A number of experiments in this course rely on radioactive materials as sources of photons of known energy. One of the skills we hope you develop in this course is the ability to read a nuclear decay scheme and identify the elements released in that decay – which may include electrons, positrons, and/or gamma particles (high energy photons) – as well as the relative intensities of each. ====== Resources ====== ---- Decay schemes provided here come from the following sources (noted beside each figure): * [1] James E. Martin, //Physics for Radiation Protection,// Wiley-VCH, 2006. * [2] C. Michael Lederer, Jack M. Hollander, and Isadore Perlman, //Table of Isotopes, 6th Edition,// John Wiley & Sons, 1967. Additional information (e.g. X-ray lines, lifetimes) can be found from the online Radioactive Table of Isotopes maintained by the International Atomic Energy Agency as an interactive table at [[https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html]] or as a static table at [[https://www-nds.iaea.org/xgamma_standards/genergies1.htm]].
How to navigate the interactive table
====== How to read a decay scheme ====== ---- | {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:na-22_annotated.png?800}} | | Annotated decay scheme for Sodium-22.  Note that decay schemes are published in black and white; the scheme above has been color-coded to highlight the different features that are present. | Horizontal lines [purple] represent energy levels and are arranged so that higher energy states are placed above lower energy states. (Note that separations are not, in general, to scale.) The value written next to a horizontal line [teal] is the energy of that state, usually in MeV, relative to the lowermost energy state in the diagram. The lowermost (ground) state is at zero energy and is the stable, final state of the decay. Some energy levels may also have an indicated lifetime [red]. If no lifetime is given, it is usually safe to assume that the decay from that state to a lower energy is nearly instantaneous. Diagonal lines [green] represent decay processes which take one nuclear species to another (e.g. ${}^{22}_{11}\textrm{Na}$  to ${}^{22}_{10}\textrm{Ne}$ ). Possible processes include the following: * **Electron Capture (EC)**: The nucleus captures an electron from one of the inner shells and the electron is used to convert one of the protons in the nucleus into a neutron. The resulting nucleus usually is left in an excited state and an electron neutrino is emitted from the proton conversion. * Note that in addition to leaving the daughter nucleus in an excited state, EC leaves a hole in an electron shell. One of the electrons in a higher electron state will quickly fall to fill that hole, releasing a photon in the process. //However, the energy of this photon will not appear on the decay scheme since it it not produced directly by the nucleus//. Such photons are typically $K_\alpha$ , $K_\beta$  or $L_\alpha$  X-rays; values for these photons can be found in standard tables like [[http://hyperphysics.phy-astr.gsu.edu/hbase/tables/kxray.html |this one]].  * $\boldsymbol{\beta}^\bf{-}$  emission: A neutron in the nucleus decays into a proton, an electron and an electron neutrino. The electron and neutrino are emitted (and carry away some kinetic energy), usually leaving the nucleus in an excited state. * ****$\boldsymbol{\beta}^\bf{+}$** emission:** A proton in the nucleus decays into a neutron, a positron and an electron antineutrino. The positron and antineutrino are emitted (and carry away some kinetic energy), usually leaving the nucleus in an excited state. * One can think of $\beta^+$  emission as a relative of EC. If the difference in energies between the initial and final nuclear states is at least $2m_ec^2$ , the excited nucleus can spontaneously form an electron-positron pair and use the electron to convert a proton into a neutron; the extra positron is then emitted. Therefore, whenever $\beta^+$  emission is a possible decay mode, EC is also a possible decay mode. The opposite is not true. * ****$\boldsymbol{\alpha}$**  emission**: A heavy nucleus may decay by releasing an alpha particle (a bare nucleus of 2 protons and 2 neutrons, i.e. ${}^{2}_{4}\textrm{He}^{2+}$ ), lowering its charge by 2 units and the number of nucleons by 4. This usually leaves the daughter nucleus in an excited state. Vertical lines [orange] represent transitions from a higher nuclear energy state to a lower nuclear energy state. In most cases, a gamma ray (high energy photon) is emitted carrying away the difference in energy. These emissions are analogous to the more familiar photons emitted when electrons transition