CINCH NucWik

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.

====== 5. Modes of radioactive decay ======
Chapter 5 from //BASICS OF NUCLEAR PHYSICS AND OF RADIATION DETECTION AND MEASUREMENT – An open-access textbook for nuclear and radiochemistry students// by Jukka Lehto

{{anchor:fission}}
{{anchor:spontaneous_fission}}

===== 5.1.Fission =====

###
In addition to spontaneous fission, which is one of the radioactive decay modes, [[textbook:nrctextbook:chapter5#induced_fission|induced fission]] is also shortly discussed here. The reason for the spontaneous fission is that the nucleus is too heavy and it is typical only for the heaviest elements (heavier than uranium). In fission, the nucleus splits into two nuclei of lighter elements, for example:
###


$$^{238}\text{U} \rightarrow ^{145}\!\text{Ba} + ^{90}\!\text{Kr} + 3^{1}\!\text{n} + 200\text{MeV}$$
;;#
[V.I]
;;#


{{:textbook:nrctextbook:spontaneous_fission_of_heavy_nuclei.png?400|}}

Figure V.1. Spontaneous fission of a heavy nucleus into two nuclei of lighter elements.

{{anchor:induced_fission}}

###
In an induced fission a nucleus is bombarded with a particle, such as a [[textbook:nrctextbook:chapter2#neutron|neutron]], which results in fission, such as
###


$$^{235}\text{U} + \text{n} \rightarrow ^{236}\!\text{U} \rightarrow ^{141}\!\text{Ba} + ^{92}\!\text{Kr} + 3^{1}\!\text{n} + 200\text{MeV}$$
;;#
[V.II]
;;#


{{:textbook:nrctextbook:induced_fission_fig_5_2.jpg?400|}}

Figure V.2. Induced fission of a heavy nucleus into two nuclei of lighter elements 
(http://chemwiki.ucdavis.edu/Physical_Chemistry/Nuclear_Chemistry/Nuclear_Reactions).

{{anchor:fission_products}}
###
In addition to the lighter elements, called fission products, fission yields into emission of 2-3 neutrons and a large amount of energy, the distribution of which is shown in Table V.I.
###


Table V.I. Distribution of the 200 MeV energy in the fission of <sup>235</sup>U.
 
^Kinetic energy of the fission products |165 MeV|
^Kinetic energy of neutrons |5 MeV|
^Energy of the instantaneously released gamma rays |7 MeV| 
^Kinetic energy of the beta particles of fission products |7 MeV| 
^Kinetic energy of the gamma rays of fission products |6 MeV| 
^Kinetic energy of neutrinos from beta decays |10 MeV|

{{anchor:uranium_spontaneous_fission}}
###
In the nature, there is only one nuclide, <sup>238</sup>U that decays spontaneously by fission. Fission is, however, not the only decay mode of <sup>238</sup>U and in fact only 0.005% of it undergoes this decay mode while the rest decays by [[textbook:nrctextbook:chapter5#alpha|alpha decay]]. Spontaneous fission of uranium has its own specific decay [[textbook:nrctextbook:chapter6#half_life|half-life]] which is 8·10<sup>15</sup> a. With transuranium and superheavy elements, spontaneous fission is more common but as with uranium, spontaneous fission is mostly a minor decay mode. For example, all plutonium [[textbook:nrctextbook:chapter2#isotope|isotopes]] with a [[textbook:nrctextbook:chapter2#mass_number|mass number]] between 235 and 244 partly decay by spontaneous fission. There are, however, some heavy radionuclides, such as <sup>256</sup>Cf and <sup>250</sup>No, which decay solely by spontaneous fission.

###

###
Fission products, the lighter nuclides formed in fission, are radioactive. The heavy elements, such as uranium, have higher [[textbook:nrctextbook:chapter3#neutron_to_proton_ratio|neutron to proton ratios]] compared to elements formed in fission. In the fission, however, only 2-3 [[textbook:nrctextbook:chapter2#neutron|neutrons]] are released and therefore the fission products have too many neutrons for stability. For example, barium [[textbook:nrctextbook:chapter2#isotope|isotopes]] formed in fission have approximately the same neutron to proton ratio as <sup>238</sup>U, 1.59. The stable barium isotopes, however, have neutron to proton ratio in the range of 1.32-1.46. To obtain stability, the fission products gradually correct their neutron to proton ratio by decaying with [[textbook:nrctextbook:chapter5#beta|beta decay]] (β<sup>-</sup>)  mode, i.e. they transform excess neutrons to [[textbook:nrctextbook:chapter2#proton|protons]] until the nuclide has [[textbook:nrctextbook:chapter3#neutron_to_proton_ratio|neutron to proton ratio]] that enables stability. An example of such decay chain is shown in [[textbook:nrctextbook:chapter5#figure_53|Figure V.3]].
###
{{anchor:figure_53}}

^ Nuclide ^ Half-life ^n/p ratio ^
| <sup>137</sup>Te | 3.5 s | 1.63 |
| ↓|||
| <sup>137</sup>I | 24.5 s | 1.58 |
| ↓|||
| <sup>137</sup>Xe | 3.8 min | 1.54 |
| ↓|||
| <sup>137</sup>Cs | 30 a | 1.49 |
|↓|||
| <sup>137</sup>Ba | stable | 1.48 |


Figure V.3. A fission product decay chain ending in stable <sup>137</sup>Ba.

###
There is a large number of fission daughter products. They are, however, not evenly formed at various [[textbook:nrctextbook:chapter2#mass_number|mass numbers]]. Instead, they are concentrated to two mass number ranges with mass numbers between 90-105 and 130-140. Graphical presentation of the fission product yields, the percentage of fissions leading to specified mass number, as a function of mass number results in the formation of a double hump curve given in [[textbook:nrctextbook:chapter5#figure_54|Figure V.4]].  The upper mass range is independent of the fissioning [[textbook:nrctextbook:chapter2#nuclide|nuclide]] while the lower mass range shifts into higher mass numbers as the mass of the fissioning nuclide increases.

