On the relation between resonances andK-matrix poles

The relation between resonances andK-matrix poles for the potential scattering problem is investigated. The analysis is carried out in two stages. We first discuss the analytic properties of aK-matrix related to a model phase-shift which embodies the relevant features of a potential scattering resonance; we then consider the specific case of a square-well potential. The result emerging from the analysis is that to each resonance two poles of theK-matrix are associated; they appear either as a real resonance-echo pair or as a complex conjugate doublet, according to the value of a suitable background parameter. The relevance of this result in connection with the Huby theory is briefly discussed.     

Collision rate of pions and kaons at finite temperature

The energy dependence of the pion and kaon collision rates at finite-temperature are calculated in the approximation that resonances dominate the scattering, as for example, ππ→?→ππ andKπ→K ^*→Kπ. A general formula is derived for the contribution of resonances with arbitrary spin and isospin. Numerical results are given. For very narrow resonances the calculation is performed analytically.     

Derivation and implications of rigorous absolute bounds for ππ partial waves up to 1 GeV

Generalized dispersion relations and axiomatic results are used to derive absolute upper bounds for the ππ partial waves in a complex energy domain containing the physical region up to 1 GeV. As applications, a new lower bound for the π⁰π⁰ S-wave scattering length is given and some ambiguities in the connection between resonances and second sheet poles are removed.     

Calculation of the elastic scattering properties for cold and ultracold 39K atoms in a triplet state

The elastic scattering properties for collisions between cold and ultracold 39K atoms in a triplet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for a triplet α3∑u^＋ ground state of K2. Our calculated value of the s-wave scattering length a by using the Numerov method for the triplet state is 79.578α0 and found to be in good agreement with the previous ones. The numbers of bound states are supported by the molecular potential. Pronounced shape resonances appear for the l = 3 partial waves for the α3∑u^＋ state. Furthermore, the s-wave scattering cross section, the total cross section and energy positions of shape resonances for the α3∑u^＋ state are calculated.     

Saddles and trajectories,and poles and surface waves in heavy-ion elastic scattering

The terms I_m^±(θ) of the Poisson summation formula are used to describe and classify the oscillatory structures of the heavy-ion elastic cross sections coming from a strong-absorption model. The method of stationary phase, which relates these terms to branches of a deflection function, is shown to be inadequate and is replaced by the saddle-point method in the plane of complex angular momenta. The positions of the saddle points are found to be fairly independent of the parametrisation and define certain “active” regions which contribute to the scattering amplitude. The complex saddle points may be thought of as corresponding to complex trajectories in the nuclear potential. If the strong-absorption parametrisation possesses poles many saddle-point contributions can be simply expressed as the residues of the poles nearest the real axis. One of these leading parametric poles has an energy dependence similar to that of the dominant Regge pole generated by a complex optical potential. Poles lying above the real axis give rise to terms which may be thought of as surface waves, i.e. they are damped as they progress around the nuclear surface. These terms possess classically equivalent paths in the sense that they correspond to deflections less than π. Terms coming from poles below the real axis have no classical equivalent, increase as they progress and can, then, only be thought of as being diffractive. Some useful formulae for the cross section are given and the limiting case of a sharp cut-off is discussed.     

Study of proton elastic and inelastic scattering from 74Se at the isobaric analogue resonances

Excitation functions of proton elastic and inelastic scattering from ⁷⁴Se were measured to investigate the isobaric analogue resonances (IAR) in ⁷⁵Br. Observed IAR correspond to the parent states of ⁷⁵Se in excitation energy from 0.29 to 1.8 MeV. For eleven resonances, resonance parameters were determined from the analysis of the elastic scattering. For three of these resonances, inelastic widths to the 2⁺ (0.635 MeV) state in ⁷⁴Se were obtained from the analysis of the angular distributions of inelastically scattered protons. Spectroscopic factors obtained from the elastic scattering were compared with those from the ⁷⁴Se(d, p)⁷⁵Se reaction. There is good agreement between the corresponding Spectroscopic factors except for the states with l_n = 1 where they were much smaller than the (d, p) ones. For the inelastic scattering, it was proved that the compound process via IAR play an important role and the analysis including the compound process explained the experimental results reasonably well.     

