Sub-barrier Fusion Cross Sections Research Articles

Polarization effects of hot nuclear matter on the fusion of heavy ions

Within the framework of the modified density-dependent Seyler–Blanchard approach in the [Formula: see text] approximation, the polarization effects of hot nuclear matter (PEHNM) are investigated on the fusion process of 16 different colliding systems in the mass range [Formula: see text]. In order to calculate the nucleus–nucleus potential, we use the double-folding (DF) model supplemented with the thermal effects of compound nucleus and also a repulsive potential that takes into account the incompressibility of the nuclear matter. The calculations of the fusion cross-sections are performed based on the couplings to the low-lying [Formula: see text] and [Formula: see text] vibrational states in both target and projectile. The sensitivity of sub-barrier fusion cross-sections to the polarization effects is evident from this study. The obtained results reveal that the modified form of the DF potential in the presence of the PEHNM appropriately reproduces the energy-dependent behavior of the experimental fusion cross-sections for the studied reactions. The role of the polarization effects on the fusion barriers as well as the inner part of the potential is also discussed.

Sub-barrier fusion dynamics in 28,30Si induced reactions with medium mass targets

The state-of-the-art technologies made it possible to reach the realms of fusion between two complex nuclei that offer an opportunity to explore a diverse spectrum of fusion phenomena. In this article, we have reported the influence of positive Q-value neutron transfer (PQNT) channels in fusion dynamics. Significant enhancement in sub-barrier fusion cross section has been observed for the 28Si+158Gd as compared to 30Si+140Ce and other similar systems with nearby mass asymmetry. Current findings include a comparison of the fusion excitation function of multiple systems on a reduced scale. The study sheds light on the influence of PQNT channels and deformation in nuclei on the sub-barrier fusion phenomenon. Further, fusion barrier parameters (barrier height and radius) extracted from the measured data demonstrate a good agreement with the empirical parameterization and proximity potential models.

Role of multi-neutron transfer channels on fusion enhancement

Fusion reactions 40Ar + 116Sn, 40Ar + 122Sn and 40Ca + 124Sn have been examined by employing coupled channel (CC) approach using code-CCFULL. Here we aim to investigate the influence of multi-neutron transfer channels in addition to coupling of collective excitations on sub-barrier fusion enhancement. Incorporation of inelastic excitations alone reproduced the experimental results for 40Ar + 116Sn system while for 40Ar + 122Sn contribution of 2n transfer channel is required to explain the experimental data. However, CC calculations with 2n transfer could not explain the enhancement at sub-barrier energies for 40Ca + 124Sn system. Therefore, the empirical coupled channel (ECC) calculations have been carried out to include the effect of multi-neutron transfer channels and it is found that the incorporation of sequential 4n transfer channel reproduced the experimental results in entire energy region. Nevertheless, it is observed that multi-neutron transfer coupling significantly contributed in raising the sub-barrier fusion cross sections particularly for the reactions where colliding partners are spherical. Importantly, it is also found that transfer of even number of neutrons play dominating role in sub-barrier fusion enhancement.

Evaporation residue cross-section measurements for 30Si+142Ce system

Evaporation residue (ER) cross-sections were measured for 30Si+142Ce reaction at laboratory energies in the range of 105 - 132 MeV using the HYbrid Recoil mass Analyzer (HYRA) at IUAC, New Delhi. The transmission efficiency of the HYRA was estimated using the calibration reaction 28Si+142Ce. Sub-barrier fusion enhancement was observed when compared with the one-dimensional barrier penetration model predictions for the present system. To explore the phenomena responsible for sub-barrier fusion enhancement, coupled-channels calculations were performed using the CCFULL code. The effect of couplings and the role of positive Q-value neutron transfer (PQNT) channels on sub-barrier fusion cross-sections were investigated. Coupled-channels calculations were able to reproduce the data by including the coupling in both projectile and target nucleus along with two neutron-transfer channels having positive Q-value. The measured ER cross-sections were compared with the nearby systems to explore the role of deformation of the colliding nuclei.