among energy levels, but the energy scales are typically much bigger. ** Multiple possible transitions**: In elements with multiple excited energy states, there may be multiple possible decays. In these instances, each vertical transition is labeled with a relative probability and **an energy**. | {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:co_annotated-01.png?400|}} | For example, looking at the cobalt-60 decay, the nickel nucleus can transition from the 2.158 MeV state to either the 1.3325 MeV excited state or the ground state. However, the transition to the 1.3325 MeV state is over ten times more likely (as indicated by the prefixes). Thus, we should expect to see substantially more 830 keV gammas than 2.158 MeV gammas. Some nuclei can also undergo a process called **internal conversion (IC)** where the excited nucleus gives its excess energy directly to an electron, liberating that electron from its shell and sending it off with some extra kinetic energy. IC is possible only in high Z nuclei (where the electron binding energy is comparable to the excited energy of the nucleus) and only from metastable states (where the lifetime for the normal photon emission is quite long, giving enough time for the probability for an electron's wavefunction to overlap with the nucleus' wavefunction to become non-negligible). Decay schemes also contain information about nuclear excitation states, Q values, and ln(ft) values that are not commonly used in this course. ====== Decay schemes used in this course ====== ---- ===== Na-22 =====
Decay Scheme Sodium-22 ($\tau$ = 2.6 years) decays either via electron capture or $\beta^+$ (positron) emission to an excited state of neon-22. The decay from this excited state releases an //E// = 1.2746 MeV photon. Note, however, that the positron created in the decay is short-lived. Once it is slowed by Coulomb interactions, it can bind with an electron to form positronium before eventually annihilating, converting all mass into energy. The most likely product of this annihilation is two back-to-back photons each of energy 511 keV, though decays of 3 or more photons are possible.
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:na-22_toi.png?400|}} | | Na-22 decay scheme (Source: [2]) |
===== Al-28  =====
Decay Scheme Aluminum-28 is a short-lived ($\tau$  = 2.31 minutes) isotope produced by bombarding aluminum-27 with thermal neutrons. It decays via $\beta^-$  (electron) emission to an excited state of silicon-28 and the decay from this excited state releases an E = 1.780 MeV photon.
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:al-28_toi.png?400|}} | | Al-28 decay scheme (Source: [2]) |
===== Co-57  =====
Decay Scheme Cobalt-57 ($\tau$ = 272 days) decays via electron capture to an excited state of iron-57. The vacancy left in the electron orbital will be filled by an electron in a higher shell, releasing a $K_\alpha$  photon of //E// = 6.4 keV. The excited Fe-57 will decay either by emitting a single photon of //E// = 137 keV or by two photons of energies //E// = 122 keV and //E// = 14.4 keV.
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:co-57_toi.png?400|}} | | Co-57 decay scheme (Source: [2]) |
===== Co-60  =====
Decay Scheme Cobalt-60 ($\tau$ = 1925 days) decays via $\beta^-$  (electron) emission into an excited state of nickel-60. In the relaxation to ground, the nucleus emits two photons, //E// = 1.1732 MeV and //E// = 1.3325 MeV in rapid succession. (The lifetime of the intermediate state (1.3325 MeV above ground) is 0.7 ps.)
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:co-60_toi.png?400|}} | | Co-60 decay scheme (Source: [2]) |
===== In-116  =====
Decay Scheme Indium-116 is a short-lived ($\tau$  = 54.0 m) isotope of indium produced by bombarding indium-115 (weakly radioactive, $\tau$  = 4.41 x 1014 years) with thermal neutrons. It decays via $\beta^-$  (electron) emission to tin-116. The relaxation to ground can produce more than a half-dozen different photons, the most likely of which are //E// = 1.0972 MeV and 1.2933 MeV.
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:in-116_toi.png?800|}} | | In-116 decay scheme (Source: [2]) |
===== Ba-133 =====
Decay Scheme Barium-133 ($\tau$  = 10.52 years) decays via electron capture to cesium-133. The vacancy left in the electron orbital will be filled by an electron in a higher shell, releasing a $K_\alpha$  photon of //E// = 31 keV. The decay of the excited Cs-133 can proceed by many paths, but the two most prominent photons emitted are //E// = 356 keV and //E// = 81 keV. Notably, gammas at //E// = 276, 302, and 382 keV will be detectable around (and may overlap with) the 356 keV peak.
