Dr Alexis Diaz-Torres FInstP FHEA

The challenge of today's nuclear physicists is to extend the nuclide chart. We produce and study exotic nuclei to understand the nature of the nuclear force, the origin of chemical elements in the universe and the energy production and evolution of stars. Beyond, exotic nuclei are used in various applications like medicine or compact power sources.

Carbon burning is crucial for the fate of massive stars and element creation in the Universe. Its understanding at stellar energies is a great theoretical challenge, as carbon fusion is a multidimensional quantum tunneling process affected by resonances whose origin is not fully understood yet. Simplified quantum dynamical coupled-channels calculations are presented, suggesting that clustering in the intermediate nuclear molecule is a source of fusion resonances.

Low-energy nuclear fusion reactions have been described using a dynami-cal coupled-channels density matrix method, based on the theory of open quantum systems. For the first time, this has been combined with an energy projection method, permitting the calculation of energy resolved fusion probabilities. The results are benchmarked against calculations using stationary Schrödinger dynamics and show excellent agreement. Calculations of entropy, energy dissipation and coherence were conducted, demonstrating the capability of this method. It is evident that the presence of quantum decoherence does not affect fusion probability. This framework provides a basis for quantum thermodynamic studies using thermal environments.

Using a classical dynamical reaction model, angular momentum (____textit{L}) values of a compound nucleus due to incomplete fusion at energies near and above the Coulomb barrier are studied. In this model, a projectile consisting of two cluster nuclei is fired at a stationary target nucleus. After breakup of the projectile due to Coulombic and nuclear forces, an ____(____alpha____)-cluster fuses with a ____textsuperscript{208}Pb target, forming an excited ____textsuperscript{212}Po compound nucleus. Results show that all incomplete fusion reactions produced higher angular momentum in the compound nucleus compared to a direct beam of ____(____alpha____) particles at the same incident energy. The highest angular momentum values produced in ____textsuperscript{212}Po for near and above Coulomb barrier energies were obtained using a ____textsuperscript{20}Ne projectile, at 16____(____hbar____) and 40____(____hbar____) respectively. This produced 25____% and 50____% ____textit{L} values above the next highest-Z projectile used, ____textsuperscript{8}Be, respectively.

In the past 85 years the number of known nuclides increased by more than a factor of ten, resulting in 4000 presently known isotopes of 118 elements. This considerable progress we owe to the discovery of new reaction types along with the development of powerful accelerators and experimental techniques for separation and identification of reaction products. Model predictions indicate that still about 4000 further nuclides are waiting for their discovery. The vastest unexplored territory is located on the neutron-rich side in the upper half of the chart of nuclides and hides the answers to some of the most fundamental questions of nuclear physics like the limits of nuclear stability, element synthesis in the universe or stellar evolution. The access to these nuclei is presently limited by available beam intensities and/or the lack of appropriate methods for their production and identification. The latter concerns particularly new neutron-rich isotopes of transuranium and superheavy elements. To extend this area, the hope is presently based on multinucleon transfer reactions and on the application of fusion reactions with radioactive ion beams. But how promising are these approaches? Based on a survey of present-day knowledge, we will treat the questions where we currently are on our journey towards new territory on the chart of nuclides, how the chances are to gain new territory in the future and which challenges we will have to face.

We investigate the fusion and scattering of a 16O projectile on 152,154Sm targets using the time-dependent coupled-channels wave-packet method. We benchmark calculations of the S-matrix elements, fusion cross sections, and scattering differential cross sections with those from the time-independent coupled-channels method, and compare the results to experimental data. We find that our time-dependent method and the time-independent method produce quantitatively similar results for the S-matrix elements and fusion cross sections, but our method cannot quantitatively explain the experimental scattering differential cross sections, mainly due to the low maximum number of partial waves produced by the time-dependent method. Nevertheless, the strong agreements between our method and the time-independent method demonstrates that the time-dependent coupled-channels wave-packet method can be used to address fusion reactions for a wide range of energies, with the advantage of being able to extend to time-dependent Hamiltonians for more advanced modeling of nuclear reactions.

Using a semiclassical dynamical model that combines a classical trajectory model with stochastic breakup with a dynamical fragmentation theory treatment of two-body clusterization and decay of a projectile, results are presented for 20 Ne-induced incomplete fusion reactions for the production of superheavy elements. Targets include 247,248,250 Cm and 251,252,254 Cf, and results include angular, excitation energy, and angular momentum distributions in addition to total integrated cross sections for heavy incomplete fusion products. The results show that at Coulomb energies, the studied Cf isotopes are generally the more favorable choice of target over the studied Cm isotopes for the production of 'colder' and more stable 263 Lr, 263,264,266 Rf, and 265 Db isotopes through the incomplete fusion mechanism. Also presented are evaporation residue cross sections for the dominant primary incomplete fusion products of each of the six reactions: 263,264,266 Rf and 267,268,270 Sg, as well as for the primary incomplete fusion products 269,270,272 Bh.

