Thermal resistance of super(4)He below but very near the superfluid transition

We report high-resolution measurements at saturated vapor pressure of the thermal resistivity R of superfluid super(4)He over the reduced-temperature range 3 x 10 super(-7) < t = 1 - T/T sub( lambda ) < 3 x 10 super(-5) (T sub( lambda ) is the transition temperature for Q identical with 0) and heat-current-density range 4 < Q < 200 mu W/cm super(2). For smaller Q and t, no thermal resistance was detectable below a transition at T sub(c)(Q) < T sub( lambda ). For Q greater than or approximate to 10 mu W/cm super(2) we find that the results can be described well by R identical with (t/t sub(0)) super(-2.8) K cm/W with t sub(0) identical with (Q/Q sub(0)) super(0.904) and Q sub(0) identical with 393 W/cm super(2). Thus R has an incipient divergence at T sub( lambda ) which is, however, supplanted by T sub(c)(Q) where R remains finite. The results imply R proportional to Q super((m-1)) with m identical with 3.53 plus or minus 0.02. This differs from the original assumption m identical with 3 of Gorter and Mellink, and from experimental results obtained well below T sub( lambda ). However, it agrees with measurements by Leiderer and Pobell at larger currents and further below but still close to T sub( lambda ). Our measurements could not resolve a critical heat current for the onset of resistance.