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:ba-133_toi-1.png?400|}} | | Ba-133 decay scheme (Source: [2]) |
===== Cs-137  =====
Decay Scheme Cesium-137 ( $\tau$  = 30.04 years) decays via $\beta^-$  (electron) emission to either the ground state of barium-137 (6%) or a //metastable// excited state, barium-137m (94%, $\tau$  = 2.6 minutes). The metastable state decays to the stable ground state primarily by the emission of a single photon with //E// = 662 keV. However, due to the long life of the metastable state, there is a small chance that the nucleus will undergo an internal conversion whereby the excess energy is used to liberate a K-shell or L-shell electron. This ejection is accompanied by an X-ray as an electron from an upper energy level falls into the vacancy and releases a photon. Several photons are possible depending on the electron ($K_\alpha$ ,$K_\beta$ ,$L_\alpha$ , etc.), but the most likely photon is the $K_\alpha$  X-ray, //E// = 32.2 keV.
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:cs-137_toi.png?400|}} | | Cs-137 decay scheme (Source: [2]) |
===== Eu-152  =====
Decay Scheme Europium-152 ($\tau$ = 19.52 y) decays via either electron capture or $\beta^+$  (positron) emission to samarium-152, or via $\beta^-$  (electron) emission to gadolinium-152. Many (many!) potential gammas are released, including samarium $K_\alpha$  x-rays. The full decay scheme is located below, but it may be more useful to use a look-up table of known emission gammas like that provided by [[http://www.spectrumtechniques.com/products/sources/europium-152/ |Spectrum Techniques]] or the [[http://nucleardata.nuclear.lu.se/toi/nuclide.asp?iZA=630152 |Lawrence Berkley National Laboratory Nuclide Database]].
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:eu-152.png?800|}} | | Eu-152 decay scheme (Source: [2]) |
===== Bi-207  =====
Decay Scheme Bismuth-207 ($\tau$  = 31.55 y) decays via electron capture to lead-207. The vacancy left in the electron orbital will be filled by an electron in a higher shell, with the most likely X-ray emissions being $K_\alpha$  photons of //E// = 72.8 keV and 75.0 keV. The three most prominent photons emitted in the decay to ground of the excited Pb-207 are //E// = 569.6 keV, 1.0634 MeV and 1.7697 MeV.
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:bi-207.png?400|}} | | Bi-207 decay scheme (Source: [2]) |
===== Am-241  =====
Decay Scheme Americium-241 ($\tau$  = 623 y) decays via α emission to neptunium-237. The mostly likely path leaves the neptunium in an excited state, which relaxes to the ground state and emits an x-ray of energy //E// = 59.54 keV. The emitted $\alpha$ -particle typically has //E// = 5.5 MeV, but will be rapidly stopped by the Coulomb interaction and will not penetrate very far.
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:am-241_toi.png?800|}} | | Am-241 decay scheme (Source: [2]) |
===== Pu-239 =====
Decay Scheme Plutonium-239 ($\tau$  = 16700 y) decays via $\alpha$ emission to uranium-235. The mostly likely path leaves the uranium either in a metastable state at just 80 eV above ground ($\tau$ = 26.1 m), or in one of a few other low level states that quickly decay to this metastable state. In addition to the 80 eV photon emitted when the metastable state relaxes to ground, other possible x-rays include $E$ = 56.6, 38.6, and 13.1 keV. (There are no statistically likely emissions in the gamma energy range.) The emitted $\alpha$-particle typically has an energy of about $E$ = 5.18 MeV, but it will be rapidly stopped by the Coulomb interactions and will not penetrate far. When mixed with beryllium in a "Pu-Be" type source, the $\alpha$ particle will bind with the beryllium to form carbon plus a neutron (carrying kinetic energy of up to about $E$ = 11 MeV) through the reaction | $\sideset{^4}{}\alpha +\sideset{^9}{}{\textrm{Be}} \rightarrow \sideset{^{12}}{}{\textrm{C}} + \sideset{^1}{}{\textrm{n}}$. | Such a source is considered purely a neutron emitter as the $\alpha$ particles and photons released by the Pu-239 decay are absorbed within the Pu-Be mixture and do not escape the source.
| {{:phylabs:lab_courses:supplemental-material:physics-and-mathematics-references:nuclear_decay_schemes:pu-239_toi.jpg?direct&400|}} | | Pu-239 decay scheme (Source: [2]) |