Complete fusion (CF) cross section measurement for the weakly bound 9Be projectile interacting with the intermediate mass target 89Y has been extended to energies greater than the fusion barrier, by implementing off-line characteristic γ -ray detection techniques. The available experimental data for the 9Be + 89Y reaction system were compared with the theoretical predictions, using the PLATYPUS code that is based on a classical dynamical model. By introducing the breakup probability that deduced in the literature from the fitting of the experimental data, the model managed to reproduce the CF cross sections of 9Be beam with targets of different atomic mass. Through the study, it is revealed that the extended CF excitation function for the 9Be + 89Y system is consistent with the systematical behavior that the prompt-breakup probability at above-barrier energies is roughly independent of the target in the reactions induced by the same weakly bound projectiles.

Nuclear physicists all over the world are searching for new exotic nuclei. But their ambitions are being hindered by the lack of effective state-of-the-art methods for laboratory nucleosynthesis. Activities are ongoing in many places to find new pathways for production and detection of exotic nuclei. But how promising are these efforts? Here we give an overview of the ongoing worldwide activities. Objects of desire Figure 1. The current Karlsruhe Chart of Nuclides, issued in 2018, contains almost 3300 different isotopes of 118 elements. The expected limits of nuclear stability (driplines) are indicated by dashed lines. Toward the driplines, the nuclei become more and more exotic. How and where are the chemical elements created in the universe? Which nuclear reactions determine the evolution and destiny of stars? And what is the nature of the still obscure nuclear force? Such fundamental questions occupy nuclear physicists. The answers are mostly hidden in the properties of exotic nuclei, like their binding energy, half-life or shape. Exotic nuclei are unstable and do not occur in our natural environment on Earth, therefore we have to produce them artificially in the lab. This is what nuclear physicists have been doing for many decades. Meanwhile, we know of the existence of more than 3000 different isotopes of 118 elements (Fig.1), with about 90 percent of them being man-made [1]. Each nuclide has its own individual combination of protons and neutrons and is governed by the sensitive interplay between the attractive nuclear force and the repulsive Coulomb force which determines its properties. Model predictions indicate that another 4000 isotopes are still awaiting their discovery, with the vastest unexplored territory located on the neutron-rich side in the upper half of the nuclide chart. Most of the astrophysical rapid neutron capture process (r-process), which is assumed to be responsible for the production of the heavy elements in stellar explosions, proceeds through this unknown territory. By studying the properties of nuclei along the r-process path we can understand the astrophysical synthesis of the heavy elements and their abundances in nature. It is still obscure where the r-process ends in the upper part of the nuclide chart. Presumably it penetrates deep into the territory of neutron-rich superheavy nuclei. New magic neutron and proton numbers are predicted in this region at N=184, Z=114 or 120-126 creating an " island of stability ". Nuclei on this " island " are expected to have higher fission barriers, resulting in an enhanced stability against fission. Is the " island of stability " the endpoint of the r-process path?

Stellar nuclear fusion reactions take place in a hot, dense plasma within stars. To account for the effect of these environments, the theory of open quantum systems is used to conduct pioneering studies of thermal and atomic effects on fusion probability at a broad range of temperatures and densities. Since low-lying excited states are more likely to be populated at stellar temperatures and increase nuclear plasma interaction rates, a 188Os nucleus was used as a target that interacts with an inert 16O projectile. Key results showed thermal effects yield an average increase in fusion probability of 15.5% and 36.9% for our test nuclei at temperatures of 0.1 and 0.5 MeV respectively, compared to calculations at zero temperature. Thermal effects could be tested in a laboratory using targets prepared in excited states as envisaged in facilities exploiting laser-nucleus interactions.

A modern two-center shell model and its usefulness for addressing low-energy reaction dynamics of light and heavy nuclei are presented. A perspective for further developments in nuclear reaction theory is given.

The cross sections for 58 Co( n , xp ) reactions have been determined in the equivalent neutron energy range of 11.7–16.8 MeV by employing the surrogate reaction ratio method and using the cross-section values for the reference reaction 60 Ni( n , xp ) from the literature. The transfer reactions 57 Fe( 6 Li, α ) at E lab = 37 MeV and 59 Co( 6 Li, α ) at E lab = 33 MeV, are used to populate compound nuclei 59 Co ∗ (surrogate of n + 58 Co) and 61 Ni ∗ (surrogate of n + 60 Ni), respectively, at similar excitation energies. The evaporated protons at backward angles measured in coincidence with the projectile-like fragment alpha provide the proton decay probabilities of the compound nuclei. The cross sections estimated using the nuclear-reactions-model code talys -1.96 are consistent with the experimental 58 Co( n , xp ) data for the entire neutron energy range. However, the predictions of the evaluated data libraries endf/b-viii , jeff -3.3, jendl -5, rosfond -2010 and tendl -2019 overestimate the present experimental data, indicating the necessity to improve the model parameters of the data libraries for this reaction.

A Fortran-90 code for solving the two-center nuclear shell model problem is presented. The model is based on two spherical Wood-Saxon potentials and the potential separable expansion method. It describes the single-particle motion in low-energy nuclear collisions, and is useful for characterizing a broad range of phenomena from fusion to nuclear molecular structures.

