ORNL Physics Division


Theoretical and Computational Physics


[hribf] [RIB Physics] [High Energy Reactions] [atomic] [theory] [nisol] [Division Operations] [Appendix] [Author Index] [Keyword Index]
Overview

Atomic Physics

Nuclear Physics and Astrophysics

Atomic Physics


Lattice, Time-Dependent Schrödinger Equation Treatment of Atomic Collisions
D. R. Schultz, M. R. Strayer, J. C. Wells
ion-atom collisions, atomic excitation, Schrödinger equation, lattice approach

Tailoring Atomic Wavefunctions with Designer Pulses
C. O. Reinhold, J. Burgdörfer
coherent control, half-cycle, wavepackets, Rydberg states

Ion-Solid Interactions
C. O. Reinhold, J. Burgdörfer
ion-solid, quantum transport, spallation, ion-surface

Spectra of Ejected Electrons
J. H. Macek, S. Yu. Ovchinnikov
ion-atom collisions, ionization, energy and angular distributions, electron spectra

Theory of Atomic Fragmentation Processes
J. H. Macek, S. Yu. Ovchinnikov
low-energy collisions, fragmentation, Sturmian

Ionization Amplitudes in Time-Dependent Calculations
J. H. Macek, S. Yu. Ovchinnikov
ion-atom collisions, ionization, energy and angular distributions, electron spectra

Abstracts of Papers Published or Submitted for Publication

Analysis of Unexplained Oscillations in Intermediate-Energy Ion-Atom Collisions
D. R. Schultz, C. O. Reinhold, P. S. Krstic
ion-atom collisions, atomic excitation

Lattice Schrödinger-Equation Approach for Excitation and Ionization of He+ by Antiproton Impact
D. R. Schultz, J. C. Wells, P. S. Krstic, C. O. Reinhold
ion-atom collisions, atomic excitation, atomic ionization, lattice methods

Coulomb Effects in the Interaction of a Charged Particle with a Two-Fragment Quantum System
V. A. Bilyk, V. L. Shablov, P. S. Krstic, D. R. Schultz
polarization potentials, three-body problem

Interference Oscillations in the Excitation Cross Section for Slow Ion-Hydrogen Collisions
P. S. Krstic, C. O. Reinhold, D. R. Schultz
ion-atom collisions, atomic excitation, molecular orbital close coupling

Binary-Encounter Electron Emission After Fast Heavy-Ion Impact on Complex Rare- and Molecular-Gas Targets
U. Bechthold, J. Ullrich, U. Ramm, G. Kraft, S. Hagmann, D. R. Schultz, C. O. Reinhold, H. Schmidt-Böcking
ion-atom collisions, atomic ionization, ion-molecule collision

Ternary Ridge of Ejected Electrons from Fast Ion-Atom Collisions
C. O. Reinhold, D. R. Schultz, U. Bechthold, G. Kraft, S. Hagmann, H. Schmidt-Böcking
ion-atom collisions, atomic ionization

Excitation and Charge Transfer in Proton-Hydrogen Collisions
Kolakowska, M. S. Pindzola, F. Robicheaux, D. R. Schultz, J. C. Wells
ion-atom collisions, atomic excitation, lattice methods, atomic charge transfer

Elastic-Elastic Scattering of Electrons from Ions and Atoms
D. R. Schultz, C. O. Reinhold
ion-atom collisions, atomic elastic scattering

Total Electron Loss, Charge Transfer, and Ionization in Proton-Hydrogen Collisions at 10-100 keV
Kolakowska, M. S. Pindzola, D. R. Schultz
ion-atom collisions, atomic excitation, lattice methods, atomic charge transfer

Lattice, Time-Dependent Approach for Electron-Hydrogen Scattering
G. D. Buffington, D. H. Madison, J. L. Peacher, D. R. Schultz
electron-atom collision, lattice methods, atomic excitation, atomic ionization

Towards a Definitive Treatment of Inelastic Ion-Atom Collisions
D. R. Schultz, M. R. Strayer, J. C. Wells
ion-atom collisions, atomic excitation, lattice methods

Dynamical Stabilization of the Periodically Kicked Rydberg Atom
C. O. Reinhold, J. Burgdörfer, M. T. Frey, F. B. Dunning
dynamical stabilization, kicked atom, half-cycle, superheavy

