Effective-range function for doublet nd scattering from an analysis of modern data

The parameters of the generalized effective-range function K(k ²) having a pole are found by using the results that were obtained by calculating the S-wave phase shift δ(E) for doublet nd scattering and the triton binding energy on the basis of Faddeev equations and within the N/D method and which were presented in the literature. The convergence of the expansion of K(k ²) in powers of momentum is studied. The binding energy of the virtual triton and the residues of the partial-wave scattering amplitudes at the poles corresponding to the bound and virtual states are calculated. Correlations between the binding energies of the bound and virtual states of the triton, on one hand, and the doublet scattering length for nd interaction, on the other hand, are considered. The function K(k ²) is also calculated within a two-body model featuring various potentials.     

Four-wave mixing and hyper-Raman scattering in CuCl

Non-degenerate four-wave mixing using two non-collinear laser beams with frequencies (wavevectors) ω_p, ω_t (k_p, k_t) respectively is studied in CuCl. Two emission lines at frequencies ω⁽¹⁾=2ω_t-ω_p, and ω⁽²⁾=2ω_p-ω_t are observed. Their excitation spectrum is sharply peaked if the phase-match condition k⁽¹⁾=2k_t-k_p is fulfilled. This is the case, if ω_p coincides with the hyper-Raman lines (R⁺_T, R^-_T) of the laser labelled (t) in a well-defined geometrical configuration.     

The vertex constant for the virtual decay of a nucleus into two charged particles within the effective range theory

Explicit expressions for the virtual a → b + c decay vertex constant (or the asymptotic normalization factor) for charged particles b and c are obtained for the first time using the effective range function K(k ²) for the standard effective range expansion and for the case where K(k ²) has a pole. The bound and resonant states of the ²He nucleus and the resonant states of the ²He and ⁸Be nuclei are considered as physical examples. A trajectory in the complex momentum plane is constructed for the transition from the resonant state to the virtual state while the Coulomb interaction gradually decreases.     

Inverse scattering with non-overdetermined data

Let A(β,α,k) be the scattering amplitude corresponding to a real-valued potential which vanishes outside of a bounded domain D⊂R³. The unit vector α is the direction of the incident plane wave, the unit vector β is the direction of the scattered wave, k>0 is the wave number. The governing equation for the waves is [∇²+k²−q(x)]u=0 in R³. For a suitable class M of potentials it is proved that if Aq₁(−β,β,k)=Aq₂(−β,β,k),∀β∈S², ∀k∈(k₀,k₁), and q₁, q₂∈M, then q₁=q₂. This is a uniqueness theorem for the solution to the inverse scattering problem with backscattering data. It is also proved for this class of potentials that if , ∀k∈(k₀,k₁), and q₁, q₂∈M, then q₁=q₂. Here is an arbitrarily small open subset of S², and |k₀−k₁|>0 is arbitrarily small.     

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V_j(x) can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k₀²±i0)|k′〉, |k| = |k′| = k₀, then each t_j is also on-shell.     

Debye-waller factor for electron scattering by surface atoms

The contribution of anharmonic atomic vibrations to the EXAFS-spectrum is described by the third cumulantσ(³) which contributes with a term proportional tok ³ to the phase in the single scattering plane wave approximation. Due to the lattice expansion and enhancedσ(²) in the surface region we get additional temperature dependent contributions, which are evaluated in a curved wave theory. Transforming this expression into the basic formula we get an additional term proportional tok ³ in the phase of the generalized scattering amplitude. This valueΔα(³) has to be subtracted to get a value forσ(³). Numerical results at the O-K-edge of NiO give a value forΔσ(³) of about 10^?4 ų.     

Measurement of the real part of the forward scattering amplitude in K±p elastic scattering at 10.4 and 14 GeV/c

The differential cross section for K^±p elastic scattering has been measured in the very low t region (0.003 < t < 0.2 GeV²) in a wire chamber spectrometer experiment at 10.4 and 14 GeV/c. The interference effect observed between the Coulomb and the nuclear interaction has been used to determine α, the ratio of real to imaginary part of the forward scattering amplitude. At 10.4 GeV/c we measure α(K⁺p) = ?0.21 ± 0.06 and α(K^?p = 0.08 ± 0.04, and at 14 GeV/c, α(K⁺p) = ? 0.13 ± 0.03 and α(K^?p) = 0.000 ± 0.04 in agreeement with the predictions of dispersion theory calculation.     

