Hyperspherical Three-Body Calculation for Exotic Atoms

Ground state energies of atomic three-body systems like negatively charged hydrogen, normal helium, positively charged-lithium, beryllium, carbon, oxygen, neon and negatively charged exotic- muonium and positronium atoms have been calculated adopting hyperspherical harmonics expansion method. Calculation of matrix elements of two body interactions needed in the hyperspherical harmonics expansion method for a three body system is greatly simplified by expanding the bra- and ket-vector states in the hyperspherical harmonics (HH) basis states appropriate for the partition corresponding to the interacting pair. This involves the Raynal–Revai coefficients (RRC), which are the transformation coefficients between the HH bases corresponding to the two partitions. Use of RRC become particularly essential for the numerical solution of three-body Schr?dinger equation where the two-body potentials are other than Coulomb or harmonic. However in the present work the technique is used for two electron atoms ¹H^?(p ⁺ e ^? e ^?), D^?(d ⁺ e ^? e ^?), Mu^?(μ ⁺ e ^? e ^?),⁴He(⁴ He ²⁺ e ^? e ^?),⁶Li(⁶ Li ³⁺ e ^? e ^?),¹⁰Be(¹⁰ Be ⁴⁺ e ^? e ^?),¹²C(¹² C ⁶⁺ e ^? e ^?),¹⁶O(¹⁶ O ⁸⁺ e ^? e ^?) etc. and the exotic positronium negative ion Ps ^?(e ⁺ e ^? e ^?) where the interactions are purely Coulomb. The relative convergence in ground state binding energy with increasing K _max for ²⁰Ne has been demonstrated as a representative case. The calculated energies at K _max ?=?28 using RRC’s have been compared with those obtained by a straight forward manner in some representative cases to demonstrate the appropriateness of the use of RRC. The extrapolated energies have also been compared with those found in the literature. The calculated binding energies agree within the computational error.     

Screening effect of the coulomb interaction on the energy levels of atomic and molecular systems

The energies of atomic and molecular systems with a screened Coulomb interaction are expressed in terms of properties of the system with a conventional Coulomb interaction to the third order in the screening constant. The energy levels of an H atom, an H^? ion, and nonadiabatic systems, namely, the positronium ion e ⁺ e ^? e ^? and the positronium molecule e ⁺ e ⁺ e ^? e ^?, are calculated for screened Coulomb interactions of charged particles. It is demonstrated that, as the screening constant of the Coulomb interaction increases, the stability of the hydrogen atom, the H^? ion, and the positronium molecule e ⁺ e ⁺ e ^? e ^? decreases, whereas the stability of the positronium ion e ⁺ e ^? e ^? increases after a slight decrease.     

On accurate computations of slowly convergent atomic properties in few-electron ions and electron-electron correlations

We discuss an approach to accurate numerical computations of slowly convergent propertiesin two-electron atoms/ions which include the negatively charged Ps^? (e^?e⁺e^?)and H^? ions, Heatom and positively charged, helium-like ions from Li⁺ to Ni²⁶⁺. All these ions areconsidered in their ground 1¹S-state(s). The slowly convergent properties selected inthis study include the electron-nulceus (r^2k_eN) and electron-electron (r^2k_ee) expectation values for k = 2, 3, 4 and 5.     

High-field EPR Study of the Effect of Chloride on Mn2+ Ions in Frozen Aqueous Solutions

The effect of chloride concentration on Mn²⁺ (S = 5/2, I = 5/2) ions in frozen aqueous solutions is studied by high-field high-frequency electron paramagnetic resonance (HFEPR). The usually six sharp lines characteristic of Mn²⁺ ions, arising from the m _s  = ?1/2 → 1/2 transition, is modified by the addition of Cl^? anions and the six resonances become much broader and more complex. This new feature likely arises from the ligation of one Cl^? anion to a hydrated Mn²⁺ ion forming a [Mn(H₂O)₅Cl]^? complex. This complex increases linearly with Cl^? concentration with an association constant of K _{a, apparent} = 61 M^?1. The structure of the putative chloride complex was studied using density functional theory calculations and the expected zero-field interaction of such a manganese center was calculated using the superposition model. The predicted values were similar to those determined from the simulation of the spectrum of the m _s  = ?5/3 → ?3/2 transition of the chloride complex. This effect of Cl^? anions occurs at biologically relevant concentration and can be used to probe the Mn²⁺ ions in cellular and protein environments.     

