Short range correlations in a one dimensional electron gas

We use the SSTL (Singwi, Sjolander, Tosi, Land) approximation to investigate the short–range correlations in a one dimensional electron gas, for the first time. Although SSTL is introduced to better satisfy the compressibility sum rule in three dimensions, the widely used STLS (Singwi, Tosi, Land, Sjolander) approximation turns out to be more successful in the case of the one dimensional electron gas.