Context : The identification of the carriers of the diffuse interstellar bands ( DIBs ) is the longest standing problem in the study of the interstellar medium . Here we present recent UV laboratory spectra of various polycyclic aromatic hydrocarbons ( PAHs ) and explore the potential of these molecules as carriers of the DIBs . Whereas , in the near IR range , the PAHs exhibit vibrational bands which are not molecule-specific , their electronic transitions occurring in the UV/vis provide characteristic fingerprints . The comparison of laboratory spectra calibrated in intensity with high S/N observational data in the UV enables us to establish new constraints on PAH abundances . Aims : From a detailed comparison of gas-phase and Ne-matrix absorption spectra of anthracene , phenanthrene , pyrene , 2,3-benzofluorene , benzo [ ghi ] perylene , and hexabenzocoronene with new interstellar spectra , we aim to infer the abundance of these PAHs in the interstellar medium . Methods : We present spectra of PAHs measured at low temperature in the gas phase and in a Ne matrix , and present methods to derive absolute absorption cross sections for the matrix and gas phase spectra . We have obtained high signal to noise ( S/N > 100 ) absorption spectra toward five lines of sight with reddenings of E _ { \mathrm { B - V } } = 1 - 1.6 mag . The spectra cover the 3050 - 3850 \AA wavelength region where the PAHs studied here show prominent absorption features . Results : From the observations , we infer upper limits in the fractional abundances of the PAHs studied here.Upper limits in the column densities of anthracene of 0.8 - 2.8 \times 10 ^ { 12 } cm ^ { -2 } and of pyrene and 2,3-benzofluorene ranging from 2 - 8 \times 10 ^ { 12 } cm ^ { -2 } are inferred . Upper limits in the column densities of benzo [ ghi ] perylene are 0.9 - 2.4 \times 10 ^ { 13 } and 10 ^ { 14 } cm ^ { -2 } for phenanthrene . The measurements indicate fractional abundances of anthracene , pyrene , and 2,3-benzofluorene of a few times 10 ^ { -10 } . Upper limits in the fractional abundance of benzo [ ghi ] perylene of a few times 10 ^ { -9 } and of phenanthrene of few times 10 ^ { -8 } are inferred . Toward CPD -32 ^ { \circ } 1734 , we found near 3584 Å an absorption line of OH ^ { + } , which was discovered in the interstellar medium only very recently . Conclusions : The fractional abundances of PAHs inferred here are up to two orders of magnitude lower than estimated total PAH abundances in the interstellar medium . This indicates that either neutral PAHs are not abundant in translucent molecular clouds , or that a PAH population with a large variety of molecules is present .