1 Instituto de Geofisica, UNAM, 04510, C.U., Coyoacan, Mexico, D.F., MEXICO

2 Ciencias Básicas, UPIICSA, I.P.N., Te 950, Iztacalco 08400, Mexico, D.F., MEXICO

The behavior of the charge of energetic ions as a function of its velocity during their passage through matter is known as Effective Charge q*. Data on q* are obtained from Stopping Power experiments in atomic media, independently of the matter temperature (T). Such data is adequately described by a well known semi-empirical expression, in terms of the atomic number and velocity of ions, and a numerical value which takes into account the kind of atomic target material. However, such an expression does not gives us information about the processes themselves that cause the evolution of charge as ion velocity is being degrading, that is, about the balance between the cross-sections for electron capture and loss. Neither can be applied in finite-T matter, nor in the case in which ions instead of stopping are undergoing an acceleration process. Extrapolations of such empirical expressions to particle acceleration studies in finite-T astrophysical sources is not justified, because the nature of the stopping (atomic) and the acceleration (electromagnetic) processes is different. Here, we propose a general expression for q* with explicit dependence on the electron capture and loss cross-sections, and the medium temperature, whatever the energy changing process may be acting on ions, acceleration or deceleration. We illustrate such analysis under two approaches, atomic matter and plasmas. T- dependence is introduced by considering the thermal velocity of the atomic or ionic targets. The interest of this research is based on the need to draw inferences about the behavior of cross-sections in finite-T matter, by adjusting the predictions of cross-sections in our analysis of q* by comparing q* to data on charge evolution. Though such data is not openly disposable, it may eventually be created in experiments on atomic interactions in plasmas, or even from the comparison with measurements of charge states of solar energetic ions at many different energies in a single event, provided that the amount of traversed matter in the source has been high enough (long confinement and/or high density) for the establishment of charge interchange interactions. Such confrontations may provide us a kind of calibration for further refinements about the nature of those cross-sections. Other implications of this work within the frame of astrophysics as well as plasma confinement research, are in association with diagnostic methods based on photon-emissions following electron capture, to infer about particle composition based on mass/charge selectivity effects, evolution of charge spectra, acceleration or deceleration scale times and so on.