Microscopic and macroscopic aspects of 135 MeV proton scattering from 16O

Differential cross sections have been measured for the scattering of 135 MeV protons from ¹⁶O and data from the transitions to 13 states (up to 19.5 MeV excitation) have been analysed using microscopic and macroscopic nuclear reaction models. Extensive collective model calculations have been made of the transitions to all natural-parity states. The deformation parameters for the 4p4h rotational band are in good agreement with theoretical models. The inelastic scattering data from the excitation of the negative-parity states have also been analysed in the distorted-wave approximation using microscopic (shell and RPA) models of nuclear structure and with density-dependent two-nucleon t-matrices. For positive-parity states, we report the first shell-model calculation using the complete 2?ω basis space and find that the triplet of 2p2h states (4⁺, 2⁺, 0⁺) around 11 MeV excitation is quite well described by this model, as may be a 1⁺ state which is observed for the first time by proton scattering from ¹⁶O.     

Analyses of inelastic proton scattering from 20Ne

Differential cross sections and analyzing powers for inelastic proton scattering to the 2⁺₁, 4⁺₁ and 6⁺₁ states of ²⁰Ne are analyzed using an antisymmetrized distorted wave approximation in direct reaction theory. The spectroscopy of these states was obtained by angular momentum projection from an axially symmetric minimal-energy Hartree-Fock intrinsic state.     

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.     

Multi-step processes in high-energy elastic and inelastic nuclear scattering

Multi-step processes in elastic and inelastic nuclear scattering at intermediate and high energies are investigated using a formulation whereby a finite number of channels are explicitly treated while all the other channels are approximately accounted for through a “second-order potential matrix”. Within the framework of the eikonal approximation the problem reduces to a finite system of first-order coupled integro-differential equations with non-local potentials which depend on the two-body density matrix of the target nucleus. The relationship of the above formulation to the DWIA, the close-coupling method, and the Glauber multiple scattering model is examined. This approach is applied to the elastic and inelastic (2⁺, 4.43 MeV) scattering of 1 GeV nucleons by ¹²C. The corrections to the DWIA are sizeable, and the inelastic scattering appears to be very sensitive to the multi-step contributions and the nuclear structure.     

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 protons from Li between 25 and 45 MeV

The elastic and inelastic scattering of protons from ⁶Li has been studied at incident energies of 25.9, 29.9, 35.0, 40.1 and 45.4 MeV. The 2.18 MeV (3⁺, T = 0) first excited state of ⁶Li was found to be strongly excited, but the 3.56 MeV (0⁺, T = 1) second excited state was quite weakly excited. Angular distributions for excitation of the 2.18 MeV level were measured at all five energies, while angular distributions for excitation of the 3.56 MeV level were extracted only at 25.9 and 45.4 MeV. To test the applicability of the optical model for the scattering of protons from such a light nucleus the elastic scattering angular distributions have been analyzed using the eleven-parameter search code SEEK. Available polarization angular distributions were included in the analysis. Reasonable fits to the data have been obtained with an average geometry potential. Theoretical estimates of the real part of the optical potential and the inelastic scattering differential cross sections have been made using the microscopic model for proton-nucleus scattering. Both phenomenological and realistic forces have been considered and the necessary nuclear transition densities have been extracted from experimental elastic and inelastic electron scattering data. An estimate of a possible spin-spin term in the optical potential has also been made.     

Wave functions for low-lying states of light deformed nuclei using a “realistic” hamiltonian and their test by inelastic scattering: The case of 20Ne

Nuclear structure wave functions for the ground and low-lying excited states of ²⁰Ne, obtained from the angular momentum projected deformed particle-hole model using a “realistic” many-nucleon hamiltonian (kinetic energy plus a Brueckner G-matrix based on the Hamada-Johnston potential), are used as input to microscopic antisymmetrised DWBA analyses of inelastic proton scattering from ²⁰Ne. This nuclear structure model, which has been previously shown able to describe the essential features of the giant multipole resonances of both ²⁰Ne and ²⁸Si, predicts angular distributions for inelastic proton scattering, exciting a number of states below 9 MeV in ²⁰Ne, in qualitative agreement with the available data; a somewhat surprising result given the nuclear structure model's completely microscopic formulation. Anomalies observed in the assignment of some predicted levels to experimental states suggest some shortcomings in the form adopted for the hamiltonian.     

High energy elastic and inelastic p-12C scattering and nuclear deformation

Starting from a microscopic deformed picture of the ¹²C nucleus, and using angular momentum projected wave functions, the elastic and inelastic 1 GeV p-scattering differential cross sections have been analysed within the framework of the Glauber theory. From a comparison of the results obtained in a full Glauber calculation and in the optical limit, it has been shown that the elastic scattering and, to a lesser extent, the transition to the 2⁺(4.44 MeV) level are only weakly affected by the long-range correlations. In contrast the scattering to the 4⁺(14.08 MeV) state includes crucial multi-step contributions which affect the differential cross section both in shape and magnitude. Similarly the corrections to the DWIA are essential for the transition to the 3^?(9.64 MeV) state and a satisfactory explanation of the qualitative differences observed between the 2⁺ and 3^? inelastic cross sections in ¹²C is given. The great sensitivity of the cross sections to the nuclear deformation is shown and a generally good agreement with experiment for both the electron form factors and 1 GeV p cross sections has been obtained for the ground-state intraband transitions using a single oblate intrinsic state. The importance of a correct treatment of the rotational motion through the angular momentum projection is underlined and the use of the adiabatic approxmation is critically examined.     

