An analysis of odd-mass rare-earth nuclei using angular momentum projection

A systematic analysis of positive-parity rotational states in odd-mass rare-earth nuclei is presented. The theory used is microscopic in the true sense and conserves both the angular momentum and the particle number as the projection technique is applied. The hamiltonian contains the quadrupole pairing interaction (in addition to the conventional (monopole) pairing and Q · Q forces) which plays an essential role in odd-mass as well as in doubly-even nuclei. Agreement between theory and experimental data is excellent.     

Formation and decay of hot nuclei

Formation and decay properties of composite-like nuclei produced by ⁵⁸Ni projectiles bombarding ²³²Th target nuclei are investigated at different energies by means of fission fragment angular correlation measurements. Experimental results are compared to the excition model and excitation energies in the fissioning nuclei are deduced. By comparing the present data with the results on other systems, the influences of entrance channel conditions and composite-like nuclei temperatures are discussed to explain the evolution of the high linear momentum transfer region. The coexistence of both massive transfer mmechanism and head-on collisions followed by preequilibrium is suggested.     

Electromagnetic decay of hot rotating nuclei

A theory of strength functions for electromagnetic multipole emission is developed. It combines the finite-temperature cranked Hartree-Fock-Bogoliubov formalism with the random-phase approximation, and is free of spurious contributions. Numerical results for ¹⁶⁴Er based on the Kumar-Baranger hamiltonian are presented. They display sizeable fluctuations of the matrix elements for the statistical transitions (contrary to the statistical model), and underline the important role of M1 transitions for good rotors.     

Angular momentum projection corrections to transition densities in rare-earth nuclei

To describe the rotational levels of even-even nuclei in the rare-earth region, states of definite angular momentum are projected from an axially symmetric intrinsic Hartree-Pock wave function calculated with a density-dependent effective interaction. An expansion is obtained in which the rotational model approximation to the transition density, $\text{ρ}{}_{\mathrm{L}}\text{(r) = ? Y}{}_{\mathrm{Lo}}\text{(Ω)ρ(r)}\text{d}\text{ω}$, is corrected to leading order in $\text{1}\text{〈J}{}_{\mathrm{y}}{}^2\text{〉}$. Evaluation of the projection corrections in ¹⁵⁶Gd, ¹⁶⁶Er and ¹⁷⁶Yb yields negligible changes in low multipoles and a cross section increase of up to 15% in 6⁺ transitions. This effect is much too small to resolve the discrepancy between density-dependent Hartree-Fock predictions and experiment in high multipoles.     

Signature effects in odd mass ytterbium nuclei in an angular momentum projected Hartree-Fock analysis

We explain the signature effects in the spectrum of odd mass Yb nuclei in a projected Hartree-Fock calculation without assuming gamma asymmetry. Rotation-alignment of nucleons in largej orbits is responsible for the signature dependence in energy and transition rates.     

Approximate projection of angular momentum and particle number in heavy nuclei

The problem of symmetry violations in Hartree-Fock-Bogoliubov wavefunctions is handled by projection techniques. For the cases of strong and weak symmetry violations, approximate formulas of the projected energy are given. They allow an approximate projection before the variation for heavy nuclei. The methods are applied numerically to some model calculations for strong and weak deformations.     

Fission barriers of Pb nuclei at high angular momentum

Fission and evaporation residue excitation functions have been measured after the nuclei ^{192, 195, 198, 200}Pb were formed by the fusion of ^{28, 30}Si with ^{164, 167, 170}Er. The fission probabilities extracted were fitted using the rotating liquid drop/statistical model codes ORNL ALICE and MBII. The range of values of the mass asymmetry, $\text{(N?Z)}\text{A}$, of the fissioning systems allows some restrictions to be placed on the value of the surface asymmetry parameter K_s, used in the liquid drop model, despite the many uncertainties and approximations in the data analysis.     

Numerical aspects of angular momentum projection for rotational nuclei

The question of complete and exact angular momentum projection from intrinsic Slater determinant representations is studied for the example ¹⁶²Er as a pilot case for the treatment of rotational nuclei. Adequate approximation schemes can be formulated.     

Average multipolarity of continuum transitions in nuclei at high angular momentum

The multipolarity of continuum transitions deexciting high-spin states has been deduced from measured conversion coefficients. The investigated ¹⁴⁶Nd(²⁰Ne, 4n or 5n) ^162,161Yb reactions were selected by gating on discrete lines. The average multipolarity gradually changes from E2 at 0.5 MeV to E1 above 1.5 MeV.     

Parity splitting in nuclei involving octupole correlations and the alignment of the angular momentum

A rotational model based on a simultaneous analysis of parity splitting and the alignment of the angular momentum is developed to describe high-spin negative-parity states. A simple formula for the energy of these states is proposed. It is shown that negative-parity states exhibit alignment, provided that the ground-state band is aligned and that the two opposite-parity bands can be considered as a single alternating-parity band.     

Excitation of nuclei by photon beams carrying orbital angular momentum

A drop in the efficiency of nuclear excitation through transitions of high multipolarity is related to the increase in the angular momentum difference between the nuclear states involved in the excitation transition. Such transitions need photons with a high angular momentum. It is well known that photon beams carrying a well-defined and arbitrarily high value of angular momentum about the beam axis can be produced. We discuss some features in the excitation of nuclei with the beams.