Shell effects on rotational damping in superdeformed nuclei

Damping of collective rotational motion in A ∼ 190 and A ∼ 150 superdeformed nuclei is studied by means of the cranked shell model with two-body residual force. Numerical calculations predict that in a typical A ∼ 190 superdeformed nucleus, ¹⁹²Hg, the rotational damping width is significantly small, Γ_rot ∼ 30 keV, and that the number of superdeformed bands in the offyrast region amounts up to 150 at a given rotational frequency. These features are quite different from the prediction for A ∼ 150 superdeformed nuclei and rare-earth normally deformed nuclei. It is shown that the single-particle alignments of the cranked Nilsson orbits have strong shell oscillation. It affects significantly the properties of rotational damping in superdeformed ¹⁹²Hg.     

Energies and electromagnetic moments of deformed nuclei in the rare-earth region

Strutinsky-type cranking calculations with inclusion of pairing correlations have been performed for the rare-earth nuclei ^{156, 158, 164}Dy and ¹⁶⁴Er. The pairing effects contribute significantly and with their inclusion the calculated yrast spectra agree very well with experiments. Using Hartree-Fock-Bogouliubov cranking wave functions we have calculated the magnetic moments and quadrupole moments for states up to spin $\text{I = 20}\text{h}\text{?}$. The quadrupole moments are found to be constant over the whole spin range. The gyromagnetic factors g(I) show a strong I-dependence for ^{156, l58}Dy, a weaker one for ¹⁶⁴Er and none for ¹⁶⁴Dy. The sensitivity of this spin dependence on the single-particle occupation and the pairing degrees of freedom is studied. It is found that the spin variation of the gyrofactors is a rotational alignment effect.     

Number-conserving treatment of the BCS-Tamm-Dancoff approximation for deformed rare-earth nuclei

The formulation for the exact number-conserving treatment of the BCS-Tamm-Dancoff approximation (NTDA) in deformed even nuclei is given. It is applied to theK ^π=0^? octupole vibrations of rare-earth nuclei and is also compared with the ordinary TDA or RPA method based on the Bogoliubov transformation which has the defect of mixing of the particle number in the wave functions. The excitation energies andB(E3) calculated by NTDA method show rather stronger dependence on the Nilsson orbits than those calculated by the usual TDA or RPA methods, especially atN=94 nuclei.     

Studies of the electric dipole transition of deformed rare-earth nuclei

Spectrum and electric dipole transition rates and relative intensities in ^152–154Sm, ^156–160Gd, ^160–162Dy are studied in the framework of the interacting boson model with s,p,d,f, bosons. It is found that E1 transition data among the low-lying levels are in good agreement with the SU(3) dynamical symmetry of the spdf interacting boson model proposed by Engel and Iachello to describe collective rotation with octupole vibration. These results show that these nuclei have SU(3) dynamic symmetry to a good approximation. Also in this work many algebraic expressions for electric dipole transitions in the SU(3) limit of the spdf-IBM have been obtained. These formulae together with the formulae given previously exhaust nearly all the E1 transitions for low-lying negative parity states. They are useful in analyzing experimental data.     

Excited rotational bands in the high-spin region of deformed nuclei

Rotational bands of deformed nuclei in the rare-earth region in the vicinity of the yrast line are investigated within the framework of the random phase approximation based on a self-consistent solution of the Hartree-Fock-Bogolyubov equations in the rotating system. For low angular momenta one finds the well-known β, δ and γ vibrational bands and non-collective two-quasiparticle bands. In the high-spin region additional aligned bands develop. They are dramatically lowered in energy by the Coriolis interaction. Several band crossings occur. The calculated spectra are in fair agreement with experimental measurements.     

Rotations and intrinsic Kπ = 1+ excitations in deformed rare-earth nuclei

The K^π = 1⁺ intrinsic excitations in deformed rare-earth nuclei are studied in the framework of the random-phase approximation, which excludes the spurious state (zero-energy excitation) related with the rotation of the whole nucleus. We take the Nilsson-plus-pairing, quadrupole and spin-dependent (magnetic dipole or spin-quadrupole) force model. Cranking-model formulae for the moment of inertia and the collective gyromagnetic ratio are derived as the zero-energy limit of the lowest K^π = 1⁺ excitation. They are modified from the usual formulae due to the spin-dependent force. The M1 and E2 transitions from the K^π = 1⁺ excited states to the ground state of ¹⁷⁰Yb are also calculated. The M1 transition strengths are concentrated almost below 6 MeV, while the E2 ones are scattered even up to 12 MeV. Several levels around 12 MeV show rather strong E2 transitions of ΔN = 2 character.     

An investigation of the odd-A rare-earth nuclei using rotational models

Using recently compiled data for band-head energies of 53 odd-A rare-earth nuclei, rotational models for strongly deformed nuclei have been used to determine the variation of deformations, spin-orbit parameter κ and the l² parameter, μ, in these nuclei. The deformation is found to be consistent with experimental deformations within 20 %. The spin-orbit parameter, κ, is found to vary from 0.037 up to 0.070, a 25 % variation from Nilsson's 0.050. The l² parameter μ is found to vary from 0.30 up to 0.71, a 30 % variation from Nilsson's 0.45. The trends observed in the values of spin-orbit strength C indicate a correlation with deformation, δ. Simultaneous shifts of the l² strength D for neutron numbers 95–97 and 101–103 may be interpreted as a sudden shift in the squareness of the potential well possibly caused by shell filling. Inclusion of hexadecapole deformation greatly improves the band-head energies for the mass region 150 ≦ A ≦ 165.     

