Phase-function method for complex potentials

We consider the scattering problem for absorptive interactions within the framework of phase-function method. A Green’s function approach is used to derive the phase equation. As a case study we apply the algorithm presented on a shallow α-α potential, the real and imaginary parts of which have been deduced from experimental data. The real and imaginary parts of theS-wave phase shift are found to vary smoothly with energy while those forD andG waves show some fluctuations in the low-energy region. It is shown that studies in spatial behaviour of the phase function provide a plausible explanation for the dynamical origin of these fluctuations.     

Complete Analysis of the ηN S-Wave Scattering-Length Values and Its Natural Limitations in Any Single-Resonance Model

We show that the S-wave ηN scattering length can be extracted in a model-independent way only if the restricting assumption is adopted that one resonance describes the behaviour of the S-wave entirely. To obtain the ηN S-wave scattering length in a model-independent way one needs only two wellknown quantities; the πN elastic S-wave T-matrix at the η-production threshold, and the near threshold π ⁻ p →ηn total cross section slope. The results are independent of the particular parametrization of the elastic πN S-wave T-matrix and of the number of channels used. These assumptions are more general than the assumptions of the existing single-resonance models employed up to now for extracting the ηN S-wave scattering length. We show that the ηN S-wave scattering length value of other single-resonance models agrees with the model-independent estimate if the input data agree with the commonly accepted values. The existence of the upper limit of the real part and the almost fixed value of the imaginary part of the ηN S-wave scattering length are demonstrated, and the nature of limitations originating directly from first principles is explained as the reduction of the full model to the single resonance in the S-wave. The expected differences from the single-resonance estimate for models that are more general is shown. A simple criterion for recognizing the importance of parts of the model that are added in addition to the single resonance in the S-wave is given as well. Received May 15, 1995; revised September 14, 1995; accepted for publication October 11, 1995     

Linear or linear plus Coulomb potential for description of quarkonium spectra?

In previous works we explained theS andP-wave data on heavy quark spectroscopy for the spin-independent potential given by the combination of linear, harmonic or power-law and colour-Coulomb potentials. In the present work, we try to understand the same quarkonium spectra when the spin-independent part of the potential contains the linear potential only and the colour-Coulombic piece is treated perturbatively. We find that the present model cannot explain all the features ofS andP-wave data even at the cost of a large value of QCD scale parameter.     

Properties of<Emphasis Type="Italic">B</Emphasis><Subscript>c</Subscript> meson

The mass spectrum ofcb meson is investigated with an effective quark-antiquark potential of the form -α_c/r +Ar ^νwith ν varying from 0.5 to 2.0. TheS andP-wave masses, pseudoscalar decay constant, weak decay partial widths in spectator model and the lifetime ofB _cmeson are computed. The properties calculated here are found to be in good agreement with other theoretical and experimental values at potential index,ν = 1     

Study of η -production reaction πp → ηn in the near-threshold region⋆

The differential cross-sections (DCS) of the η -production reaction π^- p → ηn are measured at momenta of incident π^- mesons (700, 710 and 720MeV/c) close to the threshold of this reaction. The experiment is carried out at the pion channel of the PNPI synchrocyclotron (with the momentum spread of the pion beam equal to 1.5%) using the Neutral Meson Spectrometer (NMS) designed and created at the Meson Physics Laboratory for detecting two photons from the decay η → 2γ . This spectrometer consisting of two electromagnetic total absorption calorimeter (24 CsI(Na) crystals in each calorimeter) allowed to obtain the DCS in the whole angular range from 0^° to 180^° in the c.m.s. It is shown that at 700MeV/c the DCS angular dependence is isotropic, indicating on the S -wave character of the η -production process while at higher momenta a significant contribution of the D -wave has led to the anisotropic angular dependence having a bowl-like shape.     

TheS 11-P 11 phase shifts of pion-nucleon scattering

TheS ₁₁ andP ₁₁ partial amplitude is calculated using theN/D method. The present calculation differs from the previous ones in the handling of the divergent behavior of the forces due to first-order diagrams, by parameterizing the short-range forces, and in the way of including inelasticity. We obtain the nucleon as a bound state with correct mass and residue and the correctS ₁₁ andP ₁₁ scattering lengths. The calculatedS-wave andP-wave phase shifts and absorption coefficients are in substantial agreement with those from the CERN Theoretical and Almehed-Lovelace phase shift analyses.     

