Inelastic scattering of heavy ions at intermediate energies with excitations of nuclear collective states

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of ¹⁷O from a series of nuclei with excitation of the 2⁺ level.     

Excitation of states of medium-mass nuclei in the region of giant resonances in inelastic deuteron scattering

Results are presented that were obtained by measuring a continuum in the inelastic scattering of 37-MeV deuterons on ¹²C, ⁴⁸Ti, and ^58,64Ni nuclei in the angular range 16° ≤ θ ≤ 61°. Broad excitation maxima are found for deuteron scattering angles in the range θ ≤ 21°. The region of a broad maximum includes giant resonances of target nuclei, whose levels are excited quite readily at E _d = 37 MeV. Summation of the inelastic-scattering cross sections over all final states of the excited| nucleus and the use of completeness of the wave functions for these states make it possible to express the total cross section for inelastic (incoherent) deuteron scattering only in terms of the wave functions for the ground state of the target nucleus. The corresponding quasielastic-scattering amplitude is taken in the diffraction approximation. Nucleon correlations in the target nucleus are disregarded. Upon disregarding a small contribution of multiple quasielastic scattering at small scattering angles, the cross section for incoherent deuteron scattering is represented approximately as the product of known factors—the square of the absolute value of the amplitude for diffractive quasielastic scattering and the effective number of target nucleons scattering deuterons. The results of these calculations agree qualitatively with experimental data.     

Low-energy theorems for nuclear compton and raman scattering and 0+ → 0+ two-photon decays in nuclei

Low-energy theorems for elastic photon scattering (nuclear Compton scattering) from a nucleus of arbitrary spin are derived in the nonrelativistic approximation through terms quadratic in the photon frequency. The same derivation is made for the special case of 0⁺ → 0⁺ nuclear excitation by inelastic photon scattering (nuclear Raman scattering). Use is made of the general principle of gauge invariance, which bypasses the need to specify the form of the current operator explicitly. A general discussion of the contribution of mesonic exchanges is made and their effect is isolated. The center-of-mass correction to the nuclear diamagnetic susceptibility is calculated. The 0⁺ → 0⁺ two-photon decay amplitude is obtained from the nuclear Raman amplitude and the transition rate is calculated.     

Elastic and inelastic scattering of 18O by 16O and 18O

Angular distributions have been measured for the elastic and inelastic scattering of ¹⁸O by ¹⁶O and ¹⁸O at laboratory bombarding energies of 42 and 52 MeV. The inelastic scattering data are analyzed in terms of collective excitations using a coupled channel approach. Deformation parameters are obtained for the strongly excited states. The relationship between the strength of inelastic scattering and the amount of structure in the elastic scattering distributions is discussed.     

Elastic and Raman scattering of 8.5–11.4 MeV photons from 159Tb, 165Ho and 237Np

Differential cross sections for elastic and inelastic Raman scattering from the deformed heavy nuclei ¹⁵⁹Tb, ¹⁶⁵Ho and ²³⁷Np were measured at five energies between 8.5 and 11.4 MeV. Angular distributions at four angles between 90° and 140° for both elastic and inelastic scattering at 9.0 and 11.4 MeV were also measured. The monoenergetic photons were obtained from thermal neutron capture in Ni and Cr. All the angular distributions and the elastic and Raman scattering at the higher energies are in good overall agreement with theoretical predictions. The theory is based on a modified simple rotator model of the giant dipole resonance in which the effect of Delbrück scattering was included. A trend of both the elastic and Raman scattering at lower energies to be stronger than expected are suggested by the data. However, the ratio between the Raman and elastic scattering seem to be in good agreement with theory throughout the whole energy range. This shows that there is no need to introduce a direct nonresonant component to the imaginary part of the elastic scattering amplitude to explain the experimental data.     

Eikonal description of quantal scattering

Elastic and inelastic quantal scattering is described by a theory in which the contribution of a range of impact parameters to the scattering amplitude is determined by a phase integral (“eikonal”) which is integrated along a real curved “quantal” trajectory. This amplitude reduces to the Glauber expression in the high-energy, forward-angle limit, and to the usual semiclassical amplitude in the classical limit. The formulation can be applied to the study of heavy-ion scattering. The quantal trajectories are investigated analytically for the case of Coulomb scattering. A numerical analysis of elastic ¹⁶O¹⁶O scattering is carried out. The results show appreciable improvement as compared with the Glauber approximation.     