Effect of low lying vibrational and rotational energy levels on the fusion cross-sections

In heavy-ion fusion reactions, the coupling of various degrees of freedom to the relative motion leads to an enhancement in the sub-barrier fusion cross-section compared to the 1-dimensional barrier penetration model. The present work aims to explore the exclusive effect of low-lying vibrational and rotational energy levels in the enhancement of cross-sections for 12C induced reactions at the energy below and around the Coulomb barrier using the CCFULL code. The results show that for the negative and positive values of β4, the rotational energy states up to 2+ and 6+ significantly contributed to the fusion cross-sections which leads to fusion enhancement. These results can be useful for better understanding the dynamics of heavy-ion fusion reactions.

Systematic study of the effect of individual rotational energy levels on the fusion cross-section of 16 O-based reactions of range 480 ≤ Z P Z T ≤ 592

In heavy-ion fusion reactions, the enhancement in the sub-barrier fusion cross-section has been observed as compared to the 1-Dimensional barrier penetration model due to the coupling of many degrees of freedom to the relative motion. This enhancement can be explained theoretically by including nuclear structure effects like deformation and the coupling of relative motion among two colliding nuclei. The present work aims to investigate the effect of individual rotational energy levels on the fusion cross-sections for 16O-based reaction systems, namely, 16O + 182,184,186W, 16O + 176,180Hf, 16O + 174,176Yb, 16O + 166Er, 16O + 148,152,154Sm, 16O + 150Nd at energies below the fusion barrier. Using the CCFULL code, the effect of low-lying rotational energy levels on the fusion cross-section for 16O induced reactions has been investigated at energies below and around the Coulomb barrier. The calculations are performed by assuming the fixed value of diffuseness parameter a 0 = 0.65 fm in the Woods-Saxon nuclear potential and the other two parameters are optimised by fitting the experimental data at the above barrier. Here we have determined the V 0 and r 0 as a function of Z P Z T , where experimental cross-sections are available. From our calculations, it is observed that the hexadecapole deformation (β 4) with different magnitudes has a significant influence on the fusion cross sections. For the case of the +ve value of β 4, beyond 10+, the rotational levels cease to contribute significantly and also there is a significant difference between the contribution of sequential channels. On the other hand, in the case of -ve β 4, up to 6+ levels contribute significantly. Furthermore, we have established an algebraic systematic of fitting, which one can use to determine the parameters V 0, r 0 of Woods-Saxon nuclear potential within the range of Z P Z T lie in between 480 ≤ Z P Z T ≤ 592.

Role of positive transfer Q values in fusion cross sections for O18+W182,184,186 reactions

Background: The relevance of including channel coupling effects in the form of target deformation and vibration in fusion reactions has been well established. Many reactions with positive $Q$ values for neutron transfer show enhancement in sub-barrier fusion cross sections. However, there are exceptions to these cases.Purpose: We aim to make a comprehensive list of factors influencing the sub-barrier fusion enhancement in systems with neutron transfer channels having positive $Q$ values.Method: Evaporation residue cross sections were measured for $^{18}\mathrm{O}+^{182,184,186}\mathrm{W}$ reactions in the energy range $68--104$ MeV in the laboratory frame, using a recoil mass spectrometer.Results: Inclusion of deformation of target and projectile low-level excitations in the coupled channels calculations explains the measured fusion excitation functions of $^{18}\mathrm{O}+^{182,184,186}\mathrm{W}$ reactions.Conclusions: Considering that all the targets have similar deformation, and comparing with $^{16}\mathrm{O}+^{182,184,186}\mathrm{W}$ reactions having negative $2n$ transfer $Q$ values, we can conclude that the positive $Q$ values of neutron transfer channels have no effect on the observed fusion cross sections of $^{18}\mathrm{O}+^{182,184,186}\mathrm{W}$ reactions.

