Proton Wave Function Research Articles

Solution of self-consistent equations for the N 3LO nuclear energy density functional in spherical symmetry. The program hosphe (v1.02)

We present solution of self-consistent equations for the N 3LO nuclear energy density functional. We derive general expressions for the mean fields expressed as differential operators depending on densities and for the densities expressed in terms of derivatives of wave functions. These expressions are then specified to the case of spherical symmetry. We also present the computer program hosphe (v1.02), which solves the self-consistent equations by using the expansion of single-particle wave functions on the spherical harmonic oscillator basis. Program summary Program title: HOSPHE (v1.02) Catalogue identifier: AEGK_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 45 809 No. of bytes in distributed program, including test data, etc.: 290 514 Distribution format: tar.gz Programming language: Fortran-90 Computer: PCs and workstations Operating system: Linux RAM: 50 MB Classification: 17.22 External routines: LAPACK ( http://www.netlib.org/lapack/), BLAS ( http://www.netlib.org/blas/) Nature of problem: The nuclear mean-field methods constitute principal tools of a description of nuclear states in heavy nuclei. Within the Local Density Approximation with gradient corrections up to N 3LO [1], the nuclear mean-field is local and contains derivative operators up to sixth order. The locality allows for an effective and fast solution of the self-consistent equations. Solution method: The program uses the spherical harmonic oscillator basis to expand single-particle wave functions of neutrons and protons for the nuclear state being described by the N 3LO nuclear energy density functional [1]. The expansion coefficients are determined by the iterative diagonalization of the mean-field Hamiltonian, which depends non-linearly on the local neutron and proton densities. Restrictions: Solutions are limited to spherical symmetry. The expansion on the harmonic-oscillator basis does not allow for a precise description of asymptotic properties of wave functions. Running time: 50 seconds of CPU time for the ground-state of 208Pb described by using N 0 = 50 as the maximum harmonic-oscillator shell included in the basis.

About possible contribution of intrinsic charm component to inclusive spectra of charmed mesons

We calculate differential energy spectra (xF-distributions) of charmed particles produced in proton–nucleus collisions, assuming the existence of intrinsic heavy quark components in the proton wavefunction. For the calculation, the recently proposed factorization scheme is used, based on the colour glass condensate theory and specially suited for predictions of a production of particles with large rapidities. It is argued that the intrinsic charm component can, if it exists, dominate in a sum of two components, intrinsic + extrinsic, of the inclusive spectrum of charmed particles produced in proton–nucleus collisions at high energies, in the region of medium xF, 0.15 < xF < 0.7, and can give noticeable contribution to atmospheric fluxes of prompt muons and neutrinos.

J/ ψ Production in [formula omitted] and d+Au Collisions at [formula omitted] at STAR

We present analysis of J/ ψ production over the range − 1.0 < η < 4.2 in p + p and d+Au collisions using di-electron data taken during the 2008 run with the STAR experiment at Brookhaven National Laboratory. STAR's unique forward capabilities, especially the Forward Meson Spectrometer electromagnetic calorimeter, allow us the possibility of investigating the intrinsic charm components of the proton wave function using high- x F forward particles produced in asymmetric partonic collisions. Mid-rapidity measurements in d+Au collisions extend our understanding of the mechanisms underlying heavy quarkonium production and its transport through cold nuclear matter.

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.: (VI) hfodd (v2.40h): A new version of the program

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.: (VI) hfodd (v2.40h): A new version of the program

H/D isotope effect in methyl torsional interaction of acetone as calculated by a multicomponent molecular orbital method

We analyzed the H/D isotope effect in the methyl torsional interactions accompanying two methyl internal rotations for acetone (CH(3)COCH(3)) and deuterated acetone (CD(3)COCD(3) and CH(3)COCD(3)) in the ground state by means of the multicomponent molecular orbital (MC_MO) method, which directly accounts for the quantum effects of protons and deuterons. Our estimated rotational constants and moments of inertia for CH(3)COCH(3) and CD(3)COCD(3) agreed well with the experimental results because of the adequate treatment of protonic and deuteronic quantum effects afforded by the MC_MO method. Because the C-D bond distance in the CD(3) group was shorter than the C-H distance in CH(3) owing to the anharmonicity of the potential, the difference in potential energy surfaces of CH(3)COCH(3), CD(3)COCD(3), and CH(3)COCD(3) was strongly related to the differences induced in geometrical parameters by the H/D isotope effect. The potential energy obtained by the MC_MO method was estimated as 290.88 cm(-1) for CH(3)COCH(3), which is in excellent agreement with the experimental results. For CH(3)COCD(3), two potential energies were obtained for CH(3) and CD(3) internal rotations. The MC_MO method successfully elucidated the H/D isotope effect for methyl-methyl repulsive interactions by allowing the adequate treatment of protonic and deuteronic wave functions. The potential energies and bond distances associated with methyl internal rotation induced by the H/D isotope effect were also controlled by the distribution of wave functions of protons and deuterons.

