Static field limit of excitation probabilities in laser-atom interactions

We consider the interaction of atomic hydrogen, in its ground state, with an electromagnetic pulse whose duration is fixed in terms of the number of optical cycles. We study the probability of excitation of the atom in the static field limit i.e. for field frequencies going to zero. Despite the fact that the well-known Born–Fock adiabatic theorem is valid only for a system whose energy spectrum is discrete, we show that it is still possible to use this theorem to derive, in the low frequency limit, an analytical formula which gives the probability of transition to any excited state of the atom as a function of the field intensity, the carrier envelope phase and the number of optical cycles within the pulse. The results for the probability of excitation to lowlying excited states, obtained with this formula, agree with those we get by solving the timedependent Schrödinger equation. The domain of validity is discussed in detail

Prognostic Threshold for Circulating Tumor Cells in Patients With Pancreatic and Midgut Neuroendocrine Tumors

BACKGROUND: Circulating tumour cells (CTCs) are detectable in patients with NET and are accurate prognostic markers although the optimum threshold has not been defined. OBJECTIVE: To define optimal prognostic CTC threshold in pancreatic and midgut NET. PATIENTS AND METHODS: CellSearch was used to enumerate CTCs in 199 patients with metastatic pancreatic (PanNET) (90) or midgut NET (109). Patients were followed for progression free survival (PFS) and overall survival (OS) for a minimum of 3 years or until death. RESULTS: AUROC for progression at 12 months in PanNET and midgut NET identified the optimal CTC threshold as ≥1 and ≥2 respectively. In multivariate logistic regression analysis, these thresholds were predictive for 12 month progression with OR of 6.69 (p< 0.01) for PanNET and 5.88 (p<0.003) for midgut. The same thresholds were found to be optimal for predicting death at 36 months with an OR of 2.87 (p< 0.03) and 5.09 (p<0.005) for PanNET and midgut NET respectively. In multivariate Cox hazard regression analysis for PFS in PanNET, ≥ 1 CTC had HR 2.6 (p <0.01) whilst ≥ 2 CTCs had HR 2.25 (p < 0.01) in midgut NET. In multivariate analysis OS in PanNET, ≥ 1 CTC had HR 3.16 (p < 0.01) and in midgut NET, ≥ 2 CTCs had HR of 1.73 (p < 0.06). CONCLUSIONS: The optimal CTC threshold to predict PFS and OS in metastatic PanNET and midgut NET is 1 and 2, respectively. These thresholds can be used to stratify patients in clinical practice and clinical trials

Reformulation of the strong-field approximation for light-matter interactions

We consider the interaction of hydrogen-like atoms with a strong laser field and show that the strong field approximation and all its variants may be grouped into a set of families of approximation schemes. This is done by introducing an ansatz describing the electron wave packet as the sum of the initial state wave function times a phase factor and a function which is the perturbative solution in the Coulomb potential of an inhomogeneous time-dependent Schr\"odinger equation. It is the phase factor that characterizes a given family. In each of these families, the velocity and length gauge version of the approximation scheme lead to the same results at each order in the Coulomb potential. By contrast, irrespective of the gauge, approximation schemes belonging to different families give different results. Furthermore, this new formulation of the strong field approximations allows us to gain deeper insight into the validity of the strong field approximation schemes. In particular, we address two important questions: the role of the Coulomb potential in the output channel and the convergence of the perturbative series in the Coulomb potential. In all the physical situations we consider here, our results are compared to those obtained by solving numerically the time-dependent Schr\"odinger equation.Comment: 19 pages, 9 figures, submitted for publicatio