Study of nuclear-coulomb interference effects in inelastic deuteron scattering on 238U

The angular distributions of elastically and inelastically scattered deuterons from ²³⁸U at E = 17 MeV are compared to coupled-channel calculations. The cross sections at small scattering angles are strongly influenced by nuclear-Coulomb interference effects and allow a simultaneous extraction of nuclear (optical potential) and charge quadrupole deformation parameters. Two different deformed Coulomb potentials and the parameters of the optical model are discussed.     

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.     

Quasi-free scattering in the 6Li(d,dα)2H reaction at 52 MeV

In order to study the momentum distribution of an α-cluster in ⁶Li we have investigated the quasi-free scattering of deuterons in the ⁶Li(d, dα)²H reaction, using 52 MeV deuterons. The α-particle detector was kept at a fixed position of 30° and the second detector scanned over a range of coplanar angles. The α-cluster momentum distribution has been extracted by means of the plane-wave impulse approximation, using both the energy-sharing method and the angular correlation method. The momentum distributions so obtained are in good agreement with those obtained from other reactions such as (p, pα) and (α, 2α), and are compared with the spectator model. The reasons why the model works well are discussed. For the first time, to our knowledge, quasi-free scattering of deuterons on an α-cluster of a nucleus has been measured and analysed.     

Measuring elastically scattered 18 MeV deuterons and the shape of nuclei

The angular distributions of 18 MeV deuterons elastically scattered on ⁹Be, ¹⁰B, ¹³C, ²⁴Mg, and ²⁵Mg nuclei are measured using the U-150M cyclotron at the Institute for Nuclear Physics (Almaty, Kazakhstan). The free parameters of the scattering matrix of parametrized phase analysis are determined. We estimate the sign of the nucleus??s deformation for even nuclei ⁶⁴Ni, ⁶⁴Zn, ¹⁴⁴Sm, ¹⁸²W, ¹⁸⁴W, ¹⁹²Os, ²³⁸U, and odd nuclei ⁵⁹Co, ⁶³Cu, ⁸⁹Y, ⁹³Nb, ¹⁰³Rh, ¹⁰⁷Ag, ¹⁸¹Ta, ¹⁹⁷Au, ²⁰⁵Tl, and ²⁰⁹Bi.     

Influence of Coriolis coupling on inelastic scattering of deuterons

Influence of Coriolis coupling on excitation of some Nilsson states in¹⁵⁵Gd,¹⁵⁷Gd and¹⁶⁷Er by inelastic scattering of 12·1 MeV deuterons is analysed. Expanded Nilsson potential with hexadecapolar deformation is used for the model calculations. Theoretical values of reduced transition probability,B(E2) are compared with experimental ones.     

Quasi-free inclusive processes in the two-particle splitting of tritons by deuterons with an energy of 37 MeV

The d + t → d + d + n reaction was experimentally and theoretically investigated at an incident deuteron energy of 36.9 MeV. The experiment was performed on the U-240 isochronous cyclotron at the Institute for Nuclear Research, National Academy of Sciences of Ukraine. Inclusive spectra of deuterons and their angular distributions in the range of 15° ≤ θ_d ≤ 52° were measured. Experimental spectra and angular distributions of the final deuterons from the d + t → d + d + n reaction are satisfactorily described in a diffraction approximation that considers interaction in the final state and the correct asymptotic of the wave function of colliding nuclei. The scattered deuterons are the main contributors to the cross section (up to 70–90%), while the deuterons from tritons can be seen well only at low and high energies, at the edges of the spectra.     

