Sub-barrier fusion of drip-line nuclei

We discuss the role of break-up process of a loosely-bound projectile in subbarrier fusion reactions. Coupled-channels calculations are carried out for $^{11}$Be + $^{208}$Pb and $^{4,6}$He + $^{238}$U reactions by discretizing in energy the particle continuum states. Our calculations show that the coupling to the break-up channel has two effects, namely the loss of flux and the dynamical modulation of fusion potential. Their net effects differ depending on the energy region. At energies above the Coulomb barrier, the former effect dominates over the latter and cross sections for complete fusion are hindered compared with the no coupling case. On the other hand, at below the barrier, the latter effect is much larger than the former and complete fusion cross sections are enhanced consequently.Comment: 12 pages, 3 eps figures, uses psfig.sty and sprocl.sty. To be published in the Proceedings of the international workshop on "Fusion dynamics at the extremes", Dubna, Russia, May 2000 (World Scientific Publishing Co.

Reaction dynamics for fusion of weakly-bound nuclei

We discuss several open problems of fusion reactions induced by weakly bound nuclei. For this purpose, we solve a one dimensional three-body Hamiltonian with the coupled-channels formalism. We show that the continuum-continuum couplings substantially reduce the total fusion probability at energies above the barrier compared with the no-breakup case, although the fusion probability remains enhanced at subbarrier energies. We then discuss a role of transfer process in fusion of weakly bound nuclei, and point out that removing spurious Pauli forbidden transfer components from the calculation may be crucial at energies below the barrier. Calculations based on the three-body classical trajectory Monte Carlo (CTMC) method are also presented in order to discuss how to model complete fusion process.Comment: 8 pages, 3 eps figures. Uses ptptex.sty. A talk given at the International conference FUSION03, November 12 - 15, 2003, Matsushima, Miyagi, Japan. To be published in Prog. Theo. Phys. Supp

Nuclear fusion as a probe for octupole deformation in 224^{224}Ra

$\textit{Background}$: Nuclear fusion has been shown to be a perfect probe to study the different nuclear shapes. However, the possibility of testing octupole deformation of a nucleus with this tool has not been fully explored yet. The presence of a stactic octupole deformation in nuclei will enhanced a possible permanent electric dipole moment, leading to a possible demonstration of parity violation. $\textit{Purpose}$: To check whether static octupole deformation or octupole vibration in fusion give qualitatively different results so that both situations can be experimentally disentangled. $\textit{Method}$: Fusion cross sections are computed in the Coupled-Channels formalism making use of the Ingoing-Wave Boundary Conditions (IWBC) for the systems $^{16}$O+$^{144}$Ba and $^{16}$O+$^{224}$Ra. $\textit{Results}$: Barrier distributions of the two considered schemes show different patterns. For the $^{224}$Ra case, the octupole deformation parameter is large enough to create a sizeable difference. $\textit{Conclusions}$: The measurement of barrier distributions can be an excellent probe to clarify the presence of octupole deformation.Comment: Important changes from previous version, 6 pages, 5 figures, 2 tables, submitted to Phys. Rev.

Electromagnetic selection rules in the triangular alpha-cluster model of 12C

After recapitulating the procedure to find the bands and the states occurring in the $\mathcal{D}_{3h}$ alpha-cluster model of $^{12}$C in which the clusters are placed at the vertexes of an equilateral triangle, we obtain the selection rules for electromagnetic transitions. While the alpha cluster structure leads to the cancellation of E1 transitions, the approximations carried out in deriving the roto-vibrational hamiltonian lead to the disappearance of M1 transitions. Furthermore, although in general the lowest active modes are E2, E3, $\cdots$ and M2, M3, $\cdots$, the cancellation of M2, M3 and M5 transitions between certain bands also occurs, as a result of the application of group theoretical techniques drawn from molecular physics. These implications can be very relevant for the spectroscopic analysis of $\gamma$-ray spectra of $^{12}$C

