Is your feature request related to a problem? Please describe.
The RadiativeRatesSolver class in tardis/plasma/equilibrium/rates/radiative_rates.py has no direct unit tests. A fixture radiative_rate_solver already exists in tardis/plasma/equilibrium/tests/conftest.py but no test file ever calls .solve() on it. Errors in this solver (wrong transition direction, missing spontaneous emission term A_ul, wrong output index structure) would silently corrupt all ion and level populations without any focused test catching them.

Describe the solution you'd like
Create a new test file tardis/plasma/equilibrium/tests/test_radiative_rates.py with focused unit tests for the class. Tests should cover:

• Valid construction with a correct Einstein coefficients DataFrame
• AssertionError raised when columns A_ul, B_ul, B_lu, or nu are missing
• AssertionError raised when index names are wrong
• AssertionError raised when level_number_lower >= level_number_upper
• solve() output DataFrame has the correct 6-level MultiIndex
• r_lu = B_lu × J_nu verified numerically
• r_ul = B_ul × J_nu + A_ul with spontaneous emission term present
• Full solve() output pinned against regression HDF5 data
• Zero radiation field intensity (W=0) gives r_lu=0 and r_ul = A_ul

Regression data path should be modified locally so no PR to the regression data repository is needed.

Describe alternatives you've considered

• Relying only on indirect full plasma regression tests — rejected because a failure anywhere in the plasma chain masks whether RadiativeRatesSolver is the cause.
• Only testing construction validation — rejected because the most critical logic is inside solve() and must be verified against known physical values.

Additional context
The existing fixture in conftest.py (lines 64–66) already builds a RadiativeRatesSolver from Si Chianti atomic data — the test file just needs to use it. Bonus tests to mention in the PR: pass both DilutePlanckianRadiationField and PlanckianRadiationField as inputs to solve(), assert all output rates are non-negative, and verify that both up and down transitions appear for every spectral line.