Answer Happy

Problem 4.(30 pts) A nucleus is known to be in a nuclear state with total angular momentum quantum number J = 2. A new operator is measured that is not well understood, except it is known that it is a spherical tensor operator T(K) of some integer rank K value, and component Q 0. In order to determine K, a measurement of the average value of the operator is carried out in two different |J, M) states, namely with J = 2, M = 1 and with J = 2, M = 2, and the ratio of those average values is found to equal = Q (J = 2, M = 1|T(K)|J = 2, M = 1)/(J = 2, M = 2|T(K)|J = 2, M = 2) : = -4. Use this information to deduce the value of K. Some possibly relevant Clebsch-Gordan coefficients are shown on the next page.
The following Clebsch-Gordan coefficients are tabulated in the following notation, for J=2 and all values of M and K: | Camis M K <JM JM, KO > Table[{M, K, Clebsch Gordan[{2, M}, {K, 0}, {2, M}]}, {K, 0, 4}, {M, -2, 2}] // MatrixForm 2 -1 0 1 2 0 0 0 0 1 1 1 1 -1 0 1 2 1 1 1 1 0 √6 √6 0 2 0 1 2 1 WIN -2 2 217 -2 3 1 √14 -2 4 1 3√14 - -1 2 1 √14 -1 3 VIN -1 4 2 لے س WIN 3 I 27 0 3 0 0 4 LI7 12 2 1 √14 1 13 3 1 4 2 27 WIZ V7 3 ( WIN ~~ 2 2 27 2 m √14 2 4 1 3 √14