###
{{anchor:figure_54}}
{{:textbook:nrctextbook:distribution_of_fission_products_of_235u_fig_5_4.png?400|}}


Figure V.4. Distribution of fission products of <sup>235</sup>U 
(http://www.science.uwaterloo.ca/~cchieh/cact/nuctek/fissionyield.html).

###
Most fission products have short [[textbook:nrctextbook:chapter6#half_life|half-lives]] and they decay rapidly. In a relatively short term, tens to hundreds of years after fission of uranium or plutonium material, the most-prevailing components are the fission products <sup>90</sup>Sr and <sup>137</sup>Cs, the [[textbook:nrctextbook:chapter6#half_life|half-lives]] of which are 28 y and 30 y, respectively. In the very long term, the long-lived fission products dominate the mixture, first <sup>99</sup>Tc with a [[textbook:nrctextbook:chapter6#half_life|half-life]] of 210.000 years, then <sup>135</sup>Cs with a half-life of 2.300.000 years and, finally, <sup>129</sup>I with a half-life of 16.000.000 years.
###
{{anchor:alpha}}

===== 5.2. Alpha decay =====

###
The reason for alpha decay is the same as for fission, the [[textbook:nrctextbook:chapter2#nucleus|nucleus]] is too heavy. Alpha decay is, however, typical for somewhat lighter elements than [[textbook:nrctextbook:chapter5#fission|fission]]. {{anchor:alpha_particle}}In alpha decay, an excess of mass is released by the emission of a helium nucleus, called an alpha (α) particle:
###


$$^{226}\text{Ra} \rightarrow ^{222}\!\text{Rn} + ^{4}\!\text{He} \;(\alpha)$$
;;#
[V.II]
;;#


###
Helium [[textbook:nrctextbook:chapter2#nucleus|nucleus]] has two [[textbook:nrctextbook:chapter2#proton|protons]] and two [[textbook:nrctextbook:chapter2#neutron|neutrons]] and thus in alpha decay the [[textbook:nrctextbook:chapter2#mass_number|mass number]] decreases by four units while the [[textbook:nrctextbook:chapter2#atomic_number|atomic number]] decreases by two.  Alpha decay is the most typical mode for elements heavier than lead, especially in case of [[textbook:nrctextbook:chapter3#neutron_to_proton_ratio|proton-rich]] nuclides. Also at intermediate mass region, many proton-rich nuclides decay by alpha decay. Alpha decay seldom takes place to only ground energy state of the daughter nuclide but in most cases also to its [[textbook:nrctextbook:chapter5#excited_state|excited states]]. As will be later discussed with [[textbook:nrctextbook:chapter5#internal_transition|internal transition]], these excited states relax either by emission of [[textbook:nrctextbook:chapter5#gamma|gamma]] rays or by [[textbook:nrctextbook:chapter5#internal_conversion|internal conversion]]. Below in the [[textbook:nrctextbook:chapter5#figure_55|Figure V.5]] are shown examples of the two cases: a decay purely to the daughter’s ground state (<sup>212</sup>Po) and a decay to both ground state and excited states (<sup>211</sup>Po). With the heaviest elements, alpha decay can result in emission of a number of [[textbook:nrctextbook:chapter5#alpha_particle|alpha particles]] of different energy and even a greater number of gamma rays.
###
{{anchor:figure_55}}

{{:textbook:nrctextbook:decay_schemes_of_212po_fig_5_5.png?400|}}

Figure V.5. Decay schemes of <sup>212</sup>Po and <sup>211</sup>Po (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).

###
Many alpha decay processes compete with [[textbook:nrctextbook:chapter5#beta|beta decay]] so that part of the nuclides decays by alpha decay and the rest with beta decay. Two examples of such cases are given in [[textbook:nrctextbook:chapter5#figure_56|Figure V.6]]. On the left side is the case of <sup>218</sup>Po where 99.98% of the decays go through alpha emission while a small fraction of 0.02% through beta emission. On the right side is the case of <sup>211</sup>At of which 41.9% 
decay by alpha decay and the rest 58.1% by [[textbook:nrctextbook:chapter5#electron_capture|electron capture]] mode. In some cases, such as in case of <sup>226</sup>Ac, all these three processes take place.
###
{{anchor:figure_56}}

{{:textbook:nrctextbook:decay_schemes_of_218po_fig_5_6.png?400|}}

Figure V.6. Decay schemes of <sup>218</sup>Po and <sup>211</sup>At (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).

###
The decay energy in the alpha decay Q<sub>α</sub>, which is the energy/mass difference between the ground states of the parent and daughter nuclides, can be calculated in the following way. As already mentioned, one atomic mass unit corresponds to 931.5 MeV energy. As M<sub>Z</sub> is the mass of the parent nucleus and the masses of the daughter and alpha particle are M<sub>Z-2</sub> and M<sub>He</sub>, the decay energy is
###


$$Q_{\alpha} = - 931.5 \, \text{MeV} \left( M_{Z-2} + M_{\text{He}} - M_{Z} \right)$$
;;#
[V.II]
;;#


###
For example, when <sup>238</sup>U decays by alpha emission to <sup>234</sup>Th the decay energy is:
###


$$Q_{\alpha} = - 931.5 \, \text{MeV} \, \text{amu}^{-1} \left( 234.043594 + 4.002603 - 238.0507785 \right)$$
$$= - 931.5 \, \text{MeV} \, \text{amu}^{-1} \left( -0.0045815 \, \text{amu} \right)$$
$$= 4.274 \, \text{MeV}$$
;;#
[V.III]
;;#

###
Where 234.043594, 4.002603 and 238.0507785 are the atomic masses of <sup>238</sup>U, helium and <sup>234</sup>Th. Atomic masses are used instead of nucleus masses since the masses of electrons are the same on both sides of the reaction and balance each other. Thus, in the decay above a mass of 0.0045815 amu transforms into energy of 4.274 MeV. This energy divides into two parts, into the kinetic energy of the alpha particle (E<sub>α</sub>) and into recoil energy of the daughter nuclide (E<sub>Z-2</sub>). In the decay process both the energy Q<sub>α</sub> = E<sub>α</sub> + E<sub>Z-2</sub> and the moment are preserved and we can calculate the 
kinetic energy of the alpha particle by E<sub>α</sub> = Q<sub>α</sub> (M<sub>Z-2</sub>/M<sub>Z</sub>) and that of the daughter nuclide by E<sub>Z-2</sub> = Q<sub>α</sub> (M<sub>α</sub>/M<sub>Z</sub>). For the case presented above, we get for the kinetic energy 4.202 MeV for the alpha and for the recoil energy 0.072 MeV for <sup>234</sup>Th. Even though the recoil fraction of the energy is less than 2% it is still 10.000 times higher than the energies of chemical bonds. Thus, the recoil always 
results in the breaking of the chemical bond between the daughter nuclide and the compound where the parent initially was. Energies of alpha particles are always high. The lowest observed energy 1.38 MeV is that of <sup>144</sup>Nd and the highest 11.7 MeV that of <sup>212</sup>Pb, while typically the energies range from 4 MeV to 8 MeV.

