Low-Energy Heavy-Ion Reactions and the Skyrme Effective Interaction

The Skyrme effective interaction, with its multitude of parameterisations, along with its implemen- tation using the static and time-dependent density functional (TDHF) formalism have allowed for a range of microscopic calculations of low-energy heavy-ion collisions. These calculations allow variation of the effective interaction along with an interpretation of the results of this variation informed by a comparison to experimental data. Initial progress in implementing TDHF for heavy-ion collisions necessarily used many approximations in the geometry or the interaction. Over the last decade or so, the implementations have overcome all restrictions, and studies have begun to be made where details of the effective interaction are being probed. This review surveys these studies in low energy heavy-ion reactions, finding significant effects on observables from the form of the spin-orbit interaction, the use of the tensor force, and the inclusion of time-odd terms in the density functional.Comment: submitted to Prog. Part. Nucl. Phy

Nucleon-Nucleon Interactions from Dispersion Relations: Coupled Partial Waves

We consider nucleon-nucleon interactions from chiral effective field theory applying the N/D method. The case of coupled partial waves is now treated, extending Ref. [1] where the uncoupled case was studied. As a result three N/D elastic-like equations have to be solved for every set of three independent partial waves coupled. As in the previous reference the input for this method is the discontinuity along the left-hand cut of the nucleon-nucleon partial wave amplitudes. It can be calculated perturbatively in chiral perturbation theory because it involves only irreducible two-nucleon intermediate states. We apply here our method to the leading order result consisting of one-pion exchange as the source for the discontinuity along the left-hand cut. The linear integral equations for the N/D method must be solved in the presence of L - 1 constraints, with L the orbital angular momentum, in order to satisfy the proper threshold behavior for L>= 2. We dedicate special attention to satisfy the requirements of unitarity in coupled channels. We also focus on the specific issue of the deuteron pole position in the 3S1-3D1 scattering. Our final amplitudes are based on dispersion relations and chiral effective field theory, being independent of any explicit regulator. They are amenable to a systematic improvement order by order in the chiral expansion.Comment: 11 pages. Extends the work of uncoupled partial waves of M. Albaladejo and J. A. Oller, Phys. Rev. C 84, 054009 (2011) to the case of coupled partial waves. This version matches the published version. Discussion about the deuteron enlarged. Some references adde

Minimal Forbidden Factors of Circular Words

Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have different (antifactorial) sets of minimal forbidden factors. There exist algorithms for computing the minimal forbidden factors of a word, as well as of a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an algorithm that, given the trie recognizing a finite antifactorial language $M$, computes a DFA recognizing the language whose set of minimal forbidden factors is $M$. In the same paper, they showed that the obtained DFA is minimal if the input trie recognizes the minimal forbidden factors of a single word. We generalize this result to the case of a circular word. We discuss several combinatorial properties of the minimal forbidden factors of a circular word. As a byproduct, we obtain a formal definition of the factor automaton of a circular word. Finally, we investigate the case of minimal forbidden factors of the circular Fibonacci words.Comment: To appear in Theoretical Computer Scienc

Elliptic Flow, Initial Eccentricity and Elliptic Flow fluctuations in Heavy Ion Collisions at RHIC

We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.Comment: To appear in the proceedings of the Lake Louise Winter Institute 2007. The proceedings of the institute will be published by World Scientifi

A benign, low Z electron capture agent for negative ion TPCs

We have identified nitromethane (CH$_3$NO$_2$) as an effective electron capture agent for negative ion TPCs (NITPCs). We present drift velocity and longitudinal diffusion measurements for negative ion gas mixtures using nitromethane as the capture agent. Not only is nitromethane substantially more benign than the only other identified capture agent, CS$_2$, but its low atomic number will enable the use of the NITPC as a photoelectric X{}-ray polarimeter in the 1{}-10 keV band

Saddle Points and Stark Ladders: Exact Calculations of Exciton Spectra in Superlattices

A new, exact method for calculating excitonic absorption in superlattices is described. It is used to obtain high resolution spectra showing the saddle point exciton feature near the top of the miniband. The evolution of this feature is followed through a series of structures with increasing miniband width. The Stark ladder of peaks produced by an axial electric field is investigated, and it is shown that for weak fields the line shapes are strongly modified by coupling to continuum states, taking the form of Fano resonances. The calculated spectra, when suitably broadened, are found to be in good agreement with experimental results.Comment: 9 pages Revtex v3.0, followed by 4 uuencoded postscript figures, SISSA-CM-94-00

Multipole expansion of Bessel and Gaussian beams for Mie scattering calculations

Multipole expansions of Bessel and Gaussian beams, suitable for use in Mie scattering calculations, are derived. These results allow Mie scattering calculations to be carried out considerably faster than existing methods, something that is of particular interest for time evolution simulations where large numbers of scattering calculations must be performed. An analytic result is derived for the Bessel beam that improves on a previously published expression requiring the evaluation of an integral. An analogous expression containing a single integral, similar to existing results quoted, but not derived, in literature, is derived for a Gaussian beam,valid from the paraxial limit all the way to arbitrarily high numerical apertures

On inverse construction of isoptics and isochordal-viewed curves

Given a regular closed curve α in the plane, a $\phi$-isoptic of $\alpha$ is a locus of points from which pairs of tangent lines to $\alpha$ span a fixed angle $\phi$. If, in addition, the chord that connects the two points delimiting the visibility angle is of constant length $\ell$, then $\alpha$ is said to be $(\phi,\ell)$-isochordal viewed. Some properties of these curves have been studied, yet their full classification is not known. We approach the problem in an inverse manner, namely that we consider a $\phi$-isoptic curve $c$ as an input and construct a curve whose $\phi$-isoptic is $c$. We provide thus a sufficient condition that constitutes a partial solution to the inverse isoptic problem. In the process, we also study a relation of isoptics to multihedgehogs. Moreover, we formulate conditions on the behavior of the visibility lines so as their envelope is a $(\phi,\ell)$-isochordal-viewed curve with a prescribed $\phi$-isoptic $c$. Our results are constructive and offer a tool to easily generate this type of curves. In particular, we show examples of $(\phi,\ell)$-isochordal-viewed curves whose $\phi$-isoptic is not circular. Finally, we prove that these curves allow the motion of a regular polygon whose vertices lie along the $(\phi,\ell)$-isochordal-viewed curve