Comment on the real part of the K±p forward scattering amplitude

It is observed that the K_L⁰n→K_S⁰n regeneration measurements require positivity of the real part of the K^?p forward scattering amplitude above p ～ 1.3 GeV/c. This invalidates some of the earlier dispersion relation predictions and the preliminary experimental results from Batavia.     

An application of dispersion relations to Kaon-nucleon scattering

In this paper we have made predictions for the invariant KN and $\text{K}$N scattering amplitudes in the kinematical region q_lab < 15 GeV/c and 0 >; t > -0.7 (GeV/c)².We have performed a direct fit to medium and high-energy data using a parametrization where the imaginary part of the amplitudes for energies above the phase-shift region is identical with the imaginary part of a Regge-pole amplitude, and the real part of the amplitudes has been obtained from a dispersion relation.The s-channel helicity amplitudes are compared with their counterparts in pion-nucleon scattering and other reactions. Exact exchange degeneracy can not be verified.Also the real part of the amplitudes are compared with the real part of phase-shift solutions. There is a qualitative agreement between these two real parts even though they differ in detail.     

Complex Regge poles and high energy scattering data

For the high energy data on σ_tot^pp the proton-proton total cross section, and on ?, the ratio of real to imaginary part of the forward elastic amplitude, including the recent ISR results, an excellent fit is obtained with P, P', ω Regge poles plus a pair of complex conjugate Regge poles. The complex poles describe the possible oscillatory behavior of the quantities σ_tot^pp and ?. The physical meaning of these complex poles and extrapolation to future measurements of the above quantities are discussed.     

Duality,scaling and fixed poles in virtual compton scattering

J-plane fixed poles are considered in the lepton-hadron scattering amplitudes. A relation between the scale-invariant behaviour of the virtual Compton scattering structure W₂ and the J = 1 pole is established using the wrong signature FESR. A dual mechanism for the generation of fixed poles, leading to a number of interesting implications for a singular behaviour of the pole residue in the variable q² (photon mass square), is indicated.     

Analytic parametrization of high energy forward scattering amplitude II. K±p and π±p scattering

The K^±p and π^±p forward scattering amplitudes are parametrized in terms of functions which are analytic in the cut E plane and which give the asymptotic behaviour of the total cross sections of the type c (log E/E_o)^γ, E being the lab energy. Fits to high-energy data give, in particular, the best value of γ: around it we find, however, a large interval of positive values of γ which are also admissible on the basis of the χ² estimation.Being equally good from the point of view of the existing experimental data, the different asymptotic growth rates γ do lead to different predictions, e.g., of the real part at high energies. A remarkable common feature is, however, a zero in the real part of the π⁺p and π^?p scattering amplitudes, which is predicted by all of our parametrizations to be between 52 and 80 GeV/c of the lab momentum.     

Measurement of the real part of the forward scattering amplitude in K±p elastic scattering between 0.9 and 2.6 GeV/c

The differential cross section for K^±p elastic scattering has been measured in the forward meson direction (0.0008 < t < 0.1 GeV²) in an electronics experiment at incident momenta between 0.9 and 2.06 GeV/c. The high statistics and absolute normalisation of the data allow a good determination of the real part of the forward nuclear scattering amplitude by means of the Coulomb-nuclear interference effect.     

Comment on real parts of KN and KN elastic amplitudes

It is observed that K_L⁰N→K_S⁰N regeneration measurements contain information about forward real parts, which has not been exploited hitherto, and which disagrees with some of the present Coulomb interference results. Charge exchange scattering also contains real part information, not measured by other means.     

