Mass--dependence of the Lambda hypernuclear decay widths

Two different approaches have been employed for the evaluation of the decay widths of Lambda-hypernuclei (ranging from $^5_{\Lambda}$He to $^{208}_{\Lambda}$Pb) with the polarization propagator method. In ref.[1], the two-nucleon stimulated non-mesonic decay, $\Lambda NN\to NNN$, has been parameterized phenomenologically by means of data on the pion-nucleus optical potential. The other approach [2] consisted in a fully microscopic description of the non-mesonic decays through the first order approximation of the so-called bosonic-loop-expansion. Both calculations reproduce, with approximately the same accuracy, the experimental decay rates for the whole range of mass numbers considered.Comment: 4 pages, 2 figures. Talk presented at HYP2000, Torino, 23-27 Oct. 2000. To appear in the proceedings (Nucl. Phys. A

Microscopic Approach to Nucleon Spectra in Hypernuclear Non-Mesonic Weak Decay

A consistent microscopic diagrammatic approach is applied for the first time to the calculation of the nucleon emission spectra in the non-mesonic weak decay of Lambda-hypernuclei. We adopt a nuclear matter formalism extended to finite nuclei via the local density approximation, a one--meson exchange weak transition potential and a Bonn nucleon-nucleon strong potential. Ground state correlations and final state interactions, at second order in the nucleon--nucleon interaction, are introduced on the same footing for all the isospin channels of one- and two-nucleon induced decays. Single and double--coincidence nucleon spectra are predicted for 12_Lambda^C and compared with recent KEK and FINUDA data. The key role played by quantum interference terms allows us to improve the predictions obtained with intranuclear cascade codes. Discrepancies with data remain for proton emission.Comment: 11 pages, 6 figures, 2 tables. To be published in Physics Letters

Compartmental analysis of dynamic nuclear medicine data: models and identifiability

Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment compartmental models. The second paper will utilize this framework in order to show how non-linear regularization schemes can be applied to obtain numerical estimates of the tracer coefficients in the case of nuclear medicine data corresponding to brain, liver and kidney physiology

Weak Decay of Hypernuclei

The focus of these Lectures is on the weak decay modes of hypernuclei, with special attention to Lambda-hypernuclei. The subject involves many fields of modern theoretical and experimental physics, from nuclear structure to the fundamental constituents of matter and their interactions. The various weak decay modes of Lambda-hypernuclei are described: the mesonic mode and the non-mesonic ones. The latter are the dominant decay channels of medium--heavy hypernuclei, where, on the contrary, the mesonic decay is disfavoured by Pauli blocking effect on the outgoing nucleon. In particular, one can distinguish between one-body and two-body induced decays. Theoretical models employed to evaluate the (partial and total) decay widths of hypernuclei are illustrated, and their results compared with existing experimental data. Open problems and recent achievements are extensively discussed, in particular the determination of the ratio Gamma_n/Gamma_p, possible tests of the Delta I=1/2 rule in non-mesonic decays and the puzzling asymmetric non-mesonic decay of polarized hypernuclei.Comment: 59 pages, 13 figures Lectures given at the International School of Physics "Enrico Fermi" Course on: HADRON PHYSICS, Varenna (Lake Como), June 22nd - July 2nd, 200

On the role of ground state correlations in hypernuclear non-mesonic weak decay

The contribution of ground state correlations (GSC) to the non--mesonic weak decay of $^{12}_\Lambda$C and other medium to heavy hypernuclei is studied within a nuclear matter formalism implemented in a local density approximation. We adopt a weak transition potential including the exchange of the complete octets of pseudoscalar and vector mesons as well as a residual strong interaction modeled on the Bonn potential. Leading GSC contributions, at first order in the residual strong interaction, are introduced on the same footing for all isospin channels of one-- and two--nucleon induced decays. Together with fermion antisymmetrization, GSC turn out to be important for an accurate determination of the decay widths. Besides opening the two--nucleon stimulated decay channels, for $^{12}_\Lambda$C GSC are responsible for 14% of the rate $\Gamma_1$ while increasing the $\Gamma_{n}/\Gamma_{p}$ ratio by 4%. Our final results for $^{12}_\Lambda$C are: $\Gamma_{\rm NM}=0.98$, $\Gamma_{n}/\Gamma_{p}=0.34$ and $\Gamma_2/\Gamma_{\rm NM}=0.26$. The saturation property of $\Gamma_{\rm NM}$ with increasing hypernuclear mass number is clearly observed. The agreement with data of our predictions for $\Gamma_{\rm NM}$, $\Gamma_n/\Gamma_p$ and $\Gamma_2$ is rather good.Comment: 32 pages, 9 figure

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms outperform standard methods in terms of sensitivity to noise and reliability of the estimated profile.Comment: 19 pages, 6 figure