Uniqueness of the group Fourier transform on certain nilpotent Lie groups

In this article, we prove that if the group Fourier transform of certain integrable functions on the Heisenberg motion group (or step two nilpotent Lie groups) is of finite rank, then the function is identically zero. These results can be thought as an analogue to the Benedicks theorem that dealt with the uniqueness of the Fourier transform of integrable functions on the Euclidean spaces.Comment: update

Electric dipole polarizabilities of alkali metal ions from perturbed relativistic coupled-cluster theory

We use the perturbed relativistic coupled-cluster theory to compute the static electric dipole polarizabilities of the singly ionized alkali atoms, namely, Na$^+$, $^+$, Rb$^+$, Cs$^+$ and Fr$^+$. The computations use the Dirac-Coulomb-Breit Hamiltonian with the no-virual-pair approximation and we also estimate the correction to the static electric dipole polarizability arising from the Breit interaction.Comment: 8 pages, 3 figures and 9 tables. arXiv admin note: text overlap with arXiv:1210.547

Electric dipole polarizability of alkaline-Earth-metal atoms from perturbed relativistic coupled-cluster theory with triples

The perturbed relativistic coupled-cluster (PRCC) theory is applied to calculate the electric dipole polarizabilities of alkaline Earth metal atoms. The Dirac-Coulomb-Breit atomic Hamiltonian is used and we include the triple excitations in the relativistic coupled-cluster (RCC) theory. The theoretical issues related to the triple excitation cluster operators are described in detail and we also provide details on the computational implementation. The PRCC theory results are in good agreement with the experimental and previous theoretical results. We, then, highlight the importance of considering the Breit interaction for alkaline Earth metal atoms.Comment: 13 pages, 11 figures, 9 tables, Minor changes, References update

Triple excitations in perturbed relativistic coupled-cluster theory and Electric dipole polarizability of groupIIB elements

We use perturbed relativistic coupled-cluster (PRCC) theory to compute the electric dipole polarizabilities $\alpha$ of Zn, Cd and Hg. The computations are done using the Dirac-Coulomb-Breit Hamiltonian with Uehling potential to incorporate vacuum polarization corrections. The triple excitations are included perturbatively in the PRCC theory, and in the unperturbed sector, it is included non-perturbatively. Our results of $\alpha$, for all the three elements, are in excellent agreement with the experimental data. The other highlight of the results is the orbital energy corrections from Breit interactions. In the literature we could only get the data of Hg {E. Lindroth et al., J. Phys. B 22, 2447 (1989)} and are near perfect match with our results. We also present the linearized equations of the cluster amplitudes, including the triple excitations, with the angular factors.Comment: With minor corrections, 17 pages, 4 figures and 8 table

Electric dipole polarizability from perturbed Relativistic Coupled-Cluster Theory: application to Neon

We develop a method based on the relativistic coupled-cluster theory to incorporate a perturbative interaction to the no-pair Dirac-Coulomb atomic Hamiltonian. The method is general and suitable to incorporate any perturbation Hamiltonian in a many electron atom or ion. Using this perturbed relativistic coupled-cluster (PRCC) theory we calculate the electric dipole polarizability, $\alpha$, of Neon. The linearized PRCC results are in very good agreement with the experimental value. However, the results of the nonlinear PRCC shows larger uncertainty but it is consistent with the observations from earlier works.Comment: 6 pages, 8 table

Electric dipole polarizabilities of doubly ionized alkaline Earth metal ions from perturbed relativistic coupled-cluster theory

Using perturbed relativistic coupled-cluster (PRCC) theory we compute the ground state electric dipole polarizability, $\alpha$, of doubly ionized alkaline earth metal ions $\rm{Mg}^{2+}$, $\rm{Ca}^{2+}$, $\rm{Sr}^{2+}$, $\rm{Ba}^{2+}$ and $\rm{Ra}^{2+}$. In the present work we use the Dirac-Coulomb-Breit atomic Hamiltonian and we also include the Uehling potential, which is the leading order term in the vacuum polarization corrections. We examine the correction to the orbital energies arising from the Uehling potential in the self-consistent field calculations as well as perturbatively. Our results of $\alpha$ are in very good agreement with the experimental data, and we observe a change in the nature of the orbital energy corrections arising from the vacuum polarization as we go from $\rm{Mg}^{2+}$ to Ra$^{2+}$.Comment: 10 pages, 12 table

