Nucleon transfer reactions to rotational states induced by206, 208Pb projectiles

In a systematic study of nucleon transfer reactions accompanied by Coulomb excitation we have bombarded¹⁵²Sm,¹⁶⁰Gd and²³²Th with^{206, 208}pb beams at incident energies close to the Coulomb barrier. Particle-gamma coincidence techniques were used to identify excited states of reaction products populated through inelastic scattering and in nucleon transfer reactions. One-neutron stripping and pick-up reactions on¹⁵²Sm were observed leading to known states of the rotation alignedi _13/2-bands in¹⁵³Sm and¹⁵¹Sm. In the¹⁶⁰Gd+^{206, 208}Pb systems no significant population of low lying states of product nuclei was found in the nucleon-transfer channels. Large cross sections were observed for one- and two-neutron pick-up from²³²Th at an incident energy of 6.4 MeV/u. Around the grazing angle they are of the same order of magnitude as the cross section measured for inelastic scattering. The results are analyzed in the framework of semiclassical models.     

Long range absorption and other optical-model effects from strong inelastic coupling

An optical potential component is constructed to represent the effect of a strongly coupled inelastic excitation upon elastic scattering. In the particular case of quadrupole Coulomb excitation a long range imaginary potential component is derived in closed form. The effects of long range absorption upon the elastic scattering are considered in a general way by inserting this potential into a weak absorption model and deriving an elastic scattering cross section in closed form. Below the Coulomb barrier the formula takes a simple form which may be related to the semiclassical theory of Coulomb excitation. The potential component arising from nuclear excitation of an inelastic state may be evaluated numerically on a computer. Two examples computed (50 MeV α-scattering on ¹⁵⁴Sm and 60 MeV ¹⁶O scattering on ⁴⁰Ca) exhibit strong l-dependence in the potential component.     

Coupled channel analysis of asymmetry measurements for low-lying states of Sm and Sm by inelastic proton scattering

Asymmetries and differential cross sections have been measured for elastic and inelastic scattering of 24.5 MeV polarized protons from the spherical nucleus ¹⁴⁸Sm. The comparison with the results of an asymmetry measurement at the same proton energy on the rotational nucleus ¹⁵²Sm shows significant differences for the first 2⁺ states. A coupled-channels analysis for the first 2⁺ and 3⁻ states in ¹⁴⁸Sm and for the 2⁺ and 4⁺ states of the ground-state rotational band in ¹⁵²Sm fits the experimental data very well.     

Analysis of elastic and inelastic α + <Superscript>24</Superscript>Mg scattering within the <Emphasis Type="Italic">S</Emphasis> matrix model involving regge poles

A generalization of the phenomenological S-matrix model taking into account isolated Regge poles is proposed for simultaneously describing refractive effects in the cross sections for the elastic and inelastic scattering of light nuclei. The cross sections for elastic α + ²⁴Mg scattering are analyzed at energies of 50, 54, 65.7, 81, and 119 MeV. The analysis of the cross sections for elastic scattering is supplemented with an analysis of the inelastic scattering of alpha particles that is accompanied by the excitation of the first excited state (2⁺) of ²⁴Mg nuclei. It is shown that the proposed model makes it possible to describe satisfactorily all of the aforementioned cases of elastic and inelastic scattering, correctly reproducing the refraction Airy structures and anomalous large-angle scattering that are observed at large scattering angles.     

Untersuchungen an Neutronenresonanzen im57Fe

The total neutron cross section of⁵⁷Fe in the keV region was measured in a transmission experiment using a pulsed Van de Graaff generator. Experimental data were fitted with a two channel multilevel formula to obtain the individual resonance parameters including the inelastic scattering width. The strength-function and its spin dependence are investigated. The data indicate a correlation between the phases of the reduced amplitudes for elastic and inelastic scattering. In a further experiment the 14,4 keV-γ-radiation of the (n, n′ γ)-reaction in⁵⁷Fe was detected. The application of this reaction for Möβbauer experiments is discussed.     

Quadrupole moments and nucleon excitation strengths in even-A Sm isotopes

We present a coherent coupled-channel analysis of 7 MeV neutron and 16 MeV proton elastic and inelastic scattering from ^{148, 152, 154}Sm. The optical potential and nuclear deformation parameters are determined so as to fit not only these elastic and inelastic scattering data but also the low-energy neutron scattering properties and the total cross sections over a wide energy range. This analysis provides evidence of the same excitation strengths for both projectiles in the case of ^{152, 154}Sm, and of a smaller excitation strength for the proton than for the neutron in case of ¹⁴⁸Sm. Moreover the quadrupole moments of these deformed optical potentials are in good agreement with those extracted from Coulomb excitation measurements and from nuclear matter distribution calculations.     

Inelastic proton scattering from Ba and Sm at 30 MeV

Measurements of the inelastic scattering of 30 MeV protons from ¹³⁸Ba and ¹⁴⁴Sm have been carried out with 7–10 keV energy resolution. Differential cross sections were measured for levels up through 3.4 MeV excitation energy. For most of these states J^π assignments are suggested on the basis of angular distributions distinctly characteristic of angular momentum transfer L = 2, 3, 4,or 6.     