Experimentelle Untersuchungen am Elektroneneinfang des Mangan 54 und Zink 65

The electron capture decay of Mn 54 and Zn 65 was investigated using Na I(Tl)-detectors. Spectroscopic-coincidence techniques were employed to examine theK-electron capture rates of Mn 54 and Zn 65, the branching ratio and positron rate of Zn 65. The experimental results are:P _k ω _k (Mn)=0.2492±0.0017,P _k ω _k (Zn)=0.3927±0.0026,EC ^* /EC ⁰(Zn)=53.2±1.0/46.8±1.0,γ/β ⁺=35.1±1.7,K ⁰/β ⁺=27.7±1.5. Thus electron capture to the excited state of Cu 65 occurs to the extent of 52.4±1.0% while electron capture and positron decay to the ground state were found to be associated with 46.1±1.0% and 1.49±0.05% of the disintegrations. These data partly disagree significantly from measurements of other authors. Using the fluorescence yieldsω _k (Cr)=0.279 andω _k (Cu)=0.4425, deduced from other measurements, values ofL+M/K of electron capture to the excited state could be derived:L+M/K(Mn 54)=0.120±0.015 andL+M/K(Zn 65)=0.127±0.015. These ratios agree with the calculations ofBahcall. The half-lives of Mn 54 and Zn 65 have been determined to beT _1/2(Mn 54)=312±5d,T _1/2(Zn 65)=243±4d The energy of the Zn 65-γ-rays was measured with a Ge(Li)-counter:E ^γ=1115.5±0.5 keV.     

Radiation transfer due to a point source in an isotropically scattering,inhomogeneous solid sphere

A method of analysis is presented for solving radiation transfer due to a point source in an absorbing, isotropically scattering, inhomogeneous sphere, which is subjected to a diffusely reflecting boundary. The space-dependent single-scattering albedo is represented in the form ω(r) = Σ^K_k=0 D_K r^k, where r is the optical variable and D_k are the known expansion coefficients. The effects of various functional forms of albedo on the incident radiation, angular distribution of radiation intensity and emissivity are examined.     

Effect of Coulomb forces on the position of the pole in the scattering amplitude and on its residue

The vertex constant for the virtual decay of a nucleus to two charged particles having an arbitrary orbital angular momentum l was explicitly obtained for the first time in the case of a standard expansion of the effective-range function K _l (k ²), as well as in the case where the function K ₀(k ²) has a pole. The bound state of the 3He nucleus and the resonance states of the ²He and ³He nuclei in the S wave, as well as the resonance states of the ⁵He and ⁵Li nuclei in the P wave, are studied as physical examples. For the Np and N d systems, the trajectories of the pole in the complex planes of the momentum and the corresponding renormalized vertex constant are constructed for the transition from a resonance state to a virtual state as the Coulomb interaction is switched off gradually.     

Amplitude analysis of Kaon-nucleon scattering data

The KN scattering amplitudes have been extracted from experimental data in the energy range 3 ? k ? 14 GeV/c and for transfer values between ?0.05 and ?0.6 GeV².The ω and P+f helicity-flip amplitudes and the A₂ helicity non-flip amplitude have been neglected; it is shown, that these simplifications are compatible with the data and have no significant influence on our results. One needs to assume the approximate validity of SU(3) symmetry for the ? and A₂ couplings. A very important constraint for this analysis comes from recent experimental data for the reaction K_L⁰p → K_S⁰p. The results for A₂ and ω exchanges are analysed as functions of momentum transfer and energy and we test several current theoretical ideas. Information about f-exchange is also obtained when some further assumptions are made concerning SU(3) symmetry and duality at t = 0. Extrapolating the amplitudes to t = 0 a comparison is made with dispersion relation calculations; at other t-values we compare with results obtained from finite energy sum rules and other analyses based on fixed f analyticity. The predictions for KN data which have not been considered in this analysis are shown to be in good agreement. One of our results is that the ?-ω universality rule is approximately satisfied; we also find a strong indication for a peripheral behaviour of the imaginary part of the non-flip f-exchange amplitude.     

Measurement ofK-electron capture probability (P k ) in the decay of197Hg (64.1 h)

TheK-electron capture probability (P _K ) for the 268.7 and 77.3 keV states of¹⁹⁷Au in the decay of¹⁹⁷Hg (64.1h) have been determined from theKX-ray gamma ray summing in a HPGe X-ray detector. The measured values,P _k (268.7)=0.746±0.033 andP _k (77.3)=0.774±0.036 are found to be in good agreement with the theoretical results.     

Effects of finite size and shape on scattering and thermodynamic quantities at 2D Ising critical points

Using recent results by Cardy based on the conformal invariance of critical correlation functions we calculate universal results for scattering functions S(k), susceptibilities, correlation lengths and specific heat correction terms for finite Ising systems in two dimensions with circular and rectangular shapes and free boundary conditions. Our results specify the effect of shape on these quantities at the critical point. In particular, the half-width and lineshape of the scattering function is found to be strongly influenced by geometry. For a circle, S(k) follows the infinite system behavior 1/k^2−η, η = 0.25 only for very large k. For a substantial range of intermediate k values it is well represented by 1/k^2−η_app, with an “apparent” exponent η_app. We also discuss the probable influence of end, edge and domain wall effects on the correlation lengths, susceptibilities and specific heat correction terms. The application of our results to experimental systems and other theoretical models is considered.     