194Pt(12C, 12C′) reaction and the triaxial-rotor model

Elastic and inelastic scattering differential cross sections for the ¹⁹⁴Pt(¹²C, ¹²C′) reaction at a bombarding energy of 78 MeV have been measured. Data have been obtained for 0⁺, 2⁺, 4⁺, and 2^+′, states in ¹⁹⁴Pt. The data have been analyzed using a rigid asymmetric-rotor model in coupled-channels reaction calculations. It is found that satisfactory fits to all data can be obtained but only if the hexadecapole deformation is included in the asymmetric-rotor model.     

Eikonal expansion in electron scattering

We extend a previously developed eikonal expansion method to the case of high-energy electron scattering from dynamic nuclei. Nuclear degrees of freedom can be included either by a DWBA-like expansion or by neglecting the nuclear excitation energies. The latter approach is considered in detail and applied to the elastic and inelastic scattering from deformed nuclei. The impact parameterT-matrix is calculated by diagonalizing the inelastic zeroth-order and first-order eikonal phases in the subspace of the nuclear rotational levels; static eikonal phases are included up to second order. For¹⁵²Sm,¹⁵⁴Sm coupled-channel calculations including three and four rotational states show large multi-step effects for the 0⁺→4⁺ and the 0⁺→6⁺ excitations compared to DWBA results.     

Dispersive effects in the excitation of the ground-state rotational band of deformed nuclei by medium energy protons

The effects of long-range correlations on high-energy elastic and inelastic proton-nucleus scattering are investigated using a coupled-channel (CC) formalism where dispersive effects, i.e. virtual excitations and de-excitations of the nucleus during the scattering process, are taken into account. When treated to all orders, this CC approach is completely equivalent to the Glauber multiple scattering model, whereas it reduces to the DWIA when the coupling between channels is neglected. In ¹²C, we compare the results of the CC formalism where only a finite number of collective channels are explicitly treated with those obtained in a full Glauber calculation. This permits one to get a clear appreciation of the importance of the various sequential processes. In addition it sheds light on the influence of those channels which have been omitted. This CC approach is then applied to investigate the excitation of the ground-state rotational band in the deformed samarium isotopes, ¹⁵²Sm and ¹⁵⁴Sm, by l GeV protons. It appears that the elastic scattering on deformed nuclei is only weakly affected by dispersive corrections, at least for momentum transfer less than 2 fm^?1. In contrast, inelastic scattering to the ²⁺, 4⁺ and 6⁺ rotational states proceeds not only by direct transitions, but includes also crucial multi-step contributions which strongly affect the differential cross sections.     

Study of form factors of elastic and inelastic electron scattering by 20Ne

The elastic electron scattering form factor and also the form factor of inelastic scattering accompanied by nuclear transitions to excited states of the ground rotational band are calculated within the Sp_z(2, R) model reproducing the dynamics of quadrupole nonsphericity of ²⁰Ne. The Sp_z(2, R) model is shown to describe correctly the experimental dependence of the elastic and inelastic (for the 0⁺ to 2⁺ state transition) form factors of the momentum transferred and, consequently, to remove some difficulties experienced by other dynamic models.     

Elastic and inelastic scattering of 178 MeV protons from 58Ni and 60Ni

The elastic and inelastic scattering of 178 MeV protons from ⁵⁸Ni and ⁶⁰Ni has been studied. Angular distributions were measured for the differential cross sections for elastic scattering as well as inelastic scattering from excited states below about 5 MeV, all with natural parity. For the elastic and for the inelastic scattering from the first excited state (2⁺ in both nuclei, the angular distributions for the polarization were also measured. The measurements extend out to c.m. angles of about 60°, corresponding to a momentum transfer of about 600 MeV/c.The elastic and inelastic scattering data were compared to the results of coupled-channel calculations in the vibrational model using a deformed spin-orbit interaction of the full Thomas form. Good agreement was found in general showing that the main features of the experimental results are well described in this model.     

Evidence for the importance of the nucleon-nucleon spin-orbit interaction in the inelastic excitation of high spin states in Zr

A microscopic calculation of the inelastic scattering of 61.2 MeV protons to the 6⁺ and 8⁺ states in ⁹⁰Zr has been carried out which includes the central, tensor and spin-orbit parts of the nucleon-nucleon interaction. The two-body spin-orbit force is found to play an important role in exciting these high spin states.     

Elastische und inelastische Streuung von 104 MeV Alpha-Teilchen an58,60,62,64Ni

Differential cross sections are measured for the elastic and inelastic scattering of 104 MeV α-particles from^{58, 60, 62, 64}Ni. The experimental results are analyzed in terms of coupled channels on the basis of an anharmonic vibrational model and prove to be quite sensitive to the values of the deformation parameters. For forward angles the 4⁺ angular distributions of^58,60Ni are dominated by aL=4 single excitation mechanism. This is in keeping with theE4-transitions observed in (e, e′) scattering. From the 2 ₁ ⁺ - and 3 ₁ ⁺ -results transition rates are derived which can be compared to results of electromagnetic methods and of inelastic proton scattering studies. The comparison indicates that the transition rates differ and are generally higher for the proton scattering. Especially in the case of the 3^? states of^58,60Ni the differences are obvious. The elastic cross sections are analyzed both on the basis of the usual phenomeno-logical model and in terms of a semimicroscopic folding model resulting in values of rms-radii for the nuclear matter distribution.     

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.