Trace anomaly and chiral symmetry breaking scale in the Nambu and Jona-Lasinio model

Bound state pion production in⁴⁰Ca and¹²⁰Sn nuclei in (p,2p) and (n,d) reactions is investigated. The differential and total cross sections have been obtained. It is shown that the cross sections are determined by the overlap function of the bound states of the nucleon and pion, and as consequence,s-wave part of the pion-nucleus optical potential. The contributions from the nucleons and deuteron distortions are evaluated.The authors would like to express their gratitude to R.A. Eramzhyan, S.N. Gninenko, V.B. Kopeliovich, V.M. Lobashev, B.B. Matveev and E. Oset for very useful and stimulating discussions.     

D-branes inpp-wave background

We show the existence of classical solutions ofD-branes as well as a system ofD3-branes oriented at an arbitrary angle with respect to each other, in a six-dimensionalpp-wave background obtained fromAdS ₃ × S³ ×R ⁴ , withR — R andNS — NS 3-from flux. The world volume coordinate of D5-brane lies along the six-dimensional pp-wave directions, whereas thepp-wave direction is transverse to the system of D3-branes. We also present moreD-brane bound state solutions by applyingT-duality symmetries. The system ofD3-branes oriented at an arbitrary angle is shown to preserve 1/16 supersymmetries. Finally a brief discussion of the open string construction is presented for both the cases.     

An analysis of the mass formulae forS- andP-wave mesons

Mass regularities forS- andP-wave mesons and relations between their masses are discussed. A detailed analysis is given forS-wave mesons which extends the investigations onP-wave mesons reported earlier. Masses for theS- andP-states of all interesting -systems (including toponium states) are predicted. Partial understanding of the mass formulae is obtained within a general potential model approach. Scaling arguments are presented which support the empirical scaling behaviour found for the expectation values determining the spin-splittings in the potential picture.     

Constant-cutoff approach to meson-hyperon couplings

The kaon coupling constants at hyperon-nucleon vertices and the pion coupling constants at hyperon-hyperon vertices are calculated in the framework of the constant-cutoff approach to the CHK bound-state model of hyperons, where the postive-parity hyperons such as Λ, Σ, and ∑^*=∑(1385) are theP-wave bound states of an antikaon and theSU(2) Skyrme soliton, while Λ^* is theS-wave bound state. Meson coupling constants are defined as matrix elements of the meson-source terms between two single-baryon states following the method developed for resolving the Yukawa coupling problem in theSU(2) Skyrme soliton model. The magnitudes of the meson coupling constants are found to be close to those obtained using the complete Skyrme model and the phenomenological values.     

Hadron production near threshold

Final state interaction effects inpp→ pΛK ⁺ andpd →³Heη reactions are explored near threshold to study the sensitivity of the cross-sections to thepΛ potential and theηN scattering matrix. The final state scattering wave functions between Λ andp andη and³He are described rigorously. The Λ production is described by the exchange of one pion and aK-meson between two protons in the incident channel. Theη production is described by a two-step model, where in the first step a pion is produced. This pion then produces anη by interacting with another nucleon     

Compton scattering on the charged pion and the process γγ→π0π0

The Compton scattering on a charged pion and the process γγ→π⁰π⁰ are studied using the dispersion relations. Unknown parameters of the S-wave ππ interaction and a sum and a difference of the π⁰ meson polarizabilities are found from a fit to the experimental data for the γγ→π⁰π⁰ process. The found parameters of the ππ interaction are used for the calculation of the cross section of the elastic γπ^± scattering. The analysis of the obtained results shows that the experimental data for the elastic γπ^± scattering in the energy region up to 1 GeV together with the data for the γγ→π⁰π⁰ process could be used both for a determination of the pion polarizability values and for study of the S-wave ππ interaction. Received: 20 November 1998 / Revised version: 22 January 1999     

Dipolsummenregel bei nichtlokalen Potentialen

The integrated cross section of photonuclear reactions is considered in the electricdipole approximation. The nucleon-nucleon potential used is well-behaved and nonlocal. We use the Tabakin potential, which matchesS-, P- andD-wave phase shifts up to 320 MeV without generating strong short-range correlations.     

