1. 1) The Physics of Radium and Decay & 2) Measurement of Radium and Decay products
Two lectures prepared for Galway Radium Week 18th – 22nd April 2016 Paddy Regan Department of Physics, University of Surrey, Guildford, GU2 7XH, UK & AIR Division, National Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK

2. Outline of lectures
Lecture 1: Some Physics and energetics of Radium decay.
Discovery of Radium.
NORM and the 4n+3, Actinium decay chain.
Equations of radioactive decay; Bateman equations, secular & transient equilibrium.
Revision of energetics of alpha decay; Qa and Ea values.
Brief a -decay theory refresher, selection rules and hindrances in a decay
Lecture 2: Measurement of Radium-223 and its decay products.
How does 223Ra decay ?
Alpha decay of 223Ra and other decay modes (14C decay)
Measurement of a – particles from 223Ra decay (and daughters).
Measurement of gamma rays between excited states in 219Rn and daughters.
Internal electron conversion, Internal conversion coefficients.
The energy level scheme for 219Rn (and daughters).
The current state of the art of the available nuclear data.

3. Formation / creation of 223Ra in nature.
Radium-223 (223Ra) consists of 88 protons (atomic number, Z=88) and 135 neutrons (N=135).
It is formed naturally in trace amounts following the natural decay of uranium-235 (235U) and is thus a Naturally Occurring Radioactive Material or ‘NORM’.
The decay sequence which starts with 235U decay is called the 4n+3 chain or Actinium (Ac) chain. (The radioactive decay of 227Ac was discovered before the 235U nucleus which heads the decay chain).
235U is a primordial radionuclide which makes up ~0.7% of uranium found in nature and has a radioactive decay half-life of 704 million years and decays primarily by a particle emission to create Thorium-231 (231Th).
Most ‘series’ NORM comes from 4n+2 decay series, headed by 238U (99.7% of natural U, half-life, 4.468x109 years) or 4n decays headed by 232Th (100% of natural thorium, T1/2 = 1.405x1010 years)

4. 4n+3 decay chain
‘Actinium’ decay chain,
headed by 235U.
4n+2 decay chain
Uranium/Radium decay chain
headed by 238U.

6. Synthetic production of 223Ra.
For radiopharmaceutical production, 223Ra is not taken from the natural trace amounts present in NORM/Uranium rich materials but generated synthetically by exposing (extracted ) radium-226 to neutrons to produce radioactive radium-227.
Radium-227 (T1/2=42 mins) decays by b- decay to form
actinium-227 (227Ac).
Actinium-227 (half-life 21.8 years) then b- decays to form
thorium-227 (227Th )
Thorium-227 (half-life of 18.7 days) decays to form 223Ra
This method makes it convenient to prepare radium-223 by "milking" it from an actinium-227 containing generator or "cow“, via the decay of 227Th.

8. The 235U parent was not identified until ~30 years later…..

9. By 1930 however, the main decay chains were characterised….

11. Energetics
Beta Decay to Energy minimum, then Alpha decay to different A
Some decays of odd-A nuclei populate daughter excited states with spin of parent
Leads to alpha fine structure
mass parabolas from semiempirical mass equation
cut through nuclear mass surface at constant A
Explains beta decay in decay chain
Branched Decay

13. A quick refresher on laws of radioactive decay.
Activity = number of disintegrations per second is
equal to the number of atoms present at
time t, N(t) multiplied by the probability
of decay per unit time, l.
The (mean) lifetime for the decay is t = 1/l
If N1(0) is the number at atoms of type N1 present at time t=0 (start of decay counting time),
then we can rearrange the equation above to give:
Integrating both sides and remembering that at time t=0, N1(t=0) we get,
Since the activity at time t, A(t) is given by:
A1(t) = l N1(t), then it follows that
A1(t) = N1(t=0) e -lt

