201 MeV proton excitation of giant resonances in 208Pb: Macroscopic and microscopic analysis

The region of the giant resonances in ²⁰⁸Pb has been investigated by inelastic scattering of 201 MeV protons. To test the analysis, angular distributions were measured for the low-lying 3^?, 5^?, 2⁺ and 4⁺ collective states. The giant isoscalar quadrupole resonance (ISGQR) is split into two structures, one at 9.0 MeV with a full width at half-maximum Γ = 1.0 MeV, the other one at 10.6 MeV (Γ = 2.0 MeV), with fine structures at 8.9, 9.3, 10.1, 10.6 and 11 MeV. A macroscopic analysis using the distorted-wave Born approximation (DWBA) leads for the low-lying collective levels, as well as for the ISGQR, to transition probabilities too small by a factor of two, compared with those obtained in other reactions. Microscopic analysis using the distorted-wave impulse approximation (DWIA), with three different sets of random phase approximation (RPA) transition densities, is in very good agreement with the data. At forward angles, in the 12 to 16 MeV excitation energy region, a strong resonance at 13.5 MeV (Γ = 3.6 MeV) is accounted for by the Coulomb excitation of the isovector giant dipole resonance (IVGDR); at larger angles the results are compatible with the excitation of the isoscalar monopole resonance (ISGMR) located at 13.9 MeV (Γ = 2.6 MeV).A resonance located at 21.5 MeV (Γ = 5.7 MeV) appears as the superposition of an isovector quadrupole resonance (IVGQR) excited by Coulomb interaction and a resonance of multipolarity L = 1 ΔT = 0 (ISGDR “squeezing mode”).     

Neutron scattering from 208Pb

Elastic scattering of 7, 9, 11, 20 and 26 MeV neutrons from ²⁰⁸Pb has been measured with the Ohio University Tandem Van de Graaff accelerator. Standard pulsed beam time-of-flight techniques were employed. Measurements of the incident flux at 0° were used to normalize the differential cross sections. The measured cross sections were corrected for dead time, detector efficiency, flux attenuation, multiple scattering, finite geometry, neutron source anisotropy and compound elastic contribution. Relative uncertainties are estimated to be between 5%–10% and the uncertainty in the normalization is estimated to be less than 5 %. The data were used to obtain neutron optical potential parameters. A comparison with proton optical parameters is presented, and the (p, n) quasi-elastic cross section is calculated and compared with available data. Deformation parameters for the 3^? state (Q = ?2.615 MeV) and 5ā (Q = ?3.198 MeV) in ²⁰⁸Pb were obtained at incident energies of 11 and 26 MeV.     

The 208Pb(α, 3He)209Pb reaction at 58 MeV

The ²⁰⁸Pb(α, ³He)²⁰⁹Pb reaction at 58 MeV has been used to search for high-spin states in ²⁰⁹Pb. Only three levels are excited with appreciable intensity: the ground state $\text{(2}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}$ and levels at $\text{0.781 (}\text{li}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}\text{and}\text{1.426}\text{MeV}\text{(}\text{lj}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}\text{)}$. The angular distributions for these levels have been measured and analyzed using standard DWBA calculations to obtain spectroscopic strengths. The ²⁰⁸Pb(α, α) elastic scattering was measured and optical parameters deduced from the data. A normalization value N = 50 yields spectroscopic values which are close to the values measured in the (d, p) reaction. The (α, ³He) reaction should easily pick out any appreciable components of the $\text{j}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}$ shell model state, which weak-coupling calculations predict should be fragmented. However only three weak transitions previously seen in a (d, p) experiment are observed.     

Damping of the giant spin-flip dipole and spin-flip quadrupole charge exchange modes in 90Zr

The damping of the giant spin-flip dipole (L=1, S=1, T=1, J^π=0⁻, 1⁻, 2⁻) and spin-flip quadrupole (L=2, S=1, T=1, J^π=1⁺, 2⁺, 3⁺) charge exchange resonances in ⁹⁰Zr is calculated in a microscopic nuclear structure model which includes both one-particle-one-hole (1p1h) and two-particle-two-hole (2p2h) configurations in a systematic way. It is shown that the coupling to 2p2h configurations gives rise to a strongly energy dependent spreading width which shifts a large fraction of transition strength to high excitation energies. The implications for the analysis of intermediate energy ⁹⁰Zr(p,n) data is discussed.     

