Measurement of the Proton Structure Function $F_2$ and the Extraction of the Gluon Density at Small $x$

In the following article we describe our measurement of the proton structure function $F_2$ and of the gluon momentum density $xg$ in $ep$ collisions with the ZEUS detector at HERA in 1993. The results for $F_2$ confirm our measurement from the previous year but with much higher statistics and show a strong rise towards small $x$. The gluon momentum density $xg$ is measured for the first time in a range from $ 4 \cdot 10^{-4} < x < 10^{-2}$ at a value of $Q^2 = 20$~GeV$^2$.