bei48482_FM

150

100

50

0

400 600 800 1000

Effective mass, MeV

Events per 10-MeV interval

ω

η

Figure 13.4Resonant states in the reaction p→p^0 occur at effective

masses of 549 and 783 MeV/c^2. By effective mass is meant the total energy, including mass energy, of

the three new mesons relative to their center of mass.

Let us see what is involved in a resonance in the case of elementary particles. An

experiment is performed, for instance the bombardment of protons by energetic 

mesons, and a certain reaction is studied, for instance

p→p^0

The effect of the interaction of the and the proton is the creation of three new

pions. In each such reaction the new mesons have a certain total energy that consists

of their rest energies plus their kinetic energies relative to their center of mass.

If we plot the number of events observed versus the total energy of the new mesons

in each event, we obtain a graph like that of Fig. 13.4. Evidently there is a strong

tendency for the total meson energy to be 783 MeV and a somewhat weaker tendency

for it to be 549 MeV. We can say that the reaction exhibits resonances at 549 and

783 MeV or, equivalently, we can say that this reaction proceeds via the creation of an

intermediate particle which can be either one whose mass is 549 MeV/c^2 or one whose

mass is 783 MeV/c^2.

From Fig. 13.4 we can even estimate the mean lifetimes of these uncharged

intermediate particles, which are known respectively as the and mesons. In Chap. 12

we used the formula

Mean lifetime  (12.23)

to relate the mean lifetime of an excited nuclear state to the width at half-maximum

of the corresponding resonance peak. Applying the same formula here gives a mean

lifetime of 5 10 ^19 s for the meson and one of 7 10 ^25 s for the meson.







484 Chapter Thirteen

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