to be returned to the lecture Thursday 30.04.2009,  PK 11.2

Home work 3. Hyperfine interaction. Interaction with external fields.
 

Exercise 1:  Hyperfine interaction

a)  What is the electron configuration of the ground state of  Cesium atom (Cs)? Write all possible values of the quantum numbers L, M_L, S, M_S; J, M_J for this state. Taking into consideration the magnetic interaction between the electronic spin S and the nuclear spin I and using the formulas given at the lecture, calculate the hyperfine structure of the Cs ground state.  In particular, calculate all possible quantum numbers F which refer to the Cs hyperfine structure. Draw the corresponding hyperfine energy levels and indicate the degeneracy of each hyperfine state. What is the energy splitting between the Cs hyperfine levels (in MHz)?  The obtained splitting value is very important: it is the frequency of the Quantum Frequency Standard, which is widely used for navigation, time synchronization, and military applications.

The hyperfine constant A_I for Cs ground state is equal to A_I = 2298.15 MHz, nuclear spin I_Cs = 7/2.

b)  Excite the 3s-electron in Na atom to the 3p orbital. You have obtained the electron configuration of the Na first excited state. What is the spin-orbit structure of this state?    Taking into consideration the magnetic interaction between the total electronical angular momentum J and the nuclear spin I, predict (qualitatively) the hyperfine structure of each of the 3²P_1/2 and 3²P_3/2 spin-orbit states. The Na nuclear spin I_Na is equal to 3/2.
 

Exercise 2:  Stark and Zeeman effects. Multipole transitions.

a) Assume that you observe fluorescence from the first excited states of atomic Barium (Ba) to its ground state: 6¹S₀ ← 6¹P₁. How many spectral line do you expect to observe?  Now assume that you apply an external electric field E perpendicular to the detection direction. What changes do you expect  in the observed spectrum?

b) Repeat the problem a), but now assuming that you apply an external magnetic field B perpendicular to the detection direction. What changes do you expect  in the observed spectrum?  Assume that you are observing this spectrum through a linear polarizer. What changes do you expect to see if you start rotating the polarizer around the detection axis?

c) Write down the electron configuration of the ground state of atomic Chlorine (Cl).  What are the quantum numbers L and S  for this state? (Hint: instead of considering five negatively charged p-electrons you can consider one positively charged p-hole, the result will be the same).  Consider the spin-orbit interaction between L and S and draw all possible spin-orbit states with their quantum numbers J.  What kind of radiation transitions are possible between these spin-orbit states?

d) An atomic ion with electron spin S=3/2 is placed into an external magnetic field B. Draw a qualitative picture of the ion energy level splitting as function of the magnetic field strength.  Suppose that you plan to detect the transitions between neighboring energy levels of the ion using an Electron Paramagnetic Resonance (EPR) Spectrometer which can detect only the electromagnetic radiation at the wavelength λ = 3 cm. What magnetic field value B should you use in this experiment (think of Bohr magneton µ_B)?

Auf diesem Webangebot gilt die Datenschutzerklärung der TU Braunschweig mit Ausnahme der Abschnitte VI, VII und VIII.