bei48482_FM

The formation and decay of a compound nucleus has an interesting interpretation

on the basis of the liquid-drop nuclear model described in Sec. 11.5. In terms of this

model, an excited nucleus is analogous to a drop of hot liquid, with the binding energy

of the emitted particles corresponding to the heat of vaporization of the liquid

molecules. Such a drop of liquid will eventually evaporate one or more molecules,

thereby cooling down. The evaporation occurs when random fluctuations in the energy

distribution within the drop cause a particular molecule to have enough energy to

escape. Similarly, a compound nucleus persists in its excited state until a particular

nucleon or group of nucleons happens to gain enough of the excitation energy to leave

the nucleus. The time interval between the formation and decay of a compound nucleus

fits in nicely with this picture.

Resonance

Information about the excited states of nuclei can be gained from nuclear reactions as

well as from radioactive decay. The presence of an excited state may be detected by a

peak in the cross section versus energy curve of a particular reaction, as in the neutron-

capture reaction of Fig. 12.14. Such a peak is called a resonanceby analogy with or-

dinary acoustic or ac circuit resonances. A compound nucleus is more likely to be

formed when the excitation energy provided exactly matches one of its energy levels

than if the excitation energy has some other value.

The reaction of Fig. 12.14 has a resonance at 0.176 eV whose width (at half-

maximum) is 0.115 eV. This resonance corresponds to an excited state in^114 Cd

that decays by the emission of a gamma ray. The mean lifetime of an excited state is

related to its level width by the formula

 (12.23)

This result is in accord with the uncertainty principle in the form Et2 if we

associate with the uncertainty Ein the excitation energy of the state and with the

uncertainty tin the time the state will decay. In the case of the above reaction, the

level width of 0.115 eV implies a mean lifetime for the compound nucleus of

5.73 1 ^15 s

Center-of-Mass Coordinate System

Most nuclear reaction in the laboratory occur when a moving nucleon or nucleus strikes

a stationary one. Analyzing such a reaction is simplified when we use a coordinate

system that moves with the center of mass of the colliding particles.

To an observer located at the center of mass, the particles have equal and opposite

momenta (Fig. 12.16). Hence if a particle of mass mA and speed  approaches a

stationary particle of mass mBas viewed by an observer in the laboratory, the speed V

of the center of mass is defined by the condition

mA(V)mBV

1.054 10 ^34 J s

(0.115 eV)(1.60 10 ^19 JeV)



Mean lifetime of

excited state

448 Chapter Twelve

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