14. Example for single component decay of 223Ra.
Assume a pure sample containing 1 MBq (= 106 decays per second) of 223Ra at t=0.
Literature half-life of 223Ra (Collins et al.,) is equal to (28) days (see later).
This is equal to approximately 988 thousand seconds.
The mean (average) decay lifetime is related to the half-life by 1.443*T1/2 = t .
Therefore the Mean lifetime (t) for 223Ra is approximately millions seconds.
The decay probability (l) for 223Ra is then given by 1/ 1.425x106 secs.
Therefore l (223Ra) = 7.015x10-7 s-1
Similarly l (219Rn) = / 3.96 s = s-1 for T1/2 (219Ra)= 3.96 secs ;
and l (215Po) = / = 389 s for T1/2(215Po) = ms

15. t (mean lifetime ) = 1.443 * T1/2 (half-life) = 1 / l (decay probability)
mean-life (t) = days = 9.88x105 secs
Average time for disintegration to occur.
Atoms left reduced by factor of 1/e
= 1/2.718 = from t=0.
Number of atoms of 223Ra atoms remaining →.
0.368*N1(0)
Time in days since initial separation →

16. Time (days) since t=0 →
A(t) = lN = A1(t=0)e-lt

17. What if the daughter (219Rn) also then decays?
If l2 >> l1 (i.e., t2 << t 1 , daughter much shorted lived than mother),
Then A2 (t) = l2N2 → A1 (l 2 / (l2-l1) → A1 as e (-(l2-l1)t → 0 for t >> 1/l2 .
Result is that Activity of 223Ra and 219Rn (and 215Po….) tend to equal values for
t > 30 seconds after separation….This is an example of SECULAR EQUILIBRIUM.
l1 (for 223Ra) = 7.015x10-7 s-1
l2 (for 219Rn) = therefore l2 >> l1 and we expect equilibrium

18. Number of atoms present for 1MBq of 223Ra at t = 0
Number of 223Ra atoms at time t,
Number of atoms present for 1MBq of 223Ra at t = 0
Number of 219Rn atoms at time t,
TIME (in days) since initial separation, assumes 1MBq of 223Ra at time = 0

19. Granddaughter (e.g. 215Po) can also decay…
The activity in each generation of a multiple-generation decay series
can be described the Bateman Equations. The general result is that if
the chain is headed by the longest lived member, the activity
(corrected for branching ratios) of each generation equals that of the head of the chain.

20. Grow-in of 223Ra (T1/2=11. 4 days) from 227Th (T1/2=18
Grow-in of 223Ra (T1/2=11.4 days) from 227Th (T1/2=18.7 days) (assumption of 1 MBq activity of pure 227Th at time t=0)?
227Th
Number of atoms →
223Ra
Time (in days) since t=0 →
227Th
Number of atoms →
223Ra
Time (in days) since t=0 →

21. TRANSIENT equilibrium: A2 / A1 → l2 / (l2-l1) = constant
TRANSIENT equilibrium: A2 / A1 → l2 / (l2-l1) = constant. Activity of 1MBq of pure 227Th at t=0, feeding decay of 223Ra (assumes no 223Ra present at t=0)
223Ra Activity (Bq)
227Th Activity (Bq)
227Th Activity (Bq)
223Ra Activity (Bq)
Time (days) since t=0 →
Time (days) since t=0 →

23. Refresher on Energetics of a Decay
a decay is the emission of a 4He nucleus (2 protons and 2 neutrons) from the heavy, mother nucleus (e.g., 223Ra). This is a radioactive process.
Nuclear Binding Energy is released in the form of kinetic energy of the alpha particle and recoiling daughter heavy nucleus.
The Qa-value is the DIFFERENCE in the total MASS-ENERGY of the system before and after a - particle emission. The Q-value for alpha decay is defined by
Qa = (MP – (MD+Ma) )c2 = (MP-MD-Ma)c2
Where MP = atomic mass of parent nucleus (e.g., 223Ra)
MD = atomic mass of daugher nucleus (e.g., 219Rn)
Ma = atomic mass of the alpha particle.
Measured Atomic Masses are tabulated and can be given in atomic mass units,
where 1 u = 1 Atomic Mass unit = MeV/c2 : Ma = u = MeV/c2
If Qa > 0 energy can be released and a decay can take place…..
The probability of decay (i.e., radioactive half-life for a decay) depends on others things too…

