(Abridged) We present new deep VLT/FORS optical spectra with intermediate resolution and large wavelength coverage of the GPS radio source and ULIRG PKS1345+12 (4C12.50; z=0.122), taken with the aim of investigating the impact of the nuclear activity on the circumnuclear ISM. PKS1345+12 is a powerful quasar and is also the best studied case of an emission line outflow in a ULIRG. Using the density sensitive transauroral emission lines [S II]4068,4076 and [O II]7318,7319,7330,7331, we pilot a new technique to accurately model the electron density for cases in which it is not possible to use the traditional diagnostic [S II]6716/6731, namely sources with highly broadened complex emission line profiles and/or high (Ne > 10^4 cm^-3) electron densities. We measure electron densities of Ne=2.94x10^3 cm^-3, Ne=1.47x10^4 cm^-3 and Ne=3.16x10^5 cm^-3 for the regions emitting the narrow, broad and very broad components respectively. We calculate a total mass outflow rate of 8 M_sun yr^-1. We estimate the total mass in the warm gas outflow is 8x10^5 M_sun. The total kinetic power in the warm outflow is 3.4x10^42 erg s^-1. We find that only a small fraction (0.13% of Lbol) of the available accretion power is driving the warm outflow, significantly less than currently required by the majority of quasar feedback models (~5-10% of Lbol), but similar to recent findings by Hopkins et al. (2010) for a two-stage feedback model. The models also predict that AGN outflows will eventually remove the gas from the bulge of the host galaxy. The visible warm outflow in PKS1345+12 is not currently capable of doing so. However, it is entirely possible that much of the outflow is either obscured by a dense and dusty natal cocoon and/or in cooler or hotter phases of the ISM. This result is important not just for studies of young (GPS/CSS) radio sources, but for AGN in general.
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