A study of the odd isotopes of copper using the 58, 60, 62, 64Ni(τ, d) 59, 61, 63, 65Cu and 48Ca(τ, d)49Sc reactions

Experimental measurements are reported for the ^{58, 60, 62, 64}Ni(τ, d) ^{59, 61, 63, 65}Cu and ⁴⁸Ca(τ, d)⁴⁹Sc reactions and for the elastic scattering of ³He particles from ^{58, 60, 62, 64}Ni and ⁴⁸Ca targets at an incident energy of 18 MeV. The (τ, d) angular distributions cover the angular range from approximately θ_c.m. = 5° to 90° and the elastic scattering angular distributions range from θ_c.m. = 12° to 172°. In the (τ, d) reactions several weakly excited states, not previously seen in stripping reactions, have been identified and assignments of the transferred angular momentum made. The ⁴⁸Ca(τ, d)⁴⁹Sc reaction data are used in conjunction with the theoretical sum rules of MacFarlane and French to determine the normalization factors to be used with DWBA calculations for different sets of optical potentials. These normalization factors are used to extract spectroscopic strengths and centroid energies from the Ni(τ, d)Cu data which are compared with published model calculations for the odd copper isotopes. It is concluded that these calculations invariably fail to give a consistent picture of the odd copper isotopes mainly due to the use of centroid energies as variable parameters in the model calculations.     

Signature dependence of 1/2+ bands in rare-earth nuclei: Rotation-alignment of g7/2 protons

The origin of the signature splitting of theK=1/2⁺ bands in odd Z rare-earth nuclei Ho, Tm and Lu, unexplained in previous models, is studied by angular momentum projection from deformed Hartree-Fock configurations. Energy spectra,E2 matrix elements and the rotation-aligned angular momenta of nucleons in i_{1 3/2}, h_{1 1/2} and g_7/2 orbits are calculated. Staggering in the rotation-alignment of protons in the g_7/2 orbit causes signature dependent effects in the 1/2⁺ bands.     

SU(3) coupling schemes for odd-odd nuclei in the interacting boson – fermion – fermion model with both odd proton and odd neutron in natural parity orbits

The SU^BFF(3) dynamical symmetry limits of interacting boson – fermion – fermion model are identified and they are appropriate for heavy deformed odd – odd nuclei for configurations with both the odd proton and odd neutron occupying all the natural parity orbits in the corresponding valence shells. There are three symmetry limits and their correspondence with two quasi-particle (proton-neutron) Nilsson configurations is established; one of the limits mixes both Nilsson n_z's and Λ's and other two limits mix only Nilsson Λ's. The ¹⁹¹Ir (d,t) ¹⁹⁰Ir single nucleon transfer spectroscopic strengths are well described by one of the symmetry limits that mixes only Nilsson Λ's. Received: 22 June 1998     

Direct processes in the6Li(α, d)8Be reaction

The angular distributions of deuterons from the ⁶Li(α, d)⁸Be reaction corresponding to the 0⁺ ground state and the 2.9 MeV (2⁺) state in⁸Be have been measured at E_α = 17.3, 23.3 and 25.1 MeV. The excitation functions for this reaction have been measured at seven emission angles in the region from 12 up to 25 MeV. The experimental angular distributions are compared with theoretical predictions obtained using DWBA stripping calculations and the plane wave approximation (PWA) for various direct processes. It is shown that the experimental angular distributions can be described throughout the angular region using the simple mechanisms associated with the break-up of the ⁶Li target nuc clusters and heavy-particle stripping. The interference of these processes is taken into account.     

Calculation of the wide-angle neutron spectra from the ~9Be(d,xn) reaction in a thick beryllium target

The multi-layer computing model is developed to calculate wide-angle neutron spectra, in the range from0° to 180° with a 5° step, produced by bombarding a thick beryllium target with deuterons. The double-differential cross-sections(DDCSs) for the ~9 Be(d, xn) reaction are calculated using the TALYS-1.8 code. They are in agreement with the experimental data, and are much better than the PHITS-JQMD/GEM results at 15°, 30°, 45° and 60° neutron emission angles for deuteron energy of 10.0 MeV. In the TALYS-1.8 code, neutron contributions from direct reactions(break-up, stripping and knock-out reactions) are controlled by adjustable parameters, which describe the basic characteristics of typical direct reactions and control the relative intensity and the position of the ridgy hillock at the tail of DDCSs. It is found that the typical calculated wide-angle neutron spectra for different neutron emission angles and neutron angular distributions agree quite well with the experimental data for 13.5 MeV deuterons. The multi-layer computing model can reproduce the experimental data reasonably well by optimizing the adjustable parameters in the TALYS-1.8 code. Given the good agreement with the experimental data, the multi-layer computing model could provide better predictions of wide-angle neutron energy spectra, neutron angular distributions and neutron yields for the ~9 Be(d, xn) reaction neutron source.     

