2 Calculation process

The profiles that are shown have been obtained by computer simulation techniques using particles. The simulation process generates the microfield time sequence suffered by the emitter, which then alters the emission process. The plasma model considers an ensemble of ${N_{\rm p}}$ electrons and ${N_{\rm p}}$ ions moving along rectilinear paths with constant velocity inside a spherical volume. The emitter is placed in the center of that sphere. The plasma is homogenous and isotropic. The velocities of ions and electrons are obtained using the Maxwell distribution with the equilibrium temperature T. In order to account for the correlation effects between charged perturbers, we use Debye screened electric fields. A detailed description of the simulation method can be found in Gigosos & Cardeñoso (1996). As can be seen in that reference, the simulation processes are characterized by the relationship between the mean distance between particles $r_0 = \left(\frac{3}{4\pi N_{\rm e}}\right)^{1/3}$, where $N_{\rm e}$ is the electron density, and the Debye radius $r_{\rm D}$ that fixes the parameter $\rho$ of the simulation:

$$% \rho = \frac{r_0}{r_{\rm D}} = \left(\frac{3}{4\pi}\right)^... ...repsilon_0 k}\right)^{1/2} \frac{N_{\rm e}^{1/6}}{T^{1/2}}\;.$$ (1)

Each time sequence of the electric microfield is used in the Schrödinger equation that establishes the evolution of the emitter atom. In that equation we have considered the fine structure for the level n=2 of the hydrogen atom. From this process the autocorrelation function of the emitter dipolar momentum is calculated. An average over a large number of such processes allows us to obtain the tabulated autocorrelation functions. Gigosos & González (1998) describe in detail the calculation of the two-photon absorption profiles, $A(\Delta\omega)$, the dispersion profiles, $D(\Delta\omega)$, and two-photon polarization profiles, $P(\Delta\omega)$. As can be seen there the autocorrelation function may be written as

$$% C(t) = 2 C_{\rm R}(t) \cos(\omega_0 t) + 2 C_{\rm I}(t) \sin(\omega_0 t)$$ (2)

so that the absorption or emission profiles, the dispersion profiles and polarization profiles may be obtained from

$$% A(\Delta\omega) \frac{1}{\pi} \int_0^\infty {\rm d} t [\cos(\Delta\omega t) C_{\rm R}(t) - \sin(\Delta\omega t) C_{\rm I}(t)]$$ = (3)

$$D(\Delta\omega) - \frac{1}{\pi} \int_0^\infty {\rm d} t [\cos(\Delta\omega t) C_{\rm I}(t) + \sin(\Delta\omega t) C_{\rm R}(t)]$$ =

[-2mm] (4)

$$P(\Delta\omega) A(\Delta\omega)^2 + D(\Delta\omega)^2\;.$$ = (5)

In these expressions $\Delta\omega = \omega - \omega_0$ is the frequency displacement measured from the center of the spectral line. In our calculations that center has been considered as the distance from the medium point of the upper level n=2 states to the lower level n=1. When doing the Fourier transform of Eq. (2) we do not take into account how quantities such as $\int_0^\infty {\rm d}t \cos[(\omega + \omega_0)t] C_{\rm R}(t)$ contribute to the spectrum, which would only make sense if the functions $C_{\rm R}(t)$ and $C_{\rm I}(t)$ had variations in time in that range of frequencies.

At time t=0, $C_{\rm R}(0) = 1$ so that $A(\Delta\omega)$ directly gives the areanormalized absorption or emission profile. In order to obtain the areanormalized polarization profile it is necessary to require that

$$% \int_{-\infty}^{+\infty} P(\Delta\Omega) {\rm d} \Delta\omega = 1\;,$$ (6)

which is equivalent to

$$% \frac{2}{\pi} \int_0^{\infty} {\rm d} t \left( C_{\rm R}(t)^2 + C_{\rm I}(t)^2 \right) = 1$$ (7)

for the autocorrelation function. The tables for $C_{\rm R}(t)$ and $C_{\rm I}(t)$ given in this paper are normalized so that $C_{\rm R}(0) = 1$. In order to obtain areanormalized polarization profiles, the values of $C_{\rm R}(t)$ and $C_{\rm I}(t)$ given in the tables should be properly renormalized according to Eq. (7).

In the simulation it has been considered that the correlation loss of the emission process, described by the $C_{\rm R}(t)$ and $C_{\rm I}(t)$ functions, is due exclusively to collisions with the charged particles. Whenever it may be necessary to consider aditional phenomena that were statistically independent of the Stark effect (for example collisions with neutrals or a residual Doppler effect), the supplied $C_{\rm R}(t)$ and $C_{\rm I}(t)$ functions may be modified in order to calculate the profiles that include all the existing phenomena. In this way, if $F(\Delta\omega)$ is the areanormalized profile due to another broadening mechanism independent of the Stark effect, we calculate the corresponding autocorrelation function using

$$% B(t) \equiv B_{\rm R}(t) + {\rm i}B_{\rm I}(t) \equiv \int... ...\rm i}\Delta\omega t} F(\Delta\omega) {\rm d} \Delta\omega\;.$$ (8)

The total autocorrelation functions that should be used in the calculations to obtain the complete profile would have, then,

$$% C'_{\rm R}(t) C_{\rm R}(t) B_{\rm R}(t) - C_{\rm I}(t) B_{\rm I}(t)\;,$$ =

$$C'_{\rm I}(t) C_{\rm R}(t) B_{\rm I}(t) + C_{\rm I}(t) B_{\rm R}(t)\;.$$ = (9)

  

Table 1: Correlation function file r30n2133.c1p for dipolar emission with $\rho = 0.30$ and $\log(N_{\rm e}) = 21.33$

  

Table 2: One photon dipolar emission profile r30n2133.d1p with $\rho = 0.30$ and $\log(N_{\rm e}) = 21.33$