Limitation of angular momentum transfer in adiabatic calculations of rotational excitation by inelastic scattering

A new method is proposed for quantummechanical calculations of rotational excitation of nuclei by inelastic scattering. It is based on a combination of coupled-channels method (few-states approximation) and adiabatic method. Results are presented for α scattering from ¹⁷⁶Yb.     

Excitation of nuclear collective states by heavy ions within the model of semimicroscopic optical potential

The (semi)microscopic double-folding nucleus-nucleus optical potentials are suggested for consideration of inelastic scattering with excitation of collective nuclear states by using the adiabatic approach and the elastic scattering amplitude in the high-energy approximation. The analytical expression for inelastic scattering amplitude is obtained keeping the first-order terms in the deformation parameter of a potential. Calculations of inelastic cross sections for the ¹⁷O heavy ions scattered on different nuclei at about hundred MeV/nucleon are made, and the acceptable qualitative agreement with the experimental data is obtained without introducing free parameters. The prospect of the method for further applications is discussed. The text was submitted by the authors in English.     

Intensity rules for partial widths of deformed analog resonances

Intensity rules for the escape widths of isobaric analogs of rotational states in deformed nuclei are obtained. These rules correctly take into account inelastic scattering to other states within the rotational band in the target nucleus. The simplest results are obtained in the limit of vanishing rotational energy (adiabatic approximation). First order corrections in the inverse moment of inertia are also given.     

Coulomb distortions in heavy-ion reactions

In heavy-ion scattering the Coulomb potential deviates from the potential of two point charges since vibrations, rotations and giant resonances are excited in both projectile and target nuclei as a result of their mutual electrostatic forces. In this paper this effect is calculated using a classical model. The adiabatic and the dynamical solutions of the problem are compared and discussed.     

The influence of strongly coupled pickup channels on proton elastic scattering

We show that the influence of strongly coupled deuteron channels on proton elastic scattering is large. The effect is to increase the total reaction cross section by an amount which is several times the pickup cross section. The effect is particularly large for light nuclei suggesting a reason for the breakdown of the folding model for these nuclei. We have carried out model calculations which make these results plausible in terms of the deuteron acting as a doorway for proton absorption. The effect on the real potential is considerable for lighter nuclei and consistently repulsive. Results are also presented concerning the applicability of DWBA for pickup and which illuminate the adiabatic model of Johnson and Soper. Uncertainty in very low energy deuteron propagation makes the observation of experimental effects at (p, d) threshold somewhat doubtful.     

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.     

Differential cross sections for muonic hydrogen scattering on hydrogen molecules

The results of first calculations of the differential cross sections for muonic hydrogen scattering on hydrogen molecules are presented. They are functions of the initial and final kinetic energy of the system and the scattering angle. These calculations are based on the respective set of cross sections for muonic hydrogen scattering on hydrogen nuclei, obtained within the framework of the adiabatic method. The Fermi pseudopotential method is used to estimate the molecular binding effects. The influence of electrons on the cross sections under consideration is described in terms of the effective screening potential. Rotational and vibrational transitions are taken into account. The calculated molecular differential cross sections show a strong angular dependence. This effect is very significant for the electronic contributions to the cross sections, e.g. for collision energies above approximately 0.1 eV only the cross sections of small scattering angles are influenced considerably by the screening. Since these differential cross sections give detailed information about the final energies and complicated angular distributions of the scattered muonic atoms they are the proper basis for calculations concerning the deceleration of muonic hydrogen atoms in molecular hydrogen targets and for Monte Carlo simulations of different experiments in muonic physics.     

Spin-flip cross sections in muonic hydrogen scattering on hydrogen molecules

The results of calculations of the total cross sections of spin-flip processes in low energy muonic hydrogen scattering on hydrogen molecules are presented. These calculations are based on the respective set of cross sections for muonic hydrogen scattering on hydrogen nuclei, obtained within the framework of the multichannel adiabatic method. All combinations of the three hydrogen isotopes are considered. Molecular binding effects are described in terms of the Fermi pseudopotential method. Electron screening effects are calculated in the distorted wave Born approximation. Rotational and vibrational transitions of the molecules, due to collisions with muonic hydrogen atoms, are taken into account. The molecular and electron screening corrections do not exceed a few tens per cent for lowest collision energies.     

Protonic decay of oriented nuclei

On the basis of the multiparticle theory of protonic decay, the angular distributions of protons emitted by oriented spherical and deformed nuclei in the laboratory frame and in the internal coordinate frame of deformed parent nuclei are constructed with allowance for symmetry with respect to time inversion. It is shown that, because of the deep-subbarrier character of protonic decay, the adiabatic approximation is not applicable to describing the angular distributions of protons emitted by oriented deformed nuclei and that the angular distribution of protons in the laboratory frame does not coincide with that in the internal coordinate frame. It is demonstrated that these angular distributions coincide only if the adiabatic and the semiclassical approximation are simultaneously valid.     

