Figure 1.30.

With 235U(n, f) the distribution peaks at A = 90 to 100,and A = 134 to 144. The cumulative fission yield datafor each mass number are given on the Karlsruhe Chartas percentage yields on the right-hand edge of the chart.


800.0001

0.001

0.01

0.1

1

Fis

sion

yie

ld (

%)

10

100 120

235U (thermal induced)

239Pu (thermal induced)

252Cf (spontaneous)

140 160 180

Mass number, A

Figure 1.29 Mass yield curves for the thermal neutron fissionof 235U and 239Pu, and spontaneous fission of 252Cf

38 (Sr)

Num

ber

of p

roto

ns, Z

Rb96 Rb97

Kr95 6.28 5.953

6.520

53 (I)

56 85Number of neutrons, N

Beta stabilit

y line

Figure 1.30 The location of fission products on the NuclideChart, indicatingregionsofhighindependentyield.Theinsetshowshow data are presented for the cumulative yield of each isobar

The identification problem appears difficult, but bear inmind that:

• Most fission products fall into narrow bands around thetwo peaks described above, comprising only some 20isobars.

• All are neutron rich, so that all EC/�+ nuclides can beignored.

• A large fraction of possible contenders have short half-lives, and these you may well not need to consider.On the other hand, all fission products are membersof isobaric chains and decay will usually result inother activities.

Fission product yields from fast neutron fission show avery similar distribution to Figure 1.29, the main differ-ence being that yields in the minimum between the twopeaks increase by a factor of about three.

Information on the history of the ‘unknown’, in partic-ular, its age or cooling time from the end of irradiation, ismost useful. Figure 1.31 shows how the total activity ofsome elements formed in fission varies with time. Theseare not all gamma emitters.

PRACTICAL POINTS

• Gamma spectrometry using germanium detectors isthe best technique for identifying and quantifyingradionuclides. This is due to the very sharplydefined and characteristic energies of gamma-rayswhich are produced by the great majority ofradionuclides.

• However, there are a small number of ‘pure beta emit-ters’, which do not emit gamma radiation. These cannotbe identified by gamma spectrometry. Some are tech-nologically important (3H, 14C, 90Sr).

• Most gamma-rays are a consequence of beta decay.Gamma-emission probabilities are not necessarily thesame as beta decay probabilities because of internalconversion. This latter can result in X-radiation.

• Gammas and X-rays are usually properties of thedaughter nucleus (but not with isomeric transitions).This can lead to identical gamma energies being shownby two isobaric nuclides.

• X-ray energies overlap the low-energy range of gamma-rays. X-ray peak shapes can be different from gamma-ray peak shapes.

• X-ray energies will tell you the element present, but notwhich isotope. This identification presupposes knowl-edge of the decay mode: IT −→ nuclide directly; EC,�−/IC −→ daughter.

• Decay schemes give vital information on whethergammas are in ‘cascade’. This has great significance intrue coincidence summing.


10–3

1 7 14 21 2 4 6 1 2 5 10 20 40Years

1000100501051

Time (d)

MonthsDays

Rb lnAs

Ag Cd Sn

NdI

Te SbTc

Sm

Eu

Pm

CsSrY

Total

Ce/P

r

Ru/Rh

Kr

Pd

Geln

GdTc

AsCdRb

PdSnAg

SbSm

Cs

Rh

Eu

Kr

PmNdRuTeSrYIPrCe

Total

10–2

10–1

102

103

104

1

10

10–3

10–2

10–1

102

103

104

1

10

Rel

ativ

e ac

tivity

Figure 1.31 Relative radioactivity from fission products as a function of decay time. Data are for thermal neutron fission of 235U, fluxof 1013 n cm−2 s−1 and irradiation time of 2 years. Several different nuclides may contribute to the curve for each element. Adapted withpermission from Choppin and Rydberg (1980)

• The Karlsruhe Chart of the Nuclides is a useful tool inhelping to identify nuclides, both with regard to classesof nuclide present and for the nuclear data it shows. Thedata should not necessarily be relied upon for accuratework.

FURTHER READING

• There are a number of general books that cover many of thetopics of this chapter:

Keller, C. (1988). Radiochemistry (English edition), EllisHorwood, Chichester, UK.


Ehmann, W.D. and Vance, D.E. (1991). Radiochemistry andNuclear Methods of Analysis, John Wiley & Sons, Inc., NewYork, NY, USA.

Choppin, G.R. and Rydberg, J. (1980). Nuclear Chemistry,Theory and Applications, Pergamon Press, Oxford, UK.

• A classic authoritative text on the physics of the atom that hasrun to several later editions:

Evans, R.D. (1955). The Atomic Nucleus, Mcgraw-Hill, NewYork, NY, USA.

• The following is currently the best single-volume completecompilationofnucleardecaydata. (More informationonsourcesof data, printed and Internet, are given in Appendix A):

Browne, E., Firestone R.B., Baglin, C.M. and Chu, S.Y.F. (1998).Table of Isotopes, John Wiley & Sons, Inc., New York, NY,USA (This book is now accompanied by a CD containing thenuclear data tables. See http://www.wiley.com/toi).

• Decay schemes, and hence gammas in cascade, are shownin the forerunner to the above. Numerical data are obviouslyolder and less reliable, and the format is not user-friendly:

Shirley, V.S. and Lederer, C.M. (1978). Table of Isotopes, 7thEdn, Wiley Interscience, New York, NY, USA.

• Charts of the nuclides can be found online at:An interactive online version from the US NNDC

(http://www.nndc.bnl.gov/chart/ ).

• Printed versions can be found on Amazon as:Magill, J. and Galey, J. (2004). Radioactivity, Radionuclides,

Radiation (with the Fold-out Karlsruhe Chart of the Nuclides)(Hardcover), Springer-Verlag, Berlin, Germany (a CD-ROMaccompanies the book).

The General Electric printed version (USA) can also be foundon Amazon.

• The Karlsruhe Chart of the Nuclides can be purchased on-lineat: http://www.nucleonica.net/nuclidechart.aspx

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