Precise measurement of Γ(K→e ν(γ))/Γ(K→μ ν(γ)) and study of K→e ν γ

We present a precise measurement of the ratio R _K =Γ(K→e ν(γ))/Γ(K→μ ν(γ)) and a study of the radiative process K→e ν γ, performed with the KLOE detector. The results are based on data collected at the Frascati e ⁺ e ^? collider DAΦNE for an integrated luminosity of 2.2 fb^?1. We find R _K =(2.493±0.025_stat±0.019_syst)×10^?5, in agreement with the Standard Model expectation. This result is used to improve constraints on parameters of the Minimal Supersymmetric Standard Model with lepton flavor violation. We also measured the differential decay rate dΓ(K→e ν γ)/dE _γ for photon energies 10<E _γ < 250 MeV. Results are compared with predictions from theory.     

Recent results on multiple ionization and fragmentation of negatively charged fullerene ions by electron impact

Employing the dynamic crossed-beams technique, the absolute cross sections of the electron-impact multiple ionization and fragmentation of mass-selected negatively charged fullerene ions C _m ^? → C _m?n ²⁺ (m=60, 70, 84; q=1, 2, 3; n=0, 2, 4) were measured. The electron energy varied from the respective threshold up to 1 keV. A scaling law was observed for the cross-section magnitude as a function of the fullerene size m and the charge state q of product ions. The data indicate that different mechanisms account for the detachment of an extra electron from the negatively charged fullerene and the formation of a positively charged ion, respectively. Moreover, the multiple ionization of a fullerene anion is found to be a sequential process. A novel ionization mechanism is proposed which might be expected to be valid for all negatively charged molecular or cluster ions able to shield the attached electron from the incident electron.     

S-Wave Shape Resonances in the Ps− System

We have investigated the S-wave shape resonance states of the positronium negative ion (Ps^?) system. The resonance poles are traced from H^? system to Ps^? by systematically varying the mass of the positively charged particle from infinitely heavy to one unit of the electron mass. The shape resonances that associated with and lying above the Ps(N = 2, 3, 4 and 5) thresholds are located by employing the complex-coordinate rotation method with highly correlated Hylleraas-type wave functions. It has been shown that the Ps^?(N = 3) shape resonance lies at an energy which is higher than the Ps(N = 4) thresholds and even the Ps^?(N = 4) shape resonance. An explanation was given to shed light on such phenomena.     

Calculations of Coulomb systems with optimization of nonlinear parameters

Precise variational calculations of the energy and diverse physical characteristics are performed for the ground state of a fully nonadiabatic four-particle system—the positronium molecule e⁺e^?e⁺e^?. The nonlinear exponential parameters of correlated Gaussian basis functions dependent on all interparticle separations are systematically optimized. The dependence of the calculated energy values and the expectation values of interparticle separations (as well as their degrees and Dirac delta functions of interparticle separations) on the basis size N is examined. For N=200, the ground-state energy of the positronium molecule is found to be E=?0.5160028 au. For an extended basis set with N=4700 containing 200 basis functions with the optimized parameters and 4500 additional functions with random values of nonlinear parameters, E=?.5160036 au. At present, this result is the most accurate variational energy value of the positronium molecule, and it demonstrates the high efficiency of optimization of the nonlinear parameters in calculations of atomic-molecular systems. The lifetime of the positronium molecule e⁺e^?e⁺e^? with respect to electron-positron annihilation is calculated to be τ=2.26×10^?10 s.     

