Numerical approximation of the generalized regularized long wave equation using Petrov–Galerkin finite element method

The generalized regularized long wave (GRLW) equation has been developed to model a variety of physical phenomena such as ion-acoustic and magnetohydro dynamic waves in plasma,nonlinear transverse waves in shallow water and phonon packets in nonlinear crystals. This paper aims to develop andanalyze a powerful numerical scheme for the nonlinear GRLWequation by Petrov–Galerkin method in which the elementshape functions are cubic and weight functions are quadratic B-splines. The proposed method is implemented to three ref-erence problems involving propagation of the single solitarywave, interaction of two solitary waves and evolution of solitons with the Maxwellian initial condition. The variational for-mulation and semi-discrete Galerkin scheme of the equation are firstly constituted. We estimate rate of convergence of such an approximation. Using Fourier stability analysis of thelinearized scheme we show that the scheme is uncondition-ally stable. To verify practicality and robustness of the new scheme error norms L2, L∞ and three invariants I1, I2,and I3 are calculated. The computed numerical results are compared with other published results and confirmed to be precise and effective

Structure of 13^{13}Be probed via secondary beam reactions

The low-lying level structure of the unbound neutron-rich nucleus $^{13}$Be has been investigated via breakup on a carbon target of secondary beams of $^{14,15}$B at 35 MeV/nucleon. The coincident detection of the beam velocity $^{12}$Be fragments and neutrons permitted the invariant mass of the $^{12}$Be+$n$ and $^{12}$Be+$n$+$n$ systems to be reconstructed. In the case of the breakup of $^{15}$B, a very narrow structure at threshold was observed in the $^{12}$Be+$n$ channel. Contrary to earlier stable beam fragmentation studies which identified this as a strongly interacting $s$-wave virtual state in $^{13}$Be, analysis here of the $^{12}$Be+$n$+$n$ events demonstrated that this was an artifact resulting from the sequential-decay of the $^{14}$Be(2$^+$) state. Single-proton removal from $^{14}$B was found to populate a broad low-lying structure some 0.70 MeV above the neutron-decay threshold in addition to a less prominent feature at around 2.4 MeV. Based on the selectivity of the reaction and a comparison with (0-3)$\hbar\omega$ shell-model calculations, the low-lying structure is concluded to most probably arise from closely spaced J$^\pi$=1/2$^+$ and 5/2$^+$ resonances (E$_r$=0.40$\pm$0.03 and 0.85$^{+0.15}_{-0.11}$ MeV), whilst the broad higher-lying feature is a second 5/2$^+$ level (E$_r$=2.35$\pm$0.14 MeV). Taken in conjunction with earlier studies, it would appear that the lowest 1/2$^+$ and 1/2$^-$ levels lie relatively close together below 1 MeV.Comment: 14 pages, 13 figures, 2 tables. Accepted for publication in Physical Review

Resonances in 19Ne with relevance to the astrophysically important 18F(p,{\alpha})15O reaction

The most intense gamma-ray line observable from novae is likely to be from positron annihilation associated with the decay of 18F. The uncertainty in the destruction rate of this nucleus through the 18F(p,{\alpha})15O reaction presents a limit to interpretation of any future observed gamma-ray flux. Direct measurements of the cross section of both this reaction and the 18F(p,p)18F reaction have been performed between center of mass energies of 0.5 and 1.9 MeV. Simultaneous fits to both data sets with the R-Matrix formalism reveal several resonances, with the inferred parameters of populated states in 19Ne in general agreement with previous measurements. Of particular interest, extra strength has been observed above ECM \sim1.3 MeV in the 18F(p,p)18F reaction and between 1.3-1.7 MeV in the 18F(p,{\alpha})15O reaction. This is well described by a broad 1/2+ state, consistent with both a recent theoretical prediction and an inelastic scattering measurement. The astrophysical implications of a broad sub-threshold partner to this state are discussed.Comment: 7 pages, 4 figures, 2 table

Spectroscopy of 18^{18}Na: Bridging the two-proton radioactivity of 19^{19}Mg

The unbound nucleus $^{18}$Na, the intermediate nucleus in the two-proton radioactivity of $^{19}$Mg, was studied by the measurement of the resonant elastic scattering reaction $^{17}$Ne(p,$^{17}$Ne)p performed at 4 A.MeV. Spectroscopic properties of the low-lying states were obtained in a R-matrix analysis of the excitation function. Using these new results, we show that the lifetime of the $^{19}$Mg radioactivity can be understood assuming a sequential emission of two protons via low energy tails of $^{18}$Na resonances

