Shift of the 21+^+_1 state of 10^{10}Be in the ternary cold fission of 252^{252}Cf

Recent experimental data indicate that in the ternary cold fission of $^{252}$Cf the energy of the first excited state of the accompanying light cluster $^{10}$Be is decreased by an amount ranging between $\approx$ 6 and 26 keV. A model is proposed to calculate the shift of the vibrational 2$^+_1$ state in $^{10}$Be when its heavy companions are the even-even nuclei $^{146}$Ba and $^{96}$Sr. The stiffness parameters of the $\beta$-vibrations are calculated within the self-consistent Hartree-Fock method with BCS pairing correlations taken into account, and its change is determined by the interaction of the light cluster with the heavy fragments. The results are pointing to a dependence of the shift magnitude and signature on the relative distance between the three clusters and their mutual orientation. Eventually it is the anharmonic perturbation of the spherical vibrator which is responsible for obtaining a negative energy shift of the 2$^+_1$ state.Comment: 4 pages, 3 figure

Signature of Shallow Potentials in Deep Sub-barrier Fusion Reactions

We extend a recent study that explained the steep falloff in the fusion cross section at energies far below the Coulomb barrier for the symmetric dinuclear system 64Ni+64Ni to another symmetric system, 58Ni+58Ni, and the asymmetric system 64Ni+100Mo. In this scheme the very sensitive dependence of the internal part of the nuclear potential on the nuclear equation of state determines a reduction of the classically allowed region for overlapping configurations and consequently a decrease in the fusion cross sections at bombarding energies far below the barrier. Within the coupled-channels method, including couplings to the low-lying 2+ and 3- states in both target and projectile as well as mutual and two-phonon excitations of these states, we calculate and compare with the experimental fusion cross sections, S-factors, and logarithmic derivatives for the above mentioned systems and find good agreement with the data even at the lowest energies. We predict, in particular, a distinct double peaking in the S-factor for the far subbarrier fusion of 58Ni+58Ni which should be tested experimentally.Comment: 34 pages, 10 figures, to appear in Phys. Rev.

Spectroscopic factors of cluster decays in an algebraic cluster model

Abstract We propose a new ansatz for the cluster spectroscopic factor in an algebraic cluster model. The parameters of the ansatz are fitted to the experimental and Blendowske–Walliser values of the spectroscopic factor for light emitted clusters and then applied to predict the spectroscopic factors for heavier clusters up to the spontaneous cold fission in two equal fragments. We show that due to the cluster and daughter shell structure, the calculated spectroscopic factors are strongly deviating from the empirical law for increasing cluster number. The observed gap between the alpha-like and cluster-like fission on one side and the spontaneous cold fission on the other side for actinides is explained by the moderate increase of spectroscopic factors, as computed in the present Letter, combined with the simultaneous decrease of the barriers when approaching symmetric mass division. This conclusion is inferred by computing the half-lives of cluster emission and spontaneous cold fission for 234U

Hindrance of ^{16}O+^{208}Pb fusion at extreme sub-barrier energies

We analyze the fusion data for $^{16}$O+$^{208}$Pb using coupled-channels calculations. We include couplings to the low-lying surface excitations of the projectile and target and study the effect of the ($^{16}$O,$^{17}$O) one-neutron pickup. The hindrance of the fusion data that is observed at energies far below the Coulomb barrier cannot be explained by a conventional ion-ion potential and defining the fusion in terms of ingoing-wave boundary conditions (IWBC). We show that the hindrance can be explained fairly well by applying the M3Y double-folding potential which has been corrected with a calibrated, repulsive term that simulates the effect of nuclear incompressibility. We show that the coupling to one-neutron transfer channels plays a crucial role in improving the fit to the data. The best fit is achieved by increasing the transfer strength by 25% relative to the strength that is required to reproduce the one-neutron transfer data. The larger strength is not unrealistic because the calculated inelastic plus transfer cross section is in good agreement with the measured quasielastic cross section. We finally discuss the problem of reproducing the fusion data at energies far above the Coulomb barrier. Here we do not account for the data when we apply the IWBC but the discrepancy is essentially eliminated by applying the M3Y+repulsion potential and a weak, short-ranged imaginary potential.Comment: text and 8 fifure

Decay modes of two repulsively interacting bosons

We study the decay of two repulsively interacting bosons tunneling through a delta potential barrier by direct numerical solution of the time-dependent Schr\"odinger equation. The solutions are analyzed according to the regions of particle presence: both particles inside the trap (in-in), one particle in and one particle out (in-out), and both particles outside (out-out). It is shown that the in-in probability is dominated by exponential decay, and its decay rate is predicted very well from outgoing boundary conditions. Up to a certain range of interaction strength the decay of in-out probability is dominated by the single particle decay mode. The decay mechanisms are adequately described by simple models.Comment: 18 pages, 13 figure

Role of Fragment Higher Static Deformations in the Cold Binary Fission of 252^{252}Cf

We study the binary cold fission of $^{252}$Cf in the frame of a cluster model where the fragments are born to their respective ground states and interact via a double-folded potential with deformation effects taken into account up to multipolarity $\lambda=4$. The preformation factors were neglected. In the case when the fragments are assumed to be spherical or with ground state quadrupole deformation, the $Q$-value principle dictates the occurence of a narrow region around the double magic $^{132}$Sn, like in the case of cluster radioactivity. When the hexadecupole deformation is turned on, an entire mass-region of cold fission in the range 138 - 156 for the heavy fragment arise, in agreement with the experimental observations. This fact suggests that in the above mentioned mass-region, contrary to the usual cluster radioactivity where the daughter nucleus is always a neutron/proton (or both) closed shell or nearly closed shell spherical nucleus, the clusterization mechanism seems to be strongly influenced by the hexadecupole deformations rather than the $Q$-value.Comment: 10 pages, 12 figure

Recent experimental results in sub- and near-barrier heavy ion fusion reactions

Recent advances obtained in the field of near and sub-barrier heavy-ion fusion reactions are reviewed. Emphasis is given to the results obtained in the last decade, and focus will be mainly on the experimental work performed concerning the influence of transfer channels on fusion cross sections and the hindrance phenomenon far below the barrier. Indeed, early data of sub-barrier fusion taught us that cross sections may strongly depend on the low-energy collective modes of the colliding nuclei, and, possibly, on couplings to transfer channels. The coupled-channels (CC) model has been quite successful in the interpretation of the experimental evidences. Fusion barrier distributions often yield the fingerprint of the relevant coupled channels. Recent results obtained by using radioactive beams are reported. At deep sub-barrier energies, the slope of the excitation function in a semi-logarithmic plot keeps increasing in many cases and standard CC calculations over-predict the cross sections. This was named a hindrance phenomenon, and its physical origin is still a matter of debate. Recent theoretical developments suggest that this effect, at least partially, may be a consequence of the Pauli exclusion principle. The hindrance may have far-reaching consequences in astrophysics where fusion of light systems determines stellar evolution during the carbon and oxygen burning stages, and yields important information for exotic reactions that take place in the inner crust of accreting neutron stars.Comment: 40 pages, 63 figures, review paper accepted for EPJ

Fusion hindrance for a positive Q-value system

An excitation function for the fusion reaction Si28 + Si30 (Q=14.3MeV) has been measured down to 40μb. Deviations from the behavior predicted by the optical model and standard coupled-channels calculations have been observed in this system. The fusion cross sections can be reproduced by a shallow potential model well, which was originally developed to explain the hindrance of heavy-ion fusion for systems with negative Q-values