First results obtained using the CENBG nanobeam line: performances and applications

A high resolution focused beam line has been recently installed on the AIFIRA (“Applications Interdisciplinaires des Faisceaux d’Ions en Région Aquitaine”) facility at CENBG. This nanobeam line, based on a doublet–triplet configuration of Oxford Microbeam Ltd. OM-50™ quadrupoles, offers the opportunity to focus protons, deuterons and alpha particles in the MeV energy range to a sub-micrometer beam spot. The beam optics design has been studied in detail and optimized using detailed ray-tracing simulations and the full mechanical design of the beam line was reported in the Debrecen ICNMTA conference in 2008. During the last two years, the lenses have been carefully aligned and the target chamber has been fully equipped with particle and X-ray detectors, microscopes and precise positioning stages. The beam line is now operational and has been used for its firstapplications to ion beam analysis. Interestingly, this set-up turned out to be a very versatile tool for a wide range of applications. Indeed, even if it was not intended during the design phase, the ion optics configuration offers the opportunity to work either with a high current microbeam (using the triplet only) or with a lower current beam presenting a sub-micrometer resolution (using the doublet–triplet configuration). The performances of the CENBGnanobeam line are presented for both configurations. Quantitative data concerning the beam lateral resolutions at different beam currents are provided. Finally, the firstresults obtained for different types of application are shown, including nuclear reaction analysis at the micrometer scale and the firstresults on biological sample

Solvable simulation of a double-well problem in PT symmetric quantum mechanics

Within quantum mechanics which works with parity-pseudo-Hermitian Hamiltonians we study the tunneling in a symmetric double well formed by two delta functions with complex conjugate strengths. The model is exactly solvable and exhibits several interesting features. Besides an amazingly robust absence of any PT symmetry breaking, we observe a quasi-degeneracy of the levels which occurs all over the energy range including the high-energy domain. This pattern is interpreted as a manifestation of certain "quantum beats".Comment: 12 pages incl. 7 figure

Pump-induced wavefront distortion in prototypical NIF/LMJ amplifiers-modeling and comparison with experiments

In large-aperture laser amplifiers such as those envisioned for the National Ignition Facility (NIF) and Laser Megajoules (LMJ) lasers, the geometry is such that the front and back faces of the laser slab are heated unevenly by the pump process. This uneven heating results in a mechanical deformation of the laser slab and consequent internal stresses. The deformation and stresses, along with a temperature-dependent refractive index variation, result in phase variations across the laser beam (so-called pump-induced wavefront distortions). These phase variations lead to beam steering which may affect frequency conversion as well as energy-on-target. We have developed a model which allows us to estimate the pump-induced wavefront distortion for a given amplifier configuration as well as the spatially-resolved depolarization. The model is compared with experiments taken in our amplifier development laboratory, AMPLA

A Nonperturbative Study of Inverse Symmetry Breaking at High Temperatures

The optimized linear $\delta$-expansion is applied to multi-field $O(N_1) \times O(N_2)$ scalar theories at high temperatures. Using the imaginary time formalism the thermal masses are evaluated perturbatively up to order $\delta^2$ which considers consistently all two-loop contributions. A variational procedure associated with the method generates nonperturbative results which are used to search for parameters values for inverse symmetry breaking (or symmetry nonrestoration) at high temperatures. Our results are compared with the ones obtained by the one-loop perturbative approximation, the gap equation solutions and the renormalization group approach, showing good agreement with the latter method. Apart from strongly supporting inverse symmetry breaking (or symmetry nonrestoration), our results reveal the possibility of other high temperature symmetry breaking patterns for which the last term in the breaking sequence is $O(N_1-1) \times O(N_2-1)$.Comment: 28 pages,5 eps figures (uses epsf), RevTeX. Only a small misprint in Eq. (2.10) and a couple of typos fixe

On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure

Improved perturbation theory in the vortex liquids state of type II superconductors

We develop an optimized perturbation theory for the Ginzburg - Landau description of thermal fluctuations effects in the vortex liquids. Unlike the high temperature expansion which is asymptotic, the optimized expansion is convergent. Radius of convergence on the lowest Landau level is $a_{T}=-3$ in 2D and $a_{T}=-5$ in 3D. It allows a systematic calculation of magnetization and specific heat contributions due to thermal fluctuations of vortices in strongly type II superconductors to a very high precision. The results are in good agreement with existing Monte Carlo simulations and experiments. Limitations of various nonperturbative and phenomenological approaches are noted. In particular we show that there is no exact intersection point of the magnetization curves both in 2D and 3D.Comment: 24 pages, 9 figure

Critical Exponents of the N-vector model

Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within errors of the previous evaluation. Exponents like eta (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou--Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published epsilon=4-d expansions (order epsilon^5), we have also reanalyzed the determination of exponents from the epsilon-expansion. The conclusion is that the general agreement between epsilon-expansion and 3D series has improved with respect to Le Guillou--Zinn-Justin.Comment: TeX Files, 27 pages +2 figures; Some values are changed; references update

Technical developments for computed tomography on the CENBG nanobeam line

The use of ion microbeams as probes for computedtomography has proven to be a powerful tool for the three-dimensional characterization of specimens a few tens of micrometers in size. Compared to other types of probes, the main advantage is that quantitative information about mass density and composition can be obtained directly, using specific reconstruction codes. At the Centre d’Etudes Nucléaires de Bordeaux Gradignan (CENBG), this technique was initially developed for applications in cellular biology. However, the observation of the cell ultrastructure requires a sub-micron resolution. The construction of the nanobeamline at the Applications Interdisciplinaires des Faisceaux d’Ions en Region Aquitaine (AIFIRA) irradiation facility has opened new perspectives for such applications. The implementation of computedtomography on the nanobeamline of CENBG has required a careful design of the analysis chamber, especially microscopes for precise sample visualization, and detectors for scanning transmission ion microscopy (STIM) and for particle induced X-ray emission (PIXE). The sample can be precisely positioned in the three directions X, Y, Z and a stepper motor coupled to a goniometer ensures the rotational motion. First images of 3D tomography were obtained on a reference sample containing microspheres of certified diameter, showing the good stability of the beam and the sample stage, and the precision of the motion

(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev.

Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

We use the nonperturbative linear \delta expansion method to evaluate analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime} \ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where T_0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c_1 to order-\delta^2 with the result c_1= 3.06. Here, we push the calculation to the next two orders obtaining c_1=2.45 at order-\delta^3 and c_1=1.48 at order-\delta^4. Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.Comment: 29 pages, 3 eps figures. Minor changes, one reference added. Version in press Physical Review A (2002