On magnetic dipole form factors in deformed nuclei

Properties of magnetic dipole form factors for deformed nuclei are discussed in terms of the angular momentum projected Hartree-Fock-Bogoljubov approximation and the neutron-proton interacting boson model. It is pointed out that there exists a relation between the M1 form factor for the excitation of the orbital K^π=1⁺ band, the M1 form factor for the ground-state band, and the collective M1 form factor in odd-A nuclei.     

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.     

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.     

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     

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.     

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)     

Density-dependent Brueckner-Hartree-Fock approach in deformed nuclei

Recently a method has been developed which includes into the Brueckner-Hartree-Fock (BHF) approach in a finite nucleus those terms which produce the density dependence of the effective interaction between nucleons. This method is extended to the deformed open shell nuclei ¹²C and ²⁰Ne. The results indicate that it is possible to describe these nuclei starting from a bare realistic nucleon-nucleon interaction (Reid soft-core potential). Binding energies, quadrupole moments, root mean square radii are improved compared to the usual BHF approach with the same force or the HF approach with a phenomenological effective force.     

One-nucleon transfer reactions in deformed nuclei

The one-nucleon transfer reaction on deformed nuclei has been computed with the inclusion of indirect inelastic transitions that go through intermediate rotational states. The specific examples considered are¹⁷¹Yb(d, p), ¹⁷²Yb(p, d) and ¹⁸⁶W(p, d). Anomalies in the shapes of of experimental angular distributions with respect to predictions of the distorted-wave Born approximation are shown to be reproduced when these higher-order inelastic processes are taken into account. Consideration is also given to the deuteron optical potential needed for these studies.     

Interaction and fusion of deformed nuclei

It is shown that the height of the barrier and its position, as well the depth of the capture well, are highly sensitive to the relative orientation of colliding strongly deformed nuclei. It is found that the fusion/capture cross sections and the nucleus-nucleus potential for heavy nuclear systems depend greatly on the magnitude and sign of the quadrupole deformation of nuclear surfaces. In order to describe correctly the cross section for the capture of heavy strongly deformed nuclei, it is necessary to perform averaging over all three angles that describe their relative orientation. Allowance for a hexadecapole deformation leads to a significant increase in the capture cross section for very heavy nucleus-nucleus systems.     

Effective theory for deformed nuclei

Techniques from effective field theory are applied to nuclear rotation. This approach exploits the spontaneous breaking of rotational symmetry and the separation of scale between low-energy Nambu–Goldstone rotational modes and high-energy vibrational and nucleonic degrees of freedom. A power counting is established and the Hamiltonian is constructed at next-to-leading order.     

Octupole vibrations of deformed nuclei

The octupole vibrations of deformed nuclei are studied. A strong coupling between the harmonic octupole vibrations and the quadrupole ellipsoid is assumed. This interaction gives rise to a splitting of octupole bands with different projection quantum numberK. TheE1-transitions of the octupole states are explained within the frame of the Dynamic Collective Theory ofDanos andGreiner by calculating the Coulomb interaction between octupole vibrations and giant resonances. Furthermore, theE2- andE3-transitions of the octupole states are studied. The spectrum of W¹⁸² is investigated in detail. A fair agreement between theory and experiment is obtained. Predictions for the octupole spectra of Sm¹⁵² and Gd¹⁵⁶ are given.     

Single-particle quasistationary states in spherical and deformed nuclei

A method is presented for investigation of single-particle quasistationary states of spherical and deformed nuclei in the sub-barrier energy region. The wave functions and energy levels of quasistationary sates are found as eigensolutions of the Schrödinger equation using a continuous analog of the Newton method. The formalism and the numerical results are compared to those of other methods of treating potential resonances.     

Shell structure in deformed nuclei and nuclear fission

Some new aspects in the theory of heavy nuclei emerging from studies of nuclear shell structure in the nuclear-fission process are described. Specific subjects cover general understanding of shell structure, the significance of macroscopic modes and the droplet model.     

Double giant dipole excitations in deformed nuclei

A calculation is presented for the excitation spectra of two superimposed dipole resonances for deformed nuclei by using theSU(3) limit of the interaction boson model for the case of many bosons. The results indicate that experiments to test the model may be feasible.     

Giant dipole resonance in heavy deformed nuclei

Analysis of all the experimental data on nuclear shape deformation and photonuclear reaction cross sections in the energy range of giant dipole resonance is performed. The relationship between the giant resonance width and the nuclear-quadrupole-deformation parameter value is shown.     

Electromagnetic transitions in some odd-neutron deformed nuclei

Using the reactions ^{155, 157}Gd(α,2n), ¹⁷⁸Hf(n,γ) and ^{177Hf(α, 2n}, the following half-lives of excited nuclear states have been measured: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(188.1}\text{keV in}{}^{157}\text{Dy}\text{) = 1.00 ± 0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(161.9}\text{keV in}{}^{157}\text{Dy}\text{) = 1.3 ± 0.2 μ}\text{S}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(177.6}\text{keV in}{}^{159}\text{Dy}\text{) = 9.0 ± 0.5}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(614.3}\text{keV in}{}^{179}\text{Hf}\text{) = 0.50 ± 0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(720.7}\text{keV in}{}^{179}\text{Hf}\text{) ≦ 0.3}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(516.4}\text{keV in}{}^{179}\text{Hf}\text{) < 0.2}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(309.0}\text{keV in}{}^{179}\text{W}\text{) = 1.53 ± 0.10}\text{ns}$. A Ge(Li) timing system was employed. Electromagnetic transition probabilities are calculated in the Nilsson model including pairing and band mixing effects. Comparisons between theoretical and experimental results are performed.     

Surface diffuseness of deformed and rotating nuclei

The surface diffuseness of deformed and rotating nuclei has been studied using the energy density formalism. It is shown that the surface diffuseness exhibits an anisotropy. This anisotropy in surface diffuseness can result in an anisotropic charged particle emission from highly spinning nuclei as has been seen in some recent experiments.     

Description of charge-exchange resonances in deformed nuclei

The (p, n) and (n, p) transition strength functions with excitation of the GT resonance, other 1⁺ states, spin-dipole with λ^π=0^- andE1 charge-exchange resonances in deformed nuclei in the regions 156≦A≦168 and 236≦A≦240 are calculated in the RPA. It is shown that the GT resonance has a maximum at 18–20 MeV, and in the region of 5–6 MeV around maximum (60–70)% of strength is concentrated. The spindipole resonance with λ^π=0^-, 1^- and 2^? strength is distributed within 14–33 MeV and theE1 strength within 25–29 MeV. The latter is splitted withΔE equal to 0.6–2 MeV into two peaks withI ^π I=1^-0 and 1^?1. In the region of 4–7 MeV around maximum 73–77% ofE1 strength is concentrated. The total (n,p) transition strength is 10–200 times as small as the total (p, n) transition strength.