###
{{anchor:line_spectrum_alpha}}
###
Emitting [[textbook:nrctextbook:chapter5#alpha_particle|alpha particles]] have definite energies, since the transition from the ground state of the parent to the ground and [[textbook:nrctextbook:chapter5#excited_state|excited states]] of the daughter occur between definite quantum states. Thus, the alpha particles are monoenergetic, as are the [[textbook:nrctextbook:chapter5#gamma|gamma rays]] of the transitions from the excited states of the daughter nuclide. Due to the monoenergetic nature of the alpha particles, their spectrum is called line spectrum. In [[textbook:nrctextbook:chapter5#figure_57|Figure V.7]] on left, there is the line spectrum of alpha particles emitted in the decay of <sup>241</sup>Am, where five peaks of the following alpha particles are seen 5.389 MeV (1.3%), 5.443 MeV (12.8%), 5.486 MeV (85.2%), 5.512 MeV (0.2%) and 5.544 (0.3%). Due to the limited energy resolution of the spectrometer, i.e. limited capability to respond to alpha particles of same energy in the same manner, the observed alpha spectrum gives only one observable peak.
###
{{anchor:figure_57}}

{{:textbook:nrctextbook:distribution_of_alpha_particle_energies_fig_5_7.png |}}

Figure V.7. Distribution of alpha particle energies (left), observed alpha spectrum with <sup>243</sup>Am tracer (middle) and the decay scheme (right) (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983) of <sup>241</sup>Am.

{{anchor:tunneling}}
###
As mentioned, the reason for alpha decay of nuclides is their too heavy mass. Theoretically, all nuclides with [[textbook:nrctextbook:chapter2#mass_number|mass number]] larger than 150 are unstable and should decay by alpha decay. As seen from [[textbook:nrctextbook:chapter2#figure_21|Figure II.1]], representing the potential diagram of nuclei, the nucleus has a high positive potential wall that an alpha particle has to go over to leave the nucleus. For nuclei with a mass number between 150 and 200, the energies of alpha particles are not high enough to do this. Even for heavier nuclei, the potential wall is higher than the energies of the alpha particles but nevertheless many of them decay by alpha emission. For example, for <sup>238</sup>U the height of the potential wall is about 9 MeV while the energy of the emitting alpha particle is only 4.2 MeV, which has been explained by the //tunneling// phenomenon assuming a certain probability of alpha particles crossing the potential wall.
###
{{anchor:beta}}

===== 5.3. Beta decay processes =====

###
The reason for beta decay is an unsuitable [[textbook:nrctextbook:chapter3#neutron_to_proton_ratio|neutron to proton ratio]]. There are three different types of beta decay processes:
###


  * [[#5.3.1._beta_decay|beta decay]] (β<sup>-</sup> decay)
  * [[#5.3.2.1._positron_decay|positron decay]] (β<sup>+</sup> decay)
  * [[#5.3.2.2._electron_capture|electron capture]] (EC)

###
of which the first is characteristic for neutron-rich nuclides and the two latter for proton-rich nuclides.
###


###
{{anchor:isobar}}
For all beta decay processes the [[textbook:nrctextbook:chapter2#mass_number|mass number]] does not change since a [[textbook:nrctextbook:chapter2#neutron|neutron]] in the nucleus transforms into a [[textbook:nrctextbook:chapter2#proton|proton]] in β<sup>-</sup> decay and vice versa in [[#5.3.2.1._positron_decay|positron decay]] and [[#5.3.2.2._electron_capture|electron capture]]. All beta decay processes take place on isobaric lines towards stable nuclides in the middle:
###


{{:textbook:nrctextbook:beta_decay_on_isobaric_line_2.png?400|}}

Figure V.8. Beta decays on isobaric line A=12.

{{anchor:beta_decay}}
==== 5.3.1. Beta decay ====


###
In β<sup>-</sup> decay, later called beta minus decay, the nuclide has too many neutrons for stability, i.e. the nucleus is neutron-rich. This kind of nuclides are formed in fission of heavy elements, such as uranium and plutonium, and in neutron-induced nuclear reactions. In beta minus decay, an excessive neutron in the nucleus transforms into a proton and a beta particle (β<sup>-</sup>) is emitted. Thus, the atomic number of the daughter nuclide is one unit higher than that of the parent.
###


$$(n) \rightarrow (p^+) + \beta^-$$
;;#
[V.IV]
;;#

{{anchor:beta_particle}}
###
where parentheses refer to particles within the nucleus. The emitting beta particle is physically identical to an electron and is also called negatron.

###
{{anchor:continuous_spectrum}}
{{anchor:emax_beta}}
{{anchor:antineutrino}}
###
As already mentioned when [[textbook:nrctextbook:chapter5#alpha|alpha decay]] was discussed, nuclear transformations between the parent and the daughter always occur between defined quantum (energy) states. The observed spectrum of the beta particles is, however, not a [[textbook:nrctextbook:chapter5#line_spectrum_alpha|line spectrum]] but a continuous one, ranging from zero to a maximum energy (E<sub>max</sub>) characteristic for each radionuclide ([[textbook:nrctextbook:chapter5#figure_59|Figure V.9]]). The conflict between the defined energy states of the parent and the daughter from one side and the continuous beta spectrum on the other is explained by the fact that not only beta particles are emitted in beta minus decay but also //antineutrinos// (ῡ). They have practically no mass and thus beta detectors do not detect them. In each beta decay process the total kinetic energy of beta particle plus antineutrino is the same as the maximum energy (E<sub>max</sub>) but their energy fractions varies in the 0-100% range. When, for example, 
the other gets 35% of the energy the other gets 65%. The complete beta minus decay reaction is thus:
###



$$(n) \rightarrow (p^{+}) + \beta^{-} + \bar{\nu}$$ ;;#
[V.V]
;;#
{{anchor:beta_spectrum_fig}}
{{anchor:figure_59}}

{{:textbook:nrctextbook:beta_spectrum_fig_5_9.png?400|}}

Figure V.9. A beta spectrum.

