Electromagnetic Properties of the Low-Lying States ofC6126in the Oscillating Drop Model

Abstract

The electromagnetic properties of the first four states of ${}_6{}^{}{}_{}{}^{}\mathrm{C}_6^{12}{}_{}{}^{}$ are discussed within the framework of the incompressible liquid-drop model. The radius of the drop is determined by the elastic electron scattering from the ground state. The surface tension and mass participating in the motion are treated as parameters and are fixed by the energy and lifetime of the first-excited state ($2^{+}$) at 4.43 Mev. This yields an inelastic-electron scattering cross section close to the experimental result. The $0^{+}$ state at 7.66 Mev is then identified with the two-surfon state and the inelastic electron scattering cross section and matrix element for pair emission to the ground state are found to be in quantitative agreement with the experimental results. The state at 9.63 Mev is studied as both the $2^{+}$, two-surfon state and $3^{-}$, one-surfon state which is also predicted at this energy, and it is shown that only the $3^{-}$ state has an inelastic electron-scattering cross section which is consistent with the experimental results. This total electromagnetic width of the $0^{+}$ state at 7.66 Mev, which is astrophysical interest, is calculated to be ${\Gamma }_{\mathrm{el}}=1.02\mathrm{}\times {10}^{-2\mathrm{}}$ ev. The other electromagnetic widths for the first four states are calculated and reasonable agreement is obtained with the experimental data where it exists. The other members of the $0^{+}$, $2^{+}$, $4^{+}$ triplet are unassigned. There are other levels in the vicinity of 10 Mev in ${\mathrm{C}}^{12}$. It would be of interest to know what their spins are.