Rotational branching ratios at low photoelectron energies in resonant enhanced multiphoton ionization of NO

We report calculated rotational branching ratios for very low energy (50 meV) photoelectrons resulting from (1+1′) resonant enhanced multiphoton ionization (REMPI) via the J_i =1/2, 3/2, 5/2, and 7/2 levels of the P_(11) branch of the A ^2Σ^+ (3sσ) state of NO. Even angular momentum transfer (ΔN≡N_+−N_i) peaks are dominant in these rotational distributions, in agreement with the selection rule ΔN+l=odd. Angular momentum coupling in the photoelectron wave function arising from the molecular ion potential leads to smaller but appreciable ΔN=odd peaks. The calculated ΔN=0 to ΔN=+2 peak ratios show the same strong decrease when J_i increases from 1/2 to 3/2 as seen in the experimental zero‐kinetic‐energy (ZEKE) photoelectron spectra [Sander et al., Phys. Rev. A 36, 4543 (1987)], but do not show the rapid die‐off of the ΔN≠0 peaks for higher J_i observed experimentally. The calculated trend in the ΔN=+2 vs ΔN=0 peaks could be understood on the basis of simple angular momentum transfer arguments. These same arguments indicate that this trend in the ΔN=0 and +2 peaks with increasing angular momentum is not generally expected in other branches. Spectra via the R_(21) ( J) branch are presented to support this assertion. We also present photoelectron angular distributions which show a strong dependence on ΔN reflecting the changing composition of the photoelectron wave function

The Zagier modification of Bernoulli numbers and a polynomial extension. Part I

The modified B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 introduced by D. Zagier in 1998 are extended to the polynomial case by replacing $B_{r}$ by the Bernoulli polynomials $B_{r}(x)$. Properties of these new polynomials are established using the umbral method as well as classical techniques. The values of $x$ that yield periodic subsequences $B_{2n+1}^{*}(x)$ are classified. The strange 6-periodicity of $B_{2n+1}^{*}$, established by Zagier, is explained by exhibiting a decomposition of this sequence as the sum of two parts with periods 2 and 3, respectively. Similar results for modifications of Euler numbers are stated.Comment: 35 pages, Submitted for publicatio

The finite Fourier transform of classical polynomials

The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families

Photoionization cross sections of rovibrational levels of the B^1Σ^+_u state of H_2

We report theoretical cross sections for direct photoionization of specific rovibrational levels of the B ^1Σ^+_u electronic state of H_2. The calculated cross sections differ considerably from values recently determined by resonant enhanced multiphoton ionization (REMPI) studies. In an attempt to understand the disagreement, we analyze in detail the REMPI dynamics and find that the multiphoton ionization probability is extremely sensitive to the spatial and temporal profiles of the laser pulses. Accurate characterization of laser profiles and their jitter is therefore necessary for a comparison between theory and experiment

The g-modes of white dwarfs

The neutral g-modes of a degenerate fluid at zero temperature are analyzed. The g-modes of a degenerate fluid at finite but small temperatures are then expanded in terms of those of the zero temperature fluid. For nonrelativistic degenerate fluids it is found that (1) the g-eigenvalues are proportional to T mu(6)sub e mu(-1)sub i, where T is the internal temperature of the fluid, mu sub e and mu sub i are the mean molecular weights of electrons and ions, respectively; (2) the ion pressure is solely responsible for driving the g-modes. For white dwarfs of about a solar mass, the periods of the g-oscillations are in the range of a few hundredths of seconds