Creating and Probing Coherent Atomic States
C. O. Reinhold, J. Burgdörfer, M. T. Frey, F. B. Dunning
atomic wavepackets, Rydberg states, half-cycle

Studying Atomic Dynamics with Designer Pulses
C. O. Reinhold, J. Burgdörfer, M. T. Frey, F. B. Dunning
Rydberg states, half-cycle, coherent control, non-linear dynamics

Interaction of Multicharged Ions with Insulator Surfaces
L. Hägg, C. O. Reinhold, J. Burgdörfer
neutralization, insulators

Measurements of Absolute Electron Emission Spectra for Grazing Incidence Ion-Surface Collisions
R. Minniti, S. Elston, C. O. Reinhold, J. Y. Lim, J. Burgdörfer
convoy emission

Ionization of Rydberg Atoms by Half-Cycle Pulses: Effect of Pulse Shape and Rise Time
E. Tannian, R. A. Popple, F. B. Dunning, S. Yoshida, C. O. Reinhold, J. Burgdörfer
ionization, Rydberg states, half-cycle

Accurate Ionization Threshold of Atoms Subject to Half-Cycle Pulses
S. Yoshida, C. O. Reinhold, J. Burgdörfer, B. E. Tannian, R. A. Popple, F. B. Dunning
Rydberg states, Schrödinger equation, Sturmian, ionization

Excited State Subshell Population of Hydrogen Atoms After Transmission of Relativistic H- Ions Through Thin Foils
P. Kürpick, C. O. Reinhold, J. Burgdörfer
Langevin, shell structure

Electronic Excitation in Transmission of Relativistic H- Ions Through Thin Foils
O. Reinhold, P. Kürpick, J. Burgdörfer, S. Yoshida, B. Gervais
Langevin, shell structure

Intra-Atomic Double Scattering of Binary Encounter Electrons in Heavy-Ion Collisions with Gas Targets
U. Bechthold, J. Ullrich, U. Ramm, G. Kraft, S. Hagmann, C. O. Reinhold, D. R. Schultz, H. Schmidt-Böcking
ion-atom collisions, atomic ionization, ion-molecule collisions, binary peak

Realization of the Kicked Atom
M. T. Frey, F. B. Dunning, C. O. Reinhold, S. Yoshida, J. Burgdörfer
kicked atom, half-cycle, chaos

Theory of Ionization in Ion-Atom Collisions: Spectra of Ejected Electrons
S. Yu. Ovchinnikov, J. H. Macek, D. B. Khrebtukov
ion-atom collisions, ionization, energy and angular distributions, electron spectra

Positive Energy Sturmian States for Two-Coulomb-Center Problems
S. Yu. Ovchinnikov, J. H. Macek
low-energy collisions, fragmentation, Sturmian

Threshold Law for Positron Impact Ionization of Atoms
W. Ihra, J. H. Macek, F. Mota-Furtado, P. F. O'Mahony
positrons, ionization

Harmonic Oscillator Green Functions
B. Khrebtukov, J. H. Macek
Green's functions, zero-range potentials, harmonic oscillators

Theory of Rapidly Oscillating Electron Angular Distributions in Slow Ion-Atom Collisions
J. H. Macek, S. Yu. Ovchinnikov
ion-atom collisions, ionization, energy and angular distributions, electron spectra

Hidden Crossing Theory Applied to Positronium Formation
S. J. Ward, J. H. Macek, S. Yu. Ovchinnikov
positrons, crossings, charge transfer

Radial-Decoupling Excitation Mechanism in Slow Atomic Collisions Studied Using Zero-Range Model Potentials
M. Pieksma, S. Yu. Ovchinnikov, J. H. Macek
ion-atom collisions, ionization, energy and angular distributions, electron spectra

Energy and Angular Distributions of Detached Electrons in a Solvable Model of Ion-Atom Collisions
J. H. Macek, S. Yu. Ovchinnikov, E. A. Solov'ev
ion-atom collisions, ionization, energy and angular distributions, electron spectra


Nuclear Physics and Astrophysics


Competition of Electron-Capture and Beta-Decay Rates in Supernova Collapse
G. Martinez-Pinedo, K. Langanke, D. J. Dean
electron capture, beta decay, supernova, back resonance

