Investigation of spin dependence of neutron cross sections and of strength functions for rare earth nuclei in experiments with polarized neutrons and nuclei

Experiments on the spin dependence of the interaction of resonance neutrons (up to 100 keV) with the rare earth nuclei ¹⁴¹Pr, ¹⁵⁹Tb, ¹⁶⁵Ho, ¹⁶⁷Er and ¹⁶⁹Tm are reported. The measurements were performed with polarized neutrons and nuclei. The spin dependence of S-wave strength functions was investigated, and the imaginary part of the spin-spin potential (W_ss = 0.10 ± 0.06 MeV) was estimated in optical-model calculations with a potential in the form of a rectangular well. The energy dependence of the difference of strength functions for two J-states shows possible intermediate states in the formation of the compound nucleus. The J-values of about 230 resonances were determined.     

The (p,t) reactions on nuclei in the rare earth region

The (p, t) reactions on isotopic targets of ^{178, 180}Hf and all the stable isotopes of Yb and on natural targets of Gd, Dy, Er, Hf, Ta, W, Os and Au were studied at a beam energy of 19 MeV with an average resolution of 12 keV. A split-pole magnetic spectrometer was used to measure (p, t) Q-values and absolute differential cross sections. On the basis of angular distribution shapes definite 0⁺ and tentative 2⁺ assignments were made. Rotational bands were identified assuming an I(I+1) spacing. The (p, t) reaction populates excited 0⁺ states strongly in ¹⁷⁴Yb, ¹⁷⁶Hf, ¹⁶⁶Yb and several Gd, Dy and Er isotopes. The ¹⁷⁴Yb and ¹⁷⁶Hf 0⁺ states are discussed in terms of the pairing phase transition and in terms of Nilsson orbitals with unequal (p, t) reaction amplitudes. Members of gamma and octupole vibrational bands were observed in the even-N nuclei. The lowest L = 0 transfers to states in ^{169, 171}Yb were found to have less than 55% of the strength to ground states in adjacent even-N nuclei. A strong L = 0 transfer to a state at 1513 keV in ¹⁷¹Yb indicates the presence of a possible K = 0 core vibration coupled to the unpaired $\text{5}\text{2}$[512] neutron. The natural targets have furnished information on trends in cross sections for members of ground bands, gamma bandheads, 3^? octupole states, and strongly excited 0⁺ states.     

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.     

One- and three-quasiparticle states in 171Hf and high spin rotational bands

The $\text{1}\text{2}{}^{\mathrm{?}}\text{[521]}\text{and}\text{7}\text{2}{}^{\mathrm{+}}\text{[633]}$ one-quasiparticle bands in the N = 99 nucleus ¹⁷¹Hf have been identified to spins of about $\text{45}\text{2}$ using (heavy ion, xn) reactions. The moments of inertia of these bands are consistent with the absence of backbending in the N = 98 core nucleus. The half-life of the $\text{5}\text{2}{}^{\mathrm{?}}\text{[512]}$ intrinsic state was measured as 63.6 ns. The strength of the $\text{5}\text{2}{}^{\mathrm{?}}\text{[512] →}\text{7}\text{2}{}^{\mathrm{+}}\text{[633]}\text{E}\text{1}$ transition is discussed. Two three-quasiparticle isomers with spins and parities $\text{19}\text{2}{}^{\mathrm{+}}\text{and}\text{23}\text{2}{}^{\mathrm{?}}$ have been identified and their suggested configurations are a $\text{7}\text{2}{}^{\mathrm{+}}\text{[633]}$ neutron added to the 6⁺ and 8^? two-quasiproton states of the core. The moment of inertia of a rotational band based on the $\text{23}\text{2}{}^{\mathrm{?}}$ isomer supports this suggestion, and shows the effect of partial rotation alignment of the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron.     

