Spectroscopic Characterization of Open-Shell Cations: Emission and Laser Excitation spectra of Rotationally Cooled CH3(CC)2X+, X = Cl,Br

Gas phase emission and laser excitation spectra of the òE?X?²E (Σ = +½, ?½) transition of rotationally/vibrationally cooled 1-chloro- and 1-bromo-1,3-pentadiyne cations have been obtained. The emission was excited by electron impact on a seeded helium supersonic free jet and the fluorescence by laser excitation of cations produced by Penning ionization and collisional relaxation. From these two sets of data the origin bands of the spin-orbit systems are located and for the bromo species this leads to better values of the spin-orbit splitttings in the two electronic states and of the first adiabatic ionization energy. The vibrational frequencies of many of the fundamentals of these cations in the X?²E and òE states have been obtained to within ±2 cm^?1.     

Laser Induced Excitation Spectra of the Cations of Some Fluoro-substituted Phenols (B̃2 A″ ↔ X̃2 A″) in the Gaseous Phase

Excitation spectra of the cations of pentafluorophenol, 2,3,4-trifluorophenol, 2,4,5-trifluorophenol, 2,5-difluorophenol and 3,5-difluorophenol have been obtained by pumping the B?² A″ ← X?²A″ transition with a dye laser. The cations were first produced in their ground states by Penning ionisation using argon metastables. Vibrational frequencies of some of the fundamentals have been inferred for these cations in the B?² A″ state from the excitation spectra, and in the X?² A″ state from the emission spectra. Possible applications of the reported results are suggested.     

Laser-Induced Fluorescence and Photoelectron-Photon Coincidence Studies of 3,5-Octadiyne Cation

3,5-Octadiyne cation in its lowest excited state has been studied in the gas phase by laser-induced fluorescence and photoelectron-photon coincidence techniques. The excitation spectrum of the ò″←²A″ transition has been obtained and yields vibrational frequencies of some of the fundamentals for the excited cationic state. The fluorescence quantum yields and lifetimes at selected energies within the òA″ state have been determined from the coincidence measurements. This provides quantitative data for the discussion of the relaxation behaviour of such an excited open-shell cation.     

Comparing Hecke eigenvalues of newforms

Given two distinct newforms with real Fourier coefficients, we show that the set of primes where the Hecke eigenvalues of one of them dominate the Hecke eigenvalues of the other has density \(\ge \)1/16. Furthermore, if the two newforms do not have complex multiplication, and neither is a quadratic twist of the other, we also prove a similar result for the squares of their Hecke eigenvalues.     

Fragmentation dynamics and energy disposal in photodissociation of (N2O)2+ in the 458–660 nm wavelength range

The nitrous oxide dimer cation (N₂O)₂⁺ has been studied in the visible wavelength range by photodissociation of a mass-selected high-energy ion beam followed by energy analysis of the charged photofragments. Information on the angular anisotropy of the fragmentation process has been obtained by rotating the polarization direction of the laser light. The results allow conclusions to be drawn about the lifetime of the optically accessed excited electronic state and on the energy disposal in the photofragmentation event.     

Emission and laser-excitation spectra of rotationally cooled methylcyanodiacetylene cation (A˜2EāX˜2 E) and photoelectron—photon

The A?²EāX?² E band system of rotationally cooled methylcyanodiacetylene cation has been studied by emission and excitation spectroscopies. Spectra were obtained by electron-impact ionisation of a seeded helium supersonic free jet and by Penning ionisation followed by laser excitation. These data enable the vibrational frequencies of most of the A₁ fundamentals to be inferred for the X?²E (to within ±2 cm^?1) andX?²E (to within ±4 cm?1) states. The fluorescence quantum yields and lifetimes of the cation prepared in selected levels of theA?²E andB?²A₁, excited states have been determined by photoelectron—photon coincidence measurements and yield a quantitative insight into the radiationless-decay pathways.     

Lifetimes of C-2 in rotational levels of the B̃2Σ+u state in the gas phase

Lifetimes of C^-₂ in rotational levels of the B?²Σ⁺_u:ν′ = 0, ν′ = 1 states have been measured. C^-₂ was produced from bromoacetylene and rare-gas metastables and the B?²Σ⁺_u—X?²Σ⁺_g transition was laser excited. The lifetimes are constant within a vibrational level, 77 = 8 ns for ν′= 0 and 73 = 7 ns for ν′ = 1. The oscillator strength f_νo = 0.044 ± 0.004.