Scattering length and effective range in closed form for the Coulomb plus Yamaguchi potential

From the known expression for the off-shell T-matrix corresponding to the potential consisting of the sum of the Coulomb potential and the Yamaguchi potential, the physical scattering amplitude can be derived in a satisfactory way. We derive simple exact closed formulae for the scattering length a_cs and the effective range r_cs from this amplitude. These are compared with approximate formulae derived by Harrington. Also a few numerical calculations are reported and compared with results obtained by Harrington and by Ali et al.     

A low-lying resonance in the spectrum of H

It was proved by Pekeris⁽¹⁾ that the singly excited states of H^- lie exactly at, or slightly above, the ground state of hydrogen. Using a theory of Fano,⁽²⁾ these fictitious states will have a configuration interaction with the H^- continuum. The strength of this configuration interaction is computed for the mixing of a 1s2p¹P⁰ state with the H^- continuum for different values of the fictitious binding energy of the 2p valence electron. In every case, the effect of the configuration interaction is to induce a rapid change of the phase shift of the continuum wave function by a quantity of π/2 over an energy range of a few times 0.01 eV, at an energy somewhat above the hydrogen ground state. The variation from π/2 to π is much slower. Such a swift change of the phase shift may be identified with the occurrence of a low-lying shape resonance.     

The Callan-Symanzik equation and dimensional regularization

A study is made of the Callan-Symanzik equation using the dimensional regularization method. The final equation is far more general than in the usual derivation in that the effect of mass terms is explicitly included; moreover the momenta need not be restricted to the deep-Euclidean region when considering asymptotic limits.     

Isobaric analogue resonances in proton elastic scattering from 84Sr

The cross section for the reaction ⁸⁴Sr(p, p₀)⁸⁴Sr has been measured for proton energies in the range E_p = 4.18?6.73 MeV. Resonance parameters were determined for 15 isobaric analogue resonances. Spectroscopic factors calculated for the analogues by means of the R-matrix theory and the Green function method are compared with Spectroscopic factors determined from the ⁸⁴Sr(d, p)⁸⁵Sr reaction. Angular distributions were measured at E_p = 7 and 12 MeV in order to obtain optical model parameters.     

Elastic scattering of 40Ar on 40Ca at Elab = 191, 236 and 272 MeV

Cross sections for elastic scattering of ⁴⁰Ar on ⁴⁰Ca have been measured at energies E_lab = 191, 236 and 272 MeV employing position-sensitive detectors and the method of kinematical coincidences. The experimental data are first compared with the ordinary and the generalized Fresnel models. Only the generalized Fresnel model describes the experimental data well. An optical model analysis with a Woods-Saxon potential yields an energy independent set of parameters (V_R = ?21.76 MeV, r_OR = 1.37 fm, a_R = 0.45 fm; W₁ = ?13.69 MeV, r₀₁ = 1.40 fm, a₁ = 0.36 fm) very similar to the one found in ⁴⁰Ca-⁴⁰Ca scattering at corresponding energies. Values deduced for the total reaction cross sections for the three energies are in good agreement with those predicted by the generalized Fresnel model. The data are also compared with optical model calculations with the real part of the potential replaced by various microscopically determined potentials. The proximity, Fleckner-Mosel and the Krappe-Nix-Sierk potentials like the phenomenological optical model potential reproduce the measured data fairly well over several orders of magnitude.     

Laser spectroscopic properties of Nd3+ -doped tellurite glasses

The stimulated emission cross-section σ and fluorescence lifetime for the 1.06 μm emission (⁴F_3/2 →⁴I_1/12) have been measured for a number of Nd-doped tellurite glasses. The measured value of σ ? 9 × 10^-20 cm ² for the tellurite glasses is to be compared with the value of 3.5 × 10^-20 cm ² for the ED-2 glass. Based on the measured spectroscopic parameters, an LED-pumped tellurite glass fiber laser is predicted to perform better than ED-2 glass, both in the longitudinal and transverse pumping configuration. The threshold for side-pumped tellurite glass laser can be comparable or even lower than that in Nd:YAG.