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Item Open Access Variational calculations of excited states with zero total angular momentum vibrational spectrum of H2 without use of the Born–Oppenheimer approximation(2003) Bubin, Sergiy; Adamowicz, LudwikVery accurate, rigorous and fully variational, all-particle, non-Born–Oppenheimer calculations of the vibrational spectrum of the H2 molecule have been performed. Very high accuracy has been achieved by expanding the wave functions in terms of explicitly correlated Gaussian functions with preexponential powers of the internuclear distance. An indicator of the high accuracy of the calculations is the new upper bound for the H2 nonrelativistic nonadiabatic ground state energy equal to 21.164 025 030 0 hartreeItem Open Access Non-Born–Oppenheimer calculations of atoms and molecules(2003) Cafiero, Mauricio; Bubin, Sergiy; Adamowicz, LudwikWe review a recent development in high-accuracy non-Born–Oppenheimer calculations of atomic and molecular systems in a basis of explicitly correlated Gaussian functions. Much of the recent progress in this area is due to the derivation and implementation of analytical gradients of the energy functional with respect to variational linear and non-linear parameters of the basis functions. This method has been used to obtain atomic and molecular ground and excited state energies and the corresponding wave functions with accuracy that exceeds previous calculations. Further, we have performed the first calculations of non-linear electrical properties of molecules without the Born–Oppenheimer approximation for systems with more than one electron. The results for the dipole moments of such systems as HD and LiH agree very well with experiment. After reviewing our non-Born–Oppenheimer results we will discuss ways this method can be extended to deal with larger molecular systems with and without an external perturbationItem Open Access Nonrelativistic molecular quantum mechanics without approximations: Electron affinities of LiH and LiD(2004) Bubin, Sergiy; Adamowicz, LudwikWe took the complete nonrelativistic Hamiltonians for the LiH and LiH2 systems, as well as their deuterated isotopomers, we separated the kinetic energy of the center of mass motion from the Hamiltonians, and with the use of the variational method we optimized the ground-state nonadiabatic wave functions for the systems expanding them in terms of n-particle explicitly correlated Gaussian functions. With 3600 functions in the expansions we obtained the lowest ever ground-state energies of LiH, LiD, LiH2, and LiD2 and these values were used to determine LiH and LiD electrons affinities ~EAs! yielding 0.330 30 and 0.327 13 eV, respectively. The present are the first high-accuracy ab initio quantum mechanical calculations of the LiH and LiD EAs that do not assume the Born-Oppenheimer approximation. The obtained EAs fall within the uncertainty brackets of the experimental resultsItem Open Access Non-Born–Oppenheimer study of positronic molecular systems: e¿LiH(2004) Bubin, Sergiy; Adamowicz, LudwikVery accurate non-Born–Oppenheimer variational calculations of the ground state of e1LiH have been performed using explicitly correlated Gaussian functions with preexponential factors dependent on powers of the internuclear distance. In order to determine the positron detachment energy of e1LiH and the dissociation energy corresponding to the e1LiH fragmentation into HPs and Li1 we also calculated non-BO energies of HPs, LiH, and Li1. For all the systems the calculations provided the lowest ever-reported variational upper-bounds to the ground state energies. Annihilation rates of HPs and e1LiH were also computed. The dissociation energy of e1LiH into HPs and Li1 was determined to be 0.036 548 hartreeItem Open Access Non-Born–Oppenheimer calculations of the pure vibrational spectrum of HeH+(2005) Pavanello, Michele; Bubin, Sergiy; Molski, Marcin; Adamowicz, LudwikVery accurate calculations of the pure vibrational spectrum of the HeH+ ion are reported. The method used does not assume the Born–Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are calculated as the states of the system with zero total angular momentum. The wave functions of the states are expanded in terms of explicitly correlated Gaussian basis functions multipled by even powers of the internuclear distance. The calculations yielded twelve bound states and corresponding eleven transition energies. Those are compared with the pure vibrational transition energies extracted from the experimental rovibrational spectrumItem Open Access The general solution for relativistic spherical shells(2005) Kijowski, J.; Magli, G.; Malafarina, D.The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split into two classes: a class of “astrophysically interesting” solutions describing “ordinary” matter with positive density and pressure, and a class of “phantom-like” solutions with positive density but negative active gravitational mass, which can also be of interest in several “very strong fields” regimes. Known results on linear-barotropic equations of state are recovered as particular cases.Item Open Access LCDG4 and DigiSim – Simulation activities at