Anolis chlorocyanus

Number of Pages: 6Integrative BiologyGeological Science

Error propagation in polarimetric demodulation

The polarization analysis of the light is typically carried out using modulation schemes. The light of unknown polarization state is passed through a set of known modulation optics and a detector is used to measure the total intensity passing the system. The modulation optics is modified several times and, with the aid of such several measurements, the unknown polarization state of the light can be inferred. How to find the optimal demodulation process has been investigated in the past. However, since the modulation matrix has to be measured for a given instrument and the optical elements can present problems of repeatability, some uncertainty is present in the elements of the modulation matrix and/or covariances between these elements. We analyze in detail this issue, presenting analytical formulae for calculating the covariance matrix produced by the propagation of such uncertainties on the demodulation matrix, on the inferred Stokes parameters and on the efficiency of the modulation process. We demonstrate that, even if the covariance matrix of the modulation matrix is diagonal, the covariance matrix of the demodulation matrix is, in general, non-diagonal because matrix inversion is a nonlinear operation. This propagates through the demodulation process and induces correlations on the inferred Stokes parameters.Comment: 18 pages, 3 figures, accepted for publication in Applied Optic

Description of the 11^{11}Li(p,d)10(p,d){^{10}}Li transfer reaction using structure overlaps from a full three-body model

Recent data on the differential angular distribution for the transfer reaction $^{11}$Li(p,d)$^{10}$Li at $E/A=5.7$ MeV in inverse kinematics are analysed within the DWBA reaction framework, using the overlap functions calculated within a three-body model of $^{11}$Li. The weight of the different $^{10}$Li configurations in the system's ground state is obtained from the structure calculations unambiguously. The effect of the $^{9}$Li spin in the calculated observables is also investigated. We find that, although all the considered models succeed in reproducing the shape of the data, the magnitude is very sensitive to the content of $p_{1/2}$ wave in the $^{11}$Li ground-state wave function. Among the considered models, the best agreement with the data is obtained when the $^{11}$Li ground state contains a $\sim$31\% of $p_{1/2}$ wave in the $n$-$^9$Li subsystem. Although this model takes into account explicitly the splitting of the $1^+$ and $2^+$ resonances due to the coupling of the $p_{1/2}$ wave to the $3/2^-$ spin of the core, a similar degree of agreement can be achieved with a model in which the $^{9}$Li spin is ignored, provided that it contains a similar p-wave content.Comment: 8 pages, 3 figures. Final versio