Electromagnetic scattering as a radiation reaction problem

Electromagnetic scattering is treated as a dynamical problem, by equating the external torque exerted by the incident wave on the sphere to the self torque due to the radiated (scattered) wave. ForI _mech=0,our scattering amplitude is equal to the usualP-wave amplitude of the electromagnetic scattering on an infinitely conducting sphere. The poles of the scattering amplitude, in particular their dependence onI _mech, are studied. For example, a pole on the positive imaginary axis, which usually corresponds to a bound state, corresponds to a runaway solution in our case. Non-decaying resonances are also discussed.     

Differential KL → KS regeneration cross section in coherent production model and optical model

We investigate the high-energy K_L → K_S regeneration process in nuclei in terms of a coherent production model. The angular distribution of the regenerated K_S is calculated for Pb and Cu at an incident momentum of 4 GeV/c. The experimental data are well reproduced. We have also performed an optical-model calculation which explicitly treats K_L as a mixture of K₀ and $\text{K}{}_0$ particles. We show that it is not necessary to introduce a large neutron skin in the above nuclei to interpret the data, if the finite range of strong interaction is taken into account properly in the density distribution. The coherent production model and the optical model, with seemingly very different physical interpretations, give very similar results. We also show that these models represent two ways of summing the multiple scattering series in the particular case of K_L → K_S regeneration. In conclusion, we discuss the unique and important feature of using nuclear regeneration scattering to study scattering theories, as compared to other high-energy particle-nucleus scattering.     

Dispersion analysis of the K±p forward scattering amplitudes

The currently available experimental data on the K^±p forward scattering amplitudes are analyzed by three different methods: a discrepancy-function method, the Haber-Schaim linear extrapolation method, and a method based on a once-subtracted dispersion relation. Substantially more data are used than in previous analyses. The results of the three methods are found to be in good qualitative agreement. Predictions are obtained for the value of the effective KNY coupling constant and for the real parts of the K^±p forward scattering amplitudes over a wide range of energies.     

Dynamically generated resonances from the vector octet-baryon octet interaction

We study the interaction of vector mesons with the octet of stable baryons in the framework of the local hidden gauge formalism using a coupled-channels unitary approach. We examine the scattering amplitudes and their poles, which can be associated to known J ^P = 1/2^-, 3/2^- baryon resonances, in some cases, or give predictions in other ones. The formalism employed produces doublets of degenerate J ^P = 1/2^-, 3/2^- states, a pattern which is observed experimentally in several cases. The findings of this work should also be useful to guide present experimental programs searching for new resonances, in particular in the strange sector where the current information is very poor.     

Resonance production in the reaction π±p→Ks0K±p at 30 and 50 GeV/c

The mass and momentum transfer spectra of the charged $\text{K}\text{K}$ system produced in the reaction π^±p→K_s⁰K^±p are analyzed. The data have been collected at the CERN SPS with the Geneva-Lausanne two-arm, non-magnetic spectrometer at 30 and 50 GeV/c incident momenta. The general features of the reactions at these energies and the results of partial-wave analyses of the two kaon system are presented.The channel is dominated by the diffractive production of even spin resonances. The spin 4 recurrence of the A₂(1320) is clearly observed at 2040 MeV (Γ=380 MeV. A new resonance is observed with a mass M=2450MeV and a width Γ=400 MeV; the quantum numbers of this state are found to be I^G(J^PC)=1^?(6++). The analysis also shows the decay of the decay of the meson ?′(1600) through the $\text{K}\text{K}$ channel at both energies.The production amplitudes are determined both as a function of the $\text{K}\text{K}$ effective mass and of the momentum transfer. Isoscalar natural parity exchange is dominant. The energy dependence between 10 and 50 GeV/c is shown to be well described by a Regge pole model based on the f-dominated pomeron hypothesis. We compare the production mechanisms of the 2⁺ resonances A₂(1320) and K¹(1430). Finally, we estimate the $\text{K}\text{K}$ branching ratios of the spin 4 A₂(2040) and spin 6 A₂(2450) resonances.