Microscopic study of the fusion reactions Ca40,48+Ni78 and the effect of the tensor force

We provide a microscopic description of the fusion reactions between $^{40,48}\mathrm{Ca}$ and $^{78}\mathrm{Ni}$. The internuclear potentials are obtained using the density-constrained (DC) time-dependent Hartree-Fock (TDHF) approach and fusion cross sections are calculated via the incoming wave boundary condition method. By performing DC-TDHF calculations at several selected incident energies, the internuclear potentials for both systems are obtained and the energy-dependence of fusion barrier are revealed. The influence of tensor force on internuclear potentials of $^{48}\mathrm{Ca}+^{78}\mathrm{Ni}$ is more obvious than those of $^{40}\mathrm{Ca}+^{78}\mathrm{Ni}$. By comparing the calculated fusion cross sections between $^{40}\mathrm{Ca}+^{78}\mathrm{Ni}$ and $^{48}\mathrm{Ca}+^{78}\mathrm{Ni}$, an interesting enhancement of subbarrier fusion cross sections for the former system is found, which can be explained by the narrow width of internuclear potential for $^{40}\mathrm{Ca}+^{78}\mathrm{Ni}$ while the barrier heights and positions are very close to each other. The tensor force suppresses the subbarrier fusion cross sections of both two systems.

Improving the characterization of fusion in a MuSIC detector by spatial localization

Multi-Sampling Ionization Chambers (MuSIC) provide an efficient means of measuring nuclear reactions with low beam rates (< 106 pps). However, in comparison to thin-target measurements, prior measurements using MuSIC detectors all manifest fusion excitation functions with wide error bars in the energy dimension. This uncertainty limits the applicability of these devices in measuring near and sub-barrier fusion cross-sections. Key to overcoming this limitation is spatial localization of the fusion in the detector. By comparing the measured ionization in the MuSIC detector with accurate energy loss calculations the position of the fusion in the detector is determined. The analysis not only provides the desired improvement in energy resolution, but it also allows extraction of the atomic number of the evaporation residues following fusion. The effectiveness of this approach is demonstrated for 18O+12C measured with MuSIC@Indiana.

Fusion studies in O16+Nd142,150 reactions at energies near the Coulomb barrier

Background: Enhancement in fusion cross sections over one-dimensional barrier penetration model (1D-BPM) predictions has been observed at sub-barrier energies owing to the coupling of various internal degrees of freedom to the relative motion. On the other hand, hindrance in fusion is noticed at energies well above the barrier in a few cases.Purpose: The purpose is to probe the dynamics of heavy ion fusion at energies below and well above the Coulomb barrier.Methods: Fusion excitation functions for the $^{16}\mathrm{O}+^{142,150}\mathrm{Nd}$ reactions are measured using the Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. Measurements have been performed in the range $12%$ below to $50%$ above the Coulomb barrier for both systems. The measured fusion cross sections are compared with coupled channels calculations using ccfull code. The cross sections are also compared with reactions using $^{16}\mathrm{O}$ beams with other isotopes of Nd to explore the systematic behavior of fusion.Results: Compared with 1D-BPM predictions, fusion enhancement is observed in both $^{16}\mathrm{O}+^{142}\mathrm{Nd}$ and $^{16}\mathrm{O}+^{150}\mathrm{Nd}$ reactions at below-barrier energies, with the latter reaction showing a higher enhancement. Coupled channels calculations incorporating the collective excitations of the target nuclei reproduce the fusion cross sections in both reactions. The collective excitations of the projectile nucleus do not seem to contribute to the observed fusion enhancement. Calculations using Aky\"uz-Winther potential parameters fail to reproduce the fusion cross sections at energies well above the barrier.Conclusions: Fusion enhancement is observed in both reactions studied. Degree of enhancement of sub-barrier fusion cross section is larger for the reaction using $^{150}\mathrm{Nd}$ target. Fusion hindrance is observed in both reactions at very high energies. The hindrance seems to increase with increasing beam energy. Larger value of diffuseness parameter compared with the value consistent with elastic-scattering measurements is required to reproduce the fusion excitation function at energies well above the barrier. This could be a strong indication of dynamical effects in fusion at very high energies.

