SS-HORSE method for studying resonances

A new method for analyzing resonance states based on the Harmonic-Oscillator Representation of Scattering Equations (HORSE) formalism and analytic properties of partial-wave scattering amplitudes is proposed. The method is tested by applying it to the model problem of neutral-particle scattering and can be used to study resonance states on the basis of microscopic calculations performed within various versions of the shell model.     

Elastic scattering, muon transfer, bound states and resonances in the three-body mesic molecular systems in the reduced adiabatic hyperspherical approach

The uniform method of numerical investigation of bound states and scattering processes 2→ 2 (including resonance states) in the Coulomb three-body (CTB) systems is developed. It is based on the adiabatic hyperspherical approach (AHSA) and includes the numerical realization and applications to the three-body mesic atomic systems. The results of calculations of bound states of these systems (including the local characteristics of the wave functions) and the scattering processes 2→ 2 (including the characteristics of the resonance states) are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Raman scattering of light by 2LO-phonons

A theory of resonance Raman scattering of light by 2LO-phonons in semiconductor crystals is presented. Wannier excitons are considered as intermediate states. Analytic expressions are obtained that take into account contributions from different chains of intermediate states. The scattering cross section is shown to be weakly dependent on the wave vector imparted to the phonon system. The theoretical model permits the calculation of the scattering cross section for the energy of the exciting radiation photon below the level of exciton resonances.     

The 7Li (n,γ)8Li radiative capture at astrophysical energies

The possibility to construct intercluster interaction potentials in continuous and discrete spectra is shown in one‐channel cluster model based on the classification of orbital states according to Young schemes. These potentials usually contain Pauli forbidden states, and correctly describe elastic scattering phase shifts taking into account resonance behavior and main characteristics of the bound states of nuclei in the considering cluster channel. The versions of intercluster interaction potentials describing the resonance nature of some phase shifts of the n⁷Li elastic scattering at low energies and the P₂ ground state of ⁸Li in the n⁷Li cluster channel have been constructed for the demonstration of this approach. The possibility of describing the total cross sections of ⁷Li (n,γ)⁸Li within the energies from 5 meV (5 · 10^‐3 eV) to 1 MeV, including resonance at 0.25 MeV, has been demonstrated for the potentials obtained in the potential cluster model with forbidden states.     

Evolution of the giant dipole resonance in excited 120Sn and 208Pb nuclei populated by inelastic alpha scattering

The evolution of the giant dipole resonance (GDR) in ¹²⁰Sn and ²⁰⁸Pb nuclei at excitation energies in the range of 30–130 MeV and 40–110 MeV, respectively, were studied by measuring high energy γ rays from the decay of the resonance. The excited states were populated by inelastic scattering of α particles at beam energies of 40 and 50 MeV/nucleon for ¹²⁰Sn and 40 MeV/nucleon for ²⁰⁸Pb. A systematic increase of the resonance width with increasing excitation energy was observed for both nuclei. The observed width evolution was compared to calculations employing a model that adiabatically couples the collective excitation to the nuclear shape, and to a model based on the collisional damping of nucleons. The adiabatic coupling model described the width evolution in both nuclei well, whereas the collisional damping calculation could describe the width evolution only in ²⁰⁸Pb. Light-particle inelastic scattering populates low angular momentum states in the target nucleus. The observed width increase is therefore interpreted to be predominantly due to fluctuations in the nuclear shape induced by temperature. This interpretation is consistent with the adiabatic model calculations and with recent angular momentum-gated measurements of the GDR in excited Sn isotopes.     

Quantum-mechanical analysis of resonance Raman scattering spectra of the uracil molecule

A direct quantum-mechanical calculation of the relative intensities of lines in the resonance Raman scattering (RRS) spectra of uracil is performed by a method developed earlier by the authors on the basis of the adiabatic model in the Herzberg-Teller approximation [1]. It is shown that the main regularities in the intensity distribution of spectra can be explained only by taking into account the vibronic mixing of electronic states and the contribution to the scattering tensor components from the excited electronic states adjacent to the resonance state. The calculated results are in satisfactory agreement with the results of experimental studies of the RRS spectra of uracil excited by laser radiation at 266, 240, 218, and 200 nm.     

复动量格林函数方法对n-α散射研究

在复动量表象下引入格林函数,建立了复动量格林函数方法.把这种方法应用于n-α散射系统,计算其散射相移.提取n-α系统的共振态并研究共振态对能级密度、相移和散射截面的贡献.在不引入任何非物理参数的前提下,离散化薛定谔积分方程得到束缚态、共振态和连续谱.通过分析散射态物理量可以更好地理解共振态以及非共振连续谱态.在n-α系统中的成功应用,证明了该方法的正确性.     

THE RESONANCE OF THE CHAIN STRUCTURE STATES IN A(α,αx)B TYPE THREE-BODY REACTIONS

In this Paper a calculable three-body T matrix with compact kernel is obtained by using multiplier's methods. The formulations for calculating the A（a, ax）B type three-body reaction trans-tion amplitudes are presented when plane wave or distorted wave is used for the incident and outgoing states. This T matrix also includes the resonance terms of the three-body chain struc-ture states besides quasi-free scattering terms and final states interaction terms. A calculable formulation for the resonance energy of chain structure states is presented when it is expanded approximately into two two-body bound states. For ⁸Be and ⁶Li as target nuclei, the resonance energies are calculated. The results are in good agreement with the experimental values and the theoretical values of a mole-cule-like model. In order to check this kind of resonances, some experiments are proposed.     

