Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold

A time and polarization resolved reflective interferometry measurement on femtosecond laser heated gold is presented. We deduced the electron momentum damping frequency, the conduction electron density, and finally the electron temperature in the $0.6–5\mathrm{eV}$ range in out of equilibrium, solid density warm dense gold. This allows the experimental determination of the electron-electron collision frequency variation with the electron temperature in warm dense matter conditions. The comparison with several models shows the importance of properly taking into account the $d$-band electrons in noble metals.

Figure 1

Ratio $r_p/r_s^2$ from the measured reflectivities in P and S polarizations as a function of time for a gold sample irradiated at $0.6$ and $3\mathrm{J}{\mathrm{cm}}^{-2}$.

Figure 2

Reflectivity and phase shift in S polarization relative to the cold values, measured $100\mathrm{fs}$ after heating, as a function of the heating laser fluence.

Figure 3

Conduction electron density and collision frequency deduced from the data of Fig. 2.

Figure 4

(a) Electron DOS for $T_e=3\mathrm{eV}$ (black dashed-dotted line), Fermi occupation function (blue dashed line), and occupied electron DOS (red solid line). The area of the hatched zones is the number of conduction electrons per atom. The energy origin is the Fermi energy of cold gold, and $\mu$ is the chemical potential for $T_e=3\mathrm{eV}$. (b) Number of conduction electrons per atom $Z_{\text{eff}}$, as a function of $T_e$.

Figure 5

Measured electron damping rate as a function of $T_e$ (blue experimental points), and the contributions from collision with phonons (${\nu }_{\text{ph}}$) and electrons in the conduction band (${\nu }_{ee}^c$). The sum of both contributions is depicted in the red dashed line. Also plotted are the collision frequencies due to the phonons and $d$-band electrons according to our simple model (solid line), and due to phonons and electrons according to the Petrov et al. calculation [12].