Shell-Model Monte Carlo Investigation of Rare-Earth Nuclei
J. A. White, S. E. Koonin, D. J. Dean
Dy, density of states, shell model, intruder states

Shape Coexistence and the Effective Nucleon-Nucleon Interaction
P.-G. Reinhard, D. J. Dean, W. Nazarewicz, J. Dobaczewski, J. A. Maruhn, M. R. Strayer
coexistence, superdeformation, shell model

Neutrino Interactions with Nuclei and Nuclear Matter
D. J. Dean, M. R. Strayer
nuclear matter, neutron matter, Green's function, variational Monte Carlo

Further Progress in Shell-Model Monte Carlo Studies
D. J. Dean
Xe, giant resonances, pair transfer, constrained path

Coupled-Cluster Methods
B. Mihaila, D. J. Dean, M. R. Strayer
ground state, electron scattering, coupled clusters

Characteristics of Di-Proton Emission from Light Nuclei
B. Mihaila, D. J. Dean, W. Nazarewicz, S. Y. Ovchinnikov, J. H. Macek, M. R. Strayer
proton emitters, angular distribution, dynamical evolution

Nuclear Symmetries -- Chaotic Spectra
C. Ozen, D. J. Dean, W. Nazarewicz, C. W. Johnson
random matrix theory, entropy, group symmetries

Generalized Folding Model for Elastic and Inelastic Nucleus-Nucleus Scattering Which Includes Density-Dependent Nucleon-Nucleon Interactions and Knock-On Exchange
D. T. Khoa, G. R. Satchler
folding model, heavy ions, optical potential, density-dependent interactions

Study of the Airy Pattern in 16O + 12C Elastic Scattering at 230 MeV
A. Ogloblin, D. T. Khoa, G. R. Satchler
O, C, elastic scattering, differential cross sections, Airy structure

Summary of Preliminary Results from a Mean-Field Analysis of 16O + 12C Elastic Scattering at Seven Energies from E16 = 124 to 608 MeV and its Implications for the Airy Structure of the Scattering
G. R. Satchler
O, C, elastic scattering, mean field, Airy structure, nuclear rainbow

Detailed Study and Mean-Field Interpretation of 16O + 12C Elastic Scattering at Seven Medium Energies
M. P. Nicoli, F. Haas, C. Beck, G. R. Satchler, M. E. Brandan
O, C, elastic scattering, optical potential

Separable Nuclear Multipole Interaction
P. D. Stevenson, J Rikovska, M. R. Strayer
Hartree-Fock, perturbation theory, spherical nuceli

Comparison of Neutrino-Driven Convection in Core Collapse Supernovae in Two and Three Dimensions
J. Knerr, A. Mezzacappa, J. M. Blondin, S. W. Bruenn, A. C. Calder
convection, core collapse supernova

Neutrino Signatures from Core Collapse Supernovae
S. W. Bruenn, A. Mezzacappa
neutrinos, core collapse supernova

Neutrino Mass and the Core Collapse Supernova Mechanism
A. Mezzacappa, S. W. Bruenn
neutrinos, core collapse supernova

Two-Dimensional Studies of Core Collapse Supernovae
A. Mezzacappa, W. R. Hix, S. W. Bruenn, A. C. Calder, J. M. Blondin
convection, core collapse supernova

New Precollapse Models for Core Collapse Supernovae
A. Mezzacappa, S. W. Bruenn, M. Limongi, A. Chieffi
stellar evolution, core collapse supernova

Nova Outburst and Uncertainties Due to Nuclear Reaction Rates
W. R. Hix, M. S. Smith, A. Mezzacappa, S. Starrfield, M. W. Guidry
nova, cataclysmic variables, nuclear reactions, nucleosynthesis

Simplifying Nuclear Reaction Networks with Partial Equilibria
W. R. Hix, C. Freiburghaus, F.-K. Thielemann
nuclear reactions, nucleosynthesis, abundances

One-Dimensional Newtonian Boltzmann Neutrino Transport and Core Collapse Supernovae
O.E.B. Messer, A. Mezzacappa, S. W. Bruenn
supernova, neutrinos, radiation transport, stellar evolution

General Relativistic Boltzmann Neutrino Transport and Core Collapse Supernovae
O.E.B. Messer, M. Liebendörfer, A. Mezzacappa, M. W. Guidry, S. W. Bruenn
supernova, general relativity, radiation transport

