We describe experiments where 2D atomic hydrogen gas is compressed thermally at a small "cold spot" on the surface of superfluid helium and detected directly with electron-spin resonance. We reach surface densities up to 5×10 12 cm −2 at temperatures ≈ 100 mK corresponding to the maximum 2D phase-space density ≈ 1.5. By independent measurements of the surface density and its decay rate we make the first direct determination of the three-body recombination rate constant and get the upper bound L 3b 2 × 10 −25 cm 4 /s which is an order of magnitude smaller than previously reported experimental results.PACS numbers: 05.30.Jp, 67.65.+z, 82.20.Pm When adsorbed on the surface of superfluid helium spin-polarized atomic hydrogen (H↓) is an ideal realization of a two-dimensional (2D) boson gas [1]. Helium provides a translationally invariant substrate and its surfacenormal potential supports only one bound state for hydrogen with the binding energy E a =1.14(1) K [2]. Even for such a weak interaction, lowering the surface temperature T s well below 1 K leads to a large adsorbate density σ. At high H↓ coverages three-body recombination is expected to be the dominant density decay mechanism setting the main obstacle to the achievement of the quantum degeneracy regime, where the thermal de Broglie wavelength Λ is larger than the average interatomic spacing. Degenerate 2D H↓ is expected to exhibit collective phenomena such as the Kosterlitz-Thouless superfluidity transition and the formation of a quasicondensate.Two methods of local compression of adsorbed H↓ have been employed to overcome limitations caused by recombination and its heat. Magnetic compression has been successfully used to achieve quantum degeneracy [3,4]. In this method the recombination heat is removed from the compressed H↓ by ripplons of the helium surface and the cooling efficiency depends on the length of the heat transfer path. By decreasing the size of the compressed region to 20 µm we were able to achieve σΛ 2 ≈ 9 [3]. However, the small size of the sample together with large magnetic field gradients did not allow to implement direct diagnostics of adsorbed H↓. In the thermal compression method [5,6] cooling a small part of the sample cell wall well below the temperature of the rest of the wall leads to an exponential increase of σ on such a "cold spot". In this method the recombination heat is transferred from the ripplons to the phonons of helium [7] and then to the substrate beneath the spot. Therefore a larger spot is preferable as long as the total recombination rate on the spot becomes a limitation. The larger sample size and the homogeneity of the magnetic field make thermal compression better suited for direct studies of adsorbed H↓.In the present work we use sensitive electron-spin resonance [8] to diagnose 2D H↓ gas thermally compressed to σΛ 2 ≈ 1.5 and discuss the limitations and possible improvements of the "cold spot" method to reach and detect the Kosterlitz-Thouless transition. By independent measurements of the recombination rate a...