Partial Wave Analysis Research Articles

Transport of secondary electrons through coatings of ion-irradiated metallic nanoparticles

The transport of low-energy electrons through the coating of a radiosensitizing metallic nanoparticle under fast ion irradiation is analyzed theoretically and numerically. As a case study, we consider a poly(ethylene glycol)-coated gold nanoparticle of diameter 1.6 nm excited by a carbon ion in the Bragg peak region in water as well as by more energetic carbon ions. The diffusion equation for low-energy electrons emitted from a finite-size spherical source representing the surface of the metal core is solved to obtain the electron number density as a function of radial distance and time. Information on the atomistic structure and composition of the coating is obtained from molecular dynamics simulations performed with the MBN Explorer software package. Two mechanisms of low-energy electron production by the metallic core are considered: the relaxation of plasmon excitations and collective excitations of valence d electrons in individual atoms of gold. Diffusion coefficients and characteristic lifetimes of electrons propagating in gold, water, and poly(ethylene glycol) are obtained from relativistic partial wave analysis and the dielectric formalism, respectively. On this basis, the number of electrons released through the organic coating into the surrounding aqueous medium and the number of hydroxyl radicals produced are evaluated. The largest increase of the radical yield due to low-energy electrons is observed when the nanoparticle is excited by an ion with energy significantly exceeding that in the Bragg peak region. It is also shown that the water content of the coating, especially near the surface of the metal core, is crucial for the production of hydroxyl radicals.

Differential technique for the covariant orbital angular momentum operators

The orbital angular momentum operator expansion turns to be a powerful tool to construct the fully covariant partial wave amplitudes of hadron decay reactions and hadron photo- and electroproduction processes. In this paper we consider a useful development of the orbital angular momentum operator expansion method. We present the differential technique allowing the direct calculation of convolutions of two orbital angular momentum operators with an arbitrary number of open Lorentz indices. This differential technique greatly simplifies calculations when the reaction subject to the partial wave analysis involves high spin particles in the initial and/or final states. We also present a useful generalization of the orbital angular momentum operators.

Experimental study of the γp→π0ηp reaction with the A2 setup at the Mainz Microtron

The data available from the A2 Collaboration at MAMI were analyzed to select the γp→π0ηp reaction on an event-by-event basis, which allows for partial-wave analyses of three-body final states to obtain more reliable results, compared to fits to measured distributions. These data provide the world's best statistical accuracy in the energy range from threshold to Eγ=1.45 GeV, allowing a finer energy binning in the measurement of all observables needed for understanding the reaction dynamics. The results obtained for the measured observables are compared to existing models, and the impact from the new data is checked by the fit with the revised Mainz model.11 MoreReceived 7 March 2018DOI:https://doi.org/10.1103/PhysRevC.97.055212©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle & resonance productionPhotonuclear reactionsPhysical SystemsProtonsNuclear Physics

Partial-wave analysis of proton Compton scattering data below the pion-production threshold

Low-energy Compton scattering off the proton is used as an experimental tool for determination of the proton polarizabilities. However, the present empirical determinations rely heavily on the theoretical description(s) of the experimental cross sections in terms of polarizabilities. The state-of-art determinations are based on either the fixed-t dispersion relations (DR) or chiral perturbation theory in the single-baryon sector (χPT). The two approaches obtain rather different results for proton polarizabilities, most notably for βM1 (magnetic dipole polarizability). We attempt to resolve this discrepancy by performing a partial-wave analysis of the world data on proton Compton scattering below threshold. We find a large sensitivity of the extraction to a few “outliers”, leading us to conclude that the difference between DR and χPT extraction is a problem of the experimental database rather than of “model-dependence”. We have specific suggestions for new experiments needed for an efficient improvement of the database. With the present database, the difference of proton scalar polarizabilities is constrained to a rather broad interval: αE1−βM1=(6.8…10.9)×10−4fm3, with their sum fixed much more precisely [to 14.0(2)] by the Baldin sum rule.

