bei48482_FM

Most excited nuclei have very short half-lives against gamma decay, but a few remain

excited for as long as several hours. The analogy with metastable atomic states is a

close one. A long-lived excited nucleus is called an isomerof the same nucleus in its

ground state. The excited nucleus^8738 Sr* has a half-life of 2.8 h and is accordingly an

isomer of^8738 Sr.

12.7 CROSS SECTION

A measure of the likelihood of a particular interaction

Most of what is known about atomic nuclei has come from experiments in which

energetic bombarding particles collide with stationary target nuclei. A very con-

venient way to express the probability that a bombarding particle will interact in a

certain way with a target particle employs the idea of cross sectionthat was intro-

duced in the Appendix to Chap. 4 in connection with the Rutherford scattering

experiment.

What we do is imagine each target particle as presenting a certain area, called its

cross section, to the incident particles, as in Fig. 12.12. Any incident particle that is

directed at this area interacts with the target particle. Hence the greater the cross section,

the greater the likelihood of an interaction. The interaction cross section of a target

particle varies with the nature of the process involved and with the energy of the

incident particle; it may be greater or less than the geometrical cross section of the

particle.

Suppose we have a slab of some material whose area is Aand whose thickness is

dx(Fig. 12.13). If the material contains natoms per unit volume, a total of nA dxnuclei

is in the slab, since its volume is A dx. Each nucleus has a cross section of for some

particular interaction, so that the aggregate cross section of all the nuclei in the slab is

nAdx. If there are Nincident particles in a bombarding beam, the number dNthat

interact with nuclei in the slab is therefore specified by





Cross section ndx (12.19)

nAdx



A

dN



N

aggregate cross section



target area

Interacting particles



Incident particles

Nuclear Transformations 441

1.015 MeV

0.834 MeV

0

27

12 Mg

γγ

β– β–

γ

27

13 Al

Figure 12.11Successive beta and gamma emissions in the decay of^2712 Mg to^2713 Al via^2713 Al*.

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