Phys 4910 Spectroscopy
Spring 2018 Assignment 8

For each of the following terms, what are the possible levels?

^{1}D

^{5}H

^{2}F

^{1}H

^{5}P

^{5}P

At low resolution there is a transition from a ^{5}P term (upper)
to a
^{5}D term (lower) at 450 nm. At higher resolution the fine
structure due to spin orbit coupling becomes apparent. Assume perfect LS
coupling with

for the ^{5}P term the spin orbit coupling is given by E(J) = 127
[ J(J+1)  L(L+1)  S(S+1) ]

for the ^{5}D term the spin orbit coupling is given by E(J) = 79
[ J(J+1)  L(L+1)  S(S+1) ]
where the units of E(J) is cm^{1} for both terms. What are the
wavelengths of all the allowed transition which make up this 450 nm line?
Neglect the difference between air wavelengths and vacuum wavelengths.
Hint: first draw a diagram showing all the allowed transitions from one
level from the ^{5}P term to one from the ^{5}D term. Also
the calculations are repetitive, and the use of a spreadsheet (or Maple)
can cut down on the amount of work you have to do quite considerably.
(Note: the spin orbit coupling is only a perturbation, and so all the
wavelengths should be close to 450 nm. If you get wavelengths which are
significantly different, then you have made a mistake.)