Higgs hadroproduction at large Feynman x

We propose a novel mechanism for the production of the Higgs boson in inclusive hadronic collisions, which utilizes the presence of heavy quarks in the proton wave function. In these inclusive reactions the Higgs boson acquires the momenta of both the heavy quark and antiquark and thus carries 80% or more of the projectile's momentum. We predict that the cross section d σ / d x F ( p p ¯ → H X ) for the inclusive production of the Standard Model Higgs coming from intrinsic bottom Fock states is of order 150 fb at LHC energies, peaking in the region of x F ∼ 0.9 . Our estimates indicate that the corresponding cross section coming from gluon–gluon fusion at x F = 0.9 is relatively negligible and therefore the peak from intrinsic bottom should be clearly visible for experiments with forward detection capabilities. The predicted cross section for the production of the Standard Model Higgs coming from intrinsic heavy quark Fock states in the proton is sufficiently large that detection at the Tevatron and the LHC may be possible.

Hydrogen Tunneling in an Enzyme Active Site: A Quantum Wavepacket Dynamical Perspective

We study the hydrogen tunneling problem in a model system that represents the active site of the biological enzyme, soybean lipoxygenase-1. Toward this, we utilize quantum wavepacket dynamics performed on potential surfaces obtained by using hybrid density functional theory under the influence of a dynamical active site. The kinetic isotope effect is computed by using the transmission amplitude of the wavepacket, and the experimental value is reproduced. By computing the hydrogen nuclear orbitals (eigenstates) along the reaction coordinate, we note that tunneling for both hydrogen and deuterium occurs through the existence of distorted, spherical s-type proton wave functions and p-type polarized proton wave functions for transfer along the donor-acceptor axis. In addition, there is also a significant population transfer through distorted p-type proton wave functions directed perpendicular to the donor-acceptor axis (via intervening pi-type proton eigenstate interactions) which underlines the three-dimensional nature of the tunneling process. The quantum dynamical evolution indicates a significant contribution from tunneling processes both along the donor-acceptor axis and along directions perpendicular to the donor-acceptor axis. Furthermore, the tunneling process is facilitated by the occurrence of curve crossings and avoided crossings along the proton eigenstate adiabats.

Measurement of the Shape of the Boson-Transverse Momentum Distribution inpp¯→Z/γ*→e+e−+XEvents Produced ats=1.96 TeV

We present a measurement of the shape of the Z/gamma* boson transverse momentum (q(T)) distribution in pp --> Z/gamma* --> e(+)e(-) + X events at a center-of-mass energy of 1.96 TeV using 0.98 fb(-1) of data collected with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resummation prediction at low q(T), but above the perturbative QCD calculation in the region of q(T)>30 GeV/c. Using events with q(T)<30 GeV/c, we extract the value of g(2), one of the nonperturbative parameters for the resummation calculation. Data at large boson rapidity y are compared with the prediction of resummation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function.

Relativistic wavefunctions of charged particles in a uniform magnetic field and neutrino beaming in the Urca process

We review the construction of electron and proton wavefunctions in a uniform magnetic field. Keeping charged particles in cyclotron motions in mind, we adopt the symmetric gauge and its associated harmonic oscillator operator method. Furthermore, we apply this method to study the neutrino emission in the direct Urca process, e− + p → νe + n, in very strong magnetic fields of the order of 1016 G, at a fixed temperature and appropriately chosen densities for relevant particle species to calculate the angular distributions of the neutrinos. We found some discriminative profiles of neutrino emissions peculiar to the Landau states in which the incoming particles reside. An implication on the asymmetry of the primordial neutrino emission in supernova phenomena is also discussed.

