Reference no: EM131415029
Problem -
Rydberg atoms are atoms in states with n > > 1. Their energy levels, even for complex atoms, obey a hydrogenlike formula Enl = -1/2(n- δl)2 in atomic units. Our (fictional) atom has δs = 3.3, δp = 2.8, δd = 1.5, δl>2 = 0. We also assume that the dipole matrix elements obey the approximate relation
We are interested in the energy of attraction or repulsion of two 97s atoms due to the dipole-dipole interaction. We will therefore focus on states close in energy to the 197s; 97 s) states. Fine-structure effects are negligible.
a) Identify the states that are of primary importance for dipole-dipole interactions between two 97s atoms. Will the dipole-dipole interaction be attractive or repulsive for 97s+97s states?
b) There are at least 18 possible states in your list. Use [H, L1z+ L2z] = 0 to reduce your list.
c) The exchange operator is defined as χ|ψ1ψ2) = |ψ2ψ1). Show that {H, χ] = 0, find the eigen-states and eigenvalues of χ and use that to further reduce your list of states.
d) You should now be down to just 4 states. Calculate the matrix elements and find the energy shifts in terms of the relevant unperturbed energy difference ΔE and U = e2ρ2/R5.
e) Plot your results and identify under what conditions the 97s97s energy shift can be written as C5/R5 or C6/R6. Give numerical values for C3 and C6.
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