The excitation of collective nuclear states by high energy particles

The excitation of collective nuclear states by high energy particles is considered within the framework of the Glauber theory. The approach is based on the adiabatic approximation and expansion of the scattering amplitude in powers of the nonsphericity parameter. The formulae for the excitation cross sections of the rotational and one- and two-phonon vibrational states, as well as the elastic scattering cross section with the collective motion included, are obtained. The effect of nucleon correlations in both elastic and inelastic cross sections is also studied. The theoretical predictions are compared to new data on 1 GeV proton scattering by ⁵⁸Ni, ²⁰⁸Pb, ¹²C, ⁴⁰Ca and ³⁹K. A comparison with electron scattering data is simultaneously carried out. The agreement with the experimental data is generally good.     

Anomaly in α-scattering from 6Li between 35 and 45 MeV

The elastic scattering of α-particles on ⁶Li nuclei has been measured from 20° to 170° (c.m.) and the inelastic scattering to the first excited state of ⁶Li has been measured for forward and backward angles. The elastic scattering angular distributions are calculated (i) in terms of pure potential scattering, (ii) in terms of potential scattering with an l-cut-off on the imaginary part of the potential and (iii) in terms of the coherent addition of the potential scattering amplitude and of the exchange amplitude. The third method gives the best fit to the data. The inelastic angular distributions are compatible with the macroscopic calculations, except in the very backward region where exchange phenomena are also shown to dominate.     

Structure of 6Li from high-energy proton scattering

The elastic and inelastic (2.189 MeV level) scattering of 1 GeV protons from ⁶Li is predicted using Glauber multiple-scattering theory in conjunction with an α-d cluster model capable of fitting quantitatively a large number of measured form factors, in particular the most recent high-momentum-transfer electron scattering data. The predictions, especially in the inelastic channel, are quite sensitive to the parameters of the model. A valuable opportunity is thus provided via experiments well within the capabilities of LAMPF for comparison of structure information obtained from proton scattering with that from other sources in the case of a “test” nucleus whose properties are relatively well determined and unambiguous. Moreover, proton scattering goes beyond electron scattering in possibly providing information about the effective real part of the proton-deuteron cluster amplitude, and thus indirectly about D-state effects in the deuteron cluster.     

Analisis of inelastic scattering of π-mesons from nuclei within the microscopic optical potential

Cross sections of inelastic scattering of π-mesons from Si, Ni, and Pb nuclei at energy T _lab = 291 MeV are calculated using the distorted wave approximation. The microscopic direct and transition optical potentials are determined by specifying the pion-nucleon scattering amplitude and the nuclear density distribution, where we use the in-medium πN amplitude parameters obtained earlier by analyzing the elastic scattering data for the same nuclei. The cross sections are calculated on the basis of the relativistic wave equation. The deformation parameters of the nuclei are obtained by comparing inelastic scattering cross sections with the appropriate experimental data.     

Many-body field theoretic framework for inelastic pion-nucleus scattering

We consider inelastic scattering of pions from nuclei using many-body quantum field theory methods. We find that, in an inelastic amplitude for small energy transfer, one can separate out effects of particle-hole correlations in the final nuclear state. The ratio of π⁺ and π^? inelastic cross sections can differ substantially from the analogous ratio for free πN scattering.     

Application of a folding-model optical potential to analyzing inelastic pion–nucleus scattering and the in-medium effect on a pion–nucleon amplitude

The folding-model optical potential is generalized in such a way as to apply it to calculating the cross sections for inelastic scattering of π ^±-mesons on ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, and ²⁰⁸Pb nuclei at the energies of 162, 180, 226, and 291 MeV leading to the excitation of the 2⁺ and 3^? collective states. In doing this, use is made of known nucleon-density distributions in nuclei and the pion–nucleon scattering amplitude whose parameters were obtained previously by fitting the elastic scattering cross sections for the same nuclei. Thus, the values of quadrupole (β ₂) and octupole (β ₃) deformations of nuclei appear here as the only adjustable parameters. The scattering cross section is calculated by solving the relativistic wave equation, whereby effects of relativization and distortion in the entrance and exit scattering channels are taken exactly into account. The cross sections calculated in this way for inelastic scattering are in good agreement with respective experimental data. The importance of the inclusion of in-medium effects in choosing parameters of the pion–nucleon amplitude is emphasized.     

Physics (and technique) of gas jet experiments

Recently gas jet targets have been used for the study of small momentum transfer p-p and p-d elastic and inelastic scattering. In these experiments, which were performed at Serpukhov in the USSR and at the Fermilab in the USA, the gas jet is introduced in the main ring of the accelerator. We review the techniques associated with these measurements and summarize the published results which cover 4-momentum transfers 0.001< |t|< 0.12 (GeV/c)^?2 and incident energies 8<E< 400 GeV. Elastic scattering data have yielded precise values for the slope of the nuclear scattering amplitude and for the ratio of the real to imaginary part as a function of energy. The implications of these data on the understanding of high energy hadronic interactions are discussed in some detail. We also present and discuss information on the diffractive dissociation of the proton to low mass states, obtained from inelastic scattering using the gas jet target.     