Faddeev approach to the reaction K−d→πΣn at pK=1GeV/c

The reaction $K^-d \to \pi \Sigma n$ is studied within a Faddeev-type approach, with emphasis on the specific kinematics of the E31 experiment at J-PARC, i.e. $K^-$ beam momentum of $p_K = 1$ GeV/c and neutron angle of $\theta_n=0^\circ$. The employed Faddeev approach requires as main input amplitudes for the two-body subsystems $\bar KN \to \bar KN$ and $\bar KN \to \pi\Sigma$. For the latter results from recently published chiral unitary models of the $\bar KN$ interaction are utilized. The $\bar KN \to \bar KN$ amplitude itself, however, is taken from a recent partial-wave analysis. Due to the large incoming momentum of the $K^-$, the $\bar KN$ interaction is probed in a kinematical regime where those chiral potentials are no longer applicable. A comparison of the predicted spectrum for various $\pi \Sigma$ charge channels with preliminary data is made and reveals a remarkable agreement as far as the magnitude and the line shape in general is concerned. Noticeable differences observed in the $\pi\Sigma$ spectrum around the $\bar KN$ threshold, i.e. in the region of the $\Lambda$(1405) resonance, indicate a sensitivity to the details of the employed $\bar KN \to \pi\Sigma$ amplitudes and suggest that pertinent high-precision data could indeed provide substantial constraints on the structure of the $\Lambda$(1405).

Measurement of the beam asymmetry Σ and the target asymmetry T in the photoproduction of ω mesons off the proton using CLAS at Jefferson Laboratory

The photoproduction of $\omega$ mesons off the proton has been studied in the reaction $\gamma p\to p\,\omega$ using the CEBAF Large Acceptance Spectrometer (CLAS) and the frozen-spin target (FROST) in Hall B at the Thomas Jefferson National Accelerator Facility. For the first time, the target asymmetry, $T$, has been measured in photoproduction from the decay $\omega\to\pi^+\pi^-\pi^0$, using a transversely-polarized target with energies ranging from just above the reaction threshold up to 2.8 GeV. Significant non-zero values are observed for these asymmetries, reaching about 30-40% in the third-resonance region. New measurements for the photon-beam asymmetry, $\Sigma$, are also presented, which agree well with previous CLAS results and extend the world database up to 2.1 GeV. These data and additional $\omega$-photoproduction observables from CLAS were included in a partial-wave analysis within the Bonn-Gatchina framework. Significant contributions from $s$-channel resonance production were found in addition to $t$-channel exchange processes.

Partial-wave analysis for positronium-xenon collisions in the ultralow-energy region

We propose a method to convert measured positronium annihilation rates in gaseous xenon into total and differential cross sections of positronium-xenon collisions in an ultralow-energy region of less than 80 meV where their experimental determinations as functions of the positronium kinetic energy are extremely difficult. This method makes it possible to determine not only the $s$-wave collisional parameters but also the $p$-wave and $d$-wave parameters. We have found a small positive value of the scattering length, ${A}_{0}=2.06\ifmmode\pm\else\textpm\fi{}0.10\phantom{\rule{0.16em}{0ex}}{a}_{0}$, which indicates that the positronium-xenon interaction in this energy region is repulsive and suggests that it is dominated by the scattering amplitude of the positron rather than that of the electron. An extrapolation of the analytical result into the experimentally inaccessible energy regions from 80 meV to 1.0 eV indicates that there should not be a Ramsauer-Townsend minimum but rather a peak in the total cross section at an energy of approximately 0.4 eV.

Thermoelectric phonon-glass electron-crystal via ion beam patterning of silicon

Ion beam irradiation has recently emerged as a versatile approach to functional materials design. We show in this work that patterned defective regions generated by ion beam irradiation of silicon can create a phonon glass electron crystal (PGEC), a longstanding goal of thermoelectrics. By controlling the effective diameter of and spacing between the defective regions, molecular dynamics simulations suggest a reduction of the thermal conductivity by a factor of $\approx$20 is achievable. Boltzmann theory shows that the thermoelectric power factor remains largely intact in the damaged material. To facilitate the Boltzmann theory, we derive an analytical model for electron scattering with cylindrical defective regions based on partial wave analysis. Together we predict a figure of merit of ZT$\approx$0.5 or more at room temperature for optimally patterned geometries of these silicon metamaterials. These findings indicate that nanostructuring of patterned defective regions in crystalline materials is a viable approach to realize a PGEC, and ion beam irradiation could be a promising fabrication strategy.

Cold quantum-controlled rotationally inelastic scattering of HD with H2 and D2 reveals collisional partner reorientation.