Role of metastable atoms and molecules of helium in excitation transfer to hydrogen atoms

The afterglow of a discharge in helium with a small admixture of hydrogen is studied spectroscopically (p=40 Torr, [e]≤10¹¹ cm^?3). The time-resolved measurements of intensities of the first four lines of the Balmer series are performed. The concentrations of metastable helium atoms and molecules are evaluated from the relative intensity of the absorption lines. The ratios of excitation transfer rates from atoms He(2 ³ S ₁) k ₁(n) and molecules of helium He₂(a 2sσ ³Σ _u ⁺ ) k ₂(n) to atomic hydrogen H*(n) are measured to be k ₁(n=3)/k ₂(n=3)=0.04±0.02 and k ₁(n=4)/k ₂(n=4)=0.01±0.02. The ratios of excitation rate constants k ₂(n) corresponding to different states H(n) are measured to be k ₁(n=4)/k ₂(n=3)=0.023±0.01; k ₁(n=5)/k ₂(n=3)≤0.013; and k ₁(n=6)/k ₂(n=3)≤0.007.     

A multi-channel scattering theory for some time dependent Hamiltonians,charge transfer problem

Scattering theory for time dependent HamiltonianH(t)=?(1/2) Δ+ΣV _j (x?q _j (t)) is discussed. The existence, asymptotic orthogonality and the asymptotic completeness of the multi-channel wave operators are obtained under the conditions that the potentials are short range: |V _j (x)|≦C _j (1+|x|)^?2?ε, roughly spoken; and the trajectoriesq _j (t) are straight lines at remote past and far future, and |q _j (t)?q _k (t)| → ∞ ast → ± ∞ (j≠k).     

The K+π- elastic scattering cross section as observed in K+p→K+π-Δ++ from 3 to 13 GeV/c

The four-body reaction K⁺p→K⁺π^-Δ⁺⁺ is analysed in a sample of 77 300 bubble chamber events of K⁺p→K⁺π^-π⁺p for beam momenta from 2.5 to 12.6 GeV/c to study the K⁺π^- elastic scattering cross section. The relative merits of several analytic continuations to the pion pole are discussed. Maximum likelihood method is used and, for each experiment fits are performed simultaneously over the whole range of the M(pπ⁺), m(K⁺π^-) and t variables. The K⁺π^- cross section is parametrized in terms of the down solution for the s-wave, a p-wave resonating at the K¹(890) and a d-wave resonating at the K¹(1420). Fitted values are obtained for the four-body cross section, the s-wave contribution to the K⁺π^- cross section, and the masses and widths of the K¹(890) and K¹(1420).     

Low momentum transfer theorem for two photon exchange in lepton hadron scattering

The two photon exchange contribution to lepton-hadron scattering is considered. Under the assumptions of Lorentz covariance, gauge invariance, unitarity and analyticity, we prove a low momentum transfer theorem for the relevant amplitudes. Fixed energy dispersion relations tell us that their nonanalytic part, in the neighbourhood of t = 0, is given by the contribution of the two photon cut in the t-channel. The t-channel absorptive parts are obtained from unitarity. Their calculation has as input the two amplitudes corresponding to Compton scattering on the hadron with a pole contribution, and the continuum controlled at low t by the electromagnetic polarizabilities. By means of the dispersion integral, one proves the expansion $\text{k}{}_1\text{(s)+k}{}_2\text{(s)}\text{?t}\text{+k}{}_3\text{(s)t}\text{log}\text{(?t)+O(t)}$ for the continuum contribution, where k₁(s) is the only unknown. Explicit expressions are obtained for the pole contribution as M → ∞, where M is the hadron mass, and for the continuum when (?t) <Λ and (?t) < 4m², where m is the muon mass and Λ is a characteristic parameter of the hadron structure.     

On the large order expansion for the anharmonic oscillators

Using functional approaches, we investigate the large-K behaviour of theK ^th coefficientE _k in the perturbation expansion for the ground-state energyE(g) of the generalized anharmonic oscillatorX ^2N with internalO(_n)-symmetry. We establish the equivalence between the pure functional approach and the method of Collins-Soper at any order in 1 /K. For that purpose, we first develop an algebraic treatment of perturbation series and prove a theorem on Borelsummable functions. Finally, we compute analytically the 1 /K and 1 /K ² corrections to the leading term forN=2.     

<Emphasis Type="Italic">nd</Emphasis> scattering at low energies in the two-body potential model

The S-wave phase shift δ(E) for the spin-doublet nd scattering at low energy E is calculated in the framework of the two-body approach. The effective-range-theory formula k cot δ = (1+k²/k ₀ ² )^?1(?1/α+C₂k²+C₄k⁴) is used to obtain approximate analytical results with different potentials. The corresponding coefficients C₂ and C₄ are obtained from our previous calculations of the asymptotic normalization parameter function C _t ² (aκ), where κ is the triton wave number and a is the doublet nd scattering length. The model reasonably describes δ(E), the results being quite sensitive to the choice of the effective nd potential.