Fusion and proton transfer in the B10+Al27 system at sub-barrier energies

Background: Significant enhancement in sub-barrier fusion cross sections by several orders of magnitude, in the frame of one-dimensional barrier penetration models, is observed for a variety of nuclear systems. To understand this, one needs to find the fundamental degrees of freedom relevant in the sub-barrier fusion region by incorporating nonelastic channels such as coupling of the excited target and/or projectile nuclei, particle transfer channels, threshold variation of nuclear potential, etc.Purpose: We probe what degrees of freedoms are associated with the $^{10}\mathrm{B}+^{27}\mathrm{Al}$ reaction at energies $\ensuremath{\approx}18%$ below to $\ensuremath{\approx}12%$ above the Coulomb barrier.Method: An online $\ensuremath{\gamma}$-ray spectroscopy technique is used to determine the populated excitation functions in the $^{10}\mathrm{B}+^{27}\mathrm{Al}$ reaction. The reaction cross sections obtained from these $\ensuremath{\gamma}$ rays are compared with the statistical model to explore the mechanism of fusion reactions.Results: At energies near and below the Coulomb barrier, two isotopes of sulfur ($^{34}\mathrm{S}$ and $^{32}\mathrm{S}$) were found to reproduce cross section within the frame of the pace2 model based on Hauser-Feshbach calculations, whereas isotopes of chlorine ($^{35}\mathrm{Cl}$), sulfur ($^{35}\mathrm{S}$), and phosphorous ($^{32}\mathrm{P}$) agree well but at above-barrier energies. Isotopes of Ar, Cl, S, P, and Si show significant enhancement over an entire band of energies. This enhancement (suppression) in the experimental cross section at energies above (below) the barrier points towards the involvement of some nuclear reaction mechanism other than fusion-evaporation. Distorted-wave Born approximation calculations strongly support the population of $^{28}\mathrm{Si}$ residue via the one-proton transfer process. The total fusion cross section is found to follow the theory after the inclusion of coupling of low lying excited states of projectile and target. Calculations concerning the astrophysical $S$ factor and the logarithmic derivative factor support the idea of no fusion hindrance at the studied energies. The universal fusion function benchmark shows consistency with previous data for lithium (or Li isotopes) induced systems.Conclusions: The inclusion of inelastic couplings associated with both target and projectile is important to understand the behavior of total fusion cross section. The formation of $^{28}\mathrm{Si}$ via the one-proton transfer reaction supports the present experimental technique to make inclusive transfer measurements. The calculations with the universal fusion function present a slight suppression in the higher energy region, indicating possible breakup effects in this region. The present calculations show that till $18%$ below the barrier there is no fusion hindrance. On extrapolating the theoretical values we further observed that the present system has no fusion hindrance. No connection of $^{10}\mathrm{B}+^{27}\mathrm{Al}$ fusion with astrophysics has been made, which raises the question to think of cosmic ray reactions and perhaps reactions in the early solar system, but how the fusion reaction would fit into the picture is not clear at all.

Calculation of the C12+C12 sub-barrier fusion cross section in an imaginary-time-dependent mean field theory

The 12C+12C sub-barrier fusion cross section is calculated within the framework of a Time Dependent Hartree-Fock (TDHF) based classical model using the Feynman Path Integral Method. The modified astrophysical S*-factor is compared to direct and indirect experimental results. A good agreement with the direct data is found. In the lower energy region, where recent analyses of experimental data obtained with the Trojan Horse Method (THM) lead to contrasting results, the model predicts an S* factor half way between those results. Low energy resonances revealed in the THM data are added to the calculation and the relative reaction rate in the Gamow region is calculated. The role of different resonances is discussed in detail and their influence on the reaction rate at temperatures relevant to stellar evolution is investigated.