Molecular interactions are best probed by scattering experiments. Interpretation of these studies has been limited by lack of control over the quantum states of the incoming collision partners. We report here the rotationally inelastic collisions of quantum-state prepared deuterium hydride (HD) with H2 and D2 using a method that provides an improved control over the input states. HD was coexpanded with its partner in a single supersonic beam, which reduced the collision temperature to 0-5 K, and thereby restricted the involved incoming partial waves to s and p. By preparing HD with its bond axis preferentially aligned parallel and perpendicular to the relative velocity of the colliding partners, we observed that the rotational relaxation of HD depends strongly on the initial bond-axis orientation. We developed a partial-wave analysis that conclusively demonstrates that the scattering mechanism involves the exchange of internal angular momentum between the colliding partners. The striking differences between H2/HD and D2/HD scattering suggest the presence of anisotropically sensitive resonances.

Partial wave analysis for folded differential cross sections

The value of modified effective range theory (MERT) and the connection between differential cross sections and phase shifts in low-energy electron scattering has long been recognized. Recent experimental techniques involving magnetically confined beams have introduced the concept of folded differential cross sections (FDCS) where the forward (θ ≤ π/2) and backward scattered (θ ≥ π/2) projectiles are unresolved, that is the value measured at the angle θ is the sum of the signal for particles scattered into the angles θ and π − θ. We have developed an alternative approach to MERT in order to analyse low-energy folded differential cross sections for positrons and electrons. This results in a simplified expression for the FDCS when it is expressed in terms of partial waves and thereby enables one to extract the first few phase shifts from a fit to an experimental FDCS at low energies. Thus, this method predicts forward and backward angle scattering (0 to π) using only experimental FDCS data and can be used to determine the total elastic cross section solely from experimental results at low-energy, which are limited in angular range.

The exact solution of a four-body Coulomb problem

The elastic collision between two H-like atoms utilizing an ab initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly, is studied thoroughly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. The new SEM code [Ray, Pramana 83, 907 (2014)] in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude using partial wave analysis, is utilized to study the s-, p-, d-wave elastic phase shifts and the corresponding partial cross sections. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross sections. The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The systems studied are Ps–Ps, Ps–Mu, Ps–H, Ps–D, Ps–T, Mu–Mu, Mu–H, Mu–D, Mu–T, H–H, H–D, H–T, D–D, D–T, T–T. The SEM includes the non-adiabatic short-range effects due to exchange. The MSEM code [Ray, Pramana 83, 907 (2014)] is used to study the effect of the long-range van der Waals interaction due to induced dipole polarizabilities of the atoms in H(1s)–H(1s) elastic collision. The dependence of scattering length on the reduced mass of the system and the dependence of scattering length on the strength of long-range van der Waals interaction that varies with the minimum interatomic distance are observed.

What is the right formalism to search for resonances?

Hadron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. Hereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the Brightarrow psi pi K and Brightarrow bar{D}pi pi decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.

Low energy peripheral scaling in nucleon–nucleon scattering and uncertainty quantification

We analyze the peripheral structure of the nucleon–nucleon interaction for LAB energies below 350 MeV. To this end we transform the scattering matrix into the impact parameter representation by analyzing the scaled phase shifts (L + 1/2) δJLS (p) and the scaled mixing parameters (L + 1/2)ϵJLS(p) in terms of the impact parameter b = (L + 1/2)/p. According to the eikonal approximation, at large angular momentum L these functions should become an universal function of b, independent on L. This allows to discuss in a rather transparent way the role of statistical and systematic uncertainties in the different long range components of the two-body potential. Implications for peripheral waves obtained in chiral perturbation theory interactions to fifth order (N5LO) or from the large body of NN data considered in the SAID partial wave analysis are also drawn from comparing them with other phenomenological high-quality interactions, constructed to fit scattering data as well. We find that both N5LO and SAID peripheral waves disagree more than 5σ with the Granada-2013 statistical analysis, more than 2σ with the 6 statistically equivalent potentials fitting the Granada-2013 database and about 1σ with the historical set of 13 high-quality potentials developed since the 1993 Nijmegen analysis.