The incomplete fusion dynamics of ²⁰₁₀Ne + ²⁰⁸₈₂Pb collisions at energies above the Coulomb barrier are investigated using a novel semiclassical dynamical model, which combines a classical trajectory model with stochastic breakup, as implemented in the platypus code, with a dynamical fragmentation theory treatment of two-body clusterization and decay of a projectile. A finite-difference method solution to the time-independent Schrödinger equation in the charge asymmetry coordinate is employed by way of diagonalizing a tridiagonal Hamiltonian matrix with periodic boundary conditions. Results are compared with published experimental values to indicate the success of this new model, and next steps for its development are detailed.

The α-particle production in the dissociation of 9Be on 209Bi and 64Zn at energies just above the Coulomb barrier is studied within the two-center shell model approach. The dissociation of 9Be on 209Bi is caused by a molecular single-particle effect (Landau–Zener mechanism) before the nuclei reach the Coulomb barrier. Molecular single-particle effects do not occur at that stage of the collision for 9Be+64Zn, and this explains the absence of fusion suppression observed for this system. The polarisation of the energy level of the last neutron of 9Be and, therefore the existence of avoided crossings with that level, depends on the structure of the target.

The breakup of the 9Be projectile on the 209Bi target at bombarding energies above and near the Coulomb barrier is studied in the adiabatic two-center shell model approach. The effect of 9 Be→ n+2α breakup channel on complete fusion, elastic and inelastic cross sections is investigated. Results show that the breakup of the projectile 9Be could be due to a molecular single-particle effect shortly before the colliding nuclei reach the Coulomb barrier.

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier.

The incomplete fusion dynamics of 6Li + 209Bi collisions at energies above the Coulomb barrier is investigated. The classical dynamical model implemented in the {____sc platypus} code is used to understand and quantify the impact of both 6Li resonance states and transfer-triggered breakup modes (involving short-lived projectile-like nuclei such as 8Be and 5Li) on the formation of incomplete fusion products. Model calculations explain the experimental incomplete-fusion excitation function fairly well, indicating that (i) delayed direct breakup of 6Li reduces the incomplete fusion cross-sections, and (ii) the neutron-stripping channel practically determines those cross-sections.

We investigate the fusion of 16O and 154Sm with excited states at Coulomb energies using a theoretical dynamical model. The two-body Schrödinger equation is solved using the time-dependent wave-packet coupled-channels method. The wave function of the collective motion and excitations are visualized in both position and momentum space, providing a detailed mechanism of the reaction. We benchmark our calculations of the energy-resolved fusion transmission coefficients with those from the time-independent coupled-channels method. The present results are in good agreement with the time-independent results for a wide range of energies and angular momenta, demonstrating both the reliability of the quantum wave-packet dynamical approach for fusion and its usefulness for providing additional insights into fusion dynamics.

The isomer yield ratios of 184R in the incomplete fusion of the 9Be + 181Ta system were measured at energies around the Coulomb barrier, using online activation followed by offline γ-ray spectroscopy method. The PLATYPUS code that is based on a classical dynamical model is employed to analyze the measurements. By applying a phenomenological approach, model calculation managed to fairly reproduce the order of magnitude of the yield ratios at above barrier energies. Through the study, it is shown that the PLATYPUS code in conjunction with a phenomenological analysis can provide a reasonable explanation of isomer yield ratios resulted from incomplete fusion of weakly bound projectiles.

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier.

A quantitative study of the astrophysically important sub-barrier fusion of 12C+12C is presented. Low-energy collisions are described in the body-fixed reference frame using wave-packet dynamics within a nuclear molecular picture. A collective Hamiltonian drives the time propagation of the wave-packet through the collective potential-energy landscape. The fusion imaginary potential for specific dinuclear configurations is crucial for understanding the appearance of resonances in the fusion cross section. The theoretical sub-barrier fusion cross sections explain some observed resonant structures in the astrophysical S-factor. These cross sections monotonically decline towards stellar energies. The structures in the data that are not explained are possibly due to cluster effects in the nuclear molecule, which are to be included in the present approach.

A systematic study of total fusion involving the weakly bound nuclei 6,7Li with several light to heavy mass targets at Coulomb energies is presented. Emphasis is given to the role of resonance states (l=2,Jπ=3+,2+,1+ of 6Li and l=3,Jπ=7/2−,5/2− of 7Li) on the total fusion excitation function. A comparative analysis of the effects of resonant breakup on total fusion is performed for both projectiles, using the Continuum-Discretized Coupled-Channel (CDCC) framework. The calculations demonstrate that (i) resonant breakup couplings play a more important role in total fusion than non-resonant couplings, (ii) resonance states with short half-lives are very important for total fusion, as incident energies decreases towards the Coulomb barrier energy where incomplete fusion dominates, and (iii) resonance states with long half-life act as quasi-bound inelastic states, playing a crucial role in complete fusion.

Predictions of energy-shifting formulae for partial reaction and capture probabilities are compared with coupled channels calculations. The quality of the agreement notably improves with increasing mass of the system and/or decreasing mass asymmetry in the heavy-ion collision. The formulae are reliable and useful for circumventing impracticable reaction calculations at low energies.

