depletion time integrator SICELI & SILEQI did not create statepoint file (openmc_simulation_n.h5) on each depletion step

[wahidluthfi]

Bug Description

Both stochastic implicit depletion integrator: SICELI & SILEQI did not create statepoint file named openmc_simulation_n.h5 on each depletion step as usual (other time integrators). Here I show you my log file when using SICELI in comparison to CE/LI.
In general, SICELI and SILEQI only produce the first statepoint file at t=0 (n0), and after that, they didn't produce any statepoint/openmc_simulation_n file on the following depletion steps until they generated a statepoint file for the last burnup step.
one might benefit from these state point files when tallying something for their problem, i.e: neutron flux spectrum, reaction rate, photon flux for dose and fluence calculation, ...

Steps to Reproduce

since I am just comparing each depletion method provided by the openmc, then I only use a standard integrator command in my script.
I think it would be better to use jupyter notebook to show this phenomenon
cell 14:
PIintegrator = openmc.deplete.PredictorIntegrator(operator, time_steps, power, timestep_units='d')
SICELIintegrator = openmc.deplete.SICELIIntegrator(operator, time_steps, power, timestep_units='d', solver= 'cram48', n_steps=1)
SILEQIintegrator = openmc.deplete.SILEQIIntegrator(operator, time_steps, power, timestep_units='d', solver= 'cram48', n_steps=1)
CELIintegrator = openmc.deplete.CELIIntegrator(operator, time_steps, power, timestep_units='d', solver= 'cram48')
LEQIintegrator = openmc.deplete.LEQIIntegrator(operator, time_steps, power, timestep_units='d', solver= 'cram48')

for SICELI and SILEQI, I use n_steps=1 since I have tried the default 10 value and it is a long-run simulation.
the jupyter notebook and its results can be seen here
depletion.zip

I also read a paper from 2023 that indicated a similar trend, as I quote
Tanash (2023) - Selecting Burnup Algorithms in OpenMC Using the Calculated Benchmark of LEU Assembly and MOX Fuel S1063778823110431.pdf
"Burnup modeling was performed using only six integrators. The SI-CE/LI and SI-CE/QI integrators were not used because of the extensive time of computation (requiring more than 50 computational steps per burnup step with no results obtained)."
I think the no results obtained they mean is the statepoint_n files on each burnup step.

Thank you

Environment

Openmc 0.14.1-dev