A one-dimensional forest-fire model including lightnings is studied nu
merically and analytically. For the tree correlation function, a new c
orrelation length with critical exponent nu approximate to 5/6 is foun
d by simulations. A Hamiltonian formulation is introduced which enable
s one to study the stationary state close to the critical point using
quantum-mechanical perturbation theory. With this formulation also the
structure of the low-lying relaxation spectrum and the critical behav
iour of the smallest complex gap are investigated numerically. Finally
, it is shown that critical correlation functions can be obtained from
a simplified model involving only the total number of trees although
such simplified models are unable to reproduce the correct off-critica
l behaviour.