Quadrupole moments and the structure of the even titanium and chromium nuclei

The energies of the six circular transitions (n = 13 → n = 12 through n = 8 → n = 7) of the K^?Pb exotic atom have been measured to high precision (typically ～ 50 ppm) using Ge (Li) spectrometers. The data acquisition system was computer controlled and stabilized, the energy calibration spectrum was taken simultaneously with the data spectrum. The experimental energies of the six transitions were corrected for ADC nonlinearities and data-calibration spectrum shifts, as well as the presence of unresolved noncircular transition contaminants. The energies of five of the transitions (13 → 12 through 9 → 8) were computed from quantum electrodynamics, including all significant orders of vacuum polarization, electron screening and nuclear polarization. The mass of the K^? was adjusted to achieve a best fit with the experimental energies: the result was m_K^? = 493.657 ± 0.020 MeV.     

Equilibrium temperature of hadrons

The temperatureT of hadrons frome ⁺ e ^? annihilation is analyzed using the SPEAR and the PLUTO data. Thermal equilibrium is found for π,K and ρ andT～E _c.m ^α with α=0.31±0.05. A discussion is given on the equipartition of energy between broad resonances and particles from their strong decay, and its application to estimate the quark mass difference:m _s?m_u=0.11 andm _c?m_u=1.60 GeV.     

A precise determination of the τ-mass

The energy dependence of the cross sections for e⁺e^? → e^±(μ^±) + 1 charged track has been measured for centre of mass energies between 3.60 and 4.40 GeV. The pair production of the τ-lepton is observed at all energies and the τ-mass is determined to be 1.787_?0.018^+0.010 GeV from a fit to the energy dependence of the cross section.     

Accumulation of three-body resonances above two-body thresholds

We calculate resonances in the three-body system with attractive Coulomb potential by solving homogeneous Faddeev-Merkuriev integral equations for complex energies. The equations are solved using the Coulomb-Sturmian separable expansion method. This approach allows us to study the exact behavior of the three-body Coulomb systems near the threshold. A negatively charged positronium ion is used as a test case. In addition to locating all previously known S-wave resonances of the positronium ion, we also find a large number of new resonant states that accumulate just slightly above the two-body thresholds. The pattern of accumulation of resonant states above the two-body thresholds suggests that probably they are infinite in number. We conjecture that this may be a general property of the three-body system with an attractive Coulomb potential.     

SU(2)×U(1) effects in e+e− annihilation: Generalized charge asymmetry

The observability of the SU(2)×U(1) electroweak charge asymmetry effects in e⁺e^? annihilation at $\text{s}\text{=29}\text{GeV}$ is addressed in the context of a Feynman-Field type fragmentation model. We assume three colors of five flavored quarks and one heavy lepton τ. We neglect, at this time, the hard gluon bremsstrahlung events. We take b→c+X as the b-decay mode and we assume all τ's and heavy hadrons decay within the resolution of the detector so thatonly light hadrons and leptons are detected. Allowing all these decays to occur, we then compute the expected front-back asymmetry of negatively charged particles weighted with zⁿ for z?0.0175, where n = 0.5, 1…, 7, 10, and z is the light-cone momentum fraction. We find, for example, that such an asymmetry is ≈5% for n=2for sin²θ_w=0.236 and Λ_{QCD=0.34 GeV}. In other words, due to the large number of charge particles produced per event, this SU(2)×U(1) charge asymmetry may be accessible experimentally in e⁺e^? → X already at PEP and PETRA energies.     

Study of some rare decays of the K+ meson

In a search for very rare decays of the K⁺ meson we observed the K⁺→μ⁺νe⁺e^? and K⁺→e⁺ν e⁺e^? modes with branching ratios of (10±3) ×10^?7 and (2⁺²_?2)×10^?7 respectively. We also put new limits on a decay allowed by the alternate scheme of lepton conservation K⁺→π^?μ⁺e⁺, on a decay with double charged weak current K⁺→π^? e⁺e⁺ and on other forbidden decays K⁺→μ^?νe⁺e⁺ and K⁺→π⁺μ^±e^±.     