Abstracts of Papers Published or Submitted for Publication

Shell-Model Monte Carlo Methods
S. E. Koonin, D. J. Dean, K. Langanke
shell model, Monte Carlo

Rotational and Pairing Properties of 74Rb
D. J. Dean, S. E. Koonin, K. Langanke, P. B. Radha
pairing, ground states

Spin-Dependent Neutralino-Nucleus Scattering for A ~ 127 Nuclei
M. T. Ressell, D. J. Dean
neutralino, dark matter

On the Origin of the Wigner Energy
W. Satula, D. J. Dean, J. Gary, S. Mizutori, W. Nazarewicz
Wigner energy, neutron-proton pairing

Results from Shell-Model Monte Carlo Studies
S. E. Koonin, D. J. Dean, K. Langanke
shell model, Monte Carlo

Shell-Model Monte Carlo Studies of Nuclei
D. J. Dean
neutron-proton pairing

Gamow-Teller Strength Distributions in fp-Shell Nuclei
P. B. Radha, D. J. Dean, S. E. Koonin, K. Langanke, P. Vogel
Gamow-Teller, nuclear temperature, shell model

Orderly Spectra from Random Interactions
C. W. Johnson, G. F. Bertsch, D. J. Dean
random matrix theory

Particle Identification in the Dynamical String-Parton Model of Relativistic Heavy-Ion Collisions
D. E. Malov, A. S. Umar, D. J. Ernst, D. J. Dean
relativistic strings, string decay

Electron Capture on Iron-Group Nuclei
D. J. Dean, K. Langanke, L. Chatterjee, P. B. Radha, M. R. Strayer
supernova, electron capture, shell model

Hadrons as a Distribution of Classical Strings
D. E. Malov, A. S. Umar, D. J. Ernst, D. J. Dean
relativistic strings, nucleon structure functions

Rotational Bands in the Doubly Magic Nucleus 56Ni
D. Rudolph, C. Baktash, M. J. Brinkman, E. Caurier, D. J. Dean, M. Devlin, J. Dobaczewski, P.-H. Heenen, H.-Q. Jin, D. R. LaFosse, W. Nazarewicz, F. Nowacki, A. Poves, L. L. Riedinger, D. G. Sarantites, W. Satula, C.-H. Yu
Ni, rotational bands, shell model, mean field

Identification of Excited States in the N=Z Nucleus 62Ga
S. Skoda, T. Steinhardt, D. Rudolph, D. J. Dean, J. Eberth, U. Hermkens, M. M. Aleonard, C. Baktash, F. Becker, F. Bourgine, B. Cederwall, D. M. Cullen, G. de Angelis, M. Devlin, C. Fahlander, E. Farnea, Ch. Fischbeck, A. Gadea, D. Gassmann, D. S. Haslip, D. R. LaFosse, S. D. Paul, J. N. Scheurer, O. Thelen, P. G. Thirolf, H.-G. Thomas, D. G. Sarantites, C. E. Svensson, J. C. Waddington, W. Weintraub, D. Weishaar, M. Weiszflog, J. N. Wilson, C. A. Ur
shell model, Ga, neutron-proton pairing

Shell-Model Monte Carlo Studies of Neutron-Rich Nuclei in the 1s-0d,1p-0f Shells
D. J. Dean, M. T. Ressell, M. Hjorth-Jensen, S. E. Koonin, K. Langanke, A. P. Zuker
neutron-rich nuclei, shell model, center of mass

High-Spin States in 45Sc and Coexistence of Collective and Noncollective Structures in the Odd-A f7/2 Nuclei
P. Bednarczyk, J. Styczen, R. Broda, M. Lach, W. Meczynski, W. Nazarewicz, W. E. Ormand, W. Satula, D. Bazzacco, F. Brandolini, G. de Angelis, S. Lunardi, L. Müller, N. H. Medina, C. M. Petrache, C. Rossi Alvarez, F. Scarlassara, G. F. Segato, C. Signorini, F. Soramel
shape coexistence, shell model, mean-field theory, intruder states

Equilibrium Shapes and High-Spin Properties of the Neutron-Rich A ~ 100 Nuclei
J. Skalski, S. Mizutori, W. Nazarewicz
cranked shell model, rotational bands, superdeformation, triaxiality