Possible rotational states in odd In nuclei

Levels and transitions in ¹⁰⁷In and ¹⁰⁹In have been studied in in-beam spectroscopy on the reactions ¹⁰⁶Cd(d, nγ)¹⁰⁷In and ¹⁰⁸Cd(d, nγ)¹⁰⁹In. Low-lying $\text{1}\text{2}{}^{\mathrm{+}}\text{and}\text{3}\text{2}{}^{\mathrm{+}}$ states resembling the possible rotational bands observed in the heavier In isotopes are seen in both nuclei. The potential energy has been calculated for ^107–121In with the odd proton in different orbitals, using the Strutinsky normalization procedure. A prolate minimum at a deformation ε ≈ 0.2 is obtained for the lowest $\text{1}\text{2}{}^{\mathrm{+}}$ orbital, which is in good agreement with the experimental data for ^115–119In. The excitation energy of the $\text{1}\text{2}{}^{\mathrm{+}}$ minimum shows a fairly good agreement with experimental data.     

Microscopic description of low-energy neutron scattering by nuclei

The Bloch and Gillet shell-model formalism extended to continuum states is applied to lowenergy neutron scattering by nuclei. It is shown that complete antisymmetrization leads in the r-representation to corrective terms which yield important corrections to the scattering lengths. Calculations are performed within a model restricted configuration space for the target nuclei ¹²C, ¹³C, ¹⁶O, ¹⁷O and ⁴⁰Ca. We predict values for the spin-dependent scattering amplitude for ¹³C and ¹⁷O. The antisymmetrization problem in the case of a large configuration mixing is studied for the ¹⁹F target nucleus. The resonant effects of the compound nucleus are then very important and the results become very sensitive to the configuration space and the interaction parameters.     

Heavy-ion excitation of 3− states in deformed nuclei

Previously measured data for 70.4 MeV ¹²C excitation of 3^? states in ^{148, 150}Nd are reanalyzed using a third-order rotational-vibrational model. Calculations using 3^? quadrupole moments which are expected if they are K = 0 states are in reasonable agreement with the magnitude of the large-angle data, but the quality of the fit in the Coulomb-nuclear interference region is only fair. It is found that the matrix element 〈2⁺∥M(E3)∥3^?〉 plays an important role in the calculations making the “measurement” of the 3^? quadrupole moments very difficult, if not impossible.     

Algebraic description of multiple quadrupole excitations of collective states in nuclei: (I). Representation matrices for U(6)

An algorithm for the calculation of representation matrices for the totally symmetric representations [N] of the group U(6) is described. Applications to multiple quadrupole excitation processes in nuclei are given.     

High spin states in 74Se

Gamma-ray transitions from the bombardment of ⁶⁴Ni by ¹⁶O up to 81 Me V were studied in a variety of experiments. Four transitions in coincidence with four previously known transitions in ⁷⁴Se were discovered. Information on energies, angular distributions, intensities multiplicities and lifetimes is given for these transitions. Excitation functions for this and several other channels are presented. Statistical calculations are in satisfactory agreement with experiment.     

High spin states in 105Ag

High spin states in ¹⁰⁵Ag have been studied using the ¹⁰³Rh(α, 2nγ)¹⁰⁵Ag reaction. A collective band on the $\text{9}\text{2}{}^{\mathrm{+}}$ state at 53.2 keV and a negative parity band with spins ranging from $\text{15}\text{2}$ to $\text{27}\text{2}$ were observed. Furthermore a $\text{15}\text{2}{}^{\mathrm{+}}$ isomeric state with $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>\; =\; 6.0\pm 0.2\; </mtext><mtext>ns</mtext>}}$ at 1733.8 keV was identified. The g-factor deduced for this state is g = 0.58±0.06. A comparison of the experimental results with theoretical calculations indicates that the properties of most of the positive parity states are reasonably well described by the cluster-vibrational model as well as by the triaxial rotator model.     

