Elastic and inelastic deuteron scattering from 152Sm and 162Dy

Angular distributions are measured for 12 MeV deuterons scattered to the 2⁺ and 4⁺ states in ¹⁵²Sm and ¹⁶²Dy. By including the couplings of the ground state to the low-lying excited states, it is shown that the experimental results can be explained by using optical model parameters form a spherical nucleus. Deformation amplitudes are deduced and compared to those found from inelastic α-particle scattering and from Coulomb excitation.     

Measurements ofE4 matrix elements in152Sm and154Sm

TheE4 transition matrix element from the ground state to the 4⁺ state has been measured in¹⁵²Sm and¹⁵⁴Sm, by comparing relative thick targetγ-ray intensities following Coulomb excitation with 12 MeV⁴He, 24–30 MeV¹⁶O, and 35–40 MeV³²S projectiles. Values for 〈0⁺∥?(E4)∥4⁺〉 of (+0.31 _?0.20 ^+0.12 ) barn in¹⁵²Sm and (+0.50 _?0.12 ^+0.09 ) barn in¹⁵⁴Sm are found.     

Measurement of lifetimes for high spin states in 152Sm, 154Gd and 156Gd by the Doppler broadened lineshape method

Lifetimes of the ground band levels up to spin 10⁺ in ¹⁵²Sm, ¹⁵⁴Gd and ¹⁵⁶Gd have been measured by the Doppler broadened lineshape (DBLS) analysis of peaks observed following Coulomb excitation of enriched metallic targsts by 132–143 MeV ³⁵Cl beams. The γ-ray lineshapes were measured in time coincidence with backscattered ions and were analyzed with a computer program incorporating tabulated electronic stopping powers. The nuclear stopping power of Lindhard et al and multiple scattering treatment by Blaugrund were assumed. Renormalization of the electronic stopping powers given by Northclifie and Schilling was found necessary to reproduce the accurately known lifetime of the 6⁺ state in ¹⁵²Sm. Stopping powers for Sm in Sm inferred from the tabulated ⁴He stopping power of Ziegler and Chu support this renormalization. The stretching parameter a derived from the lifetimes of the ground band are (2.0 ± 0.6) × 10^?3, (1.85 ± 0.40) × 10^?3 and (0.0 ± 0.45) × 10^?3, in ¹⁵²Sm, ¹⁵⁴Gd and ¹⁵⁶Gd, respectively.     

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.     

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.     

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.     

Nuclear deformations from inelastic α-scattering on rare earth nuclei at energies near the Coulomb barrier

Alpha particles in the energy range of 10–20 MeV and scattered at various angles were used to excite the 0⁺, 2⁺, 4⁺ members in the ground state bands of ¹⁵²Sm, ¹⁵⁴Sm and ¹⁸⁶W. The measured excitation probabilities for bombarding energies below the Coulomb barrier were analyzed in the framework of Coulomb excitation theory. The resulting matrix elements of the E2 and E4 multipole operators were interpreted in terms of charge deformation parameters β^cλ = 2, 4. The cross sections for higher energies were analyzed in terms of the deformed optical potential and resulted in potential deformation parameters β^pλ = 2, 4. The two sets of deformation parameters show the same general trend of variation with target mass number. Still, significant differences are observed in some particular cases.     

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.     

Shape evolution for Sm isotopes in relativistic mean-field theory

The evolution of shape from the spherical to the axially deformed shapes in the Sm isotopes is investigated microscopically in relativistic mean-field theory. The microscopic and self-consistent quadrupole deformation constrained relativistic mean-field calculations show a clear shape change for the even-even Sm isotopes with N = 82-96. The potential surfaces for ¹⁴⁸Sm, ¹⁵⁰Sm and ¹⁵²Sm are found to be relatively flat, which may be the possible critical-point nuclei. By examining the single-particle spectra and nearest-neighbor spacing distribution of the single-particle levels, one finds that the single-particle levels in ¹⁴⁸Sm , ¹⁵⁰Sm, and ¹⁵²Sm distribute more uniformly.     

Determination of the static quadrupole moment of the first 2+ states of 122Te, 124Te,and 130Te by heavy-ion coulomb excitation

A Coulomb excitation experiment has been performed on the first 2⁺ states of ¹²²Te, ¹²⁴Te and ¹³⁰Te. The relative excitation probabilities of the first 2⁺ states were measured at backward and forward projectile scattering angles. Particle-γ coincidences were used to identify the inelastic events. The data were analyzed with the aid of the Winther-deBoer multiple Coulomb excitation program. Separate γ-ray angular distribution measurements were made as a function of target recoil velocity to determine the influence of the deorientation effect. The projectile and bombarding energy were chosen to minimize the effect on the experiment of higher state interference due to Coulomb excitation of the first 2⁺ state via the second 2⁺ state. For positive higher state interference the extracted quadrupole moments of the first 2⁺ states are Q₂₊ = ?0.43 ± 0.08 b, ?0.49 ± 0.08 b and ?0.08 ± 0.08 b for ¹²²Te, ¹²⁴Te and ¹³⁰Te respectively. These results and other measurements of Q_2⁺ for the doubly even Te isotopes are used to discuss the model dependent calculations of Q_2⁺.     

