Alpha decay: physical background and practical applications. Open lecture in UiB.

1. ALPHA DECAY: PHYSICAL
BACKGROUND AND PRACTICAL
APPLICATIONS
Andrii Sofiienko
Ph.D. Candidate
Department of Physics and Technology
University of Bergen
March - 2015

2. CONTENTS
 Natural radioactivity
 General information about α-decay and history
 Experimental observations
 Theory of Alpha decay
 Practical applications
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3. NATURAL RADIOACTIVITY
First observations and investigations of the naturally
occurring radioactivity were performed in Becquerel's
experiments with uranium salts, 1896. The significance of
this phenomenon was perhaps rather overshadowed then
by Rontgen's discovery of X-rays and by Thomson's
demonstration of the existence of the electron.
Four different types of the radioactivity are known:
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Type Label Charge, C
Alpha α +2
Beta β- or β+ -1 or +1
Gamma & X-ray γ & X-ray Neutral
Neutron n Neutral

4. NATURAL RADIOACTIVITY
Natural radioactivity is occurring due to the
disintegration or decay of the heavy nuclei with big
numbers of the neutrons and protons. The number of
the disintegrations per time unit is proportional to the
number of nuclei:
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     
 
1/2
0 exp
ln 2
dN N dt
N t N t
T



   
   


5. GENERAL INFORMATION ABOUT 𝛂-DECAY
AND HISTORY
The early experiments of Curie and of Rutherford showed that the
radiations from radioactive substances contained components of
different penetrating power, as assessed by their absorption in matter.
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The less penetrating rays, which were
completely absorbed by a few cm of
air were called α-rays. The more
penetrating components, which were
absorbed by about 1 mm of lead were
named β-rays. Both the α- and β-rays
were shown to be corpuscular in
character by magnetic deflection
methods.
Fig. 1. Effect of a transverse magnetic field on radiations [1].
B

6. GENERAL INFORMATION ABOUT 𝛂-DECAY
AND HISTORY
Alpha particles consist of two protons and two
neutrons bound together into a particle identical to
a helium nucleus.
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α - particle
4 2
2 2 2He p n 
 
α – decay equation:
4 4 2
2 2
A A
Z ZX Y He Q 
  

7. GENERAL INFORMATION ABOUT 𝛂-DECAY
AND HISTORY
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Spontaneous alpha decay is allowed when Q>0. The energy
of the emitted alpha particle with mass Mα depends on the
mass of a daughter nucleus, Md:
4 4 2
2 2
A A
Z ZX Y He Q 
  
d
d
M
E Q
M M




The Q is given in terms of binding energies B by:
     4
22, 2 ,Q B N Z B He B N Z    
 4
2 28.296B He MeV

8. EXPERIMENTAL OBSERVATIONS
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Fig. 1: Experimental values for the alpha decay Q values [2].
The alpha
decay energy
is ranging from
2 to 12 MeV,
the mean value
for all isotopes
is about 6 MeV.

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Fig. 2: Energy release in the α-decay of the heavy elements, showing the
regularities of the ground-state α-decay energies [1].
EXPERIMENTAL OBSERVATIONS
β-stable isotopes
9

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EXPERIMENTAL OBSERVATIONS
The variation of α-energy of β-stable elements with A is
due to the closure of a neutron shell at N=126 and a
proton shell at Z=82. A maximum in α-decay energy
occurs when two loosely bound nucleons just above a
closed shell are removed by the α-emission.

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Fig. 4: Decay constant vs. range of a-emitting
nuclei known in 1921 [2].
EXPERIMENTAL OBSERVATIONS
A correlation between the
lifetime and energy of the α-
particle emission was noticed
by Geiger and Nuttall as early
as 1921:
   
3
log loga b R
R v


   


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Fig. 5: Fine structure of α-particle spectra of 212Po. α0 and α1 are the most
intense α-lines. [2].
EXPERIMENTAL OBSERVATIONS
212 208
84 82 6.2Po Pb MeV  
Fine structure in a-ray spectra
was demonstrated in the high
resolution experiments of
Rosenblum (1929) and of
Rutherford. It is due to the
excitation of levels of residual
nucleus.
The long-range
α-particles are
associated with
disintegrations of
an excited state of
the initial nucleus.

