alpha decay - physical background and practical applications

ALPHA DECAY: PHYSICAL

BACKGROUND AND PRACTICAL

APPLICATIONS

Andrii Sofiienko

Ph.D. Candidate

Department of Physics and Technology

University of Bergen

March - 2015

CONTENTS

Natural radioactivity

General information about α-decay and history

Experimental observations

Theory of Alpha decay

Practical applications

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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

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

http://awakeningthesenses.blogspot.no/2012/05/radioactivity-there-are-certain.html

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


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


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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

ME 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

EXPERIMENTAL OBSERVATIONS 2

5.0

5.2

01

5

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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

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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].


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].


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.

THEORY OF ALPHA DECAY 2

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5.2

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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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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 ikrr R A e B e

α-particle in the nucleus:

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Fig. 7: A schematic of the one-dimensional uniform step-barrier

0

0

0

0, 0;

, 0;

ikr ikrx A e B e

x aV

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.

X 0 a

E

V0 0 0x 2 x a

1 0 x a

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Fig. 7: A schematic of the one-dimensional uniform step-barrier

2

2 2

20

d x mE V x x

dx

The wave function is a solution of the Schrödinger equation:

X 0 a

E

V0 0 0x 2 x a

1 0 x a

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0 0

1 1

2 2

0 0

0

1 1 1 1 1 1

2 2 2 2

20 ,

20 , ,

2,

ik x ik x

k x k x

ik x ik x

mEx A e B e k

m V Ea A e B e k A B

mEx a A e B e k

The wave function is a solution of the Schrödinger

equation:

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2

2

02

0

2exp 2

0

x a aD 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

2exp 2

R

R

D m V r E dr

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0

2

0

,

2,

4

V r R

V r Zer R

r

The potential energy of the α-particle in Coulomb barrier is:

And the barrier penetration coefficient is [3]:

2 2

0 0

2exp 2 ,

2 2

b

R

Ze ZeD m E dr b

r E

1/3

2exp 2 arccos 1

2 [MeV]

V R V R V RRD mV R

E E E

V R ZA

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1 ,2

l l RmE

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 lV r l

mr

V R ll l

V R

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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 ZeV r R l

mr r

2

0

2exp 2 , ,

2

b

R

ZeD m V r l E dr b

E

0 0 1/63

238

0 92 0

1exp 2.027

exp 0.0849 1

l l

l l

l lD 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:


2010P 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.


.

1/2

1/2

[1;10000]Meas

Theory

THF

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.


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.


eff

X Y Q q

dQi

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.


http://blog.dnagenotek.com/blogdnagenotekcom/bid/65693/The-state-of-personalized-medicine

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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).


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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.


9 121.7 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

http://web.princeton.edu/sites/ehs/ContainedSources/AmBeSource/ambesource.htm

http://www.schoolphysics.co.uk/age14-16/Nuclear physics/text/Uses_of_radioisotopes/index.html

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!