Recent measurements of low-energy (quasi)elastic-scattering angular distribution of halo nuclei have shown a strong suppression of the Coulomb-nuclear interference peak. Examining the components of the elastic-scattering differential cross sections for 11Be + 64Zn and 6He + 208Pb at energies near the Coulomb barrier, this appears to be caused by a dramatic phase-change (destructive) of the reduced Coulomb-nuclear interference term due to continuum couplings.

The subbarrier fusion cross sections with radioactive ion beams in the systems 10,11Be+ 209Bi have been measured and compared also with the stable system 9Be+ 209Bi. All three cross sections are similar within experimental accuracy; this is somehow unexpected since, in particular, the fusion process with 11Be should be influenced by its halo structure and small binding energy and could behave in a different way from the other two Be isotopes, in particular from 10Be, well bound. Extensive calculations were undertaken within the formalism of continuum discretized coupled channel ( CDCC) that considered only the coupling to two-body breakup, into n+core, of the projectile with excitation to continuum up to 10 MeV. The results are in agreement with the 11,10Be experimental data except at low energy where the cross sections could be influenced by target/projectile collective excitations. The CCFULL theoretical approach, compared to CDCC, seems to reproduce better the subbarrier region and worse the above barrier one. The 9Be cross sections are all underestimated by the CDCC approach while are well reproduced by CCFULL calculations. This suggests that, in this last case, the schematization of the breakup process into 2 only fragments maybe is not adequate and/or other excitations, properly handed by the CCFULL code, could be relevant.

Phys.Rev. C69 (2004) 021603 A new model that includes the time-dependent dynamics of the single-particle (s.p.) motion in conjunction with the macroscopic evolution of the system is proposed for describing the compound nucleus (CN) formation in fusion of heavy nuclei. The diabaticity initially keeps the entrance system around its contact configuration, but the gradual transition from the diabatic to the adiabatic potential energy surface (PES) leads to fusion or quasifission. Direct measurements of the probability for CN formation are crucial to discriminate between the current models.

A preliminary study of the C-12 + C-12 sub-Coulomb fusion reaction using the time-dependent wave-packet method is presented. The theoretical sub-Coulomb fusion resonances seem to correspond well with observations. The present method might be a more suitable tool for expanding the cross-section predictions towards lower energies than the commonly used potential-model approximation.

We suggest new methods to extract elastic (quasi-elastic) scattering angular distribution and reaction (capture) cross sections from the experimental elastic (quasi-elastic) backscattering excitation function taken at a single angle. A novel Coulomb scattering relation between angular momentum and centrifugal energy is used. The methodology is developed for addressing complementary reaction observables, improving the description of elastic differential cross section.

Coincidence measurements of breakup fragments were carried out for the Li-7 + Sm-144 and Li-6,Li-7 + Pb-207,Pb-208, Bi-209 reactions at sub-barrier energies. Breakup modes in reactions of Li-6,Li-7 were identified through the reaction Q values, and the time-scales of each process inferred through the relative energy of the breakup fragments. Breakup was found to be predominantly triggered by nucleon transfer, with p pickup leading to alpha + alpha coincidences being the preferred breakup mode for Li-7, and n stripping leading to alpha + p for Li-6. Breakup triggered by 2n stripping was also found to be prominent in the Li-7 + Sm-144 reaction. The breakup yields were separated into prompt and delayed components based on the relative energies of the breakup fragments. This enables the identification of breakup process important in the suppression of complete fusion of Li-6,Li-7 at above-barrier energies.

Atomic nuclei are complex, quantum many-body systems whose structure manifests itself through intrinsic quantum states associated with different excitation modes or degrees of freedom. Collective modes (vibration and/or rotation) dominate at low energy (near the ground-state). The associated states are usually employed, within a truncated model space, as a basis in (coherent) coupled channels approaches to low-energy reaction dynamics. However, excluded states can be essential, and their effects on the open (nuclear) system dynamics are usually treated through complex potentials. Is this a complete description of open system dynamics? Does it include effects of quantum decoherence? Can decoherence be manifested in reaction observables? In this contribution, I discuss these issues and the main ideas of a coupled-channels density-matrix approach that makes it possible to quantify the role and importance of quantum decoherence in low-energy nuclear reaction dynamics. Topical applications, which refer to understanding the astrophysically important collision C-12 + C-12 and achieving a unified quantum dynamical description of relevant reaction processes of weakly-bound nuclei, are highlighted.

Role of cluster structures of Li-7 on reaction dynamics have been studied by performing exclusive measurements of prompt-gamma rays from residues with scattered particles at energy, E/Vb = 1.6, with Pt-198 target. Yields of the residues resulting after capture of t and He-4,He-5,He-6, corresponding to different excitation energies of the composite system were estimated. The results were compared with three body classical-dynamical model for breakup fusion, constrained by the measured fusion, alpha and t capture cross-sections. The cross-section of residues from capture of alpha and t agreed well with the prediction of the model showing dominance of the two step process - breakup fusion, while those from tightly bound He-6 showed massive transfer to be the dominant mechanism.