Quantized ATDHF and angular momentum projection: Three-dimensional applications to heavy ion scattering

The quantized adiabatic time-dependent Hartree-Fock (qATDHF) theory is extended to the calculation of observables in nuclear phenomena using general many-body techniques including angular momentum projection. All calculations are performed using three-dimensional coordinate and momentum-grid techniques. The Bonche-Koonin-Negele interaction as well as several Skyrme-type forces has been used in the simple Hartree-Fock (HF) calculations of ¹²C and ²⁰Ne nuclei. Further, the maximally decoupled collective path is evaluated within qaTDHF, and the angular momentum projected kernels are inserted into the GCM formalism. As a test case, this formalism is applied to the phase shifts of elastic α-α scattering because they can be compared to experimental values. The same techniques are applied to the α-¹⁶O system and the results are compared with those obtained by solving the collective Schrödinger equation in a Gaussian Overlap Approximation, as in a previous publication. The GCM, extended to complex energies, is used to extract the widths of the resonance levels of the 0₁⁺, 0₄⁺, 0 bands in α-¹⁶O scattering. A model calculation, in which the structure of the nuclei is kept fixed to their HF ground state, is performed for the same α-¹⁶O system. We get quite different results with this “sudden” approximation than with the adiabatic calculation. The present calculations show that it is indeed possible to connect general and symmetry conserving many-body techniques to the qATDHF theory and to obtain in this way a purely microscopic framework which can be handled numerically, thus allowing evaluation of observables which are accessible to experiments.     

Mixed-parity neutron orbits in the scattering of 12C on 13C

In the scattering process of ¹²C on ¹³C the mixing of the p-and sd-shell orbits of the valence neutron in ¹³C has been investigated by using the coupled channel theory with the adiabatic assumption. When two nuclei approach each other an extremely anisotropic density distribution of the neutron is induced due to the mixed-parity configuration similar to the sp hybrid configurations in atomic physics. The probability of the elastic transfer of the neutron is enhanced by virtue of this deformation.     

Heavy-ion inelastic scattering from deformed nuclei

Theoretical and experimental methods for studying heavy-ion inelastic scattering from deformed nuclei are described. The theoretical methods involve classical-limit approximations, while particle- γ-spectroseopy techniques are employed experimentally. With these approaches, heavy-ion excitation in the Coulomb-nuclear interference region acquires a transparent interpretation, despite the apparent complexity of the multistep excitation processes involved. The examples discussed provide a good illustration of the relationship between classical and quantum physics. The sensitivity of the inelastic scattering to details of the surface ion-ion potential due to radial and angular localization is exploited to provide a method of determining the equipotential contours in a direct manner which bypasses particular model-dependent parametrizations. The method is used to construct ion-ion potentials from inelastic scattering data for the systems ⁴⁰Ar + ¹⁶⁰Gd, ¹⁵⁶Gd, ¹⁶²Dy, ¹⁶⁴Dy, and¹⁸⁰Hf. The contribution of adiabatic giant resonance polarization to this potential is discussed. The relation between the deformed ion-ion potential and nuclear shapes is illustrated by comparing the experimental potentials to deformed double-folding and deformed proximity-potential calculations.     

On three particle stripping reactions

The formalism for the coupled-channel analysis of stripping reactions of complex nuclear projectiles by nuclei is presented. The general adiabatic approximation is developed. The indirect transitions that are considered are those which arise via intermediate rotational excitations of the target and product nuclei, i.e. the adiabatic approximation for rotational bands is used. At the same time the generalized DWBA procedure is considered for the intrinsic states. Also the antisymmetrization problem is solved. A new method for the calculation of the matrix elements of the (α,n) stripping reaction with finite range effective forces is developed. The method is based on an expansion of the radial functions which describe the relative motion in terms of harmonic oscillator wave functions multiplied by a Gauss one. Effective forces of Gauss type are assumed between the outgoing neutron and each captured nucleon     

Green function and scattering amplitudes in many-dimensional space

Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation.     

Quantum time of flight and the adiabatic limit in scattering processes

The author investigates the adiabatic limit of the exact quantum scattering problem. Various types of long-lived states are considered. The author demonstrates that the characteristic scattering time obtained from the adiabatic condition is not directly related to the quantum time of flight and that the difference between these two parameters can be quite large.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 52–58, March, 1988.The author is grateful to L. M. Baskin for helpful discussions and D. V. Glazanov for computer calculations.     

Four-body adiabatic model applied to elastic scattering

Elastic scattering of a projectile, composed of three clusters, from a spherical target is analysed using a four-body adiabatic model. The model is a generalisation of the three-body adiabatic model of Johnson and Soper. Calculations of the elastic scattering of ¹¹Li from ¹²C are compared to both experimental data and the results of recent four-body eikonal model calculations.     

Decay and fission of oriented nuclei

The angular distributions of fragments originating from the binary decay of oriented spherical and deformed nuclei are investigated with allowance for correct transformation properties of wave functions under time inversion. It is shown that, as in the case of protonic decay, the adiabatic approximation for collective rotational degrees of freedom of the systems under investigation is inapplicable in describing the angular distributions of fragments of the deep-subbarrier alpha and cluster decays of nuclei. It is demonstrated that this approximation is justified in describing spontaneous and induced low-energy nuclear fission. The dependence of partial fission widths on the orientation of intrinsic axes, spins, and projections of spins and relative orbital angular momenta of fission fragments is analyzed by using the formalism of the unified theory of nuclear reactions and the theory of open Fermi systems. It is shown that the adiabatic approximation leads to the coherent interference between the wave functions for the relative motion of fragments, whereby the universal angular distributions of fission fragments of oriented nuclei is formed. Deviations from the A. Bohr formula are investigated for these distributions.     

Adiabatic surface of self-trapping excitons

The problem of the self-trapping of the Frenkel exciton interacting with phonons is considered in the adiabatic approximation. The self-trapping is assumed to take place at a single site. The exciton scattering by phonons at this site and the nearest neighbouring sites is taken into account. Analytical expressions for the adiabatic surface of self-trapping excitons, in particular, for the barrier height separating almost free and self-trapped states, are found. The condition for the applicability of the model to the describing of the self-trapping barrier is determined. The adiabatic surface is shown to have several minima separated by a barrier, i.e. the coexistence of several types of self-trapped excitons is possible.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.