###
As seen in [[textbook:nrctextbook:chapter5#figure_59|Figure V.9]] the kinetic energy does not divide identically to [[textbook:nrctextbook:chapter5#beta_particle|beta particle]] and [[textbook:nrctextbook:chapter5#antineutrino|antineutrino]]. Instead, the average energy of beta particles is approximately one third of the [[textbook:nrctextbook:chapter5#emax_beta|maximum energy]].
###


###
The decay energy in beta decay does not go only to the kinetic energies of [[textbook:nrctextbook:chapter5#beta_particle|beta particle]] and [[textbook:nrctextbook:chapter5#antineutrino|antineutrino]] but also to the recoil energy of the daughter nuclide. Due to the small mass of emitting beta and antineutrino particles, the recoil energy is much smaller than in alpha decay. [[textbook:nrctextbook:chapter5#recoil_beta_decay|Recoil]] energies of daughter nuclides are discussed later for all three beta decay processes.
###


The energies of beta particles vary in a very wide range (Table V.II).

Table V.II. Average energies (E) and maximum energies (E<sub>max</sub>) of some beta emitters. E ≈ 0.3×E<sub>max</sub>.

^Nuclide ^E (MeV) ^E<sub>Max</sub> (MeV) ^Nuclide ^E (MeV) ^E<sub>max</sub> (MeV)^
|<sup>3</sup>H |0.0057 |0.018 |<sup>14</sup>C |0.0495 |0.180| 
|<sup>32</sup>P |0.695 |1.71 |<sup>90</sup>Y |0.935 |2.30|

{{anchor:pure_beta_emitters}}

###
Beta decays lead often to [[textbook:nrctextbook:chapter5#excited_state|excited states]] of the daughter nuclide and these excited states relax with [[textbook:nrctextbook:chapter5#internal_transition|internal transition]], which will be discussed later. Some beta emitters, such as <sup>3</sup>H, <sup>14</sup>C, <sup>32</sup>P, <sup>35</sup>S and <sup>63</sup>Ni, are, however, //pure beta emitters// as the beta transitions occur from the ground state of the parent to the ground state of the daughter. [[textbook:nrctextbook:chapter5#figure_510|Figure V.10]] shows examples of both cases: a decay only to ground state (<sup>39</sup>Ar) and a decay both to ground state and to [[textbook:nrctextbook:chapter5#excited_state|excited states]] (<sup>41</sup>Ar).
###
{{anchor:figure_510}}

{{:textbook:nrctextbook:decay_schemes_of_39_ar_fig_5_10.png?400|}}

Figure V.10. Decay schemes of <sup>39</sup>Ar and <sup>41</sup>Ar (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).

###
In β<sup>-</sup> decays, the decay energy is simply calculated from the difference between the atomic masses of the daughter nuclide and the parent nuclide:
###



$$Q_{\beta^-} = -931.5 \, \text{MeV/amu} \left( M_{Z+1} - M_{Z} \right)$$ ;;#
[V.VI]
;;#


###
The mass of emitting [[textbook:nrctextbook:chapter5#beta_particle|beta particles]] (electrons) does not need to be taken into account since the [[textbook:nrctextbook:chapter2#atomic_number|atomic number]] of the daughter nuclide is one unit higher and it needs an extra [[textbook:nrctextbook:chapter2#electron|electron]] to become electrically neutral. Daughter nuclides are initially ionized, having a charge of one positive unit, but these immediately take an electron from the surroundings to regain electroneutrality. The taken electron is of course any electron from the surrounding matter, but we can imagine that it is the emitted beta particle to rationalize the Equation V.VI.
###


==== 5.3.2. Positron decay and electron capture ====

###
Positron decay and electron capture are opposite reactions to β<sup>-</sup> decay. They occur with [[textbook:nrctextbook:chapter3#neutron_to_proton_ratio|proton-rich]] nuclides and in them a [[textbook:nrctextbook:chapter2#proton|proton]] within a [[textbook:nrctextbook:chapter2#nucleus|nucleus]] transforms into a [[textbook:nrctextbook:chapter2#neutron|neutron]]. Proton-rich nuclides are generated in [[textbook:nrctextbook:chapter16|accelerators]], especially in cyclotrons, by bombarding target nuclei with proton-bearing particles, such as protons and [[textbook:nrctextbook:chapter5#alpha_particle|alpha particles]].
###
{{anchor:positron}}
{{anchor:positron_decay}}
==== 5.3.2.1. Positron decay ====

###
In positron decay, a [[textbook:nrctextbook:chapter2#proton|proton]] turns into a [[textbook:nrctextbook:chapter2#neutron|neutron]] and a //positron particle// (β<sup>+</sup>) is emitted. Thus, in positron decay the [[textbook:nrctextbook:chapter2#atomic_number|atomic number]] decreases by one unit.
###


$$(p^+) \rightarrow (n) + \beta^+$$
;;#
[V.VII]
;;#

{{anchor:neutrino}}
{{anchor:positron_particle}}
###
Positron particle is a counter particle of [[textbook:nrctextbook:chapter2#electron|electron]]. It has the same mass as electron but its charge is plus one unit. In the [[#5.3.1._beta_decay|beta minus decay]], an [[textbook:nrctextbook:chapter5#antineutrino|antineutrino]] is emitted along with the [[textbook:nrctextbook:chapter5#beta_particle|beta particle]] and similarly to this a //neutrino// is emitted with //positron particle// in positron decay. Thus, the complete reaction is:
###