Evaporation residue cross sections for superheavy nuclei and quasifission distributions in heavy ion collisions are described within the dinuclear system concept. This concept assumes that the compound nucleus is formed by a transfer of nucleons between two touching nuclei. The calculated cross sections and quasifission distributions agree well with experimental data with exception of that for Z = 118.

The study of reactions induced by exotic weakly bound nuclei at energies around the Coulomb barrier had attracted a large interest in the last decade, since the features of these nuclei can deeply affect the reaction dynamics. The discrimination between different reaction mechanisms is, in general, a rather difficult task. It can be achieved by using detector arrays covering high solid angle and with high granularity that allow to measure the reaction products and, possibly, coincidences between them, as, for example, recently done for stable weakly bound nuclei [1, 2]. We investigated the collision of the weakly bound nucleus Be-7 on a Ni-58 target at the beam energy of 1.1 times the Coulomb barrier, measuring the elastic scattering angular distribution and the energy and angular distributions of He-3 and He-4. The Be-7 radioactive ion beam was produced by the facility EXOTIC at INFN-LNL with an energy of 22 MeV and an intensity of similar to 3x10(5) pps. Results showed that the He-4 yeld is about 4 times larger than He-3 yield, suggesting that reaction mechanisms other than the break-up mostly produce the He isotopes. Theoretical calculations for transfer channels and compound nucleus reactions suggest that complete fusion accounts for (41 +/- 5%) of the total reaction cross section extracted from optical model analysis of the elastic scattering data, and that He-3 and He-4 stripping are the most populated reaction channels among direct processes. Eventually estimation of incomplete fusion contributions to the He-3,He-4 production cross sections was performed through semi-classical calculations with the code PLATYPUS [3].

The time-dependent transition between a diabatic interaction potential in the entrance channel and an adiabatic potential during the fusion process is investigated within the two-center shell model. A large hindrance is obtained for the motion to smaller elongations of near symmetric dinuclear systems. The comparison of the calculated energy thresholds for the complete fusion in different relevant collective variables shows that the dinuclear system prefers to evolve in the mass asymmetry coordinate by nucleon transfer to the compound nucleus.

A new model that includes the time-dependent dynamics of the single-particle (s.p.) motion in conjunction with the macroscopic evolution of the system is proposed for describing the compound nucleus (CN) formation in fusion of heavy nuclei. The diabaticity initially keeps the entrance system around its contact configuration, but the gradual transition from the diabatic to the adiabatic potential energy surface (PES) leads to fusion or quasifission. Examples are given for some (near) symmetric central collisions.

The evaporation residue cross sections and the mass distributions of quasifission products in fusion reactions leading to the production of heavy and superheavy nuclei are well described in the dinuclear system model of fusion. The isotopic dependence of fusion cross section is treated.

We present a quantum reaction approach that unambiguously quantifies the complete and incomplete fusion of weakly-bound few-body nuclei. Calculations carried out within a simple model for Li + Bi at energies near the Coulomb barrier show that converged probabilities for the total, complete and incomplete fusion as well as for the scattering process can be obtained with the time-dependent wave-packet dynamics.

Complete fusion excitation functions of reactions involving breakup are studied by using the empirical coupledchannel (ECC) model with breakup effects considered. An exponential function with two parameters is adopted to describe the prompt-breakup probability in the ECC model. These two parameters are fixed by fitting the measured prompt-breakup probability or the complete fusion cross sections. The suppression of complete fusion at energies above the Coulomb barrier is studied by comparing the data with the predictions from the ECC model without the breakup channel considered. The results show that the suppression of complete fusion is roughly independent of the target for the reactions involving the same projectile.

Within the two-center shell model the potential energy of dinuclear system as a function of mass asymmetry is studied and compared with other microscopical and phenomenological driving potentials. The strong influence of the shell structure and the deformation of the dinuclear system nuclei on the evolution of system is shown. The dependence of the energy threshold for complete fusion in mass asymmetry on the isotope composition of colliding nuclei is analysed and compared with the available experimental data. The quasifission is considered as the decay of the dinuclear system. A correlation between minima of the driving potential and the peaks of the mass distribution of quasifission products is observed.

We suggest new methods to extract elastic (quasi-elastic) scattering angular distribution and reaction (capture) cross sections from the experimental elastic (quasi-elastic) backscattering excitation function taken at a single angle.

Phys.Lett. B594 (2004) 69-75 A new method of calculating unique values of ground-state shell corrections for finite depth potentials is shown, which makes use of bound states only. It is based on (i) a general formulation of extracting the smooth part from any fluctuating quantity proposed by Strutinsky and Ivanjuk, (ii) a generalized Strutinsky smoothing condition suggested recently by Vertse et al., and (iii) the technique of the Lanczos $\sigma$ factors. Numerical results for some spherical heavy nuclei ($^{132,154}$Sn, $^{180,208}$Pb and $^{298}$114) are presented and compared to those obtained with the Green's function oscillator expansion method.

