We discuss different points that are fundamental to determine the actual magnitude of the cross sections measured in two-particle transfer reactions between heavy ions. These are important issues to consider when the aim is the experimental observation of the somewhat elusive Giant Pairing Vibrations.

Partiendo de un espectro de partículas independientes razonable para los isótopos del Sn se estudió la influencia de la fuerza cuadrupolar partícula-agujero en la fuerza de pairing. También se utilizó una fuerza monopolar neutrón-neutrón para calcular las variaciones debidas al número de neutrones en los espectros de energía. Los isótopos del Cd fueron calculados teóricamente agregándole una interacción monopolar protón-neutrón entre los dos agujeros de protones y los neutrones más una interacción cuadrupolar partícula-agujero entre neutrones y protones. Este cálculo teórico fue comparado con los datos experimentales de ambos isótopos desde A= 115 hasta A = 125.

Two-particle transfer processes induced by light and heavy ions are known to be an ideal dynamical tool for extracting information on nuclear pairing correlations. The procedure is however not unique and different reaction mechanism models (ranging from microscopic correlated successive one-particle transfer to collective macroscopic models) can be introduced to establish a link with the structural aspects of initial and final states. We briefly review the subject with special attention to the novel features arising in systems close to the drip lines from the weak binding situation and the consequent role of continuum states.

The construction of differential cross sections as a function of excitation energy for systems with a collection of low- and high-lying intrinsic vibrational modes has been attempted in the past. A prescription is proposed that simplifies the implementation of such calculation schemes with a remarkable reduction in computational time.

Continued interest in learning about the giant collective dipole resonances in nuclei—both at the one- and two-phonon level—has brought about a gradual shift of the experimental bombarding energies into a higher range. As a consequence, the reactions of interest can no longer be investigated in terms of the traditional, classical formalisms but need be upgraded into the relativistic regime. This extension has been implemented correctly insofar as the Coulomb excitation mechanism is concerned. For nuclear excitation processes, on the other hand, the present stand is much less satisfactory. Very few calculations have been performed so far and these make use of boosting prescriptions of the nuclear fields that are not entirely justified. In this contribution we update the situation of this problem exploiting a recently developed approach that yields the nuclear couplings with much less uncertainty.

The angular momentum decomposition of pairs obtained using Richardson's exact solution of the pairing Hamiltonian for the deformed Yb-174 nucleus are displayed. The probabilities for low angular momenta of the collective pairs are strikingly different from the ones obtained in the BCS ground state.

The semiclassical approach is one of the fundamental tools used to investigate and analyze heavy ion reaction processes. We show in this contribution that the evolution of the motion that emerges from the knowledge of the semiclassical amplitudes for the reaction channels as a function of time cannot be taken as a reliable representation for an actual wave function of the intrinsic states.

The dominance of S and D pairs in the description of deformed nuclei is one of the facts that provided sustain to the Interacting Boson Approximation. In Ref.(J. Dukelsky and S. Pittel, Phys. Rev. Lett. 86, 4791, 2001.), using an exactly solvable model with a repulsive pairing interaction between bosons it has been shown that the ground state is described almost completely in terms of S and D bosons. In the present paper we study the excited states obtained within this exactly solvable hamiltonian and show that in order to obtain a rotational spectra all the other degrees of freedom are needed.

We investigate alternatives to the standard formalism used for the study of relativistic Coulomb excitation of the giant dipole resonance in nuclei. The idea is to obtain reasonable results for the probabilities of excitation and cross sections to the one-phonon and two-phonon levels avoiding the substantial complexity of the treatments exploited so far. This is achieved for the relevant range of partial waves up to bombarding energies of at least $5\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$ per nucleon. The transfer of energy to the center of mass of the excited nuclei is also investigated.

The use of radioactive ion beams is shown to offer the possibility to study collective pairing states at high excitation energy, which are not usually accessible with stable projectiles because of large energy mismatch. In the case of two-neutron stripping reactions induced by 6He, we predict a population of the Giant Pairing Vibration in 208Pb or 116Sn with cross sections of the order of a millibarn, dominating over the mismatched transition to the ground state.

We study the temperature dependence of the sum rules using the discontinuity of the first derivative of the Matsubara Green's functions of a bilinear particle–hole operator. Particularly we study the behavior of the dipole particle–hole operator. We applied the calculation to 114Sn, 138Ba, 154Gd and 170Yb. It is found that the energy weighted sum rule for the dipole operator changes as a function of the temperature depending on the square of the gap. This fact is related to the antipairing effect of the temperature over the nuclear system.

We discuss the validity of the Galilei invariance in nuclei. The experimentally measured changes in the dipole energy weighted sum rule, due to their magnitude, cannot be explained only by the relative motion of protons and neutrons. Additionally we reemphasize that the usual mean field descriptions introduce violations of the Galilei invariance. [S0556-2813(99)00505-1].

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.

We evaluate the spreading width of the giant multipole resonances at finite temperature using the discontinuity in the second derivative of the Green's function of the vibrational boson, in the Matsubara's framework. Our method allows us to identify the processes that contribute to the spreading width in terms of the Feynman diagrammatic expansion of the full boson propagator. We have applied the calculation of the spreading width to the Pb-208 and the Zr-90 obtaining an increment of the spreading width with the temperature. We have not reached any saturation of the spreading width increment. at least up to the temperature of our calculation.

The relation between Galilei invariance and the energy weighted sum rule for a mass dipole operator is discussed using a monopole pairing interaction. It is found that the energy weighted sum rule for the mass dipole operator changes as much as 18% in medium and heavy nuclei.

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.

We develop a self-consistent cranking formalism based on the interacting boson model intrinsic wave function. Explicit formulae are obtained for the energies and moments of inertia of the ground-state rotational band as a power expansion in the rotational frequency. The results compare well with the exact diagonalization of the hamiltonian in different transitional regions obtained by breaking the SU(3) dynamical symmetry.

We carry out an intrinsic frame analysis of octupole-deformed nuclei in the SU(3) limit of the extended interacting boson model. Excited bands associated with nuclei exhibiting permanent octupole deformation are studied, as well as the behaviour of in-band and intra-band transitions, and the results are applied to 226Ra. The coupling of an odd particle to an even core with these characteristics is also discussed.