Artificial boundary conditions for the linearized Benjamin-Bona-Mahony equation

International audienceWe consider various approximations of artificial boundary conditions for linearized Benjamin-Bona-Mahoney equation. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z-transform of an holomorphic function). In this paper, we derive explicit transparent boundary conditions both continuous and discrete for the linearized BBM equation. The equation is discretized with the Crank Nicolson time discretization scheme and we focus on the difference between the upwind and the centered discretization of the convection term. We use these boundary conditions to compute solutions with compact support in the computational domain and also in the case of an incoming plane wave which is an exact solution of the linearized BBM equation. We prove consistency, stability and convergence of the numerical scheme and provide many numerical experiments to show the efficiency of our tranparent boundary conditions

Beta-delayed proton decay of proton-rich nuclei 23Al and 31Cl and explosive H-burning in classical novae

We have developed a technique to measure beta-delayed proton decay of proton-rich nuclei produced and separated with the MARS recoil spectrometer of Texas A&M University. The short-lived radioactive species are produced in-flight, separated, then slowed down (from about 40 MeV/u) and implanted in the middle of very thin Si detectors. The beam is pulsed and beta-p decay of the pure sources collected in beam is measured between beam pulses. Implantation avoids the problems with detector windows and allows us to measure protons with energies as low as 200 keV from nuclei with lifetimes of 100 ms or less. Using this technique, we have studied the isotopes 23Al and 31Cl, both important for understanding explosive H-burning in novae. They were produced in the reactions 24Mg(p,2n)23Al and 32S(p,2n)31Cl, respectively, in inverse kinematics, from stable beams at 48 and 40 MeV/u, respectively. We give details about the technique, its performances and the results for 23Al and 31Cl beta-p decay. The technique has shown a remarkable selectivity to beta-delayed charged-particle emission and would work even at radioactive beam rates of a few pps. The states populated are resonances for the radiative proton capture reactions 22Na(p,g)23Mg and 30P(p,g)31S, respectively.Comment: Submitted on Oct. 6, 2008 for the Proceedings of the 10th Symposium on Nuclei in the Cosmos Mackinac Island, Michigan, USA 27 July - 1 August, 2008 Acceptance pendin

Observation of a correlated free four-neutron system

A long-standing question in nuclear physics is whether chargeless nuclear systems can exist. To our knowledge, only neutron stars represent near-pure neutron systems, where neutrons are squeezed together by the gravitational force to very high densities. The experimental search for isolated multi-neutron systems has been an ongoing quest for several decades(1), with a particular focus on the four-neutron system called the tetraneutron, resulting in only a few indications of its existence so far(2-4), leaving the tetraneutron an elusive nuclear system for six decades. Here we report on the observation of a resonance-like structure near threshold in the four-neutron system that is consistent with a quasi-bound tetraneutron state existing for a very short time. The measured energy and width of this state provide a key benchmark for our understanding of the nuclear force. The use of an experimental approach based on a knockout reaction at large momentum transfer with a radioactive high-energy He-8 beam was key

Isoscalar response of Ni-68 to alpha-particle and deuteron probes

Isoscalar giant resonances have been measured in the unstable Ni-68 nucleus using inelastic alpha and deuteron scattering at 50A MeV in inverse kinematics with the active target MAYA at GANIL. Using alpha scattering, the extracted isoscalar giant monopole resonance (ISGMR) centroid was determined to be 21.1 +/- 1.9 MeV and the isoscalar giant quadrupole resonance (ISGQR) to be 15.9 +/- 1.3MeV. Indications for soft isoscalar monopole and dipole modes are provided. Results obtained with both (alpha, alpha') and (d, d') probes are compatible. The evolution of isoscalar giant resonances along the Ni isotopic chain from Ni-56 to Ni-68 is discussed.</p

Spectroscopy of the unbound nucleus 18Na

Expérience GANIL, SPIRALInternational audienceThe unbound nucleus 18Na, the intermediate nucleus in the two-proton radioactivity of 19Mg, is studied through the resonant elastic scattering 17Ne(p,17Ne)p. The spectroscopic information obtained in this experiment is discussed and put in perspective with previous measurements and the structure of the mirror nucleus 18N