Compton Scattering from uc{6}{Li} at 86 MeV

Cross sections for uc{6}{Li}($gamma$,$gamma$) uc{6}{Li} have been measured at the High Intensity Gamma-Ray Source (HIGS) and the sensitivity of these cross sections to the nucleon isoscalar polarizabilities was studied. Data were collected using a quasi-monoenergetic 86 MeV photon beam at photon scattering angles of 40$^{circ}$--160$^{circ}$. These results are an extension of a previous measurement at a lower energy. The earlier work indicated that the uc{6}{Li}($gamma$,$gamma$) uc{6}{Li} reaction at 60 MeV provides a means of extracting the nucleon polarizabilities; this work demonstrates that the sensitivity of the cross section to the polarizabilities is increased at 86 MeV. A full theoretical treatment is needed to verify this conclusion and produce values of the polarizabilities.

On a functional equation appearing in characterization of distributions by the optimality of an estimate

Let $X$ be a second countable locally compact Abelian group containing no subgroup topologically isomorphic to the circle group $mathbb{T}$. Let $mu$ be a probability distribution on $X$ such that its characteristic function $hatmu(y)$ does not vanish and $hatmu(y)$ for some $n geq 3$ satisfies the equation $$ prod_{j=1}^{n} hatmu(y_j + y) = prod_{j=1}^{n}hatmu(y_j - y), quad sum_{j=1}^{n} y_j = 0, quad y_1,dots,y_n,y in Y. $$ Then $mu$ is a convolution of a Gaussian distribution and a distribution supported in the subgroup of $X$ generated by elements of order 2.