Proof of comparable K-pair and π-pair production from time-like photons of 1.5, 1.6, and 1.7 GeV and determination of the K-meson electromagnetic form factor

The observation of 21 K⁺K^? pairs in 38 hadron pair events produced at 1.5, 1.6, and 1.7 GeV total centre-of-mass energies in e⁺e^? annihilations, establishes that time-like photons produce K pairs and π pairs with comparable rates in this energy range. The K-meson electromagnetic form factor at a mean s-value of 2.4 GeV² is measured to be |F_K| = 0.50±0.08. The number of e⁺e^? pairs observed in the same angular and energy range is 5148.     

Investigation of piezoelectric properties of crystals using surface excitation of ultrasonic waves and some results for ferroelectric triglycine sulphate

The surface excitation of ultrasonic waves as a new method of investigation of piezoelectric properties of materials is suggested and experimental results specified to theZ-direction of a single crystal of triglycine sulphate (TGS) are reported. It has been found that the piezoelectric stress constant e₂₃ of TGS depends on temperatureθ as:e ₂₃=K ₂₃(θ_c?θ)^?1 whereK ₂₃=(31±0.5) As m^?2 deg andθ _c=49.6°C. The influence of an externally applied d.c. electric field has been studied in order to account for a residual excitation of ultrasonic waves in TGS at temperatures above the Curie point.     

New limits on the single-γ decay of orthopositronium

We have searched for the exotic annihilation of orthopositronium, o-Ps → a⁰ + γ, where a⁰ denotes a neutral particle of mass m_a < 2m_e. For the ratio of this decay mode to the 3γ decay mode, upper limits have been derived in the range 5 × 10^?6?1 × 10^?6 (for m_a varying from 100 to 900 keV). This result excludes the hypothesis that this exotic decay is responsible for the discrepancy between the theoretical and experimental values of the orthopositronium lifetime.     

Multipion production below 1.1 GeV by e+e− annihilation

The production of multipion events by e⁺e^? annihilation has been measured at centre of mass energies 915,990 and 1076 MeV. Both channels e⁺e^?→π⁺π^?π^o and e⁺e^?→π⁺π^?π⁺π^? have been analysed. An energy threshold effect analysed. An energy threshold effect around 919 MeV (m_ω + m_π^o) has been evidenced for the π⁺π^?π^oπ^o channel and the cross section is consistent with the quasi two-body process e⁺e^?→ωπ^o. The cross section for π⁺π^?π⁺π^? is lower by an order of magnitude and increases with the energy.     

Formation of doubly charged negative ions under the conditions of the resonant electron capture by fluorofullerenes

Doubly charged negative ions formed when electrons with controlled energies interact with isolated fluorinated fullerene molecules C₆₀F _n (n = 36, 48) have been detected and investigated by resonant electron capture mass spectrometry. The dependence of the intensity of the formation of doubly charged negative ions of fluorofullerenes on the energy of attached electrons has been measured. An original method, which is based on the experimental data and does not require additional calibration quantities, has been developed for estimating the absolute cross section for the formation of doubly charged negative ions. The absolute cross sections for the formation of the most intensely formed ions C₆₀F ₃₆ ^2? and C₆₀F ₄₈ ^2? are estimated to be about 1.1 × 10^?24 and 1.5 × 10^?24 m² at their maximum-yield energies of 2.0 and 1.6 eV, respectively.     

Crystal Structure,Luminescence and Triboluminescence of the Complex [Eu(NO<Subscript>3</Subscript>)<Subscript>2</Subscript>3hmpa] NO<Subscript>3</Subscript>·HQuin

The atomic structure of crystals of the complex [Eu(NO₃)₂3hmpa] NO₃·HQuin , (hmpa – hexamethylphosphortriamide, HQuin – quinaldic acid) characterized by intensive luminescence and triboluminescence has been determined by the X-ray method. The noncentro-symmetric crystals of the compound are rhombic : a = 16.8193(3), b = 12.2877(2), c = 27.6516(5) Å, пр. гр. Pca2(1), Z = 4, ρ _{calc. .} = 1.427 g/сm³. The crystals have a structure of the insular type which is presented by the isolated complex molecules, outer-sphere NO₃ ^? – groups, and neutral molecules of quinaldic acid. Some structural aspects of formation of the luminescent and triboluminescent properties of the compound were discussed: the role of break planes in the crystal destruction was revealed.