Carcass functions in variational calculations for few-body systems

For variational calculations of molecular and nuclear systems involving a few particles, it is proposed to use carcass basis functions that generalize exponential and Gaussian trial functions. It is shown that the matrix elements of the Hamiltonian are expressed in a closed form for a Coulomb potential, as well as for other popular particle-interaction potentials. The use of such carcass functions in two-center Coulomb problems reduces, in relation to other methods, the number of terms in a variational expansion by a few orders of magnitude at a commensurate or even higher accuracy. The efficiency of the method is illustrated by calculations of the three-particle Coulomb systems μμe, ppe, dde, and tte and the fourparticle molecular systems H₂ and HeH⁺ of various isotopic composition. By considering the example of the _Λ ⁹ Be hypernucleus, it is shown that the proposed method can be used in calculating nuclear systems as well.     

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.     

Hybridization and electron interaction in nickel compounds

The bare Coulomb interaction, defined by the reaction 2dⁿ = d^n?1 + d^{n + 1} ? U is determined for some Ni compounds. It is found that U is larger than the 3d bandwidth even for metallic compounds. More relevant to the metal nonmetal transition is the optical gap energy E_G = U ? (E(3d^n?1) ? E(L)) where E(3d^n?1) and E(L) are the d-electron and ligand electron ionization potentials respectively.     

Exponential-trigonometric basis functions in the coulomb four-body problem

Basis functions of a new type—specifically, exponential-trigonometric functions depending on all six interparticle distances—have been proposed for the Coulomb four-body problem. A method has been developed for computing nine-dimensional integrals determining the matrix elements of the Hamiltonian for a four-body system and featuring these functions. The efficiency of the approach that relies on the proposed basis functions has been tested by calculating the e ⁺ e ^? e ⁺ e ^?, p ⁺μ^? p ⁺μ^?, μ⁺ e ^?μ⁺ e ^?, and p ⁺ e ^? p ⁺ e ^? molecules.     

Leptonic polarization asymmetries ate + e − colliders inE 6 theories

We examine the left-right and azimuthal polarization asymmetries of lepton pairs produced ine ⁺ e ^? ande ^? e ^? interactions as probes of new physics resulting fromE ₆ theories. The asymmetries are calculated and compared for the processese ⁺ e ^?→µ ⁺ µ ^?,e ⁺ e ^?→e ⁺ e ^?,e ^? e ^?→e ^? e ^?, ande ⁺ e ^?→L ⁺ L ^? whereL is either anE ₆ exotic, mirror, or fourth generation heavy lepton. Our results show that lepton polarization asymmetries can be used to easily distinguish differentE ₆ models and can be used to distinguish among possible new heavy leptonsL.     

New bounds for dilepton production from heavy neutral leptons

Bounds on 〈E_?ⁿ〉/〈E₊ⁿ〈, 〉E₊E_?〈/〉E₂²〈 and 〈E₊E_?〉/〈E₊〉〈E_?〉 are direved for the processes ν_μN → μ^?μ⁺(e⁺) + X and μN → μ^?μ⁺ + X if dileptons are mediated by a $\text{spin}\text{-}\text{1}\text{2}$ heavy neutral lepton L₀. The bounds are shown to be independent of the production mechanism and mass of L₀. Useful conditional bounds are obtained relating the bounded quantities, which give information about the structure of the weak current responsible for L₀ decay.     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Signals of new gauge bosons at futuree + e − colliders

We analyze possible indirect signals of additional neutral gauge bosons at futuree ⁺ e ^? colliders, concentrating onSU(2) _L ×U(1) _y ×U(1) _y , andSU(2) _L ×SU(2) _R ×U(1) effective theories. We develop a simple formalism to describe these effects and make a careful study of radiative corrections, in particular initial state radiation, which will be shown to have important implications. To make realistic estimates of the sensitivity to the new gauge boson effects, we use a model detector fore ⁺ e ^? annihilation at a center of mass energy of 500 GeV. Using a number of selected physical observables we then show that masses considerably higher than the total energy (up to a factor of 6) can be probed and that distinction between various theoretical models is possible.     

Cross sections and angular distributions of three-jet final states ine + e − annihilation for heavy quarks

The cross sectionsdσ _U ,dσ _L ,dσ _T anddσ _I fore ⁺ e ^?→q \(\bar q\) g are calculated for heavy quarks, and the resultant angular distribution is discussed.     

Spectral and scattering theory for a class of strongly oscillating potentials

Following a recent investigation by Pearson [23] on scattering theory for some class of oscillating potentials, we consider the Schrödinger operator inL ²(IR ⁿ ) given by:H =-e ^?U?·e ^2U ?e ^?U +e ^?2U (F + (?·Q)). HereU andF are real functions ofx, andQ is a IR ⁿ -valued function ofx, such that:

1. U is bounded, and the local singularities ofF andQ ² are controlled in a suitable sense by the kinetic energy,
2. U, Q, andF tend to zero at infinity faster than ‖x‖^?1. We defineH by a method of quadratic forms and derive the usual results of scattering theory, namely: the absolutely continuous spectrum is [0, ∞) and the singular continuous spectrum is empty, the wave operators exist and are asymptotically complete. This enlarges the class of already studied strongly oscillating potentials that give rise to the scattering and spectral properties mentioned above.