We present a simple method to derive breakup probabilities of weakly bound nuclei by measuring only elastic (or quasi-elastic) scattering for the system under investigation and a similar tightly bound system. When transfer followed by breakup is an important process, one can derive only the sum of breakup and transfer probabilities.

Nucl.Phys. A757 (2005) 373-389 A realistic two-center shell model for fusion is proposed, which is based on two spherical Woods-Saxon potentials and the potential separable expansion method. This model describes the single-particle motion in a fusing system. A technique for calculating stationary diabatic states is suggested which makes use of the formal definition of those states, i.e., they minimize the radial nonadiabatic coupling between the adiabatic states. As an example the system $^{16}$O + $^{40}$Ca $\to$ $^{56}$Ni is discussed.

A quantum reaction approach to low-energy collisions of weakly bound few-body nuclei, based on the time-dependent wave-packet method, is presented in detail. In contrast to existing models that use this perspective, the approach separates the complete and incomplete fusion from the total fusion. Calculations performed within a one-dimensional model with two degrees of freedom for Li-6 + Bi-209 at energies around the Coulomb barrier demonstrate that converged reliable excitation functions for total, incomplete, and complete fusion can be obtained with this type of approach.

Following a similar approach suggested recently to derive breakup probabilities [Phys. Rev. C 92, 054620 (2015)], we present a simple method to derive transfer probabilities by measuring only elastic or quasi-elastic scattering for the system under investigation with the positive transfer Q values and a similar system with closed transfer channels. Our estimations and transfer data for the two-neutron stripping in the O-18 + Pb-206 reaction are in a reasonable agreement.

Recent dynamical fusion models for weakly bound nuclei at low incident energies, based on a time-dependent perspective, are briefly presented. The main features of both the PLATYPUS model and a new quantum approach are highlighted. In contrast to existing time-dependent quantum models, the present quantum approach separates the complete and incomplete fusion from the total fusion. Calculations performed within a toy model for Li-6 + Bi-209 at near-barrier energies show that converged excitation functions for total, complete and incomplete fusion can be determined with the time-dependent wave packet dynamics.

Based on reaction theory, we suggest a useful method for extracting total and partial reaction and capture (complete fusion) cross sections from the experimental elastic and quasi-elastic backscattering excitation functions taken at a single angle. We also propose a method to predict the differential reaction cross section from the observed elastic-scattering angular distribution.

A new method is suggested for calculating the charge and mass distributions of quasifission products. The quasifission is treated within a transport model describing the evolution of a dinuclear system in charge (mass) asymmetry and the decay of this system along the internuclear distance. The calculated yields of these products are in agreement with recent experimental data for the hot fusion reactions leading to superheavy nuclei. The quasifission distributions in cold Pb-based fusion reactions are predicted.

Coincidence measurements of breakup fragments were carried out for the Li-7 + Au-197 and Pb-204 systems at sub-barrier energies. The mechanisms triggering breakup, and time-scales of each process, were identified through the reaction Q-values and the relative energy of the breakup fragments. Binary breakup of Li-7 were found to be predominantly triggered by nucleon transfer, with p-pickup leading to Be-8 -> alpha + alpha decay being the preferred breakup mode. From the time-scales of each process, the coincidence yields were separated into prompt and delayed components, allowing the identification of breakup process important in the suppression of complete fusion of Li-7 at above-barrier energies.

Converged continuum discretized coupled-channel calculations of elastic-scattering differential cross sections for reactions induced by the Li-6 projectile on the Sm-144 target, at energies around the Coulomb barrier, are presented. The impact of the low-lying alpha-deuteron resonant states in Li-6 (l = 2, J(pi) = 3(+), 2(+), 1(+)) on those elastic angular distributions is quantified. This is done by two types of calculations, namely, (a) by omitting from the continuum energy spectrum all states where the resonances are constructed in the discretization process, and (b) by considering only the resonance discretized space. Dynamical polarization potentials are used for interpreting the effect of continuum couplings. Resonant couplings play a more significant role than nonresonance ones at back-scattering angles and at incident energies below the Coulomb barrier. However, their effect becomes weaker as the incident energy increases above the barrier energy.

This contribution provides a preliminary study of the C-12 + C-12 sub-Coulomb fusion reaction using the time-dependent wave-packet method within a nuclear molecular picture. The theoretical sub-Coulomb fusion resonances seem to correspond well with observations. The present method might be a more suitable tool for expanding the cross-section predictions towards lower energies than the commonly used potential-model approximation.

Calculations of elastic scattering angular distributions for reactions of the weakly bound projectile Li-6 with targets Si-28 and Ni-58 at energies just above the Coulomb barrier are performed with the continuum-discretized coupled-channel calculation method. Ground, resonant, and nonresonant continuum states of Li-6 are included in the convergent calculations. The effect of the resonances on elastic scattering angular distributions is studied, in an original procedure, by excluding from the continuum space those states corresponding to the resonances. When the resonances of Li-6 are considered, the calculated elastic scattering angular distributions are in good agreement with the measurements. The exclusion of the resonances, unexpectedly, has a very small effect at the energies studied. Calculation of the polarization potentials associated with the resonances show that they have a repulsive character at the long range region, where scattering occurs. It is also confirmed that couplings to continuum states of Li-6 are essential to achieve agreement with the data.