Phase shift analysis of pion-4He scattering by optimal polynomial expansion

A novel method of phase shift analysis for the scattering of charged pion from⁴He nuclei is proposed. The nuclear amplitudef _N (ϑ) has been parametrized in terms of a polynomial expansion in a conformally mapped variable, which is obtained by optimally exploiting the analytic property off _N . The method exhibits a significant reduction in the number of free parameters required for the fixed energy phase shift analysis of the differential cross-section data. The nuclear amplitude thus constructed is then used to obtain phase shifts and inelastic parameters of all possible orders. Reliable values of the real and imaginary parts of the forward amplitude are also obtained.     

Analysis of data on proton-proton scattering in the energy range 100–1300 MeV

The results of a partial-wave analysis of data on proton-proton interaction in the energy range 100–1300 MeV are presented. The real parts of phase shifts were found for states of orbital angular momentum up to L = 9, while their imaginary parts were determined for states of orbital angular momentum up to L = 5. The sixth parameter of the S matrix was introduced in order to describe states of total angular momentum J = 2 and 4. The inelasticity thresholds were chosen individually for each state and were found to be substantially different from one another. The resulting solution was characterized by χ ² = 1.155 per point in the case where the number of experimental data was 12 841 and by a large imaginary part of the phase shift in the ³ P ₂-wave state at the edge of the energy range. Special features of the interaction in orbital states are discussed along with the energy dependence of integrated amplitudes and amplitudes of the scattering matrix at zero angle.     

Weak pion production from nuclei

The charged current pion production induced by neutrinos in¹²C,¹⁶O and⁵⁶Fe nuclei has been studied. The calculations have been done for the coherent as well as the incoherent processes assuming Δ dominance and takes into account the effect of Pauli blocking, Fermi motion and the renormalization of Δ in the nuclear medium. The pion absorption effects have also been taken into account     

Optical potential in the gas approximation

Using the gas approximation the optical potential is expressed as a function of the scattering matrix of nucleon-nucleon scattering. The formalism of Green functions is used. The imaginary part of the optical potential in nuclear matter is calculated for high energies using the experimental phase shifts. In addition, a calculation of the imaginary part is made using theS-wave part of the Tabakin potential.     

Systematic trends in the line strengths and radial matrix elements of E1 transitions in the Be isoelectronic sequence

Line strengthS and radial matrix elementσ for the dipole allowed transitions withinn=2 complex of ions in the Be isoelectronic sequence have been fitted in the formsZ ² S=A+B/(Z − C) andZσ=A′ + B′/(Z − C′). The constantsA, B, C andA′, B′, C′ have been calculated by employing a non-linear least square method. The relevant data forS andσ have been taken from calculations which includes correlation effects. It is shown that the fitted yalues ofA andA′ are in excellent accord with their hydrogenic values (Z →α) provided that we express the zeroth-order wavefunction of the ground state 1s²2s^{2 1} S as a quantum-mechanical admixture of the Hartree-Fock (HF) state 1s²2s^{2 1} S and the near-degenerate state 1s²2p^{2 1} S.     

Pion-mass dependence of three-nucleon observables

We use an effective field theory (EFT) which contains only short-range interactions to study the dependence of a variety of three-nucleon observables on the pion mass. The pion-mass dependence of input quantities in our “pionless” EFT is obtained from a recent chiral EFT calculation. To the order we work at, these quantities are the ¹ S ₀ scattering length and effective range, the deuteron binding energy, the ³ S ₁ effective range, and the binding energy of one three-nucleon bound state. The chiral EFT input we use has the inverse ³ S ₁ and ¹ S ₀ scattering lengths vanishing at m _π ^crit = 197.8577 MeV. At this “critical” pion mass, the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We compute the binding energies of these states up to next-to-next-to-leading order in the pionless EFT and study the convergence pattern of the EFT in the vicinity of the critical pion mass. Furthermore, we use the pionless EFT to predict how doublet and quartet nd scattering lengths depend on m _π in the region between the physical pion mass and m _π = m _π ^crit .