$$(p^+) \rightarrow (n) + \beta^+ + \nu$$
;;#
[V.VIII]
;;#

{{anchor:pure_positron_emitters}}

###
As in [[#5.3.1._beta_decay|beta minus decay]], also positron decay often takes place via the [[textbook:nrctextbook:chapter5#excited_state|excited states]] of the daughter nuclide and the excitation energy is relaxed by [[textbook:nrctextbook:chapter5#internal_transition|internal transition]]. There are, however, some radionuclides, particularly within light positron emitters, that decay solely to ground state. Examples of //pure positron emitter nuclides// are <sup>11</sup>C, <sup>13</sup>N, <sup>15</sup>O, <sup>18</sup>F. [[textbook:nrctextbook:chapter5#figure_511|Figure V.11]] shows examples of both: a pure positron emitter (<sup>18</sup>F) and a nuclide with excited states (<sup>22</sup>Na).
###
{{anchor:figure_511}}

{{:textbook:nrctextbook:decay_schemes_of_18f_fig_5_11.png?400|}}

Figure V.11. Decay schemes of <sup>18</sup>F and <sup>22</sup>Na (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).

###
Opposite to [[#5.3.1._beta_decay|beta minus decay]], the masses of the emitting [[textbook:nrctextbook:chapter5#positron_particle|positron]] and one [[textbook:nrctextbook:chapter2#electron|electron]] need to be taken into account when calculating the decay energy. Since the daughter nuclide has one unit lower atomic number an electron needs to leave the atom. Another electron mass is lost with the emitting positron. Thus, the decay energy is:

###

$$Q_{\beta^+} = -931.5 \, \text{MeV/amu} \left( M_{Z-1} + 2M_{e} - M_{Z} \right)$$
;;#
[V.IX]
;;#

{{anchor:annihilation}}
###
The [[textbook:nrctextbook:chapter5#positron_particle|positron particle]] created in [[textbook:nrctextbook:chapter5#positron_decay|positron decay]] is unstable and, after losing its kinetic energy, it //annihilates//, i.e. it combines with its counter particle, [[textbook:nrctextbook:chapter2#electron|electron]]. In the annihilation process, the masses of the two particles turn into kinetic energy of two gamma quanta. These gamma quanta emit to opposite directions and their energy is 0.511 MeV which corresponds to the mass of an electron. These gamma rays are used to measure activities of positron emitters since their measurement is easier than measurement through detection of positron particles.
###


{{:textbook:nrctextbook:positron_emission_and_annihilation.png?400|}}

Figure V.12. Positron emission and positron annihilation.

###
Due to [[textbook:nrctextbook:chapter5#neutrino|neutrino]] emission, the spectrum of positron particles is continuous. The distribution of positron energies is, however, somewhat different from that of beta particles ([[textbook:nrctextbook:chapter5#figure_59|Figure V.9]]). The average energy of positron particles is somewhat higher, at about 0.4E<sub>max</sub>, than with beta particles for which it is round 0.3E<sub>max</sub>.
###

{{anchor:electron_capture}}
==== 5.3.2.2. Electron capture ====

###
As mentioned, electron capture (EC) is a competing process for [[textbook:nrctextbook:chapter5#positron_decay|positron decay]]. It is a prevalent process for heavier (Z>80) [[textbook:nrctextbook:chapter3#neutron_to_proton_ratio|proton-rich]] nuclides while positron decay is that for lighter (Z<30) nuclides. In between (Z=30-80) both processes take place concurrently.
###


###
In electron capture, a [[textbook:nrctextbook:chapter2#proton|proton]] within a nucleus transforms into a [[textbook:nrctextbook:chapter2#neutron|neutron]] by capturing an [[textbook:nrctextbook:chapter2#electron|electron]] from the atom's electron shell:
###
{{anchor:equation_510}}

$$(p^{+}) + e^{-} \rightarrow (n) + \nu$$
;;#
[V.X]
;;#


###
As in [[textbook:nrctextbook:chapter5#positron_decay|positron decay]], the [[textbook:nrctextbook:chapter2#atomic_number|atomic number]] of the daughter is one unit lower than that of the parent. Most typically, the captured electron comes from the inner K shell, but also from the L shell while capture from upper shells is very rare.

###

###
When calculating the decay energy the mass of the captured electron can be omitted since the [[textbook:nrctextbook:chapter2#atomic_number|atomic number]] of the daughter is one unit lower and thus needs an electron less than the parent needs. The decay energy is simply the mass difference of the daughter and the parent.
###


$$Q_{\text{EC}} = -931.5 \left( M_{Z-1} - M_{Z} \right)$$
;;#
[V.XI]
;;#

{{anchor:auger_electrons}}
###
As seen from [[textbook:nrctextbook:chapter5#equation_510|Equation V.X]] there are neutrinos emitted in electron capture. In fact, all decay energy goes to the kinetic energy of emitted neutrinos. Thus, no detectable radiation is emitted in the primary decay process. In many cases the electron capture, however, leads to [[textbook:nrctextbook:chapter5#excited_state|excited states]] of the daughter. These excited states relax by [[textbook:nrctextbook:chapter5#internal_transition|internal transition]] and the [[textbook:nrctextbook:chapter5#gamma|gamma rays]] emitted in this process can be used to measure the activities of such EC nuclides, such as <sup>85</sup>Sr. There are, however, also EC nuclides without any daughter nuclide's excitation states. Measurement of these nuclides is based on the secondary radiations created in all EC processes.  As the hole of the captured electron is filled by an electron from upper shells, X-rays are emitted and the energy of these rays is the energy difference between the shells ([[textbook:nrctextbook:chapter5#figure_513|Figure V.13]] left). Thus, these rays are characteristic X-rays of the daughter nuclide and they can be measured by an X-ray detector to determine the activity of the parent ([[textbook:nrctextbook:chapter5#figure_513|Figure V.13]] right). An example of a pure EC nuclide is <sup>55</sup>Fe for which the decay scheme is given in [[textbook:nrctextbook:chapter5#figure_514|Figure V.14]]. Another way to determine the activity of pure EC nuclides is to measure //Auger electrons// by [[textbook:nrctextbook:chapter12|liquid scintillation counting]]. Auger electrons are created when the energy of the X-rays is transferred to shell electrons, which are thereby emitted. These electrons are mono-energetic having energy of the X-ray minus the binding energy of the electron.

