Physics Commons^™

Renormalization And Mixing Of Staple-Shaped Wilson Line Operators On The Lattice Revisited, Yao Ji, Jian-Hui Zhang, Shuai Zhao, Ruilin Zhu

Physics Faculty Publications

Transverse-momentum-dependent parton distribution functions and wave functions (TMDPDFs/TMDWFs) can be extracted from lattice calculations of appropriate Euclidean matrix elements of staple-shaped Wilson line operators. We investigate the mixing pattern of such operators under lattice renormalization using symmetry considerations. We perform an analysis for operators with all Dirac structures, which reveals mixings that are not present in one-loop lattice perturbation theory calculations. We also present the relevant one-loop matching in a renormalization scheme that does not introduce extra nonperturbative effects at large distances, both for the TMDPDFs and for the TMDWFs. Our results have the potential to greatly facilitate numerical calculations …

The Gauge Principle From The Schrodinger-Born Wave Mechanics, P. T. Leung

Physics Faculty Publications and Presentations

We propose an elementary way of introducing the gauge principle to beginners with a background in only mechanics, electromagnetism, and quantum mechanics. This evolves from an apparent conflict in the Schrodinger-Born formulation of wave mechanics, and does not have to resort to advanced concepts like covariant derivative and minimal coupling. With such an approach, one would have appreciated how interactions can be dictated from consideration of internal symmetry of a physical system, which serves as a principle underlying the foundation of almost all modern physics. In addition, the gauge principle also serves as a resource providing consistency between the Born …

Electron- And Positron-Impact Ionization Of Inert Gases, R. I. Campeanu, H. R. J. Walters, Colm T. Whelan

Physics Faculty Publications

Triple-differential cross sections (TDCS) are presented for the electron and positron impact ionization of inert gas atoms in a range of geometries where a number of significant few body effects compete to define the shape of the TDCS. Using both positrons and electrons as projectiles has opened up the possibility of performing complementary studies which could effectively isolate competing interactions which cannot be separately detected in an experiment with a single projectile. A comparison is presented between theory and the recent experiments of [Gavin, deLucio, and DuBois, Phys. Rev. A95, 062703 (2017)] for e^± and contrasted with the …

Quantum Monte Carlo Calculations Of Weak Transitions In A=6-10 Nuclei, S. Pastore, A. Baroni, S. Gandolfi, R. Schiavilla, R. B. Wiringa

Physics Faculty Publications

Ab initio calculations of the Gamow-Teller (GT) matrix elements in the β decays of ⁶He and ¹⁰C and electron captures in 7Be are carried out using both variational and Green's function Monte Carlo wave functions obtained from the Argonne v18 two-nucleon and Illinois-7 three-nucleon interactions, and axial many-body currents derived from either meson-exchange phenomenology or chiral effective field theory. The agreement with experimental data is excellent for the electron captures in ⁷Be, while theory overestimates the ⁶He and ¹⁰C data by ~2% and ~10%, respectively. We show that for these systems correlations in the nuclear …

Many-Particle Systems, 1, David Peak

Many Particles

Wavefunctions for more than one particle: Different kinds of particles

Introductory examples of quantum mechanical wavefunction calculations involve a single particle moving about in a “magic” potential energy—e.g., a particle trapped inside a square well or an electron in a hydrogen atom. But, potential energy arises from interaction, so these situations must inevitably include more than one particle. Even the simplest atom—hydrogen— consists of two particles: the electron and the proton. So, how should the Schrödinger Equation be generalized to account for multiple particles?

Hohenberg-Kohn Theorems In Electrostatic And Uniform Magnetostatic Fields, Xiao-Yin Pan, Viraht Sahni

Publications and Research

The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle …

Simultaneous Analysis Of The Ballik-Ramsay And Phillips Systems Of C2 And Observation Of Forbidden Transitions Between Singlet And Triplet States, Wang Chen, Kentarou Kawaguchi, Peter F. Bernath, Jian Tang

Chemistry & Biochemistry Faculty Publications

6229 lines of the Ballik-Ramsay system (b₃Σ_g^--a₃Π_u) and the Phillips system (A¹Π_u-X¹Σ_g⁺) of C₂ up to v = 8 and J = 76, which were taken from the literature or assigned in the present work, were analyzed simultaneously by least-squares fitting with 82 Dunham-like molecular parameters and spin-orbit interaction constants between the b₃Σ_g^- and X¹Σ_g⁺ states with a standard deviation of 0.0037 cm^-1 for the whole data set. As a …

The Schrödinger Equation With Friction From The Quantum Trajectory Perspective, Sophya V. Garashchuk, Vaibhav Dixit, Bing Gu, James Mazzuca