Calculations of inelastic cross sections for rotational excitation

Cross sections for scattering of N₂ (j=0) molecules on He atoms have been calculated for relative energies below 5 · 10^?3 eV (58 °K). The time independent scattering formalism ofArthurs andDalgarno was used together with an assumed Lennard-Jones type potential with anisotropicP ₂(cos?) terms in the attractive and repulsive parts. The resulting system of coupled differential equations was solved in the distorted wave and close coupling approximations for the differential and integral cross sections for elastic and inelastic (j=0→j=2) scattering. In the integral inelastic cross section several sharp resonances were found to contribute 40% to the cross section at energies below 40 °K. The resonance peaks are attributed to orbiting or short-lived compound states since they are also observed in the elastic cross section at energies which are lower by the excitation energy of 1.5 · 10^?3 eV. Finally, the effect of varying the potential parameters on the integral inelastic cross section was studied at 50 °K and a rough formula for the cross section as a function of the parameters is obtained. The formula shows that a certain ratio of repulsive and attractive anisotropies leads to a small inelastic cross section indicating a mutual cancellation.     

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.     

Elastic and inelastic scattering of nucleons from 16O

Measurements of differential elastic and inelastic cross sections for neutron scattering from ¹⁶O at incident energies 18 to 26 MeV are presented. In addition to cross sections for neutron scattering differential cross sections for proton scattering up to 66 MeV are described in terms of phenomenological optical model potentials. At 24.5 MeV incident energy inelastic scattering up to 11.5 MeV excitation was measured. The elastic and inelastic compound nucleus contributions were examined. Direct inelastic scattering from the normal parity states was calculated using the DWBA and coupled-channel formalisms. The inelastic scattering cross section from non-normal parity state 2⁻ was calculated using the coupled-channel formalism via multi-step processes. Cross sections due to inelastic scattering from some of the states, which are thought to be members of an excited state rotational band were calculated using both vibrational and rotational approaches and were compared.     

A QCD analysis of the prompt photon away-side jet cross section measured in pp collisions

A QCD analysis of the recently measured double inclusive cross section for pp → γ + away-side jet + X at √s = 63 GeV is presented. It is pointed out that these data are indeed compatible with a gluon distribution in the proton, which is (i) determined from deep inelastic lepton-proton scattering, and (ii) which is required to describe all available data for pN → γX.     

Mechanism of elastic and inelastic proton scattering on a 15C nucleus in diffraction theory

The amplitudes for elastic and inelastic proton scattering on the neutron-rich nucleus ¹⁵C (to its J ^?? = 5/2⁺ level in the latter case) in inverse kinematics were calculated within Glauber diffraction theory. First- and second-order terms were taken into account in the multiple-scattering operator. The ¹⁵C wave function in the multiparticle shell model was used. This made it possible to calculate not only respective differential cross sections but also the contribution of proton scattering on nucleons occurring in different shells. The differential cross sections for elastic and inelastic scattering were calculated at the energies of 0.2, 0.6, and 1 GeV per nucleon.     

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.     

Possible mesonic effects on inelastic proton scattering to the 10.24 MeV 1+ state in 48Ca

Differential cross sections and analyzing powers were measured for inelastic scattering of 160 MeV protons to the ⁴⁸Ca 10.24 MeV, 1⁺ state. DWIA calculations with shell-model wave functions which fit inelastic electron scattering form factors predict too much cross section at small q and too little at large q for inelastic proton scattering. These results are consistent with the q-dependent modification of magnetic transitions anticipated from mesonic effects such as virtual Δ(1232)-hole excitations.     

Elastic and inelastic scattering of K+ mesons on deformed nuclei

Various aspects of the scattering of medium energy K⁺ mesons on deformed nuclei are investigated in the light of a specific example, viz. the scattering of 800 MeV/c positive kaons on ¹⁵²Sm. The effects of coupled channels are found to be significant despite the fact that the K⁺ meson is a rather weakly interacting hadronic probe. The localization of the reaction mechanism on a deformed target is discussed for both protons and K⁺ mesons to compare the extent of surface and volume probing capability of these two projectiles. The results show the remarkable sensitivity of the elastic and inelastic K⁺ differential cross sections to the differences between the neutron and proton density distributions in deformed nuclei.     

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.     

Measurement of spin-alignment of excited12C2+ nuclei in interactions of16O with12C usingγ-decay in flight

Measuring energy spectra of nuclei afterγ-decay of excited states in flight the spin alignment of¹²C₂₊ states has been measured. Inelastic scattering,¹⁶O(¹⁶C,¹²C₂₊)¹⁶O and the reaction¹²C(¹⁶O,¹²C₂₊)¹⁶O leading to¹²C₂₊ (4.43 MeV) state have been studied. Characteristic line shapes of the¹²C₂₊ peak were observed using a Q3D magnetic spectrometer. The magnetic substate (m-states) population has been deduced from the spectra as function of reaction angle. A comparison of the measuredm-state population with reaction models shows that the first reaction is consistent with inelastic scattering although discrepancies remain. Discrepancies are also obtained if the reaction¹²C(¹⁶O,¹²C₂₊)¹⁶O is interpreted using a FRDWBA transfer calculation. At least 1/3 of the cross section can be attributed toα-transfer. A calculation which couples transfer and inelastic scattering channels seems to be necessary.     

Electromagnetically induced alpha-emission in an analytically solvable model

Alpha emission induced byγ-absorption or inelastic electron scattering on²⁰Ne is examined in an analytically solvable model. The exact results are compared with an approximation recently proposed by Fliessbach. The model is used as a testing case to decide which definition of alpha-spectroscopic amplitudes is appropriate. A method for handling center of mass effects is presented.