Context :

Aims : We derive accurate parameters related to the CMD , structure and dynamical state of M 52 and NGC 3960 , whose fields are affected by differential reddening .
Previous works estimated their ages in the ranges 35 - 135 Myr and 0.5 - 1.0 Gyr , respectively .

Methods : J , H and K _ { s } 2MASS photometry with errors < 0.2 mag is used to build CMDs , radial density profiles , luminosity and mass functions , and correct for differential reddening .
Field-star decontamination is applied to uncover the cluster ’ s intrinsic CMD morphology , and colour-magnitude filters are used to isolate stars with high probability of being cluster members .

Results : The differential-reddening corrected radial density profile of M 52 follows King ’ s law with core and limiting radii of \mbox { $R _ { core } $ } = 0.91 \pm 0.14 pc and \mbox { $R _ { lim } $ } = 8.0 \pm 1.0 pc .
NGC 3960 presents an excess of the stellar density over King ’ s profile ( \mbox { $R _ { core } $ } = 0.62 \pm 0.11 pc and \mbox { $R _ { lim } $ } = 6.0 \pm 0.8 pc ) at the center .
The tidal radii of M 52 and NGC 3960 are \mbox { $R _ { tidal } $ } = 13.1 \pm 2.2 pc and \mbox { $R _ { tidal } $ } = 10.7 \pm 3.7 pc .
Cluster ages of M 52 and NGC 3960 derived with Padova isochrones are constrained to 60 \pm 10 Myr and 1.1 \pm 0.1 Gyr .
In M 52 the core MF ( \chi _ { core } = 0.89 \pm 0.12 ) is flatter than the halo ’ s ( \chi _ { halo } = 1.65 \pm 0.12 ) .
In NGC 3960 they are \chi _ { core } = -0.74 \pm 0.35 and \chi _ { halo } = 1.26 \pm 0.26 .
The mass locked up in MS/evolved stars in M 52 is \sim 1200 M _ { \odot } , and the total mass ( extrapolated to 0.08 M _ { \odot } ) is \sim 3800 M _ { \odot } .
The total mass in NGC 3960 is \sim 1300 M _ { \odot } .

Conclusions : Compared to open clusters in different dynamical states studied with similar methods , the core and overall parameters of M 52 are consistent with an open cluster more massive than 1 000 M _ { \odot } and \sim 60 Myr old , with some mass segregation in the inner region .
The core of NGC 3960 is in an advanced dynamical state with strong mass segregation in the core/halo region , while the somewhat flat overall MF ( \chi \approx 1.07 ) suggests low-mass star evaporation .
The excess stellar density in the core may suggest post-core collapse .
The dynamical evolution of NGC 3960 may have been accelerated by the tidal Galactic field , since it lies \approx 0.5 kpc inside the Solar circle .