26. M (223Ra) = 223.0185 u ; M (219Rn) = 219.0095 u; M (4He) = 4.002603
Qa (223Ra) = ( – )uc2 = uc2 = MeV

28. Alpha-particle Emission energies ?
Qa value must be positive for alpha decay to occur.
Qa value split between (recoil) kinetic energy of daughter and emitted alpha particle such that:
Qa = Ta + Td
Conservation of linear momentum requires a particle and daughter (d) to be emitted back to back; this leads to
mava = mdvd
Kinetic energy (non-relativistic) of particles is given by T= ½ mv2, from which it follows that
maTa = mdTd
Due to mass difference between a and daughter nucleus (A>210); most (>98%) of the Qa energy goes to the alpha particle kinetic energy.
Eg. in 223Ra decay, Qa = MeV;
For ‘ground-state-to-ground-state’ alpha decay,
Ta = MeV : Td = MeV

29. The Geiger-Nuttall Rule
There are relatively small variations
for a decay energies across all measured,
heavy cases.
Typical a decay energies lie between
4 and 9 MeV for heavy nuclei.
The corresponding range in radioactive
decay half-lives is by contrast, ENORMOUS,
ranging from > 1010 years to less than
microseconds.
When plotted on a semi-log plot of
decay half-life verses Ta, a correlation
becomes clear.
This empirical relation underpins our best
theoretical understanding of the a decay
process in terms of a NUCLEAR QUANTUM
MECHANICAL TUNNELLING PROCESS.

31. Basic Theory of a Emission.

33. Alpha Decay Theory
Include idea of an additional factor that describes probability of preformation of alpha particle inside parent nucleus prior to decay.
No clear way to calculate preformation probability
theoretical estimates of emission rates are higher than observed rates
Estimate frequency for alpha particle to reach edge of a nucleus can be made using the alpha-particle velocity divided by the nuclear diameter (from basic idea that the time taken = distance travelled divided by the speed ).
twice the nuclear radius, is the order of order of m
lower limit for velocity obtained from kinetic energy of emitted alpha particle (from Ea = ½ mava2, for a 6 MeV alpha particle from A=223, this is approximately va ~ 1.7x107 ms-1
particle is moving inside a potential energy well and its velocity should be larger and correspond to well depth plus external energy.
‘Knocking frequency’ of hitting the barrier is then shown to be ~1021 s-1
Reduced mass

34. Alpha Decay Calculations
Alpha particle barrier penetration from Gamow
T=e-2G
Determination of decay constant from potential information
Using square-well potential, integrating and substituting
Z daughter, z alpha

35. Alpha Decay Theory
The closer particle energy is to the barrier height, the more likely the particle will penetrate barrier.
More energetic alpha particles will encounter barrier more often, since
Geiger Nuttall law of alpha decay
constants A and B have Z dependence.
simple relationship describes α-decay
over 20 orders of magnitude in decay constant or half-life
1 MeV change in -decay energy results in a change of 105 in half-life

37. Gamow calculations From Gamow
Calculated emission rate typically one order of magnitude larger than observed rate
observed half-lives are longer than predicted
Observation suggest a route to evaluate alpha particle pre-formation factor linked to other ‘selection rules’ / nuclear structure effects?

