Static Quadrupole Deformation Research Articles

Global study of quadrupole correlation effects

We discuss the systematics of ground-state quadrupole correlations of binding energies and mean-square charge radii for all even-even nuclei, from ${}^{16}$O up to the superheavies, for which data are available. To that aim we calculate their correlated $J=0$ ground state by means of the angular-momentum and particle-number projected generator coordinate method, using the axial mass quadrupole moment as the generator coordinate and self-consistent mean-field states restricted only by axial, parity, and time-reversal symmetries. The calculation is performed within the framework of a nonrelativistic self-consistent mean-field model by use of the same Skyrme interaction SLy4 and to a density-dependent pairing force to generate the mean-field configurations and to mix them. These are the main conclusions of our study: (i) The quadrupole correlation energy varies between a few 100 keV and about 5.5 MeV. It is affected by shell closures, but varies only slightly with mass and asymmetry. (ii) Projection on angular momentum $J=0$ provides the major part of the energy gain of up to about 4 MeV; all nuclei in the study, including doubly magic ones, gain energy by deformation. (iii) The mixing of projected states with different intrinsic axial deformations adds a few 100 keV up to 1.5 MeV to the correlation energy. (iv) Typically nuclei below mass $A\ensuremath{\le}60$ have a larger correlation energy than static deformation energy whereas the heavier deformed nuclei have larger static deformation energy than correlation energy. (v) Inclusion of the quadrupole correlation energy improves the description of mass systematics, particularly around shell closures, and of differential quantities, namely two-nucleon separation energies and two-nucleon gaps. The correlation energy provides an explanation of ``mutually enhanced magicity.'' (vi) The correlation energy tends to decrease the shell effect on binding energies around magic numbers, but the magnitude of the suppression is not large enough to explain the relative overbinding at $N=82$ and $N=126$ neutron-shell closures in mean-field models. (vii) Charge radii are also found to be sensitive to the quadrupole correlations. Static quadrupole deformations lead to a significant improvement of the overall systematics of charge radii. The dynamical correlations improve the local systematics of radii, in particular around shell closures. Although the dynamical correlations might reduce the charge radii for specific nuclei, they lead to an overall increase of radii when included, in particular in light nuclei.

Empirical nucleus-nucleus potential deduced from fusion excitation functions

Existing data on near-barrier fusion excitation functions for 48 medium and heavy nucleus-nucleus systems have been analyzed using a simple ``diffused-barrier formula'' derived assuming the Gaussian shape of the barrier height distributions. The obtained mean values of the barrier height have been used then for determination of the parameters of the empirical nucleus-nucleus potential, assumed to have Woods-Saxon shape. The mean barrier heights calculated with this potential are reproduced with an accuracy of about $1\phantom{\rule{0.3em}{0ex}}\text{MeV}$, while other frequently used potentials, i.e., the proximity potential and the Aky\"uz-Winther potential, considerably overpredict the experimental values, especially for heavy systems. In order to predict fusion excitation functions with the diffused-barrier formula, we propose a simple method of theoretical prediction of the second parameter of the barrier distribution, its width. The proposed formula accounts for the quantum effect of sub-barrier tunneling, static quadrupole deformations, and collective surface vibrations of the colliding nuclei. With the theoretical knowledge of the mean height and width of the barrier distributions, one can predict cross sections for overcoming the barrier (``sticking'' or ``capture'') in reactions of very heavy systems used to produce superheavy nuclei.

Near-barrier transfer reactions in the 36S+144,154Sm systems.

Angular distributions and Q-value spectra for transfer reactions in the systems $^{36}\mathrm{S}$${+}^{144,154}$Sm have been measured at two energies close to the Coulomb barrier. Mass and charge identification was achieved using a time-of-flight system followed by an ionization chamber. Transfer probabilities were analyzed considering direct and sequential barrier penetration mechanisms. The dependence of the cross sections on the static quadrupole deformation of the targets was compared with the predictions of a semiclassical approach. The relative yields of the different channels were analyzed in the light of a random-walk approach based on the reaction Q values.

Onset of static quadrupole deformation in the light actinides

We examine the transition from spherical to deformed structure in even-even Ra and Th nuclei as a function of the number of valence neutron and proton paris. While the onset of collectivity is delayed, the onset of static quadrupole deformation occurs for values of the product of valence neutron and proton numbers similar to those in other mass regions.

Nuclear structure and double beta decay: Two neutrino mode.

The decay rate of the 2\ensuremath{\nu} double beta decay is calculated. The effects of pairing, static quadrupole deformation, spin-isospin polarization, and the ${\ensuremath{\Delta}}_{33}$ isobar admixtures on the nuclear matrix elements are studied and the relation of the 2\ensuremath{\nu} \ensuremath{\beta}\ensuremath{\beta} rate and the ${\ensuremath{\beta}}^{\mathrm{\ensuremath{-}}}$ and ${\ensuremath{\beta}}^{+}$ strength is stressed. In agreement with other calculations, we predict a faster decay rate than has been observed experimentally in $^{82}\mathrm{Se}$, $^{130}\mathrm{Te}$, and $^{150}\mathrm{Nd}$.

Inelastic proton scattering at 30-40 MeV fromC12

Elastic and inelastic proton differential cross sections for excitation of the following levels of /sup 12/C: 2/sub 1//sup +/(4.43 MeV), 4/sub 1//sup +/(14.08 MeV), 0/sub 2//sup +/(7.65 MeV), and 3/sub 1//sup -/(9.64 MeV) have been measured at three incident energies between 30 and 40 MeV. The data have been described by coupled channel calculations and form factors obtained by coupling surface vibrations to static deformations. The reproduction of the 0/sub 2//sup +/ state data, if this state is assumed to be a ..beta..-vibrational state, requires a quadrupole ..beta..-vibrational amplitude which is 57% of the static quadrupole deformation and a mixing of the breathing mode of the nucleus with an amplitude that would correspond to about 1% of the E0 energy weighted sum rule. For the 3/sub 1//sup -/ state it is found that the performed calculations are sensitive to the K projection, with the angular distribution of the 3/sub 1//sup -/ state being better fitted assuming K/sup ..pi../ = 3/sup -/ band. Coupled channel calculations using microscopic form factors obtained from wave functions generated using the resonating group method have also been performed and are compared to the experimental data.