  Spherical or cylindrical convergent shock waves in imploding materials are
one of the most effective ways to produce extremely high pressures, densities
and temperatures, hardly attainable in plane shock waves generated by chemical
high explosives or by the impact of high velocities objects. Pressure of the
order of tens of megabars, densities many times greater than the normal density
of solids and temperatures of hundreds of thousands degree can be easily
produced in the convergence central region of the imploding shock wave.
  In this work we perform a hydrodynamic analysis of a spherical mass of lead
imploded by an external constant pressure of 1 Mbar acting on its surface. The
aim is to monitor the rise of pressure, density, velocity and temperature with
the convergence and reflection of the shock wave at the centre. The analysis
was carried out by a hydrodynamic code and by making use of the three-term
equation of state for solids. This equation of state takes into account the
elastic pressure, the thermal pressure of atoms and the thermal pressure of
electrons in solids submitted to strong shock compressions.