Scattering and transfer reactions for 6, 7Li + 90, 91Zr

Elastic scattering data have been measured for the ⁷Li + ⁹⁰Zr, ⁶Li + ⁹⁰Zr, and ⁶Li + ⁹¹Zr systems at E(Li) = 34 MeV. Inelastic scattering data for the ⁷Li + ⁹⁰Zr and ⁶Li + ⁹⁰Zr systems were also measured for the 2⁺(2.18 MeV) and 3^?(2.75 MeV) states in ⁹⁰Zr and the $\text{1}\text{2}{}^{\mathrm{?}}\text{(0.48}\text{MeV}\text{)}$ state in ⁷Li. Optical model analyses of the elastic scattering data and DWBA analyses for the states in ⁹⁰Zr were performed. The deduced deformation lengths for the 2⁺ state agreed with those extracted in other studies but the deformation length for the 3^? state was smaller. The ⁹⁰Zr(⁷Li, ⁶Li)⁹¹Zr angular distributions were measured for the 1.21 and 2.03 MeV states and the 2.19 MeV doublet in ⁹¹Zr. Also, ⁹⁰Zr(⁷Li, ⁶He)⁹¹Nb angular distributions were measured for the ground states, 0.10, 3.41 and 4.82 MeV states in ⁹¹Nb. The transitions well matched in angular momentum were described by finite-range DWBA calculations, while other transitions displayed the same phase problems seen with heavier ions. The extracted spectroscopic information was consistent with the results of other reaction studies. At the present energy, it was not possible to determine whether the l = 1 phase problem that occurs for heavy-ion single-nucleon transfer reactions on 2s-1d shell nuclei occurs in ⁹¹Zr also.     

Angular correlations from 6Li break-up near the Coulomb barrier of 118Sn and 208Pb

Absolute coincidence cross sections for three-particle final states have been measured inplane in the ⁶Li + ¹¹⁸Sn and ⁶Li +²⁰⁸Pb reactions at incident energies of 22.2 and 23.0 MeV, respectively. Most strongly populated is the α + d branch, proceeding sequentially through the first excited state (E_x = 2.18 MeV, J^π = 3⁺) of ⁶Li. The angular distributions are fitted by DWBA calculations including Coulomb interaction in the excitation of the projectile. The main competing reaction channels above and at the Coulomb barrier (¹¹⁸Sn: E/E_c ≈ 1.3; ²⁰⁸Pb: E/E_c ≈ 0.9) are: neutron transfer (⁶Li, αp) and the non-sequential α + d break-up of ⁶Li. The latter spectra are consistent with a quasi-free break-up mechanism. No ³He or tritons have been found in the coincidence spectra, as well as no evidence for a three-particle dissociation of ⁶Li into α + p + n.     

Cross sections and reaction mechanisms of (p,pxn) reactions on 208Pb in the 24–52 MeV range

The cross sections for the reactions ²⁰⁸Pb(p, pn)^207mPb, ²⁰⁸Pb(p, p2n)^206mPb have been measured for 24, 28, 36, 44 and 52 MeV incident protons. The experimental results are shown to be consistent with the clean knockout mechanism for the (p, pn) reaction and with knockout of one neutron followed by evaporation of another for the (p, p2n) reaction. We deduce a theoretical formula for the cross section for these reactions.     

Excitation of ΔL = 0 spin-flip transitions in the N = 28 isotones by 201 MeV proton inelastic scattering

The effect of the three-nucleon forces on the triton binding energy (E_T) is investigated. Two different types of three-nucleon potentials are considered, one involving 2π-exchange (V_ππF) and the other involving 2σ-exchange (V_SSF) which is an approximation to 3π exchange. Both V_ππF and V_SSF are constructed using the πN scattering amplitude extrapolated to off (pion) mass shell subject to PCAC. The contribution of V_ππF and V_SSF to e_t are calculated in the first-order perturbation using the triton wave function obtained by solving the Faddeev equations with the Reid soft-core potential. The Fujita-Miyazawa force is also investigated as a special case. We find that the effect of V_ππF on E_T is sensitive to the assumed pionic form factor and is small due to cancellation between the πN s-d wave and p-wave contributions. The effect of V_SSF is also found to be small.     

Excitation of low-lying levels and giant resonances in 90Zr via 57.5 MeV polarized proton inelastic scattering

Differential cross section and analyzing power angular distributions have been measured for transitions to low-lying bound states with J^π = 2⁺, 3^?, 4⁺ and 5^?, and the giant resonance region from 6 to 27 MeV excitation energy. Collective model calculations using a full Thomas form factor reproduce the data fairly well. The so-called LEOR turns out not to be seen as pure E3 in (p, p′). In the giant resonance region the data do not reveal the presence of a sizeable monopole strength, 10–20% of the energy-weighted sum rule at most. There is strong indication for a mixture of E2 (18% of the EWSR) and E4 (16% of the EWSR). Calculations were also carried out using RPA (1p1h) wave functions. They reproduce the experimental data rather poorly, except for the general behaviour of the cross-section angular distributions.     

High-spin states in 208Rn

The yrast decay scheme of ²⁰⁸Rn has been investigated up to spin $\text{≈ 20}\text{h}\text{?}$ and an excitation energy of ≈ 6 MeV. Several different γ-ray spectroscopic techniques were used to determine the properties of excited states and transitions in the nucleus. Significant changes to the previously established level scheme are proposed, based on the existence of an unobserved 3.1 keV transition. Simple empirical shell-model calculations of level energies aided in the assignment of shell-model configurations to excited states and the decay scheme is discussed in terms of these configurations. The energy level systematics for the even radon isotopes, from A = 206 to 212 are discussed, as are core polarization effects in the even radon isotopes (A = 204 to 210) and polonium isotopes (A = 202–208).     