###
{{anchor:figure_513}}
{{:textbook:nrctextbook:electron_capture_fig_5_13.png?400|}}

Figure V.13. Electron capture, formation of Auger electrons and characteristic X-rays and the ensuing X-ray spectrum.

{{anchor:figure_514}}
{{:textbook:nrctextbook:decay_scheme_of_55fe_fig_5_14.png?400|}}

Figure V.14. Decay scheme of <sup>55</sup>Fe (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).

{{anchor:odd_even_problem}}
==== 5.3.3. Odd-even-problem ====


###
As mentioned in [[textbook:nrctextbook:chapter3|chapter III]] the plot of the semi empirical equation of [[textbook:nrctextbook:chapter3#nuclear_mass|nuclear mass]] for defined [[textbook:nrctextbook:chapter2#mass_number|mass number]] is parabola. The beta decaying nuclides lay on the edges of the parabola, β<sup>-</sup> nuclide on the left edge and β<sup>+</sup>/EC nuclide on the right while stable nuclide/s locate at the bottom. These parabolas are cross-sections of the energy valley presented in [[textbook:nrctextbook:chapter3#figure_33|Figure III.3]]. Depending on the mass 
number, there are either one or two parabolas: one for odd nuclides and two for even nuclides.  For odd mass numbers, there is only one stable nuclide at the bottom while for even numbers there are two or three. For even mass numbers, the nuclides on the upper parabola have both odd atomic number and odd neutron number and thus these nuclides are odd-odd nuclides. In turn the nuclides on the lower parabola the both numbers are even and these nuclides are thus even-even nuclides.

###

==== 5.3.3.1. Beta decay at odd mass numbers ====


###
[[textbook:nrctextbook:chapter5#figure_515|Figure V.15]] shows an isobaric cross-section for the mass number 145. Since the mass number is odd, there is only one parabola. [[textbook:nrctextbook:chapter5#beta_decay|β-]] decays occur on the left edge of the parabola: <sup>145</sup><sub>58</sub>Ce decays to <sup>145</sup><sub>59</sub> Pr and this further to stable <sup>145</sup><sub>60</sub>Nd. [[textbook:nrctextbook:chapter5#positron_decay|β+]] and [[textbook:nrctextbook:chapter5#electron_capture|EC]] decays occur on the right edge: <sup>145</sup><sub>62</sub>Sm decays to <sup>145</sup><sub>61</sub>Pm and this further stable <sup>145</sup><sub>60</sub>Nd . The nuclide at the bottom of the parabola <sup>145</sup><sub>60</sub>Nd has the lowest mass, which means that it is the most stable of these nuclides. In this case, it has an even [[textbook:nrctextbook:chapter2#atomic_number|atomic number]] and an odd [[textbook:nrctextbook:chapter2#neutron_number|neutron number]] and is thus an even-odd nuclide. 
There are 105 of this kind of isobaric cross-sections (parabolas) and the number of stable nuclides in them is obviously the same.
###
{{anchor:figure_515}}

{{:textbook:nrctextbook:beta_decay_with_mass_number_of_145_fig_5_15.png?400|}}

Figure V.15. Beta decays with a mass number of 145.

==== 5.3.3.2. Beta decay at even mass numbers ====


###
Isobaric cross-sections with even mass numbers have two parabolas, the upper for odd-odd [[textbook:nrctextbook:chapter2#nuclide|nuclides]] and the lower for even-even nuclides. As with odd mass numbers and also with even mass numbers, the beta decays occur along the edges of the parabolas, but in this case the decay takes place from one parabola to another since in each decay the nuclide changes from even-even nuclide to odd-odd nuclide or vice versa. The rarest case in this kind of beta decay processes end up to the bottom of the upper parabola where the nuclide has an odd-odd nature. There are only four such cases and all are among the lightest elements, <sup>2</sup>H, <sup>6</sup>Li, <sup>10</sup>B and <sup>14</sup>N. Heavier odd-odd nuclides are unstable due to their imparity of both [[textbook:nrctextbook:chapter2#proton|protons]] and [[textbook:nrctextbook:chapter2#neutron|neutrons]]. An example of these with the mass number 142 is presented in [[textbook:nrctextbook:chapter5#figure_516|Figure V.16]]. Here the bottom nuclide of the upper parabola is <sup>142</sup><sub>59</sub>Pr, being an odd-odd nuclide, is heavier than the adjacent nuclides on the lower parabola, <sup>142</sup><sub>58</sub>Ce and <sup>142</sup><sub>60</sub>Nd. Therefore <sup>142</sup><sub>59</sub>Pr decays to both directions, though the [[textbook:nrctextbook:chapter5#beta_decay|beta minus decay]] is clearly prevalent by 99.98%. Another example of these is <sup>64</sup>Cu ([[textbook:nrctextbook:chapter5#figure_517|Figure V.17]]) for which 61% of decays take place with β<sup>+</sup> and EC and the rest (39%) with β<sup>-</sup> decay. In the isobaric cross-section with mass number 142 ([[textbook:nrctextbook:chapter5#figure_516|Figure V.16]]) we also see that <sup>142</sup><sub>58</sub>Ce is heavier than <sup>142</sup><sub>60</sub>Nd and thus the decay to this lighter [[textbook:nrctextbook:chapter2#nuclide|nuclide]] should take place. This would, however, require that the decay process goes through a heavier <sup>142</sup><sub>59</sub>Pr nuclide, which is impossible. The only possibility is double beta decay and this kind of decay has indeed been observed. An example of this is the decay of <sup>82</sup>Se to <sup>82</sup>Kr where two [[textbook:nrctextbook:chapter5#beta_particle|beta particles]] are emitted and the [[textbook:nrctextbook:chapter2#atomic_number|atomic number]] increases by two units. The decay is, however, very slow, the [[textbook:nrctextbook:chapter6#half_life|half-life]] for it being as long as 1.7×10<sup>20</sup> years.

