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.     

Solving the two-center nuclear shell-model problem with arbitrarily oriented deformed potentials

A general new technique to solve the two-center problem with arbitrarily oriented deformed realistic potentials is demonstrated, which is based on the powerful potential separable expansion method. As an example, molecular single-particle spectra for (12)C+(12)C-->(24)Mg are calculated using deformed Woods-Saxon potentials. These clearly show that nonaxial symmetric configurations play a crucial role in molecular resonances observed in reaction processes for this system at low energy.     

Statistical properties of fusion reactions involving deformed nuclei

The statistical properties of the ¹⁶⁵Ho(α,2nγ) ¹⁶⁷Tm reaction were investigated. It was found that both the slopes of the excitation functions and the side-feeding intensities are independent of the K quantum number. Regular behaviour of these quantities as a function of the spin I and of the excitation energies of the observed levels provide a means for spin assignments, just as for spherical nuclei. The analysis, in the present case, however, is much more involved.     

The odd-even shifts in odd-odd deformed nuclei based on residual interaction studies

Residual interaction calculations have been made for predicting the sign and the magnitude of the odd-even shifts observed in the rotational levels of theK=0 bands in the doubly-odd rare earth nuclei. It is shown that, contrary to the conclusions reached in earlier studies, the same zero-range spin-dependent residual interaction can reproduce the odd-even shifts as well as the GM splitting energies. This has been made possible with the inclusion of the phase factors for the total intrinsic spin and the total parity of the two-quasi-particle states in the Newby matrix elements. Predictions are made for the odd-even shifts for otherK=0 bands arising from several configurations not confirmed or observed so far.     

The effect of a hexadecapole term of the residual interaction in even deformed nuclei

To explain some experimental properties of even deformed nuclei a two-separable component force is needed. Instead of using the sophisticated forces generally introduced in the literature, we simply take into account the hexadecapole term of the multipole expansion of the residual interaction. Using then simple R.P.A. technics we are able to explain a second 0⁺ state below the gap. The rather weakB(E2) values from the first excited 0⁺ state to members of the ground state band in the middle of the rare earth region are also well described.     

The finite size effects in fusion of deformed nuclei at incident energies near the barrier

By the end of the last century, the precision of heavy-ion-fusion cross-section measurement had been increased up to 1%. This allowed the measured cross sections to be converted into experimental fusion-barrier distributions. In the experimental analysis, the barrier distributions were analyzed using a Woods-Saxon shape for the nuclear part of the bare nucleus-nucleus potential. This potential was defined along the line joining the centers of the two nuclei (“centerline potential”), which, for deformed nuclei, contradicts the short-range character of the nucleon-nucleon (N N) nuclear interaction. We present the results of our theoretical study of the significant deviations of the simplified potential from a “realistic” nuclear potential. The finite-size effects on the potential for deformed nuclei were first investigated in an approximate geometrical way. Then a more rigorous approach, namely, a semimicroscopic double-folding model, was applied to calculate the nucleus-nucleus potential. The angle-dependent fusion barriers calculated with a simple delta-function-like exchange term of the N N M3Y interaction was found to be very similar to those calculated with a finite-range expression. This circumstance enables us to perform rather quick calculations of the fusion cross sections and the corresponding barrier distributions. Comparison of the results with the experimental data showed that the finite-size effects are substantial and cannot be ignored in a quantitative analysis of experimental fusion cross sections and barrier distributions. The text was submitted by the authors in English.     

Angular distribution of fission fragments in reactions of complete fusion of deformed nuclei

Formation of angular distributions of fission fragments for the ¹⁶O + ²³²Th and ¹²C + ^235,236U reactions has been analyzed within a dynamic approach. In this approach, the component of the total angular momentum along the fission axis K is considered as a fluctuating quantity and the corresponding relaxation time is assumed to be the main parameter controlling the evolution of this mode. Particular attention is paid to the analysis of the effect of initial distributions over K (formed during fusion) on the angular distribution of fission fragments of nuclei having fission barriers comparable with the nuclear temperatures.     

The hydrogen molecule in an arbitrarily oriented magnetic field

Summary The modifications induced by a magnetic field of arbitrary direction and intermediate strength (i.e not larger than 2.35·10⁵ tesla, the ?atomic tesla?) on the lowest singlet and triplet energy states of the hydrogen molecule are studied. Using a linear combination of products of field-modified atomic orbitals, it is found that increasing the field strength the depth of the singlet energy well increases and the equilibrium internuclear distance decreases, yielding more rigid and localized nuclear vibrations. For sufficiently strong fields perpendicular to the internuclear axis, the triplet state exhibits a bonding behaviour. An explanation of the above results is given in terms of the field-modified electronic-charge distributions in the internuclear region. Based on the thesis submitted by S. Basile to the University of Palermo for graduation in Physics.     

Nuclear quadrupole-quadrupole interaction in the inelastic scattering of aligned deuterons from deformed nuclei

The 2 ₁ ⁺ -excitation of deformed nuclei by tensor polarized deuterons provides an alignment of both nuclei and thus a means to study specifically the quadrupole-quadrupole interaction between both nuclei. The tensor analyzing powerA _xz (θ) has been measured for the elastic and inelastic scattering on²⁴Mg and²⁸Si. The coupled channel analysis including a deformed tensor potential reveals a clear signature of the quadrupole-quadrupole part of the nuclear projectile-target interaction.     

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.     

The amplitudes of s and d bosons in deformed nuclei

It is shown that the ground state of deformed nuclei can be considered as a condensate of bosons that do not have a well defined angular momentum. The projection on well defined angular momentum states shows that the s and d bosons take care of nearly 90% of the boson wave function.     

The general theory for calibrating two arbitrarily oriented phase plates

The general expressions for the retardances of two phase plates arbitrarily oriented between two polarizing prisms are presented. It is shown that more accurate results are obtained if measurements are performed at particular orientations of the plates. Compact formulas for the retardances at these orientations are directly derived as special cases from the general expressions. Also, some aspects related to the calibration model like the sensitivity of measurements to the relative orientations of the plates can only be treated using the general expressions.     

The splitting of giant multipole states of deformed nuclei

A vibrating potential model is applied to deformed nuclei with a deformed harmonic oscillator potential in order to discuss the splitting of isoscalar giant quadrupole states. Eigenfrequencies of the collective states are estimated to be $\text{√2ω(1 ?}\text{1}\text{3}\text{δ)}$, $\text{√2ω(1 ?}\text{1}\text{6}\text{δ)}\text{and}\text{√2ω(1 +}\text{1}\text{3}\text{δ)}\text{fo and 2}{}^{\mathrm{+}}$ modes, respectively. The splitting of isovector dipole and isovector quadrupole states is also studied according to a schematic model as proposed by Bohr and Mottelson. It is shown that. isovector dipole states are split, as in a hydrodynamic model, while isovector quadrupole states with the same scaling factors as those of isoscalar quadrupole modes.     

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.     

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.     

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.     

On the shape of deformed nuclei

Shape observables measuring the intrinsic quadrupole deformation of the nucleus are identified. The consequences of these shape operators for the collective rotational and SU(3) models are derived. The operator measuring the square of the K quantum number is given.