Spherical Proton Emitters
S. Åberg, P. B. Semmes, W. Nazarewicz
proton emitters, tunneling, spectroscopic factors, optical potential

Physics of Radioactive Nuclear Beams: Theoretical Perspective
W. Nazarewicz
radioactive beams, nuclear structure, drip lines

Shell Effects in Superdeformed Minima
P.-H. Heenen, J. Dobaczewski, W. Nazarewicz, P. Bonche, T. L. Khoo
superdeformed states, separation energies, shell structure, Hartree-Fock

Frontiers of Nuclear Structure
W. Nazarewicz
nuclear structure, radioactive beams, high spins, superheavy elements

Shell Corrections for Finite Depth Potentials: Particle Continuum Effects
T. Vertse, A. T. Kruppa, R. J. Liotta, W. Nazarewicz, N. Sandulescu, T. R. Werner
shell structure, extended Thomas-Fermi

Rotating Pseudo-Oscillator Scheme: Pseudo-Spin Symmetry and Identical Bands
Z. Szymanski, W. Nazarewicz
rotational bands, pseudo-spin, superdeformation

New Discrete Basis for Nuclear Structure Studies
M. V. Stoitsov, W. Nazarewicz, S. Pittel
harmonic oscillator, Hartree-Fock, halo nuclei

Odd-Even Staggering of Nuclear Masses: Pairing or Shape Effect?
W. Satula, J. Dobaczewski, W. Nazarewicz
pairing, deformation, binding energies, mean field

Structure of Neutron-Rich Nuclei
W. Nazarewicz
radioactive beams, neutron drip line, shell structure, superheavy

Theoretical Aspects of Science with Radioactive Nuclear Beams
J. Dobaczewski, W. Nazarewicz
radioactive beams, nuclear structure, drip lines

Periodic Numerical Solutions of the Time-Dependent Hartree-Fock Equations
J.-S. Wu, K. C. Wong, M. R. Strayer, M. Baranger
Hartree-Fock, RPA, monopole giant resonances

A Thermal LBGK Model for Large Density and Temperature Differences
J. Huang, F. Xu, M. Vallières, D. H. Feng, Y.-H. Qian, B. Fryxell, M. R. Strayer
hydrodynamics, nova

Prompt Muon-Induced Fission: A Probe for Nuclear Friction in Large-Amplitude Collective Motion
V. E. Oberacker, A. S. Umar, J. C. Wells, M. R. Strayer, J. A. Maruhn, P.-G. Reinhard
muon capture, fission, Hartree-Fock

Excitation Spectrum and Superexchange Pathways in the Spin Dimer VODPO4 · 1/2 D2O
D. A. Tennant, S. E. Nagler, A. W. Garrett, T. Barnes, C. C. Torardi
neutron scattering, spin ladder, spin waves

Magnetic Excitations in the S=1/2 Alternating Chain Compound (VO)2P2O7
W. Garrett, S. E. Nagler, D. A. Tennant, B. C. Sales, T. Barnes
neutron scattering, spin ladder, spin waves

Magnetic Excitations in (VO)DPO4 · 1/2 D2O
W. Garrett, S. E. Nagler, D. A. Tennant, T. Barnes, C. C. Torardi
neutron scattering, spin dimer

Phenomenology of Light Quarks
T. Barnes
meson spectroscopy, quarkonia, exotic mesons

Mechanisms of Photoproduction
T. Barnes
photoproduction, CEBAF, meson spectroscopy

A Study of the S=1/2 Alternating Chain Using Multiprecision Methods
T. Barnes, J. Riera, D. A. Tennant
quantum spin systems, neutron scattering

Photoproduction of Hybrid Mesons
T. Barnes
photoproduction, CEBAF, meson spectroscopy

Heavy Quarkonium Production and Propagation in Nuclei
C. Y. Wong
high-energy nuclear collisions, quarkonia, J/y production

Signatures of Absorption Mechanisms for J/y and y' Production in High-Energy Heavy-Ion Collisions
C. Y. Wong
high-energy nuclear collisions, J/y production

J/y Suppression as a Signal for the Quark-Gluon Plasma
C. Y. Wong
high-energy nuclear collisions, quark-gluon plasma, J/y production

Possible Mechanism of Formation and Stability of Anomalous States of Water
C. Y. Wong, S. Y. Lo
polymorphic states, clustering