NICADD/NIU(2005) Beznosko, Dmitriy; Blazey, G.; Chakraborty, D.; Dyshkant, A.; Francis, K.; Kubik, D.; Lima, J.G.R.; McCormick, J.; McIntosh, R.; Rykalin, V.; Zutshi, V.We present two software packages developed to support detector R&D studies for the International Linear Collider. LCDG4 is a full-detector simulator that provides energy deposits from particles traversing the sensitive volumes of the detector. It has been extensively used within the American ILC community, providing data for algorithm development and detector optimization studies. DigiSim models real-life digitization effects, converting the idealized response into simulated detector readout. It has many useful features to improve the realism in modeling detector response. The main characteristics of these two complementary packages are discussed.Item Open Access Functionalization of single-walled carbon nanotubes using isotropic plasma treatment: Resonant Raman spectroscopy study(2005) Utegulov, Z. N.; Mast, David B.; He, Peng; Shi, Donglu; Gilland, Robert F.Functionalization of single-walled carbon nanotubes sSWNTsd by isotropic plasma treatment was studied using resonant Raman spectroscopy. It was shown that plasma-induced functionalization results in the uniaxial isotropic constriction of the nanotubes but preserves their overall structural integrity. It was demonstrated that NH3 ·H2O and hexamethyldisiloxan plasmas yield various types of conductivity for semiconducting SWNTs.Item Open Access Non-Born–Oppenheimer variational calculations of HT+ bound states with zero angular momentum(2005) Bednarz, Eugeniusz; Bubin, Sergiy; Adamowicz, LudwikWe report fully nonadiabatic calculations of all rotationless bound states of HT+ molecular ion st+p+e−d carried out in the framework of the variational method. We show that, in all the states, except the two highest ones, the bond in the system can be described as covalent. In the highest two states the bond becomes essentially ionic and HT+ can be described as a T+H+ complex. The wave function of the system was expanded in terms of spherically symmetric, explicitly correlated Gaussian functions with preexponential multipliers consisting of powers of the internuclear distance. Apart from the total energies of the states, we have calculated the expectation values of the t-p, t-e, and p-e interparticle distances, their squares, and the nucleus-nucleus correlation functionsItem Open Access Charge asymmetry in HD+(2005) Bubin, Sergiy; Bednarz, Eugeniusz; Adamowicz, LudwikExpanding the wave functions of the ground and excited states of HD1 ~or pde) in terms of spherically symmetric explicitly correlated Gaussian functions with preexponential multipliers consisting of powers of the internuclear distance, and using the variational method, we performed very accurate nonadiabatic calculations of all bound states of this system corresponding to the zero total angular momentum quantum number ~vibrational states; v50 – 22). The total and the transition energies obtained agree with the best available calculations. For each state we computed the expectation values of the d-p, d-e, and p-e interparticle distances. This is the first time these quantities were computed for HD1 using rigorous nonadiabatic wave functions. While up to the v520 state some asymmetry is showing in the d-e and p-e distances, for v521 and v522 we observe a complete breakdown of the Born–Oppenheimer approximation and localization of the electron almost entirely at the deuteron.Item Open Access An accurate non-Born–Oppenheimer calculation of the first purely vibrational transition in LiH molecule(2005) Bubin, Sergiy; Adamowicz, Ludwik; Molski, MarcinIn this work we study the ground and the first vibrationally excited states of LiH molecule. We performed an extensive nonrelativistic variational calculations of the two states without using the Born–Oppenheimer approximation. The results are analyzed and compared with the data extracted from recent experiments. The 0←1 transition energy obtained in the calculations converged to a value which is less than a wave number above the transition energy estimated from the available experimental data concerning the LiH rovibrational transitions. We discuss the remaining discrepancy and the procedure used to determine the “experimental” transition frequenciesItem Open Access Convergence of Experiment and Theory on the Pure Vibrational Spectrum of HeH(2006) Stanke, Monika; Kedziera, Dariusz; Molski, Marcin; Bubin, Sergiy; Barysz, Maria; Adamowicz, LudwikVery accurate quantum mechanical calculations of the pure vibrational spectrum of the HeH molecular ion are reported and compared with newly obtained pure vibrational transitions extracted from the available experimental data. The calculations are performed without assuming the Born-Oppenheimer approximation regarding separability of the nuclear and electronic motions and include the first order relativistic mass-velocity and Darwin corrections. For the two lowest transitions, whose experimental energies are established with the highest precision, the calculated and the experimental results show very good agreementItem Open Access Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters(2006) Bubin, Sergiy; Adamowicz, LudwikIn