Comparison between formulas of rotational band for axially symmetric deformed nuclei

The experimental rotational spectra of the deformed nuclei available in even-even and odd-A nuclei in the rare-earth and actinide regions are systematically analyzed with several rotational spectra formulas,including Bohr-Mottelson's I(I+l)-expansion,Harris'w2-expansion,ab and abc formulas.It is shown that the simple 2-parameter ab formula is much better than the widely used 2-parameter Bohr-Mottelson's AB formula and Harris'αβ formula.The available data of the rotational spectra of both ground-state band in even-even nuclei and one-quaasiparticle band in odd-A nuclei can be conveniently and rather accurately reproduced by ab formula and abc formula.The moment of inertia and the variation with rotational frequency of angular momentum can be satisfactorily reproduced by ab and abc formulas.     

Comparison between formulas of rotational band for axially symmetric deformed nuclei

The experimental rotational spectra of the deformed nuclei available in even-even and odd-A nuclei in the rare-earth and actinide regions are systematically analyzed with several rotational spectra formulas, including Bohr-Mottelson's I(I+1)-expansion, Harris' ω²-expansion, ab and abc formulas. It is shown that the simple 2-parameter ab formula is much better than the widely used 2-parameter Bohr-Mottelson's AB formula and Harris'αβ formula. The available data of the rotational spectra of both ground-state band in even-even nuclei and one-quasiparticle band in odd-A nuclei can be conveniently and rather accurately reproduced by ab formula and abc formula. The moment of inertia and the variation with rotational frequency of angular momentum can be satisfactorily reproduced by ab and abc formulas.     

A description of the dynamics and thermodynamics of vibration damping in axially deformed nuclei

The Quantal Brownian Motion (QBM) model of nuclear vibration damping is adapted to describe an axially deformed nucleus where a giant oscillatory mode becomes excited. Several simplifying assumptions are imposed in order to obtain an operative version of the QBM model. Within the restrictions posed by this set of hypothesis, it is found that a system resembling the nucleide¹⁶⁶Er, as an illustration, undergoes both dynamical and thermodynamical behavior in a consistent scheme of magnitudes. The value of energies, temperatures and entropies at equilibrium fit a closed thermodynamical model concerning oscillators coupled to fermionic reservoirs. In the present approach, it is seen that the nucleonic excitations that provide the doorways to mode decay can be clearly split into two sets, or separate heat baths, for the components of the axially symmetric vibration.     

Analysis of the energy spectra of ground states of deformed nuclei in the rare-earth region

The ₆₂Sm, ₆₄Gd, ₆₆Dy, ₇₀Yb, ₇₂Hf and ₇₄W nuclei are classified as deformed nuclei. Low-lying bands are one of the most fundamental excitation modes in the energy spectra of deformed nuclei. In this paper a theoretical analysis of the experimental data within the phenomenological model is presented. The energy spectra of ground states are calculated. It is found that the low-lying spectra of ground band states are in good agreement with the experimental data.     

Orbital motion in deformed nuclei

Collective and microscopic properties of the low-lying, scissors-like, M1 excitations are studied. The collective features are analyzed in RPA using an energy-weighted M1 sum rule. Presented at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

gR and gK factors in deformed nuclei

The static and dynamic magnetic dipole moments of odd-mass and even-mass nuclei with 150R and intrinsic g-factors g_K.     

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.     

Doublet splitting in even-A deformed nuclei

The doublet splittings between excited two-quasiparticle states with parallel and antiparallel angular-momentum coupling in some even-A deformed rare earth nuclei have been calculated and compared with the experimental values. The influence of the various exchange forces is investigated, and results with both finite-range and zerorange forces are presented. Qualitative agreement is obtained when finite-range forces are used; but the SDI results—especially the spin-dependent ones—are also satisfactory if the states of the doublets are sufficiently pure two-quasiparticle states. This condition seems to be fulfilled by the doublet states considered in¹⁶²Dy, but not by those considered in the nuclei¹⁶⁸Er and¹⁷²Yb for which the experimental level splittings are rather large (about 450 keV) and could not reproduced at all. These discrepancies are discussed. It is argued that they are not due do the choice of the residual interactions but rather are due to configuration mixing, which is expected to be strong in these high-lying states.     

Effective nucleon mass in deformed nuclei

The coupling of vibrations to nucleons moving in levels lying close to the Fermi energy of deformed rotating nuclei is found to lead to a number of effects: (i) shifts of the single-particle levels of the order of 0.5 MeV towards the Fermi energy and thus to an increase of the level density, (ii) single-particle state depopulation of the order of 30%, and thus spectroscopic factors approximately 0.7, etc. These effects, which we have calculated for 168Yb, can be expressed in terms of an effective mass, the so-called omega mass ( m(omega)), which is approximately 40% larger than the bare nucleon mass in the ground state. It is found that m(omega) displays a strong dependence with rotational frequency, eventually approaching the bare mass for Planck's over 2piomega(rot) approximately 0.5-0.6 MeV.     

Superheavy nuclei in deformed mean--field calculations

The ground–state properties of superheavy nuclei are investigated within various parametrisations of relativistic and nonrelativistic nuclear mean–field models. The heaviest known even–even nuclei starting with Z = 98 are used as a benchmark to estimate the predictive power of the models and forces. From that starting point, deformed doubly magic nuclei are searched in the region 100 ≤ Z ≤ 130 and 142 ≤ N ≤ 190. Received: 6 April 1998 / Revised version: 16 June 1998     

Vibrational states in odd deformed nuclei

The energies and wave functions of the nonrotational states in odd deformed nuclei are calculated in the quasiparticle-phonon model of the nucleus. It is shown that the number of vibrational states in odd nuclei is many times larger than the number of vibrational states in even-even nuclei. The wave functions of the overwhelming majority of these states with excitation energies in the range 1.5–2.5 MeV possess a dominant term of the type quasiparticle⊗phonon. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 575–578 (25 April 1996)