A simplified, reliable and useful method, based on reaction theory, for calculating a number of integrated and differential cross sections in low-energy heavy-ion collisions is presented. Simplified formulae provide predictions of reaction, capture and elastic-scattering differential cross sections, using experimental information about elastic and quasi-elastic back-scattering excitation functions.

This paper addresses the critical importance of an unambiguous separation of the different components of the total fusion cross-section, which is a great theoretical and experimental challenge, in order to make further progress in the field of low-energy fusion of weakly bound nuclei. Recent theoretical developments in this area are reviewed. Calculations based on a classical dynamical reaction model indicate that the contribution of sequential fusion to the complete fusion cross-section is very substantial. A toy quantum model is presented, which introduces position projection operators. These can be useful for a quantitative understanding of complete and incomplete fusion of weakly bound nuclei within a more realistic quantum model.

The dinuclear system model considers a configuration of two touching nuclei which exchange nucleons. The microscopical justification of the model is presented. The fusion and quasifission processes are described in the reactions of synthesis of heavy and superheavy nuclei. The dependence of evaporation residue cross sections on isotopic composition of colliding nuclei is analyzed. The results agree with the available experimental data.

Recent progress in a quantitative study of the (12)c + C-12 sub-Coulomb fusion is reported. It is carried out using full-dimensional, time-dependent wave-packet dynamics, a quantum reaction model that has not been much exploited in nuclear physics, unlike in chemical physics. The low-energy collision is described in the rotating center-of-mass frame within a nuclear molecular picture. A collective Hamiltonian drives the time propagation of the wave-packet through the collective potential-energy landscape that is calculated with a realistic two-center shell model. Among other preliminary results, the theoretical sub-Coulomb fusion resonances for (12)c + C-12 seem to correspond well with observations. The method appears to be useful for expanding the cross-section predictions towards stellar energies.

The effect of breakup is investigated for the medium weight Li-6+Co-59 system in the vicinity of the Coulomb barrier. The strong coupling of breakup/transfer channels to fusion is discussed within a comparison of predictions of the Continuum Discretized Coupled-Channels model which is also applied to He-6+Co-59 a reaction induced by the borromean halo nucleus He-6.

An interpretation of the cold fission events in thermal-neutron-induced fission of heavy nuclei is given. The descent from the saddle point is considered as a dynamical process with reversible coupling between collective and intrinsic degrees of freedom. The distribution function for the collective variables is expressed as a product of two terms: the adiabatical and the dynamical factors. A simple model for symmetric fission to study the mass distribution is presented. As example, the calculations are performed for the nucleus Fm-264. Gross features of the cold fission are discussed as well as the dependence of the theoretical mass distribution on the parameters of the model.

Exclusive measurements of prompt gamma-rays from the heavy-residues with various light charged particles in the Li-7 + Pt-198 system, at an energy near the Coulomb barrier (E/V-b similar to 1.6) are reported. Recent dynamic classical trajectory calculations, constrained by the measured fusion, alpha- and t-capture cross-sections have been used to explain the excitation energy dependence of the residue cross-sections. These calculations distinctly illustrate a two-step process, breakup followed by fusion, in case of the capture of t and alpha clusters; whereas for He-6+p and He-5+d configurations, massive transfer is inferred to be the dominant mechanism. The present work clearly demonstrates the role played by the cluster structures of Li-7 in understanding the reaction dynamics at energies around the Coulomb barrier. (C) 2012 Elsevier B.V. All rights reserved.

The competition among reaction processes of a weakly-bound projectile at intermediate times of a slow collision has been unraveled. This has been done using a two-center molecular continuum within a semiclassical, time-dependent coupled-channel reaction model. Dynamical probabilities of elastic scattering, transfer and breakup agree with those derived from the direct integration of the time-dependent Schrödinger equation, demonstrating the usefulness of a two-center molecular continuum for gaining insights into the reaction dynamics of exotic nuclei.

We investigate the fusion and scattering of a 16 O projectile on 152,154 Sm targets using the time-dependent coupled-channel wave-packet method. We benchmark calculations of the S-matrix elements, fusion cross sections and scattering differential cross sections with those from the time-independent coupled-channel method, and compare the results to experimental data. We find that our time-dependent method and the time-independent method produce quantitatively similar results for the S-matrix elements and fusion cross sections, but our method cannot quantitatively explain the experimental scattering differential cross sections, mainly due to the low maximum number of partial waves produced by the time-dependent method. Nevertheless, the strong agreements between our method and the time-independent method demonstrates that the time-dependent coupled-channel wave-packet method can be used to address fusion reactions for a wide range of energies, with the advantage of being able to extend to time-dependent Hamiltonians for more advanced modelling of nuclear reactions.