13. THEORY OF ALPHA DECAY
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Classical Physics
cannot explain how
the particles with
energy of up to 12
MeV can penetrate
through the Coulomb
barrier of 20-40 MeV.
Fig. 6: A simplified schematic of the Coulomb barrier in the nucleus.
 
 
 
1/3
238
92
108
52
2 [MeV]
, 29.7
, 21.8
V R ZA
V R U MeV
V R Te MeV





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THEORY OF ALPHA DECAY
By 1928, George Gamow (from Ukraine,
Odessa) had solved the theory of the
alpha decay via tunneling.
The alpha particle is trapped in a potential
well by the nucleus. Classically, it is
forbidden to escape, but according to the
(then) newly discovered principles of
quantum mechanics, it has a tiny
probability of "tunneling" through the
barrier and appearing on the other side to
escape the nucleus.
Gamow solved a model potential for the
nucleus and derived, from first principles, a
relationship between the half-life of the
decay, and the energy of the emission, which
had been previously discovered empirically

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THEORY OF ALPHA DECAY
Fig. 7: A representation of α-particle as a wave
function the amplitude of which decreases behind
the Coulomb barrier after the tunneling through it
[1].
 0 r R 
 0
ikr ikr
r R A e B e
     
α-particle in the nucleus:

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THEORY OF ALPHA DECAY
Fig. 7: A schematic of the one-dimensional uniform step-barrier
 
 
 
0
0
0
0, 0;
, 0;
ikr ikr
x A e B e
x a
V
V x a

     
 
 

To explain the tunneling of α-particles
through the Coulomb barrier we can
solve the same but more simple
problem for the one-dimensional
uniform step-barrier.
X0 a
E
V0 0 0x   2 x a 
 1 0 x a  

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THEORY OF ALPHA DECAY
Fig. 7: A schematic of the one-dimensional uniform step-barrier
 
    
2
2 2
2
0
d x m
E V x x
dx

   
The wave function is a solution of the Schrödinger equation:
X0 a
E
V0 0 0x   2 x a 
 1 0 x a  

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THEORY OF ALPHA DECAY
 
 
 
 
0 0
1 1
2 2
0 0
0
1 1 1 1 1 1
2 2 2 2
2
0 ,
2
0 , ,
2
,
ik x ik x
k x k x
ik x ik x
mE
x A e B e k
m V E
a A e B e k A B
mE
x a A e B e k




       

 
        


       

The wave function is a solution of the Schrödinger
equation:

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THEORY OF ALPHA DECAY
 
 
 
2
2
02
0
2
exp 2
0
x a a
D m V E
x
   
    
  
The barrier penetration coefficient D represents the decay of intensity
of the α-particle wave over the barrier region:
The solution has the same form for any other barrier, V(r):
  
2
1
2
exp 2
R
R
D m V r E dr
 
   
 


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THEORY OF ALPHA DECAY
 
0
2
0
,
2
,
4
V r R
V r Ze
r R
r
 

 


The potential energy of the α-particle in Coulomb barrier is:
And the barrier penetration coefficient is [3]:
2 2
0 0
2
exp 2 ,
2 2
b
R
Ze Ze
D m E dr b
r E 
  
     
   

 
     
  1/3
2
exp 2 arccos 1
2 [MeV]
V R V R V RR
D mV R
E E E
V R ZA
   
       
      


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THEORY OF ALPHA DECAY
 1 ,
2
l l R
mE
    
If α decay takes place to or from an excited state, the angular
momentum of the α-particle may equal to different values limited by
the nucleus size:
where λ and l ≤ 10 are the de Broglie wave of the α-particle and the
orbital moment, respectively. It leads to the increase of the total
potential barrier due to the additional component – angular momentum
barrier of the α-particle [3]:
 
 
 
 
 
2
2
1
,
2
,
0.002 1
l
l
Coulomb
l l
V r l
mr
V R l
l l
V R


  

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THEORY OF ALPHA DECAY
The barrier penetration coefficient , D, depends on the both barriers:
The following approximation can be used for the range of orbital
moment l<7 [3]:
 