Electric and magnetic response to the continuum for A=7 isobars in a dicluster model

Mirror isobars $^7$Li and $^7$Be are investigated in a dicluster model. The magnetic dipole moments and the magnetic dipole response to the continuum are calculated in this framework. The magnetic contribution is found to be small with respect to electric dipole and quadrupole excitations even at astrophysical energies, at a variance with the case of deuteron. Energy weighted molecular sum rules are evaluated and a formula for the molecular magnetic dipole sum rule is found which matches the numerical calculations. Cross-sections for photo-dissociation and radiative capture as well as the S-factor for reactions of astrophysical significance are calculated with good agreement with known experimental data.Comment: Accepted in EPJ

The electron screening puzzle and nuclear clustering

Accurate measurements of nuclear reactions of astrophysical interest within, or close to, the Gamow peak, show evidence of an unexpected effect attributed to the presence of atomic electrons in the target. The experiments need to include an effective "screening" potential to explain the enhancement of the cross sections at the lowest measurable energies. Despite various theoretical studies conducted over the past 20 years and numerous experimental measurements, a theory has not yet been found that can explain the cause of the exceedingly high values of the screening potential needed to explain the data. In this letter we show that instead of an atomic physics solution of the "electron screening puzzle", the reason for the large screening potential values is in fact due to clusterization effects in nuclear reactions, in particular for reaction involving light nuclei.Comment: 6 pages, 2 figures, accepted for publication in Physics Letters

Pairing in the continuum: the quadrupole response of the Borromean nucleus 6He

The ground state and low-lying continuum states of 6He are found within a shell model scheme, in a basis of two-particle states built out of continuum p-states of the unbound 5He nucleus, using a simple pairing contact-delta interaction. This accounts for the Borromean character of the bound ground state, revealing its composition. We investigate the quadrupole response of the system and we put our calculations into perspective with the latest experimental results. The calculated quadrupole strength distribution reproduces the narrow 2+ resonance, while a second wider peak is found at about 3.9 MeV above the g.s. energy.Comment: 5 pages, 5 figure

Electric multipole response of the halo nucleus 6^6He

The role of different continuum components in the weakly-bound nucleus $^6$He is studied by coupling unbound spd-waves of $^5$He by means of simple pairing contact-delta interaction. The results of our previous investigations in a model space containing only p-waves, showed the collective nature of the ground state and allowed the calculation of the electric quadrupole transitions. We extend this simple model by including also sd-continuum neutron states and we investigate the electric monopole, dipole and octupole response of the system for transitions to the continuum, discussing the contribution of different configurations.Comment: 22 pages, 10 figure

Pair-transfer probability in open- and closed-shell Sn isotopes

Approximations made to estimate two-nucleon transfer probabilities in ground-state to ground-state transitions and physical interpretation of these probabilities are discussed. Probabilities are often calculated by approximating both ground states, of the initial nucleus A and of the final nucleus A\pm 2 by the same quasiparticle vacuum. We analyze two improvements of this approach. First, the effect of using two different ground states with average numbers of particles A and A\pm2 is quantified. Second, by using projection techniques, the role of particle number restoration is analyzed. Our analysis shows that the improved treatment plays a role close to magicity, leading to an enhancement of the pair-transfer probability. In mid-shell regions, part of the error made by approximating the initial and final ground states by a single vacuum is compensated by projecting onto good particle number. Surface effects are analyzed by using pairing interactions with a different volume-to-surface mixing. Finally, a simple expression of the pair-transfer probability is given in terms of occupation probabilities in the canonical basis. We show that, in the canonical basis formulation, surface effects which are visible in the transfer probability are related to the fragmentation of single-particle occupancies close to the Fermi energy. This provides a complementary interpretation with respect to the standard quasiparticle representation where surface effects are generated by the integrated radial profiles of the contributing wave functions.Comment: 12 pages, 7 figure