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.     

Coulomb-nuclear interference for inelastic deuteron scattering

The interference between Coulomb excitation and nuclear excitation has been observed for ^{54, 56}Fe, ⁶⁰Ni, ¹¹⁴Cd, ¹⁵²Sm, and ¹⁹²Os by measuring excitation functions of elastic and inelastic deuteron scattering at back angles. The interference is strongly constructive, indicating a predominantly imaginary nuclear form factor. DWBA calculations using the collective model, although predicting constructive interference, are unable to predict the magnitude of the observed effect.     

Comparison of the elastic and inelastic scatterings between152Sm+12C and148 Nd+16O

Angular distributions of elastic and inelastic scattering have been measured for¹⁵²Sm+¹²C at 63.2 MeV and¹⁴⁸Nd+¹⁶O at 90.9 MeV. An evident interference pattern in the inelastic scattering has been observed for the first time in a strong Coulomb coupling system.We are indebted to Dr. S. Pieper for supplying the Ptolemy Program. One of us (Chenglie Jiang) would like to acknowledge the Argonne National Laboratory for the opportunity given, to perform theoretical calculations with the code Ptolemy during his visit there. Thanks are also due to Mr. H. Folger (GSI, Germany) for supplying the targets. This work was supported in part by China National Nature Science Fundation.     

A muonic X-ray study of the charge distribution of 144, 148, 150, 152, 154Sm

We report the measurement of the energies of the 4f → 3d, 3d → 2p and 2p → Is muonic atomic transitions in separated isotopes of ^{144, 148, 150, 152, 154}Sm, and that of the 2s → 2p transitions of ¹⁵²Sm as well. Using these transition energies as well as the hyperfine splittings of the 2p levels, we have interpreted our data in terms of a deformed Fermi distribution for the charge density and obtained good fits. A model independent analysis of the isotope shifts in terms of generalized R_h moments has been made and is in good agreement with electronic X-ray and optical isotope shifts. The static quadrupole moments and the isomer shifts of the first excited state of ^{152, 154}Sm have been determined from the 2p hyperfine structure.     

Measurement of nuclear deformation parameters from elastic and inelastic scattering of α and 3He ions on Te isotopes

Cross sections for the elastic scattering of ⁴He by ^{122, 124, 126, 128}Te and ³He by ¹²⁸Te and for inelastic transitions to the lowest 2⁺ states of Te isotopes were measured for several scattering angles at bombarding energies in the vicinity of the Coulomb barrier. The data were analyzed in the framework of the optical model and the DWBA from which optical potential and deformation parameters were extracted. A detailed study of the fit procedure is presented with emphasis on the significance of the extracted parameters and the correlations among them.     

Decay of the 4.2-min152Pm into levels of152Sm

After bombardments of enriched¹⁵²Sm with 14-MeV neutrons, three isomers of¹²⁵Pm reaction, have been observed with half-lives of 4.2±0.2 min, 7.5±0.2 min and 15.0±1.0 min. Sources of pure 4.2-min¹⁵²Pm were obtained by separating the promethium from its parent 11-min¹⁵²Nd produced by thermal-neutron induced fission of²³⁵U. The beta and gamma radiations of the 4.2-min¹⁵²Pm have been investigated using semiconductor and scintillation spectrometers. Most of theγ-ray transitions could be placed in a level scheme for 152Sm. Especially interesting is a level at 1083 keV for which the assignmentI ^π=0⁺ is proposed. In a 4πβγ experiment, the ground state feeding of¹⁵²Sm in theβ ^?-decay of the 4.2-min¹⁵²Pm has been measured to be 61% of allβ-ray transitions. AQ _β-value of 3.4±0.2 MeV has been obtained.     

Large-angle 6Li + 28Si elastic and inelastic scattering at 27 and 34 MeV

Elastic and inelastic scattering data extending to θ_c.m ≈ 175° are reported for ⁶Li + ²⁸Si at 27 and 34 MeV. Optical model analyses of the elastic data were made using a variety of real potential forms. The large-angle data cannot be fitted with a Woods-Saxon real potential, but are well described by Woods-Saxon squared, double-folded or Fourier-Bessel potentials. The real potential is the same at both energies, but the imaginary potential is weaker at 27 MeV. The inelastic data were analyzed using the DWBA and coupled channels techniques with folded real form factors and deformed Woods-Saxon imaginary potentials, with the deformations taken from electron scattering. The 2⁺ state was fitted well at both energies with the DWBA, while the prediction decreased too rapidly at large angles for the 4⁺ state. The large-angle 4⁺ data were better described when two-step excitations were included in the coupled-channels calculations. The forward-angle 2⁺ data are sensitive to the interference between Coulomb and nuclear scattering and show that the nuclear and Coulomb deformation parameters β₂ are equal for this transition.