The charge-distribution differences of 209Bi, 208, 207, 206, 204Pb and 205, 203Tl investigated by elastic electron scattering and muonic X-ray data

Elastic electron scattering cross sections and cross-section ratios have been measured for the stable Bi, Pb and T1 isotopes. The data are analysed with the Fourier-Bessel method and the charge-distribution differences of the isotonic and isotopic pairs are presented as well as the Fourier-Bessel coefficients of the seven single nuclei. To improve the accuracy of the results, muonic X-ray data are incorporated into the analysis. The measured Δρ(r) are compared with the simple shell model, where the stretching due to the additional nucleons is taken into account, and with more sophisticated HF calculations.     

Time-dependent quantum description of few-nucleon transfers upon nuclear reactions 40Ca + 96Zr, 40Ca + 208Pb, and 90Zr + 208Pb

The time-dependent Schrödinger equation is solved numerically using the difference approach for outer nucleons of the spherical nuclei ⁴⁰Ca, ⁹⁰Zr, and ²⁰⁸Pb upon their grazing collisions. The neutron and proton transfer probabilities are determined for energies near the Coulomb barrier as functions of the minimum internuclear distance and quantum numbers of initial nucleon states.     

The excitation functions and Isomer ratios for neutron-induced reactions on Mo and Zr

Absolute cross sections of the reactions ⁹²Mo(n, 2n)^91m,91gMo, ⁹²Mo(n, p)⁹²Nb and ⁹²Mo(n, α)^{89m, 89g}Zr, relative cross sections of the reaction ⁹⁰Zr(n, 2n) ^89mZr and isomer ratios of the ⁹⁰Zr(n, 2n) reaction have been measured in the neutron energy range 13–15 MeV. The results for the (n, 2n) reactions are in good agreement with those of the previous studies. The present results for the (n, p) and (n, α) reactions are in disagreement with the previous works. The experimental data are analysed by the statistical model to determine the level-density parameter a, the moment of inertia ? and the strength of the γ-ray transition S_l in order to simultaneously reproduce the experimental data on the excitation function and the isomer ratio in the (n, 2n) reaction. The γ-ray competition, the yrast level and the experimental information on the excited levels of the residual nucleus in the (n, 2n) reaction are taken into account. The obtained values of a, ? and S_l are consistent with those deduced from other types of nuclear data.     

Core-polarization and open-shell effects in E6 transitions

The problem of isomeric E6 transitions recently measured in the fp shell is investigated. In the shell model these E6 decay rates require negative proton polarization charges and are quite anomalous in the context of usually enhanced E2 and E4 transitions. We demonstrate that usual core-polarization mechanisms cannot be invoked to explain the data and that the quadrupole deformations of the open shell that must be taken into account are instrumental in yielding negative P₆ moments.     

Elastic electron scattering on Zr and Mo

Elastic electron scattering on ⁹⁰Zr and ⁹²Mo has been measured at 200 and 300 MeV up to 2 fm⁻¹ momentum transfer. Data analysis led us to adopt the parabolic Gaussian shape as a valuable charge distribution for these nuclei. For ⁹⁰Zr, we have compared this model with charge distributions given by recent Hartree-Fock calculations.     

Rotation-induced shape transitions in Dy nuclei

Lifetimes of states with spins up to 30? have been measured in the nuclei ¹⁵⁶Dy, ¹⁵⁷Dy, and ^ll58Dy using the recoil-distance technique together with inverse reactions of the type $\text{Mg}\text{(}{}^{136}\text{Xe}\text{, x}\text{n}\text{)}$. The applied method, which benefited from the high velocities of the fusion residues as well as from improvements of the recoil-distance technique, allowed us to determine lifetimes and feeding times down to 0.1 ps. Below the first backbending the resultant B(E2) values in the ground-state band of ^{156, 158}Dy increase faster with increasing rotational frequency than expected for rigid rotors, reaching values similar to those observed for the well-deformed neutron-rich Dy isotopes. In contrast to this, the E2-transition probabilities between high-spin states are clearly retarded. The retardation gradually evolves from the rotation alignment of nucléons and indicates deformation changes most likely towards a triaxial shape. From the analysis of the side-feeding times of the high-spin yrast states it could be furthermore deduced that the E2 component of the preyrast γ-decay stems from transitions along highly collective bands.     

The Zr(d,n)Nb and Zr(d,n)Nb reactions

The (d, n) reaction on ⁹⁰Zr and ⁹⁶Zr has been studied at 12 MeV deuteron bombarding energy using the neutron time-of-flight technique with an overall neutron time resolution of 1.9 ns. Angular distributions of neutron groups leading to states in ⁹¹Nb and ⁹⁷Nb were measured in the angular range between 15° and 60°. The measured cross sections were analyzed in the framework of the distorted-wave theory of stripping reactions to deduce l-values and proton spectroscopic factors of states in the residual nuclei. The results are compared with the corresponding data available from (³He, d) studies. The fractionation of the single-particle proton states and their centroid energies are determined.