Effects of Parton Intrinsic Transverse Momentum on Photon Production in Hard-Scattering Processes
C. Y. Wong, H. Wang
partons, photon production, photon transverse momentum distribution

Unresolved Questions in J/y Production and Propagation in Nuclei
C. Y. Wong
quarkonia

Drell-Yan Cross Section and J/y Production in High-Energy Nucleus-Nucleus Collisions
C. Y. Wong
high-energy nuclear collisions, Drell-Yan, J/y production

Nuclear Incompressibility and Density-Dependent N-N Interaction in the Folding Model for Nucleus-Nucleus Potentials
D. T. Khoa, G. R. Satchler, W. von Oertzen
optical potentials, folding model, density dependence, incompressibility

Pronounced Airy Structure in Elastic 16O + 12C Scattering at Elab = 132 MeV
A. A. Ogloblin, D. T. Khoa, Y. Kondo, Yu. A. Glukhov, A. S. Dem'yanova, M. V. Rozhkov, G. R. Satchler, S. A. Goncharov
O, C, elastic scattering, Airy structure, optical potential, folding model

Shape Resonances and Deep Optical Potentials: A Mean-Field Description of 12C + 12C Scattering at Low Energies
Y. Kondo, M. E. Brandan, G. R. Satchler
C, elastic scattering, reaction cross sections, optical potential, resonances, cluster bound states

Ion Screening Effects and Stellar Collapse
S. W. Bruenn, A. Mezzacappa
neutrinos, core collapse supernova

Simulations of Core Collapse Supernovae in One and Two Dimensions Using Multigroup Neutrino Transport
A. Mezzacappa
neutrinos, convection, core collapse supernova

A Comparison of Boltzmann and Multigroup Flux-Limited Diffusion Neutrino Transport During the Postbounce Shock Reheating Phase in Core-Collapse Supernovae
O.E.B. Messer, A. Mezzacappa, S. W. Bruenn, M. W. Guidry
neutrinos, core collapse supernova

The Effects of General Relativity on Core Collapse Supernovae
K. R. De Nisco, S. W. Bruenn, A. Mezzacappa
general relativity, core collapse supernova

Neutrino-Driven Supernovae: Boltzmann Neutrino Transport and the Explosion Mechanism
O.E.B. Messer, A. Mezzacappa, S. W. Bruenn, M. W. Guidry
neutrinos, core collapse supernova

Neutrino Transport in Core Collapse Supernovae
A. Mezzacappa
neutrinos, core collapse supernova

The Interplay Between Proto-Neutron Star Convection and Neutrino Transport in Core-Collapse Supernovae
A. Mezzacappa, A. C. Calder, S. W. Bruenn, J. M. Blondin, M. W. Guidry, M. R. Strayer, A. S. Umar
convection, core collapse supernova

An Investigation of Neutrino-Driven Convection and the Core Collapse Supernova Mechanism Using Multigroup Neutrino Transport
A. Mezzacappa, A. C. Calder, S. W. Bruenn, J. M. Blondin, M. W. Guidry, M. R. Strayer, A. S. Umar
convection, core collapse supernova

Cosmic Closure: Relating the Ultimate Fate of Massive Stars and the Ultimate Fate of the Universe
A. Mezzacappa, S. W. Bruenn
neutrinos, core collapse supernova

Numerical Methods for Nucleosynthesis
W. R. Hix, F.-K. Thielemann
nuclear reactions, nucleosynthesis, abundances

Silicon Burning II: Quasi-Equilibrium and Explosive Burning
W. R. Hix, F.-K. Thielemann
nuclear reactions, nucleosynthesis, abundances, stellar evolution

Simplifying Silicon Burning: Application of Quasi-Equilibrium to a Network Nucleosynthesis
W. R. Hix, F.-K. Thielemann, A. M. Khokhlov, J. C. Wheeler
nuclear reactions, nucleosynthesis, abundances

A Reduced Quasi-Equilibrium Network for Silicon Burning
C. Freiburghaus, W. R. Hix, F.-K. Thielemann
nuclear reactions, nucleosynthesis, abundances


[hribf] [RIB Physics] [High Energy Reactions] [atomic] [theory] [nisol] [Division Operations] [Appendix] [Author Index] [Keyword Index]