Uniform analytic approximation of Wigner rotation matrices

We derive the leading asymptotic approximation, for low angle {\theta}, of the Wigner rotation matrix elements $d^j_{m_1m_2}(\theta)$, uniform in $j,m_1$ and $m_2$. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

Fixed- t analyticity as a constraint in single-energy partial-wave analyses of meson photoproduction reactions

Partial wave amplitudes of meson photoproduction reactions are an important source of information in baryon spectroscopy. We investigate a new approach in single-energy partial wave analyses of these reactions. Instead of using a constraint to theoretical models in order to achieve solutions which are continuous in energy, we enforce the analyticity of the amplitudes at fixed values of the Mandelstam variable $t$. We present an iterative procedure with successive fixed-$t$ amplitude analyses which constrain the single-energy partial wave analyses and apply this method to the $\gamma p \to \eta p$ reaction. We use pseudo data, generated by the EtaMAID model, to test the method and to analyze ambiguities. Finally, we present an analytically constrained partial wave analysis using experimental data for four polarization observables recently measured at MAMI and GRAAL in the energy range from threshold to $\sqrt{s}=1.85$ GeV.

Comment on ``Solution of the Specific Model of Five-body Problem to Investigate the Effective Alpha--Nucleon Interaction in a Partial-wave Analysis''

Comment on ``Solution of the Specific Model of Five-body Problem to Investigate the Effective Alpha--Nucleon Interaction in a Partial-wave Analysis''

Light Hadron Spectroscopy at BESIII

The BESIII has collected 1.3 billion J/ψ and 478 million ψ(3686) data since 2009. In this talk, we will introduce five recent analyses on light hadron spectroscopy at BESIII, including two studies on the X(1835), two partial wave analyses that are related to searching and studying glueball candidates, and one study on χc1.

Dalitz Plot Analysis of Three-body Charmonium Decays at BABAR

We present results on the measurement of the I=½ Kπ S-wave through a model independent partial wave analysis of ηc decays to K0sK+π− and K+K−π0 produced in two-photon interactions. We also perform Dalitz plot analyses of the J/Ψ decays to π+π−π0, K+K−π0 and K0sK±π∓ produced in the initial state radiation process.

Study of J/ψ and ψ(3686) decays to π+π−η′

Using the data samples of 1.31×109 J/ψ events and 4.48×108 ψ(3686) events collected with the BESIII detector, partial wave analyses on the decays J/ψ and ψ(3686)→π+π−η′ are performed with a relativistic covariant tensor amplitude approach. The dominant contribution is found to be J/ψ and ψ(3686) decays to ρη′. In the J/ψ decay, the branching fraction B(J/ψ→ρη′) is determined to be (7.90±0.19(stat)±0.49(sys))×10−5. Two solutions are found in the ψ(3686) decay, and the corresponding branching fraction B(ψ(3686)→ρη′) is (1.02±0.11(stat)±0.24(sys))×10−5 for the case of destructive interference, and (5.69±1.28(stat)±2.36(sys))×10−6 for constructive interference. As a consequence, the ratios of branching fractions between ψ(3686) and J/ψ decays to ρη′ are calculated to be (12.9±1.4(stat)±3.1(sys))% and (7.2±1.6(stat)±3.0(sys))%, respectively. We also determine the inclusive branching fractions of J/ψ and ψ(3686) decays to π+π−η′ to be (1.36±0.02(stat)±0.08(sys))×10−4 and (1.51±0.14(stat)±0.23(sys))×10−5, respectively.Received 3 September 2017DOI:https://doi.org/10.1103/PhysRevD.96.112012© 2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle decaysParticles & Fields

Measurement of the helicity asymmetry E in ω→π+π−π0 photoproduction

The double-polarization observable $E$ was studied for the reaction $\gamma p\to p\omega$ using the CEBAF Large Acceptance Spectrometer (CLAS) in Hall B at the Thomas Jefferson National Accelerator Facility and the longitudinally-polarized frozen-spin target (FROST). The observable was measured from the charged decay mode of the meson, $\omega\to\pi^+\pi^-\pi^0$, using a circularly-polarized tagged-photon beam with energies ranging from the $\omega$ threshold at 1.1 to 2.3 GeV. A partial-wave analysis within the Bonn-Gatchina framework found dominant contributions from the $3/2^+$ partial wave near threshold, which is identified with the sub-threshold $N(1720)\,3/2^+$ nucleon resonance. To describe the entire data set, which consisted of $\omega$ differential cross sections and a large variety of polarization observables, further contributions from other nucleon resonances were found to be necessary. With respect to non-resonant mechanisms, $\pi$ exchange in the $t$-channel was found to remain small across the analyzed energy range, while pomeron $t$-channel exchange gradually grew from the reaction threshold to dominate all other contributions above $W \approx 2$ GeV.