46.8MeV的p+12C非弹性散射

在Glauber多重散射理论框架下，使用跃迁密度方法和三种N湮没势，计算了46.8MeV的反质子在¹²C上的非弹性散射微分截面. 理论曲线与实验数据符合得较好. 关键词： Glauber理论 反质子 非弹性散射 湮没势 跃迁密度     

Polarization effects in inelastic deuteron scattering in the region of baryon-resonance excitation

Within the impulse approximation, polarization effects in inelastic deuteron scattering on nuclei are investigated in the region around the resonance of mass about 2190 MeV/c ². It is shown that the spin-dependent part of the NN → NN*(2190) amplitude plays a significant role at high momentum transfers. Predictions are obtained for some polarization observables and cross sections for various deuteron-spin-flip processes.     

High-energy approach for heavy-ion scattering with excitations of nuclear collective states

A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach, analytical expressions for elastic and inelastic scattering amplitudes are obtained, where all the orders in the deformation parameters are included. The multistep effect of the 2⁺ rotational state excitation on elastic scattering is analyzed. Calculations of inelastic cross sections for the ¹⁷O ions scattered on different nuclei at about tens of MeV/nucleon or higher are compared with experimental data, and the important role of the Coulomb excitation is established. The text was submitted by the authors in English.     

Closed-form quantal description of inelastic heavy ion scattering

The amplitude for inelastic heavy ion scattering, given by the distorted-wave theory for excitation of low-lying collective states, is evaluated in closed form. Use is made of the Austern-Blair relation and of other approximations appropriate for strongly absorptive interaction to express the inelastic partial-wave amplitude entirely in terms of the elastic S-matrix elements in the initial and final channels. The resulting formulae display explicitly the various contributions to the transition amplitude, whose superposition gives rise to the variety of interference patterns observable in the angular distributions and excitation functions of inelastic heavy ion scattering. It is shown that, as for elastic scattering, the dominant mechanism in inelastic heavy ion collisions near and above the Coulomb barrier is diffractive scattering of Fresnel type.     

Scattering times in AlGaN/GaN two-dimensional electron gas from magnetotransport measurements

The various scattering times of two-dimensional electron gas were investigated in modulation-doped Al_0.22Ga_0.78N/GaN quantum wells by means of magnetotransport measurements. The ratio of transport and quantum scattering times, τ_t/τ_q∼1, shows that the dominant mobility-limiting mechanisms are short-range scattering potentials. The low-field magnetoresistance shows the weak antilocalization and localization phenomenon from which the spin-orbit scattering and inelastic scattering times are obtained. The inelastic scattering time is found to follow the T⁻¹ law, indicating that electron-electron scattering with small energy transfer is the dominant inelastic process.     

Reaction spectroscopy with even tin isotopes

The two-particle transfer reactions ^{116, 118}Sn(t, p) and the inelastic scattering of 55 MeV protons from ¹¹⁶Sn and 16 MeV protons from ^{116, 118, 120}Sn are analysed for various transitions to collective and non-collective states in the final nucleus using DWBA. Form factors have been calculated with wave functions containing two-quasiparticle excitations of neutrons in open and closed shells as well as 1p-1h transitions from closed proton shells. In the inelastic scattering, generally a Serber-type Gaussian effective interaction was inserted. The results are compared with those obtained on the assumption of two-quasiparticle excitations in a restricted configuration space only. For both types of reaction, reasonable agreement with experimental data is obtained for the angular distribution. In the (t, p) reaction the measured and calculated relative cross sections agree within a factor of two. For the inelastic scattering, apart from relative cross sections the mass dependence of the collective excitations and the influence of four-quasiparticle excitations have been examined. The transition to the collective 2⁺ level in ¹¹⁶Sn was calculated with the proton component of the wave function corrected according to electromagnetic measurements. From inelastic scattering it follows that the transitions to negative-parity states especially are not described satisfactorily by the wave functions used. Cross sections for unobserved higher excited levels have been estimated.     

Path integral methods for inelastic scattering

Corrections to the primitive semi-classical amplitude for multiple inelastic scattering are obtained from a path integral formulation of scattering theory. The path integrals are calculated by making an expansion about a classical orbit describing elastic scattering. Terms are collected to give a series in inverse powers of the reduced mass m of relative motion of the target and projectile. The leading term is the primitive semi-classical amplitude for multiple excitation and explicit formulae are given for the corrections of order $\text{1}\text{m}$. These are calculated in detail for a one-dimensional model. It is shown that some, but not all, of the corrections can be included by evaluating the primitive amplitude with a symmetrized orbit.