Evaporation residue cross section in the Cl37+Zn68 fusion reaction near the Coulomb barrier

Background: The measured subbarrier fusion cross sections in heavy-ion reactions are found to be significantly large as compared with those expected from the one-dimensional barrier penetration model (1d-BPM). Although attempts have been made to comprehend the enhancement in terms of different intrinsic degrees of freedom of the colliding nuclei, a clear understanding of the same is yet to come.Purpose: The objectives of this study is to understand the interplay of the channel coupling effect on fusion excitation function and explore the decay dynamics of the excited compound nucleus in the sub-and-near barrier region.Method: Fusion excitation function has been measured at energies from 7% below to 38% above the Bass barrier using a recoil mass spectrometer. Furthermore, cross sections of the different evaporation residues, such as 98, 99, 100, and 101 u, have been extracted.Results: The observed enhancement in the subbarrier fusion cross sections over the 1d-BPM predictions has been explained by considering the low-lying inelastic excitations among the interacting partners using ccfull code and by the barrier modification using the dynamical cluster-decay model (DCM). The cross sections of individual residual mass fractions (98, 99, 100, and 101 u) have been compared with the Hauser-Feshbach model.Conclusion: Coupled-channel calculations and DCM have successfully explained the total fusion cross sections data. The measured total fusion cross section ${\ensuremath{\sigma}}_{\mathrm{fus}}$ was found to be approximately equal to the sum of various residual mass fractions ($\mathrm{\ensuremath{\Sigma}}{\ensuremath{\sigma}}_{\mathrm{ER}}$) at energies above the Bass barrier. One-dimensional barrier height and radius parameters extracted from the measured data are in good agreement with the Bass model and DCM parameters.

Role of neutron transfer in the sub-barrier fusion cross section in O18 + Sn116

Background: In heavy-ion-induced fusion reactions, cross sections in the sub-barrier region are enhanced compared to predictions of the one-dimensional barrier penetration model. This enhancement is often understood by invoking deformation and coupling of the relative motion with low-lying inelastic states of the reaction partners. However, effects of nucleon transfer on fusion below the barrier, especially for the systems having positive $Q$ value neutron transfer (PQNT) channels, are yet to be disentangled completely.Purpose: We intend to study the role of the PQNT effect on the sub-barrier fusion of the $^{18}\mathrm{O} + ^{116}\mathrm{Sn}$ system having positive $Q$ value for the two-neutron stripping channel. Also we reflect on the interplay of couplings involved in the system around the Coulomb barrier.Method: The fusion excitation function was measured at energies from $11%$ below to $46%$ above the Coulomb barrier for $^{18}\mathrm{O} + ^{116}\mathrm{Sn}$ using a recoil mass spectrometer, viz., the Heavy-Ion Reaction Analyser (HIRA). Fusion barrier distributions were extracted from the data. Results from the experiment were analyzed within the framework of the coupled-channels model.Results: Fusion cross sections at energies below the Coulomb barrier showed strong enhancement compared to predictions of the one-dimensional barrier penetration model. The fusion process is influenced by couplings to the collective excitations with coupling to single- and two-phonon vibrational states of the target and the projectile respectively. Inclusion of the two-neutron transfer channel in the calculation along with these couplings could reproduce the data satisfactorily.Conclusions: The significant role of PQNT in enhancing the sub-barrier fusion cross section for the chosen system is not observed. It simply reduced the sub-barrier fusion cross section. Therefore, a consistent link between PQNT and sub-barrier fusion enhancement could not be established vividly while comparing the fusion excitation function from this work with the same from other $^{16,18}\mathrm{O}$-induced reactions. This clearly points to the need for more experimental as well as theoretical investigation in this field.

Influence of the tensor interaction on heavy-ion fusion cross sections

[Background] While the tensor interaction has been shown to significantly affect the nuclear structure of exotic nuclei, its influence on nuclear reactions has only recently been investigated. The primary reason for this neglect is the fact that most studies of nuclear dynamics do not include the tensor force at all in their models. Indeed, only a few Skyrme parametrizations consider the tensor interaction in parameter determination. With modern research facilities extending our ability to probe exotic nuclei, a correct description of nuclear dynamics and heavy-ion fusion is vital to both supporting and leading experimental efforts. [Method] Fusion cross sections are calculated using ion-ion potentials generated by the fully microscopic density-constrained time-dependent Hartree-Fock (DC-TDHF) method with the complete Skyrme tensor interaction. [Results] For light nuclei, the tensor force only slightly changes the sub-barrier fusion cross sections at very low energies. Heavier nuclei, however, begin to exhibit a substantial hindrance effect in the sub-barrier region. This effect is strongest in spin-unsaturated systems, though can manifest in other configurations as well. Static, ground state deformation effects of the tensor force can also affect cross sections by shifting the fusion barrier. [Conclusions] The tensor interaction has a measurable effect on the fusion cross sections of nuclei spanning the nuclear chart. The effect comes from both static effects present in the ground state and dynamic processes arising from the time evolution of the system. This motivates the development of a modern Skyrme parameter set that includes all time-odd and tensor terms and that studies moving forward should include the tensor force to ensure a more robust and complete description of nuclei.