     

Bounds on the masses of neutral generation-changing gauge bosons

The existence of several generations of quarks and leptons suggests the possibility of a gauge symmetry connecting the different generations. The neutral gauge bosons of such a scheme would mediate rare processes such as K_L⁰→μ^±, K⁺→π⁺e^?π⁺, μN→eN and would contribute to ΔM(K_S⁰?K_L⁰). We study these and other processes within a simple theoretical framework and derive bounds involving the masses and coupling constants of the generation-changing gauge bosons and various generation-mixing angles. The lower bounds for the relevant masses lie in the 10–100 TeV region. Various remarks concerning the relevance of these bounds to currently popular theoretical ideas and to future experiments are presented.     

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.     

Natural left-right symmetry,atomic parity experiments and asymmetries in high energy e+e− collisions in petra and pep regions

The previously proposed left-right-symmetric SU(2)_L × SU(2)_R × U(1) theory permits one of the two neutral gauge particles N₁ and N₂ to be particularly light (<mW⁺_L) compatible with all neutrin-data and the present atomic parity experiments. Distinguishing features of this theory (with the light mass solution) for e^?e⁺ → μ⁺μ^? and π⁺π^? at PETRA and PEP energies as compared to the SU(2) × U(1) predictions are given.     

Analytical structure and properties of Coulomb wave functions for real and complex energies

The radical Coulomb wave functions are analysed in their dependence on the energy E considered as a complex parameter. Repulsive and attractive fields are both considered. First turning to the function Φ_l ∝ r^?l?1F_l introduced by Briet, slightly modifying its definition, and assuming that the angular momentum is also a complex parameter, for which the notation L is used, it is proved that Φ_L is an entire function of both E and L. From an expansion of the regular Whittaker function given by Buchholz, the Taylor expansion of Φ_L in powers of E and a simple recurrence relation for its coefficients are easily obtained. The expansion of the regular function F_l is readily obtained from that of Φ_L for L = l, but the irregular function G_l contains Φ_l and $\text{?Φ}{}_{\mathrm{L}}\text{?L}$ for L = l and ?l?1. Having proved that the expansion obtained for Φ_L in powers of E can also be regarded as a uniformly convergent series of entire functions of L, the derivative $\text{?Φ}{}_{\mathrm{L}}\text{?L}$ can be obtained by term-by-term derivation. This method for obtaining the expansion of G_l is straightforward and leads to a final result involving essentially: (i) the conventional function $\text{h(η) =}\text{1}\text{2}\text{ψ(1 + iη) +}\text{1}\text{2}\text{ψ(1 ? iη) ?}\text{ln}\text{η}$ which is singular at η = ∞, i.e., at k = 0; (ii) two entire functions of E, namely Φ_l and Ψ_l; the terms of the expansion of the latter in powers of E contain only Bessel functions multiplied by Bernoulli numbers and coefficients easily obtained from a simple recurrence relation. As an application of the above results, the last sections contain: (i) an alternate from of G_l expansion useful in numerical computations; (ii) the definition and expansion of two linearly independent solutions of the Coulomb equation which are entire in E; (iii) the expansion and threshold properties of the outgoing and incoming solutions, O_l and I_l, corresponding to those we have obtained for F_l and G_l.     

Angular distributions of electrons in the (γ, 2e) reaction andee-correlations in the atom

The cross sectionsd ³ σ/dE ₁ d n ₁ d n ₂ for the Ar (γ, 2e) Ar⁺⁺ process are calculated on the basis of the diagram approach within the energy intervalω=400–650 eV as functions of the angleθ ₁₂ between final electrons with equal energiesE ₁=E ₂ for several levels of the final Ar⁺⁺ ion. It has been elucidated that the interference of amplitudes corresponding to the interaction in the final and initial states is of prime importance. The angular distributions over the angleθ ₁₂ are very sensitive to the term of the final ion. There are numerous data for the experimental verification of the theory, in particular, for the selection of leading diagrams. The (e, 3e) experiment is also desirable.     

Relationship between charge transfer energies of Yb and Sm and crystal environmental factor

Relationship between charge transfer energies E_CT of Yb³⁺ and Sm³⁺ and environmental factors h_e in various crystals was investigated using a dielectric chemical bond method. Both results show that they have an exponential relation E_CT=A+B exp(−kh_e), but the exponential factors are different, which indicates that the interaction between the rare earth ions and environment is connected with the kind of rare earth ion. This result provides a method of determining charge transfer energies of Yb³⁺ and Sm³⁺ from a crystal structure.     

The upper and lower bounds of energy for nuclear and coulomb few-body systems

The upper and lower bounds of energy are found for three-, four-, and five-particle nuclear and Coulomb systems in the framework variational method with the trial functions of exponential and Gaussian types. The two-sided estimates of energy not only allow one to fix the limits for the exact value of energy but also provide an additional opportunity for extrapolation of the variational estimates to the exact value of energy. This allows one to reduce the volume of calculations by shortening the number of trial functions without the loss of accuracy.     

Bounds on fourth-generation fermion masses in the standard model

In the standard model, if the ratios of Yukawa couplings to gauge couplings are bounded functions of the renormalization point, then the fourth-generation fermion massesm _U , m _D , andm _L (in GeV) are constrained to lie within a domain approximately given by (m _U /213)^4.8+(m _D /209)^4.8+(m _L /161)^2.4<1.