Alpha-decay of atomic nucleus (English)

Top of Part 1

Last page

Nest page

1-7: Alpha Decay of Atomic Nuclei

In the preceding section,

we learned

a surprising phenomenon,

the tunnel effect,

which is never seen

in classical mechanics.

If we could actually

discover this phenomenon

in the microscopic world,

it would be strong evidence

of the correctness

of quantum mechanics

and we could justify

the probability interpretation of the wave function.

G. Gamow

(Russia, USA, 1904 - 68)

discovered that

the alpha decay of atomic nuclei

is well explained

by the tunnel effect

(1928).

This was one of the

strong indications of the success

of quantum mechanics.

[Half Life of an Alpha Emitter]

An alpha particle

is the nucleus

of the helium atom.

The radioactive decay

of atoms was discussed

on the page

2-1: The Discovery of Radioactivity

in the preceding Seminar

(Microscopic World -1-).

When we deal

with alpha decay,

we sometimes use

a concept named

half life,

which means the time

in which the amount of

a radioactive nuclide

of a sample decays to

half of its original value.

The half life

is very dependent

on the kind of nuclide.

Geiger and others

measured the half lives of

various alpha radioactive atoms

and discovered

a close relation between

the energy of the emitted

alpha particles and

the half life.

The relation was written

where E

is the energy of

the emitted alpha particles

and A

and C

are the constants

to be adjusted

to agree with experiment.

It is clearly seen

in Fig. (A)

that the empirical

formula (1)

fits well to

the experimental data.

Half lives of alpha decays

The black dots

are experimental data.

The

solid curve

shows

the value of

the empirical formula (1).

(The constants, A

and C ,

are adjusted to

the experimental data.)

It should be noted

from the experimental data

in Fig. (A)

that

the half life of

the alpha emitter

changes to be shorter

by a factor of about

as the energy of

the emitted alpha particles

drops by a factor of 2.5 times.

For example,

the energy of the alpha

particles emitted from

is about 4 MeV and

its half life is very long as .

On the other hand,

for

the alpha particle energy

is about 10 MeV

which is about 2.5 times

larger than the case of

and the half life of

is very short as .

Is it possible

to explain this extreme

difference?

[The Explanation of Alpha Decay by Gamow]

Gamow thought of

the mechanism of the alpha decay

as follows:

The alpha decay of atoms

is nothing else than

the decay of an atomic nucleus by

radiating alpha particles.

The alpha particles

in an atomic nucleus

are considered to be

bound in a nuclear potential

as shown in the following Fig. (B).

The potential exerted to alpha particles in a nucleus.

The alpha particles

in a level with negative energy

cannot go out

from the nucleus, but

those in a positive energy level

penetrate out

with the tunnel effect.

The above figure is drawn

in a one-dimensional space,

but it must be

three-dimensional in practice.

However, it is somewhat

troublesome to discuss in the

three-dimensional space,

so that we consider

in a one-dimensional space

(only on the x

axis) here.

In Fig. (B),

the region

|x| < a

is the inner part

of a nucleus where

alpha particles are bound

by a strong nuclear potential.

The region of

|x| > a

shows the Coulomb repulsive potential

between the charge of an alpha particle,

+2e,

and

the charge of the rest of the nucleus,

+(Z - 2)e.

This means that only

the Coulomb repulsive potential

works between the alpha particle and

the rest of the nucleus

at the region in which

|x| is large enough.

The potential in

Fig. (B)

is extremely simplified.

Although the precise potential

must be

more complicated,

this simplified one

seems sufficient to

qualitatively understand

the mechanism of

the alpha decay.

Fig. (B)

three energy levels, ,

and ,

are drawn

as examples.

If the alpha particle

is on the level ,

the energy is negative.

Then it cannot go out of

the region of

the nucleus, and no alpha decay occurs.

If the alpha particle is on the level ( > 0 )

or ( > 0 ),

then the alpha particle

would penetrate

the potential barrier

by the tunnel effect

and alpha decay occurs.

The question is what effect

on the penetration coefficients

results

from the difference between

the energies,

and .

The half life is

inversely proportional

to the penetration coefficient.

Because it is somewhat

troublesome to estimate

the penetration

coefficient of the tunnel effect

in such a case as the potential

barrier shown in

the following Fig. (C),

let us substitute

the following square potential

for the potential barrier.

This figure

is just the same as what

is shown by Fig. (E)

on the preceding page.

For this square potential,

the penetration coefficient

has already been given by

Eq. (16) on the last page.

This is approximately

proportional to

This exponential function

is strongly dependent on

the value aK ,

In this expression,

is the width of the barrier

and

the energy difference

between the top of the barrier and

the energy of the alpha

particle under consideration.

The penetration coefficients

for the states of energies

and

therefore differ very much;

i.e.,

the half life for each case

varies considerably,

and its energy dependence

well matches

the experimental data.

Carrying out a precise calculation

of the penetration coefficient

for such a potential as in

Fig. (B),

Gamow

obtained the values

of the constants

and

in Eq. (1) that are well suited to

the experimental data.

Gamow's result

was one of the strong evidences of

the correctness

of the probability interpretation

and contributed greatly

to the development

of quantum mechanics.

Top
	Go back to the top page of Part 1. Go back to the last page. Go to the next page.