Hypernuclear excitation through kaon photoproduction

The $\Lambda$ hypernuclear spectrum excited in the weakly interacting electromagnetic production process $A{(\gamma , {\mathrm{K}}^{+})}_{\Lambda }B$ is theoretically surveyed. Plane wave impulse approximated multiple-scattering calculations for hypernuclear formation from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ targets are presented for a wide range of lab and excitation energies. Excitation energies and transition densities are calculated within a lambda-particle, proton-hole model using Woods-Saxon basis wave functions. The transition operator is constructed using the free (bare) amplitudes for the elementary process $\gamma +\mathrm{p}\to {\mathrm{K}}^{+}+\Lambda$ which are evaluated from Feynman diagrams including both strange meson (K,K*) and baryon ($\Lambda , \Sigma$) exchange. These amplitudes are dominated by $\Lambda$ and scalar K exchange; however, effects from $\Sigma$ and vector K* exchange are found to be significant even near threshold. The hypernuclear selective excitation is documented in detail for $\theta =0\mathrm{}°$. Transitions to unnatural parity states and substitutional states with medium to high spin are predicted to be strong. Because of large momentum transfer (≥200 MeV/c), the ($\gamma$, K) reaction is highly quasielastic and a low, roughly 0.1, $\Lambda$ "sticking probability" is estimated using an approximate hypernuclear sum rule. The excitation process is sensitive to the interior as cross section calculations for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(\gamma , {\mathrm{K}}^{+}){}_{\Lambda }{}^{208}{}_{}{}^{}\mathrm{Tl}$ involving bound $\Lambda$, $1s$, $2s$, and $3s$ configurations, unrestricted by the Pauli exclusion principle, reveal markedly different signatures. Cross section sensitivity is also investigated and discussed for off-shell amplitude effects, variations in the $\Lambda$-nucleus spin-orbit interaction, and different sets of phenomenological coupling constants which equivalently describe the $\gamma +\mathrm{p}\to {\mathrm{K}}^{+}+\Lambda$ process. Finally, estimates for electroproduction, $A{(\mathrm{e}, {\mathrm{e}}^{\prime }{\mathrm{K}}^{+})}_{\Lambda }B$, are also presented and discussed. Both photoproduction and electroproduction cross sections are calculated to be measurably large for the beam energies, 1 to 3 GeV, of proposed intense electron accelerators.