NuclearE1Overtones

Abstract

The magnitude and energy distribution of nuclear $E1$ cross sections are considered in the light of recent evidence for a large, positive collective shift in the giant resonance energy. Two secondary mechanisms appear relevant: quasi-deuteron or two-particle effects; and overtones of the fundamental $E1$ resonance, representing vibration of the nucleus as a whole. These overtones must exist on any mechanical model, and one object of the present paper is to point out their probable importance for real nuclei. Four types of rough experimental data now available indicate a first overtone intensity of order 25% relative to the fundamental. The parameters obtained are applied to yield (a) an estimate of ${W}_{0}\ensuremath{\sim}60$ MeV for the energy at which quasi-deuteron effects become predominant; (b) predicted curves of $\ensuremath{\int}\ensuremath{\sigma}\mathrm{dW}$ to finite upper limits, suitable for immediate comparison with experiment, in contrast to sum rules that require infinite upper limits in principle; (c) a corrected estimate $y\ensuremath{\sim}1$ for the nuclear exchange force parameter, indicating two-body forces in the nucleus that are relatively weak (attractive) in odd states; and (d) an improved formula for nuclear polarizability.