Spectroscopic study of 75Se by the (d,p) reaction

The (d, p) reaction on ⁷⁴Se was investigated with 6.0 MeV deuterons. Many new levels of the ⁷⁵Se nucleus were found up to 4.7 MeV excitation energy. From a DWBA analysis of the cross sections and the angular distributions, spectroscopic factors and l_n values were obtained for forty levels. A sum rule analysis was applied to the results and the emptiness of low-lying shell model states was extracted.     

High spin spectroscopy in odd-odd 170Lu

High-spin states in doubly odd ¹⁷⁰Lu have been studied through the ¹⁶⁰Gd(¹⁴N, 4nγ) fusion-evaporation reaction at a beam energy of 68 MeV. γγ-coincidences, Eγ,Iγ and angular distribution are measured. For the first time a high-spin level scheme consisting of three rotational structures is proposed. In the πh_9/2Θvp_3/2 yrast band, the (ab) neutron crossing occurs at a rotational frequency of ≈0.27 MeV. This is indicative of the partial disappearance of the blocking effect of the odd neutron. Another signature-split πh_9/2Θvi13/2 band exhibits normal signature-dependence and delayed (bc) neutron crossing is anticipated to occur at h?ω > 0.39 MeV in this structure.     

Photodeuterons from C

Cross sections and angular distributions for the reaction ¹²C(γ, d)¹⁰B have been measured using solid-state detectors mounted in the focal plane of a magnetic spectrometer. The angular distribution of the deuterons restricted to ground or near ground-state transitions is consistent with an E2 reaction; however at deuteron energies not so restricted the reaction appears to be different from pure E2. Deuteron emission was also studied as a function of incident electron energy. A comparison with simple models is made and an estimate of the 2p-2h contribution to the ground state of ¹²C is presented.     

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.     

The magnetic hyperfine field and the electric field gradient at181Ta impurities in Gd metal

The magnetic hyperfine fieldH _hf and the electric field gradientV _zz at¹⁸¹Ta impurties in metallic Gd were determined by time differential perturbed angular correlation measurements with the 133 keV K-conversion electron 482 keV -cascade of¹⁸¹Ta. The sources for these measurements were prepared by implantation of radioactive¹⁸¹Hf ions into Gd. The results are: |H _hf(TaGd; 77 K)|=285(14)kG, and |V _zz(TaGd; 330 K)|=5.32(15)·10¹⁷V/cm². The value ofH _hf fits well into the systematics for 5d impurities in Gd and indicates a positive core polarisation contribution, which is expected if the conduction electrons of Gd have to a large extent d-character. The electric field gradients of the 5d impurities in Gd are not consistent with a proportionality between the ionic and the electronic contribution.     

Hyperfine field of156Gd in TbFe2, TbFe3, TbCo2 and TbCo3 compounds

Time integral γ-γ angular correlation measurements have been made on¹⁵⁶Gd in Tb-3d metal compounds, TbFe₂, TbFe₃, TbCo₂ and TbCo₃, using two Ge(Li) detetctors. From the observation of a linear relation between magnetic hyperfine fields at Gd and Tb nuclei in corresponding compounds, it is inferred that crystalfield induced variations of the Tb moment are negligible. The experimental results are discussed in terms of the conduction electron polarization caused by the magnetic moment of 3d metals.     

Level structure of 76As

The energy-level structure of ⁷⁶As has been studied by the ⁷⁵As(d, p) reaction with 12.0 MeV incident deuterons. Eighty-seven excited energy levels up to 2.5 MeV have been identified. The angular distributions for thirty-nine of the observed transitions are compared with distorted-wave Born approximation calculations. Angular momentum transfers are determined and spectroscopic strengths are deduced from the data. The results are compared with shell-model sum rules and with (d, p) results on N = 42 isotones. Possible spin values are assigned for some of the levels based on the present results, (n, γ), (p, n) and (p, nγ) studies.