Alpha decay and identificationof nuclides produced
November 2023

OutlineRiccardo Orlandi

・ Key Points of Alpha Decay
・ Isotope Identification Examples

1About Alpha Collapse
α Decay is a process by which an unstable nucleus gains stability by emitting an α particle,
that is a nucleus of helium made of 2 protons and 2 neutrons

AZ→(A-4)(Z-2)+4He

Mothernucleus

Daughternucleus

Alpha decay occurs spontaneously if the Q-value for the reaction is positive, i.e. Qα > 0.
The Q-value is the difference of the mass of the mother (mM) and the combined mass of thedaughter (mD) and α particle (mα), multiplied by c2, i.e. :Qα = mMc2 − (mDc2 + mαc2)

In terms of the binding energies of the mother (BM), daughter (BD) and alpha (Bα)

Qα =(BD + Bα) − BM2

Mode of decay from ground state (experimental data)

82
Proton number Z

126
50
82
28208820

Main decay mode
β+/EC, β- , α, SF, p50
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Neutron number N

Alpha decay (yellow) in proton-rich, heavy nuclei

3About Alpha Collapse

Experimental observables: Eα and T1/2Alpha energy can be derived from the law of conservation ofmomentum:

𝑚𝑚𝐷𝐷𝐴𝐴𝐷𝐷
Eα =Qα ≈𝑄𝑄 α
𝑚𝑚𝐷𝐷＋𝑚𝑚α
𝐴𝐴𝐷𝐷+4

Example A=238, Eα ≈ 238/242 Qα = 0.983 Qα4About Alpha Collapse：

Very large variation in half-life

Th Experimental data for isotope
4.4 x 1017 s
232

230
228
226
224

222

1.1 x 10-7 s
218

Even a slight change in Eα changes T1/2 by many orders of magnitude.
Example ) 232Th : Eα = 4.01 MeV, T1/2 = 1.4 x 1010 years = 4.4 x 1017 seconds
218Th : E = 9.68 MeV, T
0.11 μs = 1.1 x 10-7 seconds
α1/2 =5

Gamow's explanation of alpha decay

Eα< Vb→ Collapse due to tunnel effe

TunnelingExample）Th Against isotopes
R ~ 1.2 x (2301/3+ 41/3) = 9.26 fm

𝑞𝑞1 𝑞𝑞2
𝑞𝑞1 𝑞𝑞2
88 × 2= 27.3 MeV≅ 1.44= 1.44 ×𝑉𝑉𝑏𝑏 =9.26
4𝜋𝜋𝜋𝜋0𝑟𝑟
𝑟𝑟

Eα(Th): 4~10 MeV !

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Relationship between half-life and element number

ThCm

Transuranium
element
280Rg

Po260Sg

For the same energy, the alpha decay half-life increases with proton number(Longer half-lives are one evidence of the formation of superheavy elements) 7

Gamow's explanation of alpha decay

Eα< Vb→ Collapse due to tunnel effectTunnelingトンネリング

Eα EαThe larger the atomic number, the larger the potential barrier.
The same Qα may also be due to the tunneling effect,
A slight increase in barrier height significantly increases the half-life8

Blanching of alpha decay
Some radionuclides undergo multiple forms of decay, called branched decay
例

0+1-1.2%
6.77 MeV0224Th

19(2)%
7 MeV2+0+220Ra

79(2)%
7.17 MeV

When calculating cross sections,
Branching must be taken into account9

Nuclide identification based on alpha decayenergy and half-life
Generated in the reaction

34S Beam(150 MeV)

169Tm

JAEA RMS

TargetFocus Chamber

RMS
DSSD
（ Si strip detector ）MCP （ Timing detector ）t0 : The nucleus is hammering away. 10

Nuclide identification based on alpha decayenergy and half-life
Generated in the reaction

34S Beam(150 MeV)

169Tm

JAEA RMS

TargetFocus Chamberalpha decay
DSSD（ Si strip detector ）MCP （ Timing detector ）t > t0 : Alpha decay

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Exampleα3α2 7900 keV
7200 keV
t1/2 = 100 s
t1/2 = 3 sα18300 keV
t1/2 = 0.1 s

11Example

Elapsed time since strike [s]Log Scale

α3α2 7900 keV
7200 keV
t1/2 = 100 s
t1/2 = 3 sAlpha energy (keV)α18300 keV
t1/2 = 0.1 s

11Example

Elapsed time since strike [s]Log Scale

α3α1

α2 7900 keV
7200 keV
t1/2 = 100 s
t1/2 = 3 s

8300 keV
t1/2 = 0.1 sα3α2
α1
Alpha energy (keV)11Number of events Elapsed time since strike [s]ExampleAlpha energy (keV)
X projection

α3α2

Alpha energy confirmed with database
For example

α1National Nuclear Data Center （NNDC）
Radiation Searchhttps://www.nndc.bnl.gov/nudat3/indx_dec.jsp

Alpha energy (keV)

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YprojAlpha energy (keV)

Number of events

Elapsed time since strike [s]Examplet1/2= 0.1 s

t1/2= 3 s

t1/2= 100 s

Elapsed time since strike [s]Number of events

X projection

α3α2

α1

ln 2− 𝑏𝑏 𝑥𝑥
𝑓𝑓 = 𝑐𝑐 ∗ 𝑥𝑥 ∗ 𝑒𝑒

Parameterx is Timeb is t1/2

K.-H. Schmidt et.al.,Z. Phys. A 316, 19-26(1984)

Alpha energy (keV)

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Exampleα18300 keV
For decay chains,
t1/2 = 0.1 s
Correlated measurement of alpha signalkeV
α2 7200
t1/2 = 100 s

α2energy (keV)∆t = t(α2)-t(α1) < ~300 sec(Figured on the same strip）

α1energy (keV)

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Example Important point

Elapsed time since strike [s]t1/2～ ?

t1/2～100 s

Alpha energy (keV)15

Number of events

The t1/2 appears to be ~350 sec, which is wrong, but ...

Elapsed time since strike [s]16Example Important point

Elapsed time since strike [s]t1/2～350 s ?

t1/2～100 s

Alpha energy (keV)17

Elapsed time since strike [s]Actually constant background(from nuclei with very long half-lives)

Linear Scale Appears inAlpha energy (keV)
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