38. Alpha Decay Selection Rules.
Alpha decay to excited states in nuclei is observed empirically.
Alpha particle spectra from odd-A and odd-odd nuclei can become (very) complex, with a number of characteristic alpha decay energies up to the the ground state to ground state decay Ea value.
In order to conserve angular momentum, alpha particles can be emitted with some additional orbital angular momentum value, l, relative to the daughter nucleus.
This also gives rise to an effective increase in the potential energy barrier height for that decay (called the centrifugal barrier).
Any orbital angular momentum adds l(l+1)ħ2/2mr2 to potential barrier for that decay.
Angular momentum selection rule in a decay required that the spins of the state populated by direct decay must be equal to the vector sum of the spin of the emitting state in the mother, plus any relative orbital angular momentum carried away from the a particle, la.
l = 0 alpha decays would be favored. (i.e., same spin/parity for mother decaying state and daughter state populated directly in alpha decay).
Excited energy states in daughter can have different spin (and parity) values which affect the relative population in a decay.

39. Hindered -Decay Assumes existence of pre-formed -particles
Ground-state transition from nucleus containing odd nucleon in highest filled state can take place only if that nucleon becomes part of -particle
therefore another nucleon pair is broken
less favorable situation than formation of an -particle from already existing pairs in an even-even nucleus
may give rise to observed hindrance
-particle is assembled from existing pairs in such a nucleus, product nucleus will be in an excited state
this may explain higher probability transitions to excited states
Hindrance from difference between calculation and measured (partial) half-life
Hindrance factors between 1 and 30,000
Hindrance factors determined by
ratio of measured alpha decay half life over calculated alpha decay half life
ratio of calculated alpha decay constant over measured alpha decay constant

40. I. Ahmad et al., Phys. Rev. C68 (2003) 044306
a-decay, example of hindrance effect.
4/28/2017
I. Ahmad et al., Phys. Rev. C68 (2003)
even-even nuclei:
0+ -> 0+; la=0
odd-A:
1/2+ -> 1/2+; la=0,1
1/2+ -> 3/2+; la=1,2
1/2+ -> 9/2-; la=4,5
Strong dependence on la
fastest decay for la=0
Configuration dependence
fastest for the same configurations
Test

41. Hindrance Factors Transition of 241Am (5/2-) to 237Np
states of 237Np (5/2+) ground state and (7/2+) 1st excited state have hindrance factors of about 500 (red circle)
Main transition to 60 keV above ground state is 5/2-, almost unhindered
Hindrance Factors

42. Hindrance Factors
5 classes of hindrance factors based on hindrance values
hindrance factors increase with increasing change in spin
Parity change also increases hindrance factor
Between 1 and 4, transition is called a “favored”
emitted alpha particle is assembled from two low lying pairs of nucleons in parent nucleus, leaving odd nucleon in its initial orbital
Hindrance factor of 4-10 indicates a mixing or favorable overlap between initial and final nuclear states involved in transition
Factors of indicate that spin projections of initial and final states are parallel, but wave function overlap is not favorable
Factors of indicate transitions with a change in parity but with projections of initial and final states being parallel
Hindrance factors of >1000 indicate that transition involves a parity change and a spin flip

43. Part 2: How does 223Ra decay ? Characteristic signatures of decay include: i) Alpha decay (and rare 14C cluster emission) Ii) Fine structure in alpha decay to 219Rn excited states. iii) Gamma ray emission from excited states in the 219Rn daughter. Iv) Internal electron conversion emission in competition with gamma ray emission. V) Daughter (219Rn), granddaughter (215Po) and subsequent decays….

44. Very complex alpha decay fine structure, many alpha lines to excited states in 219Rn.
(from ENSDF nuclear data based from 2001 evaluation in Nuclear Data Sheets).

45. Evaluated nuclear decay data for 223Ra; how does it decay?
(Evaluation from Nuclear Data Sheets (2001).

47. Alpha decay of 227Th parent used to give spin/parity for 223Ra ground state as Jp = 3/2+
Expect to see most favoured decays to Dl=0 Jp = 3/2+ (excited) states in 219Rn daughter

48. Alpha decay spectrum of 223Ra and daughters (courtesy Sean Collins, NPL).

49. Interesting aside: (rare) Heavy-particle decay
Possible to calculate Q values for emission of heavier nuclei
Is energetically possible for a large range of heavy nuclei to emit other light nuclei.
14C emission observed from 222,223Ra
emission probability is much smaller than alpha decay
Simple barrier penetration estimate can be attributed to very small probability to preform 14C residue inside heavy nucleus