We report on an isomer yield ratio study of biologically important 94 Tc following the fusion of the 9 Be + 89 Y system, carried out using the offline γ-ray spectroscopy in continuation to the online activation method. The incident beam energies considered are above the Coulomb barrier for the present study. The PLATYPUS model in conjunction with a potential model calculation was employed to analyze the data. An agreement in the order of magnitude between the experimental data and theoretical predictions has been achieved, by applying a phenomenological approach. The approach was further tested with isomer yield ratios of 94 Tc formed through 3 He + 93 Nb reactions. Possible factors that relate to the isomer yield ratios are also presented.

The quantum dynamics of a particle in a one-dimensional box with an oscillating wall (the Fermi accelerator) is investigated. The model is applied to the motion of a single nucleon in the mean-field potential of a heavy atomic nucleus whose surface vibrates. By directly solving the time-dependent Schrödinger equation, both the state of the particle and its mean-energy are studied. The effects of the frequency of the wall oscillation on the nucleon’s energy are addressed. Its energy oscillates in phase with the moving wall for all frequencies, showing no chaotic behaviour. There is a large initial peak of the nucleon’s energy as the particle adjusts to the sudden change in the size of the box and a varying relaxation time as it plateaus towards lower energy and a partial equilibrium. Small oscillations in energy continue, since there cannot be a true equilibrium while the wall is moving. The quantum coherence between the different parts of the nucleon’s wave-function in real space is very much preserved. This research lays the foundation for future investigations into quantum tunnelling in the Fermi accelerator.

The mechanism of reactions with weakly-bound proton-rich nuclei at energies near the Coulomb barrier is a long-standing open question owing to the paucity of experimental data. In this study, a complete kinematics measurement was performed for the proton drip-line nucleus .sup.17F interacting with .sup.58Ni at four energies near the Coulomb barrier. Thanks to the powerful performance of the detector array, exhaustive information on the reaction channels, such as the differential cross sections for quasielastic scattering, exclusive and inclusive breakup, as well as for fusion-evaporation protons and alphas, was derived for the first time. The angular distributions of quasielastic scattering and exclusive breakup can be described reasonably well by the continuum-discretized coupled-channels calculations. The inclusive breakup was investigated using the three-body model proposed by Ichimura, Austern, and Vincent, and results indicate the non-elastic breakup is the dominant component. The total fusion cross sections were determined by the fusion-evaporation protons and alphas. Based on the measured exclusive breakup data, the analysis of the classical dynamical simulation code PLATYPUS demonstrates that the incomplete fusion plays a minor role. Moreover, compared with .sup.16O+.sup.58Ni, both the reaction and total fusion cross sections of .sup.17F+.sup.58Ni exhibit an enhancement in the sub-barrier energy region, which mainly arises from couplings to the continuum states. This work indicates that the information of full reaction channels is crucially important to comprehensively understand the reaction mechanisms of weakly bound nuclear systems.

The compound nuclei 58 Co* and 61 Ni* have been populated at overlapping excitation energies by transfer reactions 56 Fe(6 Li,α) 58 Co * (surrogate of n+ 57 Co) at E lab = 35.9 MeV and 59 Co(6 Li,α) 61 Ni * (surrogate of n+ 60 Ni) at E lab = 40.5 MeV respectively. The 57 Co(n,xp) cross sections in the equivalent neutron energy range of 8.6-18.8 MeV have been determined within the framework of surrogate reaction ratio method using 60 Ni(n,xp) cross section values from the literature as reference. The proton decay probabilities of the compound systems have been determined by measuring evaporated protons at backward angles in coincidence with projectile-like fragments detected around the grazing angle. The measured 57 Co(n,xp) cross sections are in good agreement with both the predictions of talys-1.8 statistical model code with default parameters using different microscopic level densities and data evaluation library jeff-3.3 up to equivalent neutron energy ≈ 12.6 MeV, while for higher energies the measured 57 Co(n,xp) cross sections are found to be consistently higher than the predictions. However, the talys-1.8 calculations with modified values of input potential parameters provide a reasonable reproduction of the measured 57 Co(n,xp) cross sections for the entire neutron energy range. The observed discrepancies at higher energies between the experimental data and the predictions of both the jeff-3.3 library and the talys-1.8 calculations with default parameters indicate the need of new evaluations for this reaction.

Some of my recent works on the two-center shell model and its application to describing low-energy nuclear collisions within time-dependent approaches are reviewed and a perspective for their further use is given.

A novel quantum dynamical model based on the dissipative quantum dynamics of open quantum systems is presented. It allows the treatment of both deep-inelastic processes and quantum tunneling (fusion) within a fully quantum mechanical coupled-channels approach. Model calculations show the transition from pure state (coherent) to mixed state (decoherent and dissipative) dynamics during a near-barrier nuclear collision. Energy dissipation, due to irreversible decay of giant-dipole excitations of the interacting nuclei, results in hindrance of quantum tunneling

A quantitative study of the astrophysically important sub-barrier fusion of 12C+ 12C is reported. Lowenergy collisions are described in the body-fixed reference frame using wave-packet dynamics within a nuclear molecular picture. In contrast to conventional methods, such as the potential model and the coupled-channels approach, these new calculations reveal three resonant structures in the S-factor, explaining some structures observed in the data. The structures in the data that are not explained are possibly due to cluster effects in the nuclear molecule, which need to be included in the new approach.