Hypernuclear excitation through kaon photoproduction

Abstract

The $\ensuremath{\Lambda}$ hypernuclear spectrum excited in the weakly interacting electromagnetic production process $A{(\ensuremath{\gamma}, {\mathrm{K}}^{+})}_{\ensuremath{\Lambda}}B$ 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 $\ensuremath{\gamma}+\mathrm{p}\ensuremath{\rightarrow}{\mathrm{K}}^{+}+\ensuremath{\Lambda}$ which are evaluated from Feynman diagrams including both strange meson (K,K*) and baryon ($\ensuremath{\Lambda}, \ensuremath{\Sigma}$) exchange. These amplitudes are dominated by $\ensuremath{\Lambda}$ and scalar K exchange; however, effects from $\ensuremath{\Sigma}$ and vector K* exchange are found to be significant even near threshold. The hypernuclear selective excitation is documented in detail for $\ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{}$. Transitions to unnatural parity states and substitutional states with medium to high spin are predicted to be strong. Because of large momentum transfer (\ensuremath{\ge}200 MeV/c), the ($\ensuremath{\gamma}$, K) reaction is highly quasielastic and a low, roughly 0.1, $\ensuremath{\Lambda}$ "sticking probability" is estimated using an approximate hypernuclear sum rule. The excitation process is sensitive to the interior as cross section calculations for $^{208}\mathrm{Pb}(\ensuremath{\gamma}, {\mathrm{K}}^{+})_{\ensuremath{\Lambda}}^{208}\mathrm{Tl}$ involving bound $\ensuremath{\Lambda}$, $1s$, $2s$, 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 $\ensuremath{\Lambda}$-nucleus spin-orbit interaction, and different sets of phenomenological coupling constants which equivalently describe the $\ensuremath{\gamma}+\mathrm{p}\ensuremath{\rightarrow}{\mathrm{K}}^{+}+\ensuremath{\Lambda}$ process. Finally, estimates for electroproduction, $A{(\mathrm{e}, {\mathrm{e}}^{\ensuremath{'}}{\mathrm{K}}^{+})}_{\ensuremath{\Lambda}}B$, 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.NUCLEAR REACTIONS Kaon photoproduction and $\ensuremath{\Lambda}$ hypernuclear formation. Theoretical survey of $\ensuremath{\sigma}({E}_{\mathrm{lab}}, {E}_{x})$ for $_{\ensuremath{\Lambda}}^{4}\mathrm{H}$, $_{\ensuremath{\Lambda}}^{12}\mathrm{B}$, and $_{\ensuremath{\Lambda}}^{208}\mathrm{Tl}$. Plane wave impulse approximation and particle-hole wave functions. Investigation of cross section sensitivity to theoretical uncertainties. Application of hypernuclear sum rule. Electroproduction hypernuclear cross section estimates.