Faculty Publications

Similarity of equations of motion for the classical and quantum trajectories is used to introduce afriction term dependent on the wavefunction phase into the time-dependent Schrödingerequation. The term describes irreversible energy loss by the quantum system. The force offriction is proportional to the velocity of a quantum trajectory. The resulting Schrödinger equationis nonlinear, conserves wavefunction normalization, and evolves an arbitrary wavefunction into the ground state of the system (of appropriate symmetry if applicable). Decrease in energy is proportional to the average kinetic energy of the quantum trajectory ensemble. Dynamics in the high friction regime is suitable for simple models of …

Comparison Of Forward And Backward Pp Pair Knockout In 3He(E,E'Pp)N, H. Baghdasaryan, L. B. Weinstein, J. M. Laget, K. P. Adhikari, M. Aghasyan, M. J. Amaryan, M. Anghinolfi, J. Ball, M. Battaglieri, A. S. Biselli, G. Dodge, C. E. Hyde, S. E. Kuhn, H. Seraydaryan

Physics Faculty Publications

Measuring nucleon-nucleon short range correlations (SRCs) has been a goal of the nuclear physics community for many years. They are an important part of the nuclear wave function, accounting for almost all of the high-momentum strength. They are closely related to the EMC effect. While their overall probability has been measured, measuring their momentum distributions is more difficult. In order to determine the best configuration for studying SRC momentum distributions, we measured the ³He(e,e'pp)n reaction, looking at events with high-momentum protons (p_p > 0.35 GeV/c) and a low-momentum neutron (p …

Simulations Of The Dipole-Dipole Interaction Between Two Spatially Separated Groups Of Rydberg Atoms, Thomas J. Carroll, Christopher Daniel, Leah Hoover, Timothy Sidie, Michael Noel

Physics Faculty Research and Scholarship

The dipole-dipole interaction among ultracold Rydberg atoms is simulated. We examine a general interaction scheme in which two atoms excited to the x and x(') states are converted to y and y(') states via a Förster resonance. The atoms are arranged in two spatially separated groups, each consisting of only one species of atom. We monitor the state mixing by recording the fraction of atoms excited to the y(') state as the distance between the two groups is varied. With zero detuning a many-body effect that relies on always resonant interactions causes the state mixing to have a finite range. …

Relativistic (Zα)2 Corrections And Leading Quantum Electrodynamic Corrections To The Two-Photon Decay Rate Of Ionic States, Benedikt J. Wundt, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

We calculate the relativistic corrections of relative order (Zα) 2 to the two-photon decay rate of higher excited S and D states in ionic atomic systems, and we also evaluate the leading radiative corrections of relative order α (Zα) 2 ln [(Zα) -2]. We thus complete the theory of the two-photon decay rates up to relative order α3 ln (α). An approach inspired by nonrelativistic quantum electrodynamics is used. We find that the corrections of relative order (Zα) 2 to the two-photon decay are given by the Zitterbewegung, by the spin-orbit coupling and by relativistic corrections to the electron mass, …

General Validity Of Reciprocity In Quantum Mechanics, P.T. Leung, H. Y. Xie, D. P. Tsai

Physics Faculty Publications and Presentations

The concept of reciprocity symmetry for matter-wave propagation is established for nonrelativistic quantum mechanics with previous results in the literature extended to include nonlocal interactions. Examples are given for cases with both local and nonlocal potentials, where we show in particular that reciprocity can be violated for the motion of a charged particle in an external electromagnetic field. In addition, this symmetry is applied to interpret a recent analysis [Phys. Rev. A 64, 042716 (2001)] on the symmetry of transmission through one-dimensional complex potentials, with the emphasis that the validity of reciprocity can go beyond that of time-reversal symmetry, such …

Form Factors And Wave Functions Of Vector Mesons In Holographic Qcd, Hovhannes R. Grigoryan, Anatoly V. Radyushkin

Physics Faculty Publications

Within the framework of a holographic dual model of QCD, we develop a formalism for calculating form factors of vector mesons. We show that the holographic bound states can be described not only in terms of eigenfunctions of the equation of motion, but also in terms of conjugate wave functions that are close analogues of quantum-mechanical bound state wave functions. We derive a generalized VMD representation for form factors, and find a very specific VMD pattern, in which form factors are essentially given by contributions due to the first two bound states in the Q² -channel. We calculate electric …

Geminal Model Chemistry Ii. Perturbative Corrections, V. A. Rassolov, F. Xu, Sophya V. Garashchuk

Faculty Publications

We introduce and investigate a chemical model based on perturbative corrections to the product of singlet-type strongly orthogonal geminals wave function. Two specific points are addressed (i) Overall chemical accuracy of such a model with perturbative corrections at a leading order; (ii) Quality of strong orthogonality approximation of geminals in diverse chemical systems. We use the Epstein–Nesbet form of perturbation theory and show that its known shortcomings disappear when it is used with the reference Hamiltonian based on strongly orthogonal geminals. Application of this model to various chemical systems reveals that strongly orthogonal geminals are well suited for chemical models, …

Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov

Faculty Publications

We present a time-dependent semiclassical method based on quantum trajectories. Quantum-mechanical effects are described via the quantum potential computed from the wave function density approximated as a linear combination of Gaussian fitting functions. The number of the fitting functions determines the accuracy of the approximate quantum potential (AQP). One Gaussian fit reproduces time-evolution of a Gaussian wave packet in a parabolic potential. The limit of the large number of fitting Gaussians and trajectories gives the full quantum-mechanical result. The method is systematically improvable from classical to fully quantum. The fitting procedure is implemented as a gradient minimization. We also compare …

Reduced Form For Coulomb-Wave Multicenter Integrals, Jack C. Straton

Physics Faculty Publications and Presentations

In a previous paper [J. C. Straton, Phys. Rev. A 41, 71 (1990)] an integro-differential transform was introduced and utilized to obtain the analytically reduced form for multicenter integrals composed of general-state hydrogenic orbitals, Yukawa or Coulomb potentials, and plane waves. The present paper extends this result to include Coulomb waves.

The Exchange Potential In Path Integral Studies: Analytical Justification, Randall W. Hall

Collected Faculty and Staff Scholarship

We present analytical justification for our previously described exchange pseudopotential. We show how the fermi quantum partition function can be constructed from the Boltzmann (distinguishable particle) wave functions if the states that correspond to like‐spin electrons occupying the same quantum state are excluded. A class of weighting functions that satisfy this constraint approximately is discussed. Our previous pseudopotential falls under this class. Essentially, our pseudopotential forces the unwanted states to have high energy and, hence, to make negligible contribution to the partition function. Exchange potentials of the form discussed in this article should be useful for studying systems where the …

Quasidegenerate Variational Perturbation Theory And The Calculation Of First‐Order Properties From Variational Perturbation Theory Wave Functions, Robert J. Cave, Ernest R. Davidson

All HMC Faculty Publications and Research

In previous work on the treatment of correlation in molecular systems we have applied a multireference version of second‐order Hylleraas variational perturbation theory. The choice made for the partitioning of H treated the interactions between the correlating functions to infinite order and gave the corrections to the wave function to first order. The method was shown to be accurate in many cases, but became less so when near degeneracies occurred between the reference energy and other eigenvalues of H0. In this article we introduce an effective Hamiltonian method that is analogous to variational perturbation theory, but which is significantly more …

Ionization Of K-Shell Electrons By Highly Relativistic Protons, M. L. Rustgi, P.T. Leung, S. A. Long

Physics Faculty Publications and Presentations

A comparative study of three decent theoretical formalisms by Anholt, Scofield, Becker, and coworkers (1978-85) for K-shell ionization by highly relativistic protons has been carried out. The importance of the spin-flip mechanism is emphasized. It is concluded that in the analysis of such inner-shell ionization processes, an accurate description of the projectile-target interaction is of much more significance than the accuracy of the wave functions of the atomic electrons.

Theoretical Studies Of Electron Transfer In Metal Dimers: Xy+→X+Y, Where X, Y=Be, Mg, Ca, Zn, Cd, Robert J. Cave, David V. Baxter, William A. Goddard Iii, John D. Baldeschwieler

All HMC Faculty Publications and Research

The electronic matrix element responsible for electron exchange in a series of metal dimers was calculated using ab initio wave functions. The distance dependence is approximately exponential for a large range of internuclear separations. A localized description, where the two nonorthogonal structures characterizing the electron localized at the left and right sites are each obtained self‐consistently, is found to provide the best description of the electron exchange process. We find that Gaussian basis sets are capable of predicting the expected exponential decay of the electronic interactions even at quite large internuclear distances.

Shell Correction For The Stopping Power Of K Electrons, P.T. Leung, M. L. Rustgi, S. A. Long

Physics Faculty Publications and Presentations

In view of the inapplicability of the asymptotic expressions for the stopping number available in the literature at high energies, an alternative approach is taken to compute the shell correction to the stopping number of K electrons. Anholt's formula (1979) for the K-shell ionization has been used to calculate the excitation function for longitudinal interaction and numerical integration over energy has been carried out to evaluate the shell correction. Comparison with other theoretical calculations is made. It is proposed that, with the inclusion of relativistic effects, an asymptotic expansion of the stopping number with a leading-term logarithmic in the energy …

A Model For Orientation Effects In Electron‐Transfer Reactions, Paul Siders, Robert J. Cave, R.A. Marcus

All HMC Faculty Publications and Research

A method for solving the single‐particle Schrödinger equation with an oblate spheroidal potential of finite depth is presented. The wave functions are then used to calculate the matrix element T_BA which appears in theories of nonadiabatic electron transfer. The results illustrate the effects of mutual orientation and separation of the two centers on T_BA. Trends in these results are discussed in terms of geometrical and nodal structure effects. Analytical expressions related to T_BA for states of spherical wells are presented and used to analyze the nodal structure effects for T_BA for the spheroidal wells.