NuclearE1Peak Energies

The peak energies $E_g$ of electric dipole giant resonances in photonuclear reactions considerably exceed the shell-model spacings $E_s$ in the same nuclei: The discrepancy $\delta =\frac{(E_g-E_s)}{E_s}$ is of order unity, although the giant resonances are supposed to arise mainly from transitions of nucleons between successive shells. The present note attempts to understand $\delta$ by noting that $|E_g-E_h|\ll E_g$ and considering sum rule expressions for the harmonic energy $E_h$. These sum rule expressions are well known to yield $E_h=E_d+E_x$, where $E_x$ is special to the $E1\mathrm{}$ operator and the charge exchange component of nuclear forces. Theoretical and empirical arguments are adduced that ($E_g-E_s$) comprises mainly $E_x$, plus two secondary corrections which happen practically to cancel. Comparison with experiment gives a constant $E_x\approx 8$ Mev and thence a satisfactory account of $\delta$. Previous discussions of $\delta$ appear to have neglected $E_x$ and hence have failed to obtain even the right order of magnitude of $\delta$ for real nuclei. The use of a constant $E_x$ also allows an improved fit to the curve of $\int \sigma \mathrm{dE}$ as a function of $A$. It is pointed out that the value of $E_x$ is comparable in significance with the average nuclear potential $V$: By virtue of the $E1\mathrm{}$ excitation mode, $E_x$ represents the difference of even-parity and odd-parity two-nucleon interactions, while $V$ represents a sum of even and odd interactions. The effective mass for the model ground-state wave function is treated as a derived quantity and turns out to be $\frac{M^{*}}{M}\gtrsim 1$; this large value is attributed to a Thomas shift associated with finite nuclear boundaries.