The 3-dimensional cored and logarithm potencials: Periodic orits

Agraïments: The first author is partially supported by CNPq grant 201802/2012-0.We study analytically families of periodic orbits for the cored and logarithmic Hamiltonians H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (1+x2 +(y2 +z2)/q2)1/2, and H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (log(1+x2 +(y2 + z2)/q2))/2, with 3 degrees of freedom, which are relevant in the analysis of the galactic dynamics. First, after introducing a scale transformation in the coordinates and momenta with a parameter ε, we show that both systems give essentially the same set of equations of motion up to first order in ε. Then the conditions for finding families of periodic orbits, using the averaging theory up to first order in ε, apply equally to both systems in every energy level H = h > 0. The averaging method used proves the existence of at most three periodic orbits, for ε small enough, and gives an analytic approximation for the initial conditions of these periodic orbits

Coherent phase control in ionization of magnesium by a bichromatic laser field of frequencies ω and 2ω

We have investigated the coherent phase control on the $3p^{2}$ autoionizing state (AIS) resonantly coupled with the ground state for Mg through a two- and a four-photon transition simultaneously, using a bichromatic linearly polarized laser field. The frequency is chosen such that the lasers are tunable around resonance with the transition $3s^{2}(^{1}{\rm S^e})\rightarrow 3p^{2}(^{1}{\rm S^e})$, which implies $\omega _{f}=2.11$ eV and $\omega _{h}=4.22$ eV. We are interested in the modification of autoionizing (AI) line shape through the relative phase and laser intensities. A strong phase dependence on the total ionization yield and ionization rate is found. We also performed a time-dependent calculation which takes into consideration all the resonant states of the process

Multiphoton ionization of magnesium in a Ti-sapphire laser field

In this paper we report the theoretical results obtained for partial ionization yields and the above-threshold ionization (ATI) spectra of magnesium in a Ti:sapphire laser field (804 nm) in the range of short pulse duration (20-120 fs). Ionization yield, with linearly polarized light for a 120 fs laser pulse, is obtained as a function of the peak intensity motivated by recent experimental data [9]. For this, we have solved the time-dependent Schrödinger equation nonperturbatively on a basis of discretized states obtained with two different methods; one with the two-electron wavefunction relaxed at the boundaries, giving a quadratic discretized basis and the other with the two-electron wavefunction expanded in terms of Mg+-orbitals plus one free electron allowing the handling of multiple continua (open channels). Results, obtained with the two methods, are compared and advantages and disadvantages of the open-channel method are discussed