Time multiplexing: a new single shot femtosecond pump-probe technique

Received: 26 August 1996/Revised version: 13 November 1996     

Fast observation of primary triplets in naphthalene vapor with tandem laser pulse absorption

A sharply tuned pulsed laser absorption experiment is described involving two dye lasers synchronized in tandem (TLPA) which enables one to produce molecules in defined excited states and then follow the immediate production of subsequent molecular species. Measurements of transient TT absorption were carried out in naphthalene at pressures down to 20 mtorr with a precision of 0.2%. The results demonstrate the feasibility of TLPA and here specifically that triplets are formed in naphthalene as a prompt process, and that collisions do not aid the formation of these primary product species.     

Bernoulli convolutions and an intermediate value theorem for entropies of<Emphasis Type="Italic">K</Emphasis>-partitions

We establish a strong regularity property for the distributions of the random sums Σ±λ ⁿ , known as “infinite Bernoulli convolutions”: For a.e. λ ∃ (1/2, 1) and any fixed ℓ, the conditional distribution of (w _n+1...,w _n+ℓ) given the sum Σ _n=0 ^∞ w _n λ ⁿ , tends to the uniform distribution on {±1}^ℓ asn → ∞. More precise results, where ℓ grows linearly inn, and extensions to other random sums are also obtained. As a corollary, we show that a Bernoulli measure-preserving system of entropyh hasK-partitions of any prescribed conditional entropy in [0,h]. This answers a question of Rokhlin and Sinai from the 1960’s, for the case of Bernoulli systems. The authors were partially supported by NSF grants DMS-9729992 (E. L.), DMS-9803597 (Y. P.) and DMS-0070538 (W. S.).     

Theory of Multi-Photon Ionization of Atoms and Molecules

In this paper we present a density matrix formalism to treat one-photon ionization and multiphoton ionization of atoms and molecules in the presence of an external field. It is shown that Fano's results for one-photon ionization without an external field can easily be obtained from our formulation. For comparison, the Green's function method applied to multiphoton ionization of molecules is also presented.     

Lower bounds for the absolute value of random polynomials on a neighborhood of the unit circle

Let where stands for a random choice of sign with equal probability. The first author recently showed that for any and most choices of sign, , provided is large. In this paper we show that the power is optimal. More precisely, for sufficiently small and large most choices of sign satisfy . Furthermore, we study the case of more general random coefficients and applications of our methods to complex zeros of random polynomials.

     

Spectroscopy of molecular ions: Laser induced predissociation of O 2 +

The technique of laser induced predissociation and laser induced fluorescence is applied to study spectra of gas-phase molecular ions. The main feature of the experiment is a beam of mass selected molecular ions illuminated by a pulsed dye laser. Over an extended range of excitation energies spectroscopic information can be obtained about positive and negative ions including transient species. As a first result we present predissociation spectra of O ₂ ⁺ ,b ⁴ bE _g ^? ?a ⁴ π _u Δv=3 andgDv=2 which can well be simulated by calculated spectra assuming a rotational ion temperature of 300δK.     

The spectrum of collision free triplets and its temporal evolution

A tandem laser experiment now enables one to follow the time history of the radiationless formation of triplets from inception to the final relaxed state known from flash photolysis. The TT absorption spectrum is measured shortly after excitation of the singlet and then at different times up to full relaxation at 14 μs. This spectrum is totally different from the well known flash photolysis spectrum, both in spread and its structure. The spectrum reveals both a relaxation process to thermalized triplets, as well as direct evidence for overall loss of triplets by a further radiationless process. Quantitative data can here be presented for these processes.