###
{{anchor:figure_516}}

{{:textbook:nrctextbook:beta_decay_at_the_isobaric_cross-section_a142_fig_5_16.png?400|}}

Figure V.16. Beta decay at the isobaric cross-section A=142. Two stable nuclides, both even-even nuclides.

{{anchor:figure_517}}

{{:textbook:nrctextbook:decay_scheme_of_64cu_fig_5_17.png?400|}}

Figure V.17. Decay scheme of <sup>64</sup>Cu (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).

###
Below in [[textbook:nrctextbook:chapter5#figure_518|Figure V.18]] there are plots for the other cases of even mass numbers. On the left-hand side there is the case with only one stable [[textbook:nrctextbook:chapter2#nuclide|nuclide]] and on the right a case with three stable nuclides. The former is a typical case and there are altogether 78 of them. The latter, however, is rare and only three cases are known, for example at mass number 96 there are three stable nuclides <sup>124</sup>Xe, <sup>124</sup>Te and <sup>124</sup>Sn.
###
{{anchor:figure_518}}

{{:textbook:nrctextbook:beta_decay_processes_at_even_mass_numbers_fig_5_18.png?400|}}

Figure V.18. Beta decay processes at even mass numbers. Left: one stable nuclide. Right: three stable nuclides.

{{anchor:recoil_beta_decay}}
==== 5.3.4. Recoil of the daughter in beta decay processes ====

###
The direction where [[textbook:nrctextbook:chapter5#neutrino|neutrinos]] are emitted is not known, since we do not observe them, but if it emits to opposite direction to [[textbook:nrctextbook:chapter5#beta_particle|beta particle]] the recoil energy of the daughter atom is zero. In case they both are emitted to same direction the recoil energy is its maximum (E<sub>d</sub>). Decay energy in this case is
###


$$Q = E_{d} + E_{max}$$
;;#
[V.XII]
;;#


###
where E<sub>max</sub> is the maximum energy of the [[textbook:nrctextbook:chapter5#beta_particle|beta particle]]. As already mentioned, the recoil energies in beta decay processes are small due to the small mass of [[textbook:nrctextbook:chapter5#beta_particle|electron]]/[[textbook:nrctextbook:chapter5#positron_particle|positron]]. Thus, Q and E<sub>max</sub> are practically identical. For example, in the beta decay of <sup>14</sup>C where E<sub>max</sub> is 156 keV, E<sub>d</sub> is only 7 eV (0.004%). Compared to energies of chemical bonds, this recoil energy is, however, considerable and therefore the beta decay recoil often results in breaking chemical bonds.
###

{{anchor:secondary_processes_beta_decay}}
==== 5.3.5. Consequences of beta decay processes ====

###
Beta decay processes result in the formation of [[textbook:nrctextbook:chapter5#beta_particle|beta particles]], [[textbook:nrctextbook:chapter5#positron_particle|positrons] and [[textbook:nrctextbook:chapter5#neutrino|neutrinos]]/[[textbook:nrctextbook:chapter5#antineutrino|antineutrinos]] as primary emissions. After primary processes, there are secondary processes, which lead to additional emission of radiation. These are:
###


  * Beta decay often occurs to the [[textbook:nrctextbook:chapter5#excited_state|excited states]] of the daughter nuclide. Relaxation of the excitation occurs by [[textbook:nrctextbook:chapter5#internal_transition|internal transition]] (described in next section) and emission of [[textbook:nrctextbook:chapter5#gamma|gamma rays]] and [[textbook:nrctextbook:chapter5#internal_transition|conversion electrons]].
  * As the positrons [[textbook:nrctextbook:chapter5#annihilation|annihilate]] with electrons 0.511 MeV gamma rays are formed.
  * {{anchor:x_rays}}In electron capture, X-rays are formed as the hole in the electron shell is filled with an electron from the upper shells. The X-rays are characteristic of the daughter atom and their energies correspond to the energy differences between the shells.
  * [[textbook:nrctextbook:chapter5#auger_electrons|Auger electrons]] are formed as a consequence of [[textbook:nrctextbook:chapter5#electron_capture|electron capture]] as the X-rays, formed as explained above, transfer their energy to electrons in the upper electron shells and these electrons are emitted. These Auger electrons are mono-energetic and their energies are fairly low, at most a few tens of electron volts.

{{anchor:internal_transition}}
===== 5.4. Internal transition  -  Gamma decay and internal conversion  =====


###
As mentioned, [[textbook:nrctextbook:chapter5#beta_decay|beta]] and [[textbook:nrctextbook:chapter5#alpha|alpha]] decays in most cases do not lead only to the ground state of the daughter but also to its excited states. These excitations are relaxed by two ways:
###


  * [[#5.4.1._Gamma_decay|gamma decay]]
  * [[#5.4.2._Internal_conversion|internal conversion]]
  
These two processes together are called internal transition (IT).

{{anchor:gamma}}
{{anchor:excited_state}}
==== 5.4.1. Gamma decay ====

###
In gamma decay, the daughter nuclide releases its excitation energy by emitting electromagnetic gamma radiation (γ). When, for example, <sup>232</sup>Th decays ([[textbook:nrctextbook:chapter5#figure_519|Figure V.19]]) by [[textbook:nrctextbook:chapter5#alpha|alpha]] mode to <sup>228</sup>Ra only a fraction (76.8%) of [[textbook:nrctextbook:chapter5#alpha_particle|alpha particles]] receive the maximum energy of 4.011 MeV, the rest being decayed by emission of 3.952 MeV alpha particles (23.0%) and 3.828 MeV alpha particles (0.2%). These latter alpha energies are a cause of decay to excited states of <sup>228</sup>Ra. The energies of gamma rays emitted in the de-excitation can be calculated from the energy differences of the alpha particles, for example, 4.011 MeV - 3.952 MeV = 0.059 MeV. There are also gamma transitions from one excitation state to another, for example, 0.126 MeV gamma rays are emitted from this kind of transition in case of <sup>232</sup>Th decay.
###
{{anchor:figure_519}}

{{:textbook:nrctextbook:decay_scheme_of_232_th_fig_5_19.png?400|}}

Figure V.19. Decay scheme of <sup>232</sup>Th (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).