Deformed states of neutron-deficient cerium and neodymium nuclei

High-spin levels in Ce and Nd isotopes excited by the reactions ^120,122Sn(¹⁶O, 3n) ^{133, 135}Ce and ^{122, 124}Te(¹⁶O, 3n)^{135, 137}Nd have been studied by in-beam γ-ray spectroscopic methods (prompt and delayed spectra, excitation functions, angular distributions and γ-γ coincidences). Bands built on the $\text{11}\text{2}{}^{\mathrm{?}}$ isomeric levels in ¹³⁵Ce and ¹³⁷Nd and on the $\text{9}\text{2}{}^{\mathrm{?}}$ground states in ¹³³Ce and ¹³⁵Nd have been found. A prolate deformation is required for these nuclei in order to explain the E2/M1 mixing ratios and the level ordering of these bands.     

High spin states in 57Co

High spin states of ⁵⁷Co have been studied via prompt γ-ray spectroscopy in the reactions ⁴⁸Ti(¹²C, p2n) and ⁵⁴Fe(α, p) at 26–48 MeV and 12–24 MeV, respectively. The energies and decay modes of these levels were determined from the analysis of γ-ray singles and γ-γ coincidence spectra, excitation functions, angular distributions and correlations. The relevant lifetimes were measured by the Doppler-shift attenuation method. The new levels established in this work are at 4037, 4814 and 5918 keV with the most probable J^π assignment of $\text{15}\text{2}{}^{\mathrm{?}}$, if $\text{17}\text{2}{}^{\mathrm{?}}$ and $\text{19}\text{2}{}^{\mathrm{?}}$, respectively. The previously known level at 2524 keV was assigned to have $\text{J}{}^{\mathrm{\pi }}\text{=}\text{13}\text{2}{}^{\mathrm{?}}$. These together with the known $\text{9}\text{2}{}^{\mathrm{?}}$(1224 keV) and $\text{11}\text{2}{}^{\mathrm{?}}$(1690 keV) levels constitute the yrast states of ⁵⁷Co. The measured lifetimes of the above six levels are (in order of increasing energies) 0.085±0.030, 0.32±0.10, 0.16±0.06, 0.10_?0.07^+0.06, 1.5_?0.5⁴ and 0.17_?0.07^+0.08 ps, respectively. Comparisons with some theoretical calculations are presented.     

Neutron inelastic scattering to octupole states in single-closed-shell nuclei

Differential cross sections for the excitation of the first octupole-vibrational state in the closed- neutron-shell nuclides ⁸⁸Sr and ⁹⁰Zr and in the closed-proton shell-nuclei ^{116, 118, 120, 124}Sn by 11 MeV neutrons are presented. The distorted-wave Born approximation is used to obtain deformation lengths, σ(3^?), for each state. Results are compared with earlier measurements of inelastic proton scattering to the same states. Although limited resolution in the neutron time- of-flight spectrometer complicates the interpretation of the Sn data, the overall conclusion that σ_nn′(3^?) ≈ σ_pp′(3^?) is supported by all of the measurements.     

High spin states of 83Sr

The reactions ⁸⁰Kr(α, n)⁸³Sr and ⁸²Kr(α, 3n)⁸³Sr were used to populate excited states of high spin in ⁸³Sr. The de-excitation of these states was studied by in-beam γ-ray spectroscopy. A number of new high-spin states have been observed. The results are discussed within the framework of the Coriolis-coupling model and the cluster-core coupling model.     

Relativistic description of deformed rare earth nuclei

Ground state properties of heavy deformed nuclei in the rare earth region are described in the framework of the relativistic Hartree approximation. Both linear and non-linear parameter sets of the lagrangian are used. The non-linear sets reproduce the experimentally observed binding energies, the charge radii and the quadrupole moments, with the same quality as non-relativistic density dependent mean field calculations with Skyrme forces.     

Search for highly excited states in light nuclei with three-body reactions

Various three-body break-up reactions resulting from the bombardment of ⁷Li with 120 MeV ³He have been measured simultaneously in a kinematically complete experiment. Missing-mass spectra have been deduced for ⁴H, ⁴He, ⁴Li, ⁵He, ⁵Li, ⁶He, ⁶Li and ⁷Li. The ground states of ⁴H and ⁵He are well described as n-t and n-α P-wave final-state interactions, respectively. Evidence is found for relatively narrow states at very high excitation energies in several nuclei. The results are compared with those of other authors and with various theoretical predictions.     