 2 2
2
0
1 2
,
2 4
l l Ze
V r R l
mr r

  
  
2
0
2
exp 2 , ,
2
b
R
Ze
D m V r l E dr b
E
 
    
 

 
 
    
0 0 1/63
238
0 92 0
1
exp 2.027
exp 0.0849 1
l l
l l
l l
D D
Z A
D U D l l
 
 
     
  
    

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The decay constant, λ, is proportional to the barrier
penetration coefficient as follows:
THEORY OF ALPHA DECAY
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10P D D     
where P is the probability of the formation of α-particle in
the nucleus and ν is the frequency of the interactions of
α-particle with the nucleus walls.
 log A E B   
The theoretical prediction for the decay constant has the
same form as the empirical low of Geiger and Nuttall.

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The odd nucleon α-emitters, especially in ground
state transitions, decay at a slower rate than that
suggested by the simple one-body theory.
The decays of the odd nuclei are referred to as
“hindered decays” and a “hindrance factor” may be
defined as the ratio of the measured partial half-life to
the calculated one.
THEORY OF ALPHA DECAY
.
1/2
1/2
[1;10000]
Meas
Theory
T
HF
T
 
The hindered decays can be explained by the detailed
quantum mechanical analysis of the formation of a-
particles in the nuclei with different energies and
orbital momenta.

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Alpha particle sources are used in variety of practical
applications:
 Energy
 Medicine
 Science
 Industry
PRACTICAL APPLICATIONS

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 Energy:
Nuclear battery is a device which uses energy from the decay of a
radioactive isotope to generate electricity. Compared to other batteries
they are very costly, but have extremely long life and high energy density,
and so they are mainly used as power sources for equipment that must
operate unattended for long periods of time, such as spacecraft,
pacemakers, underwater systems and automated scientific stations in
remote parts of the world. First industrial batteries were developed in
1954.
PRACTICAL APPLICATIONS
X Y Q q
  

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 Energy:
As an example, the composed nuclear battery VERIIT was
developed in Kharkiv Institute of Physics and Technology,
2011, Ukraine [4]. It is based on the transformation of the
kinetic energy of α-particles into the charge through the
ionization process in several thin Me-layers of the battery.
 The source is 210Po (Eα = 5.3 MeV, T1/2 = 138.3 d);
 The efficiency is about 10%;
 Pe = 89 μW, Uout = 15 V.
PRACTICAL APPLICATIONS
eff
X Y Q q
dQ
i
dt w


  
 

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 Medicine:
The 𝛂-particles emitted by isotope of radium (233Ra, half-life 11.4
days) for example, can be directly injected in tiny quantities into
tumourous tissue to directly irradiate and kill cancer cells, an
excellent medical use of an alpha emitter. Since they are not very
penetrating, there is less chance of damaging healthy cells.
This is an example of internal radionuclide therapy.
PRACTICAL APPLICATIONS

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 Science:
The monoenergetic 𝛂-particles emitted by 210Po (Eα =
5.3 MeV (100%), T1/2 = 138.3 d) for example, can be
used for the energy calibration of alpha-spectrometric
detectors (surface barrier detectors).
PRACTICAL APPLICATIONS

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 Industry:
The α-particle sources is used in the smoke detectors because the α-
particles have small penetration depth in the air and its sensitive to the
density change of the gaseous environment.
PRACTICAL APPLICATIONS
  9 12
1.7 5.71E MeV Be C n MeV     
The nuclear reaction (α, n) is used to generate
neutrons that can be used in the down hole
applications, for NDT devices, in nuclear
materials identification systems, etc. The
neutron emission for Am-Be source is ~2.2 x 106
n/s per Ci

31. REFERENCES
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[1] W.E. Burcham. Nuclear physics: an introduction.
Longman.; 1973.
[2] B.A. Brown. Lecture notes in nuclear structure physics.
Michigan State University.; 2005
[3] K.N. Mukhin. Nuclear physics. Macdonald & Co.; 1970.
[4] V.I. Karas, S.I. Kononenko, V.I. Muratov, V.T. Tolok, New
type radionuclide battery VERIIT for the space
applications (Report), Kharkiv Institute of Physics and
Technology, 2011.

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Thank you for your attention!