强场中NO分子回归谱的长程散射矩阵的理论研究

采用半经典散射矩阵方法研究外磁场中高里德伯态双原子分子在能量范围为77010—77050cm^-1的回归谱.通过引进模型势简化强磁场中NO分子的高里德伯电子的势函数,找出其在核转动量子数分别为N=1,3,5的三个通道中的闭合轨道,重点分析了强磁场中NO分子的长程散射矩阵元实部的傅里叶变换谱与闭合轨道之间的一一对应关系.     

Nuclear resonance flourescence in 22Ne

States at 5.328, 6.851, 8.553, 9.165 and 10.203 MeV in ²²Ne have been observed in a nuclear resonance fluorescence experiment using bremsstrahlung and high resolution Ge(Li) diodes. Photon scattering cross sections, γ-ray decay widths to the ground and first excited states, and lifetimes are derived. The results are compared with inelastic electron scattering data and shell model calculations.     

Algebraic solution of the Hubbard model on the infinite interval

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2) ) and that the bound states are Yangian singlet.     

The resonance pole and the residue of the scattering amplitude while the Coulomb forces gradually decrease

Trajectories for the S-wave pole of the scattering amplitude are constructed in the complex planes of the resonance momentum and of the renormalized vertex constant squared. They correspond to transitions from the resonance states to the virtual states of the singlet deuteron and the doublet triton while the Coulomb interaction gradually decreases to zero. The effective-range theory and a Yukawa-potential model are used. Physical reasons for the differences between the corresponding trajectories for Np and Nd systems are found. The results obtained explain why the resonances in the doublet Nd scattering are more difficult to detect in experiments in comparison with the well-studied singlet NN resonances.     

A microscopic model analysis of the 90Zr(p,n) IAS transition

Direct reaction (p, n) data to the isobaric analogue of the ground state of ⁹⁰Zr is analysed within a DWA using a complex effective two-nucleon transition interaction, the real part of which has been used in many previous inelastic scattering analyses. Using collective model form factors in the ansatz for the imaginary part of the transition interaction and allowing for virtual resonance excitation, the differential cross sections from the scattering of 18.5–45 MeV protons are well reproduced. The parameters of the required complex interaction have a smooth energy variation similar to that required by a microscopic model analysis of proton inelastic scattering to collective states in nuclei.     

Resonance Raman scattering at the saddle points of semiconductors

An approximate theory is formulated to describe resonance Raman scattering near the critical points of semiconductors using a model density of states. Large resonance enhancements and absolute scattering cross sections are predicted near the saddle points.     

Investigation of low-energy scattering in the nnpp system on the basis of differential equations for Yakubovsky components in configuration space

The s-wave differential equations for the Yakubovsky components characterizing the nnpp system have been solved by the method of cluster reduction. Two-cluster scattering at energies below the three-particle threshold in the singlet and triplet spin states has been considered. The MT I–III potential model has been used to simulate nucleon-nucleon interaction, and the Coulomb interaction between the protons has been taken into account. The singlet and triplet scattering lengths have been calculated for proton interaction with the triton (³H) and for neutron interaction with the ³He nucleus, and the deuteron-deuteron scattering length has also been determined. The low-energy behavior of the phase shifts and inelasticity factors in the corresponding scattering channels has been investigated. The features of the 0⁺ resonance in the ⁴He nucleus have been determined.     

Interaction Energy of Two Trapped Bosons with Long Scattering Lengths

 I study two interacting bosons confined to a harmonic trap. The interaction is assumed to be of zero range and is expressed in terms of the s-wave scattering length. The energy shifts of the harmonic-oscillator states due to the atom-atom interaction are calculated analytically. It is found that for an ordinary potential the interaction energy depends only on the scattering length, while if the scattering length is modified by a near-threshold Feshbach resonance there is also a dependence on the width of the resonance. Received October 25, 2001; accepted for publication November 9, 2001     

Die Winkelabhängigkeit der Resonanzstreuung niederenergetischer Elektronen an He,Ne, Ar und N2

The energy dependence of the elastic resonance scattering of low energy electrons from He, Ne, Ar, and N₂ has been measured in the angular range from 8° to 110°. From the measurements are derived the total angular momenta and hence the configurations of the quasistationary negative ion states. The line shapes depend very strongly on the phase shifts for the potential scattering and on the interference of different partial waves. In the cases of He and Ne phase shifts are determined. The resonance structure in the elastic scattering from N₂ in the energy range from 1.75 eV to about 3,5 eV seems to be due to the formation of the N ₂ ^? -ion in its electronic ground state with a²Π configuration. The separations of its first few vibrational states are 237±10 meV, the natural half-width of these states being approximately 150 meV.     

Possible resonance structure in the elastic scattering of neutrons by Y near En = 1 MeV

The total cross section as well as the differential cross section and polarization in the elastic scattering of 0.8–1.4 MeV neutrons by Y have been measured with neutron beams of energy spread less than 20 keV. Rather weak structure with widths ≈ 50 keV was observed at a few energies within this range. The data were analyzed by use of a model in which the scattering process is described in terms of resonance amplitudes superimposed on an optical-potential background. Although not completely definitive, this analysis indicates the existence of three intermediate-width resonances (two 1^? and one 1⁺) at neutron energies between ≈ 1.0 and 1.2 MeV. The properties of the 1^? resonances suggest that these are the parent states of the proposed T_> components of the El giant resonance observed near 21 MeV excitation energy in ⁹⁰Zr produced in the ⁸⁹Y(p,γ₀) reaction. The resolved resonance structure in this energy region is in reasonable agreement with a recent calculation of the energies and widths of negative-parity states in ⁹⁰Y.