Abstract:
The response function to an external prove is evaluated using the ring approximation in nuclear matter. Contrary to what it is usually assumed, it is shown that the summation of the ring series and the solution of the Dyson's equation are two different approaches. The numerical results exhibit a perceptible difference between both approximations.

Abstract:
Single and double coincidence nucleon spectra in the $\Lambda$-hypernuclei weak decay are evaluated and discussed using a microscopic formalism. Nuclear matter is employed together with the local density approximation which allows us to analyze the $^{12}_{\Lambda}C$ hypernucleus non-mesonic weak decay. Final state interactions (FSI) are included via the first order (in the nuclear residual interaction) terms to the RPA, where the strong residual interaction is modelled by a Bonn potential. At this level of approximation, these FSI are pure quantum interference terms between the primary decay $(\Lambda N \to NN)$ and $(\Lambda N \to NN \to NN)$, where the strong interaction is responsible for the last piece in the second reaction. Also the Pauli exchange contributions are explicitly evaluated. We show that the inclusion of Pauli exchange terms is important. A comparison with data is made. We conclude that the limitations in phase space in the RPA makes this approximation inadequate to reproduce the nucleon spectra. This fact, does not allow us to draw a definite conclusion about the importance of the interference terms.

Abstract:
We have performed a many-body calculation of the longitudinal nuclear $(e,e')$ reaction employing a Second RPA (SRPA) formalism which contains the $\Delta$(1232). More explicitly, our scheme contains RPA correlations as well as Hartree-Fock and second order self-energies, where an accurate evaluation of exchange terms is achieved. Using this formalism we have evaluated the longitudinal response function for $^{40}Ca$. We give final results at momentum transfers ranging from 300 up to 500 MeV/c, obtaining a good agreement with data.

Abstract:
The nonmesonic weak decay width of $^{12}_{\Lambda}C$ hypernucleus has been evaluated within a nuclear matter formalism, using the local density approximation. In addition to the one-body induced decay $(\Lambda N \to n N)$, it has been also considered the two-body induced decay $(\Lambda NN \to n N N)$. This second decay is originated from ground state correlations, where a renormalization procedure to ensure a ground state normalized to one has been implemented. Our results show that the plain addition of the two-body induced decay implies a lost in the ground state-norm, which adds $\sim 38%$ of spurious intensity to the nonmesonic weak decay width. By an adequate selection of the $\Lambda N$-transition potential, our result for the nonmesonic weak decay width of $^{12}_{\Lambda}C$ is 0.956, in good agreement with the most recent data.

Abstract:
The nonmesonic weak decay of $\Lambda$ hypernuclei is studied using nuclear matter. We have developed a formalism which gives a microscopic interpretation of the process of emission of particles originated in this decay. More specifically, our scheme provides a unified treatment of $\Gamma(\Lambda N \to NN$) and $N_{N}$ ($N_{NN}$), the $\Lambda$ non-mesonic weak decay widths and the number of emitted particles (pair of particles) of kind $N$ ($NN$), respectively. We have also evaluated for the first time the quantum interference terms between the $n$- and $p$-induced weak decay amplitudes. Explicit expressions for $N_{N}$ and $N_{NN}$ are shown within the ring approximation. Using the local density approximation together with the ring approximation, we report results for the decay of the $^{12}_{\Lambda}C$ hypernucleus. We have obtained values for the ratio $N_{n}/N_{p}$ ($N_{nn}/N_{np}$) in the range $1.4-1.6$ ($0.2-0.3$), where no energy threshold have been employed. The $n$- and $p$-induced interference terms modify in less than $\sim 3 %$ these results.

Abstract:
The transverse nuclear response to an electromagnetic probe which is limited to create (or destroyed) a particle-hole ($ph$) or delta-hole ($\Delta h$) pair is analyzed. Correlations of the random phase approximation (RPA) type and self energy insertions are considered. For RPA correlations we have developed a scheme which includes explicitly the $\Delta$ and the exchange terms. Self energy insertions over $ph$ and $\Delta h$ bubbles are studied. Several residual interactions based on a contact plus a ($\pi + \rho$)-meson exchange potential are used. All calculations are performed in non-relativistic nuclear matter. The main effect of the $\Delta$ is to reduce the intensity over the nuclear quasi-elastic peak. Exchange RPA terms are very important, while the self energy depends strongly on the residual interaction employed. We compare our final result with data for $^{40}Ca$ at momentum transfer $q=410$ and $q=550$ MeV/c.

Abstract:
Foot problems in patients with diabetes remain a major public health issue and are the commonest reason for hospitalization of patients with diabetes with prevalence as high as 25%. Ulcers are breaks in the dermal barrier with subsequent erosion of underlying subcutaneous tissue that may extend to muscle and bone, and superimposed infection is a frequent and costly complication. The pathophysiology of diabetic foot disease is multifactorial and includes neuropathy, infection, ischemia, and abnormal foot structure and biomechanics. Early recognition of the etiology of these foot lesions is essential for good functional outcome. Managing the diabetic foot is a complex clinical problem requiring a multidisciplinary collaboration of health care workers to achieve limb salvage. Adequate off-loading, frequent debridement, moist wound care, treatment of infection, and revascularization of ischemic limbs are the mainstays of therapy. Even when properly managed, some of the foot ulcers do not heal and are arrested in a state of chronic inflammation. These wounds can frequently benefit from various adjuvants, such as aggressive debridement, growth factors, bioactive skin equivalents, and negative pressure wound therapy. While these, increasingly expensive, therapies have shown promising results in clinical trials, the results have yet to be translated into widespread clinical practice leaving a huge scope for further research in this field. 1. Introduction Approximately, 26 million people, comprising 8.3% of the US population are estimated to have diabetes [1]. In 2010 alone, there were 2 million new cases of diabetes diagnosed. This becomes even more significant with increasing age as the prevalence of diabetes increases to 27% in the population over age 65 [1]. The American Diabetes Association consensus group identified increased risk in patients with diabetes for >10 years, which are males, having poor glucose control or having cardiovascular, retinal, or renal complications [2].Of the US diabetic population, it is estimated that 15% will develop manifestations of diabetic foot disease in their lifetime [3]. Foot ulcers are common in patients with diabetes mellitus with a prevalence as high as 25% and an annual incidence of 2%-3% [3]. Although cancer and trauma can result in amputations, chronic diabetic foot ulcers lead to more than 80% of nontraumatic amputations and account for 46% of the 162,000 hospital admissions for foot ulcers annually [3]. This prevalence of foot disease in the diabetic population results in significant clinical and economic impact.

Abstract:
The ratio N_{nn}/N_{np} between the number of neutron-neutron and neutron--proton pairs emitted in the non--mesonic weak decay of \Lambda-hypernuclei is calculated within a nuclear matter formalism extended to ^{12}_{Lambda}C via the local density approximation. The single--nucleon emission spectra, N_p and N_n, are also evaluated. Our formalism takes care of both ground state correlations (gsc) and final state interactions (FSI). The evaluation of N_{nn}/N_{np} which, unlike Gamma_n/Gamma_p = Gamma(Lambda n -> nn)/Gamma(Lambda p -> np), is an actual observable quantity in non--mesonic decay is performed within a fully microscopic model where a proper treatment of FSI, gsc and ground state normalization is considered. All the isospin channels contributing to one-- and two--nucleon induced decays are included. Our final result for the coincidence number ratio, N_{nn}/N_{np}=0.374, is in agreement with the KEK--E508 datum, (N_{nn}/N_{np})^{\rm exp}=0.40 +/- 0.10.

Abstract:
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.