bei48482_FM

Nuclear Transformations 435

George Gamow (1904–1968),

born and educated in Russia, did

his first important work at Göttin-

gen in 1928 when he developed

the theory of alpha decay, the first

application of quantum mechanics

to nuclear physics. (Edward U.

Condon and Ronald W. Gurney,

working together, arrived at the

same theory independently of

Gamow at about the same time).

In 1929 he proposed the liquid-

drop model of the nucleus. After periods in Copenhagen,

Cambridge, and Leningrad, Gamow went to the United States

in 1934 where he was first at George Washington University

and later at the University of Colorado. In 1936 Gamow

collaborated with Edward Teller on an extension of Fermi’s

theory of beta decay. Much of his later research was concerned

with astrophysics, notably on the evolution of stars, where he

showed that as a star uses up its supply of hydrogen in ther-

monuclear reactions, it becomes hotter, not cooler. Gamow also

did important work on the origin of the universe (he and his

students predicted the 2.7-K remnant radiation from the Big

Bang) and on the formation of the elements. His books for the

general public introduced many people to the concepts of

modern physics.

The basic notions of this theory are:

1 An alpha particle may exist as an entity within a heavy nucleus.

2 Such a particle is in constant motion and is held in the nucleus by a potential

barrier.

3 There is a small—but definite—likelihood that the particle may tunnel through the

barrier (despite its height) each time a collision with it occurs.

According to the last assumption, the decay probability per unit time can be

expressed as

Decay constant T (12.12)

Here is the number of times per second an alpha particle within a nucleus strikes

the potential barrier around it and Tis the probability that the particle will be

transmitted through the barrier.

If we suppose that at any moment only one alpha particle exists as such in a nucleus

and that it moves back and forth along a nuclear diameter,

Collision frequency  (12.13)

where is the alpha-particle velocity when it eventually leaves the nucleus and R 0 is

the nuclear radius. Typical values of and R 0 might be 2  107 m/s and 10^14 m

respectively, so that

 1021 s^1

The alpha particle knocks at its confining wall 10^21 times per second and yet may have

to wait an average of as much as 10^10 y to escape from some nuclei!

As developed in the Appendix to this chapter, the tunnel theory for the decay

constant gives the formula

log 10 log (^10) 1.29Z^1 ^2 R 01 ^2 1.72ZE^1 ^2 (12.14)


2 R 0
Alpha decay
constant


2 R 0
bei48482_ch12.qxd 1/23/02 12:07 AM Page 435 RKAUL-9 RKAUL-9:Desktop Folder: