Scaling Limits for the System of Semi-Relativistic Particles Coupled to a Scalar Bose Field

In this paper, the Hamiltonian for the system of semi-relativistic particles interacting with a scalar Bose field is investigated. A scaled total Hamiltonian of the system is defined and its scaling limit is considered. Then, a semi-relativistic Schrödinger operator with an effective potential is derived.     

Analysis of Photoexcitation Energy Dependence in the Photoluminescence of Firefly Luciferin

The whole pathways for photoluminescence, which include absorption, relaxation and emission, of firefly luciferin in aqueous solutions of different pH values with different photoexcitation energies were theoretically investigated by considering protonation/deprotonation. It is experimentally known that the color of fluorescence changes from green to red with a decrease in the photoexcitation energy. We confirmed with the theoretical analysis that the peak energy shift in the fluorescence spectra with varying photoenergies is due to a change in photoluminescence pathway. When the photoexcitation energy is decreased, the red emission from a monoanion form of firefly luciferin with carboxylate and phenolate groups and N‐protonated thiazoline ring occurs irrespective of the pH values. However, because the species abundant in the solution and those excited by the photon depend on the solution pH, the pathway leading to the monoanion form changes with the solution pH.