Isobaric spin mixing in the analog states of 90Zr

A 90° photoproton energy spectrum has been obtained from the reaction ⁹⁰Zr(γ, p)⁸⁹Y using an isotopically enriched target foil. Previously unreported proton groups are observed at E_p = 6.95, 9.55, 10.68 and 11.03 MeV. A total photoneutron cross section and a low-energy neutron energy spectrum are also presented, and isospin mixing is demonstrated by comparison with the photoproton data. The possibility of T_> strength in the region 23–24 MeV excitation is noted.     

High-spin negative parity states in doubly even Hg,Pt and Os nuclei

A systematic study of the level structure of ²⁰⁰Hg, ¹⁹⁸Hg, ¹⁹⁶Hg, ¹⁹⁴Pt, ¹⁹²Pt, ¹⁹⁰Pt, ¹⁸⁸Os, ¹⁸⁶Os and ¹⁸⁴Os has been performed by means of (α, 2nγ) and (p, 2nγ) in-beam γ-ray spectroscopy. Much new information has been obtained about the individual level spectra, and arguments based on level energy and population intensity systematics have been used to trace the behaviour of interesting spectral features through this series of transitional nuclei. Of particular interest is a 5^?, 7^?, 9^? … sequence of levels which appears to be a recurring feature in the spectra of the doubly even Pt and Hg nuclei in the mass range A = 190–200. These negative parity levels are connected by enhanced E2 transitions and they are very strongly populated in the de-excitation of the residual nuclei formed in (α, 2n) reactions. It is proposed that the 5^?, 7^?, 9^? … sequences constitute rotation-aligned bands analogous to the decoupled bands identified by Stephens and co-workers in odd-A transitional nuclei. In the doubly even nuclei, the bands may arise from the coupling of an $\text{i}\text{13}\text{2}$ neutron with a low-j neutron partner (from the $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ orbitals). Negative parity levels in the Os nuclei are populated much less strongly in the (α, 2nγ) reactions. While 5^? levels corresponding to those in the Pt and Hg nuclei appear to be fairly well established in ¹⁸⁶Os, ¹⁸⁸Os (and ¹⁹⁰Os), it is not yet clear whether the 5^?, 7^?, 9^? … band sequence extends into the Os nuclei.     

Inelastic electron scattering from low-lying states in the nuclei 36Ar and 40Ar

The low-lying level structure of ³⁶Ar and ⁴⁰Ar has been investigated using the technique of inelastic electron scattering. Data were collected at the National Bureau of Standards Linear Accelerator with incident electron energies between 65 and 115 MeV and scattering angles of 92.5° and 110°. The data span a range of momentum transfer squared between 0.29 and 0.92 fm^?2. Tassie model and Helm model analyses have been applied to data for levels at 1.97 and 4.18 MeV in ³⁶Ar and at 1.46, 2.52, 3.21 and 3.68 MeV in ⁴⁰Ar. A 2⁺ assignment to the 3.21 MeV state in ⁴⁰Ar is suggested. Transition strengths, transition radii, and mean lifetimes for these states are computed and compared with results of previous experiments.     

Yrast isomers and very high spin states in 148, 149, 151, 152Dy and 147Gd

We have studied level schemes for the feeding and decay of high-spin isomers in the nuclei ^{148, 149, 151, 152}Dy and ¹⁴⁷ Gd. A variety of techniques involving γ-ray spectroscopy with pulsed heavy-ion beams have been applied including linear polarization, γ-γ correlations and recoil distance measurements.The general aspect of these level schemes is in accordance with the idea that the states near and along the yrast line can be described by a spheroidal shell model in which the nucleus is axially symmetric with respect to the total spin. In these cases the spin is generated not by collective rotation, but by alignment of many single-particle orbits around a common axis.