###
Typically, gamma decays take place very rapidly, in less than 10<sup>-12</sup> seconds, i.e. practically at the same time as the alpha and beta emissions. Sometimes, the gamma decays are delayed and if their life-times are so long that they can be measured, the excited states are considered as individual nuclides, isomeric states of the daughter. These nuclides are marked with "m" with the mass number. The life-times for the isomers are expressed as half-lives since their rate of decay behaves in an identical manner with other radionuclides. For example, when <sup>137</sup>Cs decays to stable <sup>137</sup>Ba, there is in between an isomer of barium <sup>137m</sup>Ba which has a half-life of 2.6 minutes. The half-lives of isomeric radionuclides vary in a wide range and the longest [[textbook:nrctextbook:chapter6#half_life|half-life]] of 900 years is known for <sup>192m</sup>Ir.
###


###
As mentioned already, the gamma decays occur from excited states to ground state or between the excited states. Since all these states have defined energy levels, the gamma rays have defined energies. Thus, also the spectrum obtained is a //line spectrum//. [[textbook:nrctextbook:chapter5#figure_520|Figure V.20]] shows the decay scheme and the gamma spectrum of <sup>241</sup>Am. As seen, all three gamma transitions are seen in the spectrum. The heights of the peaks depend on the intensity of each transition. Intensities are the fractions of each transitions from total decay events. For example, the intensities of the three gamma transition in the case of <sup>198</sup>Au are 96% for γ<sub>1</sub> (412 keV), 0.8% for γ<sub>2</sub> (676 keV) and 0.2% for γ<sub>3</sub> (1088 keV). The sum of the intensities is not 100% because part of de-excitations takes place by [[textbook:nrctextbook:chapter5#internal_conversion|internal conversion]], as described later.
###
{{anchor:figure_520}}

{{:textbook:nrctextbook:decay_scheme_214am_fig_5_20.png?400|}}

Figure V.20. Decay scheme (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983) and gamma spectrum <sup>241</sup>Am (http://www.amptek.com/products/x-123-cdte-complete-x-ray-gamma-ray-spectrometer-with-cdte-detector/).

###
Gamma-emitting radionuclides are not only constituted of the [[textbook:nrctextbook:chapter5#beta|beta]] and [[textbook:nrctextbook:chapter5#alpha|alpha]]-decaying radionuclides with excitation states of the daughter. They can also be obtained by activation of a nuclei by electromagnetic and particles bombardments, for example with [[textbook:nrctextbook:chapter2#neutron|neutrons]]. In [[textbook:nrctextbook:chapter5#fission|fission]], gamma rays are also emitted as primary emission, i.e. instantly during the fission process.
###


###
The recoil energy of the daughter in gamma decay is very small, being only less than 0.1% of the energy of the gamma ray. Thus, practically all decay energy goes to gamma radiation.
###

{{anchor:internal_conversion}}
==== 5.4.2. Internal conversion ====

###
As mentioned above, a competing process to gamma decay is internal conversion (IC). In it, excitation energy is not released by gamma ray emission but transferred to a shell electron, which is then emitted. The phenomenon is analogous to formation of [[textbook:nrctextbook:chapter5#auger_electrons|Auger electrons]], which are emitted by the action of energy released from electron transitions from upper to lower shells. The electrons emitted in internal transitions are called //conversion electrons//. They are monoenergetic and their energy is the excitation energy minus the binding energy of the emitted electron. Most conversion electrons come from the inner K-shell since it has a strongest interaction with the nucleus. For example, in the decay of <sup>137m</sup>Ba the conversion electrons come five times more from K shell than from the L shell. In a [[textbook:nrctextbook:chapter5#continuous_spectrum|continuous beta spectrum]], the conversion electrons are seen as peaks. An example is given in [[textbook:nrctextbook:chapter5#figure_521|Figure V.21]] where the beta spectrum of <sup>137</sup>Cs is shown. The conversion electrons, from both K and L shells, are seen as individual peaks at higher energies.
###
{{anchor:figure_521}}

{{:textbook:nrctextbook:beta_and_conversion_electron_spectrum_of_137cs_fig_5_21.png?400|}}

Figure V.21. Beta and conversion electron spectrum of <sup>137</sup>Cs.

###
The ratio of the intensity of internal conversion to that of gamma decay is called conversion coefficient (α<sub>IC</sub>)
###


$$\alpha_{\text{IC}} = \frac{I_{\text{IC}}}{I_{\gamma}}$$
;;#
[V.XIII]
;;#


###
[[textbook:nrctextbook:chapter5#figure_521|Figure V.22]] shows the decay scheme of <sup>137</sup>Cs. 94.6% of the beta transitions go through the 662 keV excitation state of <sup>137</sup>Ba. This excitation state relaxes by emission of 662 keV gamma rays with an intensity of 89.8% (85.1% intensity of all decay events) and the rest 10.2% (9.6%) by internal conversion. Thus, the conversion coefficient is 89.8/10.2 = 0.11.
###
{{anchor:figure_522}}

{{:textbook:nrctextbook:decay_scheme_of_137cs_fig_5_22.png?400|}}

Figure V.22. Decay scheme of <sup>137</sup>Cs (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).

{{anchor:particles_and_rays_in_decay_processes}}
===== 5.5. Particles and rays in radioactive decay processes =====


Table V.III. Primary and secondary particles and rays present in radioactive decay processes.

^Particle/quant ^Symbol ^Mass (amu) ^Charge^
|proton |p |1.007277 |+1|
|neutron |n |1.008665 |0|
|electron, negatron, beta particle |e, e<sup>-</sup>, β<sup>-</sup> |0.00054859 |-1| 
|positron |β<sup>+</sup> |0.00054859 |+1|
|neutrino |υ |~0 |0|
|antineutrino |ῡ |~0 |0|
|gamma ray| γ|
|X-ray |rtg, X|
CINCH NucWik

Sidebar

A-CINCH Consortium

CINCH NucWik

User Tools

Site Tools

Sidebar

Page Tools

A-CINCH Consortium