Electric dipole polarizability of group-IIIA ions using PRCC: Large correlation effects from nonlinear terms

We compute the ground-state electric dipole polarizability of group-IIIA ions using the perturbed relativistic coupled-cluster (PRCC) theory. To account for the relativistic effects and QED corrections, we use the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy. The effects of triple excitations are considered perturbatively in the PRCC. Our PRCC results for $\alpha$ are good in agreement with the previous theoretical results for all the ions. From our computations we find that the nonlinear terms in PRCC have significant contributions and must be included to obtain the accurate value of $\alpha$ for group-IIIA ions. For the correction from the Breit interaction, we find that it is largest for Al$^+$ and decreases as we go towards the heavier ions. The corrections from the vacuum polarization and the self-energy increase from lighter to heavier ions.Comment: 12 pages, 2 figures, 10 table

Sb concentration dependent structural and resistive properties of polycrystalline Bi-Sb alloys

Polycrystalline Bi-Sb alloys have been synthesized over a wide range of antimony concentration (8 at% to 20 at%) by solid state reaction method. In depth structural analysis using X-Ray diffraction (XRD) and temperature dependent resistivity measurement of synthesized samples have been performed. XRD data confirmed single phase nature of polycrystalline samples and revealed that complete solid solution is formed between bismuth and antimony. Rietveld refinement technique, utilizing MAUD software, has been used to perform detail structural analysis of the samples and lattice parameters of synthesized Bi-Sb alloys have been estimated. Lattice parameter and unit cell volume decreases monotonically with increasing antimony content. The variation of lattice parameters with antimony concentration depicts a distinct slope change beyond 12 at% Sb content sample. Band gap has been estimated from the thermal variation of resistivity data, with the 12% Sb content sample showing maximum value. It has been observed that, with increasing antimony concentration the transition from direct to indirect gap semiconductor is intimately related to the variation of the estimated lattice parameters. Band diagram for the polycrystalline Bi-Sb alloy system has also been proposed.Comment: To be published in J. Applied Physic

Evolution of texture and microstructure during accumulative roll bonding of aluminum AA5086 alloy

In the present investigation, a strongly bonded strip of an aluminium-magnesium based alloy AA5086 is successfully produced through accumulative roll bonding (ARB). A maximum of up to eight passes has been used for the purpose. Microstructural characterization using electron backscatter diffraction (EBSD) technique indicates the formation of submicron sized (~200-300 nm) subgrains inside the layered microstructure. The material is strongly textured where individual layers possess typical FCC rolling texture components. More than three times enhancement in 0.2% proof stress (PS) has been obtained after 8 passes due to grain refinement and strain hardeningComment: 13 pages, 9 figure

A new multi line-cusp magnetic field plasma device (MPD) with variable magnetic field for fundamental plasma studies

One of the fundamental problems is the understanding of physics of electrostatic and electromagnetic fluctuations in multi-scale plasma turbulence. Especially so, in continuously connected plasma regions with varying degree of magnetization. Examples range from multiscale plasmas in Magnetron-like devices to astrophysical plasmas confined by magnetic dipole structures, solar wind driven collision-less and weakly collisional plasmas around Earth, to mention a few. Such plasmas are dominated by both electron scale and ion scale physics as well as finite beta effects. To investigate such processes in laboratory experiments requires excellent control of continuously connected regions of nearly zero plasma beta with finite beta regions as well as the gradient length scales of mean density and temperatures. To address some of these phenomena at laboratory scale, a new multi-line cusp configured plasma device (MPD) consisting of electromagnets with core material has been constructed with a capability to experimentally control the relative volume fractions of magnetized to unmagntized plasma volume as well as accurate control on the gradient length scales of mean density and temperature profiles. The hot tungsten cathode produced Argon plasma in the MPD has been characterised using single Langmuir probes. Argon plasma has been produced in the device over a wide range of pressure 5 x 10-5 mBar to 1 x 10-3 mBar, achieving plasma density range from 109 to 1011cm-3 and temperature in the range 1eV to 8eV