Diffractive excitation in DIS andppcollisions

We have in earlier papers presented an extension of Mueller's dipole cascade model, which includes subleading effects from energy conservation and running coupling as well as colour suppressed effects from pomeron loops via a ``dipole swing''. The model was applied to describe the total cross sections in pp and gamma*p collisions. In this paper we present a number of improvements of the model, in particular related to the confinement mechanism. A consistent treatment of dipole evolution and dipole--dipole interactions is achieved by replacing the infinite range Coulomb potential by a screened potential, which further improves the frame-independence of the model. We then apply the model to elastic scattering and diffractive excitation, where we specifically study the effects of different sources for fluctuations. In our formalism we can take into account contributions from all different sources, from the dipole cascade evolution, the dipole--dipole scattering, from the impact-parameter dependence, and from the initial photon and proton wavefunctions. Good agreement is obtained with data from the Tevatron and from HERA, and we also present some predictions for the LHC.

Measuring C-odd correlations at lepton–proton and photon–proton collisions

We consider the charge-odd correlations (COC) in cross sections of charged particle production. The cases of a muonic pair and pion systems π+π−, π+π−π0 production are considered in detail for electron–proton or photon–proton collisions in the proton fragmentation region kinematics. COC arise from the interference of amplitudes which describe the different mechanisms of charged leptons (pions) production. One of them corresponds to the production of particles in the charge-odd state (one virtual photon or vector meson annihilation to this system of particles) and the other corresponds to the charge-even state of produced particles (creation by two photons). COC for a muon–antimuon pair creation have a pure QED nature and can be considered as a normalization process. The processes with pion production are sensitive to some characteristics of proton wavefunctions and, besides, can be used for checking the anomalous and normal parts of the effective pionic Lagrangian. The matrix element of three electromagnetic current operators can be measured in photon–proton interactions with lepton pair production. For this aim a charge-odd combination of cross sections can be constructed as a conversion of leptonic 3-rank tensor with hadronic ones. These experiments can be considered as an alternative to deep virtual Compton scattering.

ELASTIC SCATTERING AND THE PROTON FORM FACTOR

We use the QCD pomeron model proposed by Landshoff and Nachtmann to compute the differential and the total cross-sections for pp scattering in order to discuss a QCD-based approach to the proton form factor. This model is quite dependent on the experimental electromagnetic form factor, and it is not totally clear why this form factor gives good results even at moderate transferred momentum. We exchange the electromagnetic form factor by the asymptotic QCD proton form factor determined by Brodsky and Lepage (BL) plus a prescription for its low energy behavior dictated by the existence of a dynamically generated gluon mass. We fit the data with this QCD inspired form factor and a value for the dynamical gluon mass consistent with the ones determined in the literature. Our results also provide a determination of the proton wave function at the origin, which appears in the BL form factor.

Higher twists in polarized DIS and the size of the constituent quark

The spontaneous breaking of chiral symmetry implies the presence of a short-distance scale in the QCD vacuum, which phenomenologically may be associated with the size of the constituent quark, $\ensuremath{\rho}\ensuremath{\approx}0.3\text{ }\text{ }\mathrm{fm}$. We discuss the role of this scale in the matrix elements of the twist-4 and 3 quark-gluon operators determining the leading power ($1/{Q}^{2}$)-corrections to the moments of the nucleon spin structure functions. We argue that the flavor-nonsinglet twist-4 matrix element, ${f}_{2}^{u\ensuremath{-}d}$, has a sizable negative value of the order ${\ensuremath{\rho}}^{\ensuremath{-}2}$, due to the presence of sea quarks with virtualities $\ensuremath{\sim}{\ensuremath{\rho}}^{\ensuremath{-}2}$ in the proton wave function. The twist-3 matrix element, ${d}_{2}$, is not related to the scale ${\ensuremath{\rho}}^{\ensuremath{-}2}$. Our arguments support the results of previous calculations of the matrix elements in the instanton vacuum model. We show that this qualitative picture is in agreement with the phenomenological higher-twist correction extracted from an NLO QCD fit to the world data on ${g}_{1}^{p}$ and ${g}_{1}^{n}$, which include recent data from the Jefferson Lab Hall A and COMPASS experiments. We comment on the implications of the short-distance scale $\ensuremath{\rho}$ for quark-hadron duality and the $x$-dependence of higher-twist contributions.