this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximationItem Open Access Non-Born-Oppenheimer variational calculation of the ground-state vibrational spectrum of LiH+(2006) Bubin, Sergiy; Adamowicz, LudwikVery accurate, rigorous, variational, non-Born-Oppenheimer non-BO calculations have been performed for the fully symmetric, bound states of the LiH+ ion. These states correspond to the ground and excited vibrational states of LiH+ in the ground 2 + electronic state. The non-BO wave functions of the states have been expanded in terms of spherical N-particle explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance and 5600 Gaussians were used for each state. The calculations that, to our knowledge, are the most accurate ever performed for a diatomic system with three electrons have yielded six bound states. Average interparticle distances and nucleus-nucleus correlation function plots are presentedItem Open Access Nonrelativistic variational calculations of the positronium molecule and the positronium hydride(2006) Bubin, Sergiy; Adamowicz, LudwikHighly accurate ground-state nonrelativistic variational calculations of Ps2, 1HPs, and HPs are reported. The calculations have been performed using 5000 explicitly correlated Gaussian basis functions and yielded the lowest variational energy upper bounds for these systems to date. The relative accuracies of the energies obtained are of the order of 4 10−10 a.u. for Ps2 and 2 10−9 a.u. for HP. Several expectation values have also been computed for each system, as well as electron-positron annihilation ratesItem Open Access Quality Control Studies of Wavelength Shifting Fibers for a Scintillator- based Tail-Catcher Muon-Tracker Linear Collider Prototype Detector(2006) Dyshkant, A.; Beznosko, Dmitriy; Blazey, G.; Rykalin, V.; Zutshi, V.Detailed measurements of the wavelength shifting fiber response to a stable and reliable light source are presented. Details about materials, a double reference method, and measurement technique are included. The fibers studied were several hundred KURARAY, Y-11, multiclad, 1.2mm outer diameter wavelength shifting fibers each cut from a reel to about one meter length. The fibers were polished, mirrored, and the mirrors were UV epoxy protected. Each fiber passed quality control requirements before installation. About 94% of the fibers have a response within 1% of the overall meanItem Open Access Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations(2006) Kedziera, Dariusz; Stanke, Monika; Bubin, Sergiy; Barysz, Maria; Adamowicz, LudwikThe Pauli approach to account for the mass-velocity and Darwin relativistic corrections has been applied to the formalism for quantum mechanical molecular calculations that does not assume the Born-Oppenheimer BO approximation regarding separability of the electronic and nuclear motions in molecular systems. The corrections are determined using the first order perturbation theory and are derived for the non-BO wave function of a diatomic system expressed in terms of explicitly correlated Gaussian functions with premultipliers in the form of even powers of the internuclear distance. As a numerical example we used calculations of the transition energies for pure vibrational states of the HD+ ionItem Open Access Extruded scintillator for the Calorimetry applications(2006) Dyshkant, A.; Rykalin, V.; Pla-Dalmau, A.; Beznosko, DmitriyAn extrusion line has been installed and successfully operated at FNAL (Fermi National Accelerator Laboratory) in collaboration with NICADD (Northern Illinois Center for Accelerator and Detector Development). This new Facility will serve to further develop and improve extruded plastic scintillator. Recently progress has been made in producing co-extruded plastic scintillator, thus increasing the potential HEP applications of this Facility. The current R&D work with extruded and co-extruded plastic scintillator for a potential ALICE upgrade, the ILC calorimetry program and the MINERvA experiment show the attractiveness of the chosen strategy for future experiments and calorimetry. We extensively discuss extruded and co-extruded plastic scintillator in calorimetry in synergy with new Solid State Photomultipliers. The characteristics of extruded and co-extruded plastic scintillator will be presented here as well as results with non-traditional photo read-outItem Open Access Quantum entanglement via nilpotent polynomials(2006) Mandilara, Aikaterini; Akulin, Vladimir M.; Smilga, Andrei V.; Viola, LorenzaWe propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed.Item Open Access Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H2(2006) Ke¸dziera, Dariusz; Stanke, Monika; Bubin, Sergiy; Barysz, Maria; Adamowicz, LudwikThe Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the H2 using the perturbation theory and very accurate variational wave functions obtained without assuming the Born-Oppenheimer BO approximation. Expansions in terms of explicitly correlated Gaussians with premultipliers in the form of even powers of the internuclear distance were used for the wave functions. With the inclusion of the two relativistic corrections to the non-BO energies the transition energies for the highest states agree more with the experimental results