The material liyf4 is a laser host that crystallizes in the i41/a group. the y site can be substituted with a range of rare-earth ions and sits on the 4b wycoff site. for a rare earth ion with the transition of 4h5/2 to 4g5/2, three peaks are observed at 562, 557 and 553 nm. what are these peaks in cm-1? the first two peaks are strong but the peak at 553 nm is very weak. perform a spin orbit coupling and determine the stark levels and explain these observations. the authors say for transitions of 4h5/2 to a 4f9/2 state there is a strong polarization effect in polarized light. can you justify this from your stark level analysis? what would you expect to see in polarized light? for this problem just use the same approach as you did in 2 above.