  The collapse of Hall gaps in the integer quantum Hall liquid in a quantum
wire is investigated. Motivated by recent experiment [Pallecchi et al. PRB 65,
125303 (2002)] previous approaches are extended to treat confinement effects
and the exchanged enhanced g-factor in quantum wires. Two scenarios for the
collapse of the $\nu =1$ state are discussed. In the first one the $\nu =1$
state becomes unstable at $B_{cr}^{(1)}$, due to the exchange interaction and
correlation effects, coming from the edge-states screening. In the second
scenario, a transition to the $\nu =2$ state occurs at $B_{cr}^{(2)}$, with a
smaller effective channel width, caused by the redistribution of the charge
density. This effect turns the Hartree interaction essential in calculating the
total energy and changes $B_{cr}^{(2)}$ drastically. In both scenarios, the
exchange enhanced g-factor is suppressed for magnetic fields lower than
$B_{cr}$. Phase diagrams for the Hall gap collapse are determined. The critical
fields, activation energy, and optical $g$-factor obtained are compared with
experiments. Within the accuracy of the available data, the first scenario is
most probable to be realized.