50. ‘Best’ study of a-g coincidences to date…

51. Most intense a decay energies associated with 223Ra decay have Ea=5176(4) and 5607(4) keV.
These correspond to the direct population from spin/parity 3/2+ ground state of 223Ra
to (a) the 7/2+ excited state at Ex=( ) = 155(5) keV (Dl=2) and
(b) the 3/2+ excited state at Ex=( ) = 264(5) keV (Dl=0) above the 219Rn ground state.
Note a large observed hindrance (~2800) for the decay to the ground state (5781 keV).

52. 223Ra ground state, 3/2+
Ea=5607(4) keV
Ea=5607(4) keV

54. Gamma-ray multipoles determine the
angular momentum (spin) and parity
differences between the initial and final
nuclear states linked by gamma-ray emission.
E1 = one unit change in spin ; chain in parity
M1 = one change in spin ; no change in parity
E2 = two unit change in spin ; no change in parity.
Selection rules in a decay (of 223Ra) mean that different excited states are populated in the daughter nucleus. These can then subsequently decay to the ground state of the daughter (219Rn) by characteristic gamma-ray emission Nuclear states are labelled by angular momentum (or ‘spin’) and parity (+ or -) quantum numbers. The angular momentum removed by the emitted gamma-ray (DL) from the nucleus is related to the spin difference between the initial and final nuclear states (usually the lowest order decay DL = |Ii-If| dominates).

55. Excited states populated in 219Rn following 223Ra decay.

56. Determination of Absolute Pg values

57. Radon (Z=86) Internal Conversion Coefficients
Internal electron conversion is a COMPETING PROCESS with gamma-ray emission.
Instead of a discrete gamma-ray energy photon of energy Eg being emitted, the nuclear
excitation energy is transferred to a bound atomic electron, which is then emitted from the
Atom with an energy Ee- = Eg – EBE, where EBE is the ELECTRONIC BINDING ENERGY for that
particular electronic atomic state.
The internal electron conversion coefficient, a, is defined as
the ratio between the probability of the nuclear state decaying
Internal conversion (le) to gamma-ray emission (lg).
This means that some excited nuclear states decay but a discrete
gamma-ray is always emitted in the process. This usually explains
why some excited states appear to have ‘missing’ gamma-ray
Intensity balances in the

58. Atomic Electronic biding energies (in eV)
For internal conversion to result in the emission of a bound atomic electron due to a
transition between excited nuclear states in 219Rn, the minimum energy difference between the states (i.e. equivalent gamma-ray energy) must be at least:
98.4 keV for internal conversion from the K electron (1s) shell in Radon (Z=88)
14.6 keV for internal conversion from the L3 electron shell and
2.9 keV for internal conversion from the M5 electronic shell .

60. a Transition energy (keV)
K-shell IC contribution to atot is significant (above K-binding energy) Calculated values for Radon (Z=86) using BRICC. a
Transition energy (keV)

61. Need to know mixing ratios to account properly for ICC and get absolute Pg values consistent with a-decay feeding.

62. What happens to the (other) atomic electrons following Internal Conversion?
In the internal conversion process, a bound atomic electron is emitted, usually from either the K (1s) or L (2s,2p) atomic shells.
This emission results in a vacancy in this atomic electron orbit which can be filled de-excitation of higher lying electron.
This is usually followed by the emission of characteristic K or L X-ray lines. This explains the presence of characteristic K X-ray lines for Rn (and Po and Pb daughter nuclei) in the 223Ra sample high-resolution gamma-ray spectra.
Competing processes with characteristic X-ray emission are the release of characteristic AUGER electrons. The ratio of gamma-ray emission to auger emission for an atomic vacancy is given by the FLUORSCENT YIELD for that transition.

63. Characteristic X-ray energies (emitted following internal conversion)

64. Most up to date, accurate data on 223Ra decay?