A fragment molecular-orbital–multicomponent molecular-orbital method for analyzing H∕D isotope effects in large molecules

We have developed a fragment molecular orbital (FMO)-multi-component MO (MC_MO) method to analyze isotope effect due to differences between the quantum effects of protons and deuterons for large molecules such as proteins and DNA. The FMO-MC_MO method enables the determination of both the electronic and the protonic (deuteronic) wave functions simultaneously, and can directly express isotope effects, including coupling effects between nuclei and electrons. In our calculations of two polyglycines, which serve as prototypes for biological molecules, by this method, we clearly observed the geometrical relaxation induced by the HD isotope effect in the intramolecular hydrogen bonding portions of the molecules. The HD isotope effect on the interfragment interaction energy, including that of the hydrogen bonding parts, was also demonstrated: the hydrogen bond was weakened by replacement of hydrogen with deuterium. We also developed electrostatic potential approximations for use in the FMO-MC_MO calculations, and the accuracy of the energy differences induced by the isotope effect was independent of the approximation level of the FMO-MC_MO. Our results confirmed that the FMO-MC_MO method is a powerful tool for the detailed analysis of changes in hydrogen bonding and interaction energies induced by the HD isotope effect for large biological molecules.

Proton Diffusion in Perovskite-Type Oxides Based on Small Polaron Model

The ground state energy and the wavefunction of proton in the cubic perovskite-type oxides ABO 3 are studied by using the double-well potential constructed from the one-dimensional O–H–O bond. We h...

Isotope Effect on Hydrogen (Deuterium)-Absorbing Pt Clusters Calculated by the Multi-Component Molecular Orbital Method

We analyzed isotope effects on the geometrical and electronic relaxations of hydrogen/deuterium-absorbing Pt n H(D) - ( n =1–4, 6) clusters using the first principles multi-component molecular orbital (MC_MO) method, which can take into account the quantum effect of the proton/deuteron. The average of Pt–Pt bond distances of the Pt n H - clusters was calculated to be no more than 0.004 A longer than the bond distances of corresponding Pt n D - clusters. Calculations on Pt n H(D) 2 ( n =2–4, 6) clusters clearly demonstrated that significant geometrical differences between Pt–Pt bond distances caused by the isotope effect depend on the number of hydrogen/deuterium atoms. Slight relaxation of the electronic charge densities was observed by the replacement from H to D. The exponent values indicate that the distribution of the wavefunction of proton and deuteron reflected the geometrical changes and electronic charge densities around the proton and deuteron.

Relativistic theory of inverse beta-decay of polarized neutron in strong magnetic field

The relativistic theory of the inverse beta-decay of polarized neutron,ν e +n → > p +e -, in strong magnetic field is developed. For the proton wave function we use the exact solution of the Dirac equation in the magnetic filed that enables us to account exactly for effects of the proton momentum quantization in the magnetic field and also for the proton recoil motion. The effect of nucleons anomalous magnetic moments in strong magnetic fields is also discussed. We examine the cross-section for different energies and directions of propagation of the initial neutrino accounting for neutron polarization. It is shown that in the super-strong magnetic field the totally polarized neutron matter is transparent for neutrinos propagating antiparallel to the direction of polarization. The developed relativistic approach can be used for calculations of cross-sections of the other URCA processes in strong magnetic fields.

Kinetic and geometrical isotope effects in hydrogen-atom transfer reaction, as calculated by the multi-component molecular orbital method

To estimate the kinetic isotope effect (KIE) for hydrogen (or deuterium) abstraction from H(D)OR (R = H, CH 3, and CN) by an OH radical, we have considered the geometrical isotope effect (GIE) induced by the difference of the protonic and deuteronic wavefunctions using the multi-component MO method. The difference by the GIE of hydrogen bond was about 0.005 Å. The ratio ( k a H / k a D ) of the rate constant of the reaction for R = H, HO + HOR → HOH + OR and HO + DOR → HOD + OR, is estimated as 4.4 by our calculation, which is reasonable agreement with experimental result of 6.0 ± 2.0. We have found that the difference of the nuclear wavefunction of the proton and deuteron affects the changes of geometry and electronic charge density, which plays an important role to theoretically determine the effective potential energy surfaces and the corresponding KIE between H and D compounds.

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) HFODD(v2.08k)

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) HFODD(v2.08k)

Proton emission from triaxial nuclei

Proton decay from triaxially deformed nuclei is investigated. The deformation parameters corresponding to the mother nucleus are determined microscopically and the calculated decay widths are used to probe the mean-field wave function. The proton wave function in the mother nucleus is described as a resonant state in a coupled-channel formalism. The decay width, as well as the angular distribution of the decaying particle, are evaluated and their dependence upon the triaxial deformation parameters is studied in the decay of $^{161}\mathrm{Re}$ and $^{185}\mathrm{Bi}$. It is found that the decay width is very sensitive to the parameters defining the triaxial deformation while the angular distribution is a universal function which does not depend upon details of the nuclear structure.