The resonance fluorescence of thin crystal films is studied by the method of Heitler and Ma, with the resonant interaction between the crystal and the radiation field properly taken into account in a nonperturbative way. Owing to the violation of the lattice symmetry by the thin film geometry, it is found that not only the usual polariton type eigenstates characteristics of a bulk crystal cannot be found, but the crystal film once excited by the absorption of a photon will fluoresce with a superradiatively enhanced rate as a consequence of the coherent action of the atoms within roughly a wavelength of each other. Absorption and emission spectra are given explicitly.

Percolation models have been briefly discussed. The two dimensional continuum percolation model was applied to the analysis of the area1 electrical conductance as well as the bulky electrical conductivity of an ultra-thin bismuth film. The results of the normalized area1 electrical conductance against the area fraction covered by islands on the substrate have been found to behave m&h smoother and reasonable in the slope and curvature than those based on the corresponding bulky conductivity, indicating again that the system be a two-dimensional film.

The resistivity of an ultrathin bismuth film has been observed and analyzed according to a two-dimensional continuum percolation model. This novel approach has produced interesting results such as the critical area fraction ${x}_{c}=0.67$, the critical exponent $\ensuremath{\alpha}=1.15$, and other features consistent with the two-dimensional continuum model of percolation.

Assuming that the trajectories on which $\ensuremath{\rho}$ and ${f}^{0}$ mesons lie are degenerate [i.e., assuming exchange degeneracy and $\mathrm{SU}(3)$ symmetry for the $\ensuremath{\rho}$ and ${P}^{\ensuremath{'}}$ trajectories], the zeroth-moment finite-energy sum rule is used for $I=1$ in the crossed channel of the $\ensuremath{\pi}\ensuremath{\pi}$ system. If we ignore the $I=2$ contribution and assume resonance saturation in the direct channel, then a single trajectory, assumed to be of the form $\ensuremath{\alpha}(x)=\overline{a}+bx$ (where $x=s or t$), dominates the direct channel ($s$ channel) at low energies. We also assume that a single trajectory dominates the crossed channel ($t$ channel). It is found that for any given $t$ in the sum rule, there is no unique (bootstrap) solution but rather a continuous range of solutions for $\overline{a}$ and $b$. The solutions depend on the choice of $t$ and are sensitive to the functional form of the residue $\ensuremath{\beta}$. Even with the most complete form of $\ensuremath{\beta}$, a unique bootstrap solution is not possible within the single-trajectory approximation. For a given $t$, a unique solution is obtained only when $b$ (and ${m}_{\ensuremath{\pi}}$) are given a priori. For $t'\mathrm{s}$ such that $\ensuremath{\alpha}(t)=1$, where the results are independent of the functional form of $\ensuremath{\beta}$, if $b$ is assumed to have the experimental value of 1 Be${\mathrm{V}}^{\ensuremath{-}2}$, then $\overline{a}$ turns out to be 0.64, which is close to the experimental value of \ensuremath{\simeq} 0.5. For $\ensuremath{\alpha}(t)$ in the neighborhood of 1, if $b$ varied from 0 to 5 Be${\mathrm{V}}^{\ensuremath{-}2}$, $\overline{a}$ varies only between 0.5 and 0.7.