Assessment of the quality of different pocket formulas in reproducing experimental sub-barrier fusion cross sections

In the frame of a new introduced energy scaling method, the Coulomb barrier heights calculated by using thirteen different forms of the pocket formulas are systematically analyzed for sub-barrier fusion cross sections of 58 heavy-ion fusion reactions, including O, Al, Si, S, Cl, Ca and Ti projectiles. It is found that the barrier heights, which are generated by the parameterized formulas based on the Zhang 2016, Sahu 1999, Puri 2015 and Puri 1992 approaches, seem to be more suitable for description of the experimental fusion cross sections at energies below the Coulomb barrier. The present obtained results show the importance of the projectile mass and surface energy coefficients in heavy-ion fusion at sub-barrier energies. A discussion concerning the fusion Q-value rule below barrier energies is presented for some fusion systems.

Sub-barrier fusion in the Cl37+Te130 system

Background: In heavy-ion induced reactions, the sub-barrier fusion cross sections are found to be higher as compared to the predictions of the one-dimensional barrier penetration model. Attempts have been made to explain sub-barrier fusion enhancement by including the static deformations, the couplings to inelastic excitations, and non-fusion channels.Purpose: To investigate factors which influence the sub-barrier fusion in the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system and to understand the interplay of couplings, the fusion excitation function was measured at energies from $10%$ below to $15%$ above the Bass barrier.Method: The fusion excitation function was measured by employing a recoil mass spectrometer, the Heavy-Ion Reaction Analyser (HIRA), at the Inter-University Accelerator Centre, New Delhi. To study the behavior of the fusion excitation function and the effect of couplings at sub-barrier energies, the excitation function was analyzed in the framework of the coupled-channels code ccfull.Results: In the present work, the fusion cross section was measured down to 1 $\ensuremath{\mu}\mathrm{b}$ at the lowest measured energy, i.e., $10%$ below the barrier. It was found that the inclusion of couplings of low-lying excited states along with the modified barrier between interacting nuclei satisfactorily reproduces the fusion excitation function of the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system. For better insight into the sub-barrier fusion, the fusion barrier distribution, the logarithmic derivative L(E) factor, and the astrophysical S factor were extracted from the analysis of the experimentally measured fusion excitation function.Conclusions: The analysis of the fusion excitation function in terms of the astrophysical S factor and the L(E) factor suggests the absence of fusion hindrance in the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system down to a 1 $\ensuremath{\mu}\mathrm{b}$ cross section achieved at the lowest measured energy. The excitation function of the present system is compared with the existing measurements in which $^{37}\mathrm{Cl}$ has been used as a projectile to understand the interplay of entrance-channel parameters in sub-barrier fusion enhancement.

The STELLA apparatus for particle-Gamma coincidence fusion measurements with nanosecond timing

The STELLA (STELlar LAboratory) experimental station for the measurement of deep sub-barrier light heavy-ion fusion cross sections has been installed at the Andromède accelerator at the Institut de Physique Nucléaire, Orsay (France). The setup is designed for the direct experimental determination of heavy-ion fusion cross sections as low as tens of picobarn. The detection concept is based on the coincident measurement of emitted gamma rays with the UK FATIMA (FAst TIMing Array) and evaporated charged particles using a silicon detector array. Key developments relevant to reaching the extreme sub-barrier fusion region are a rotating target mechanism to sustain beam intensities above 10μA, an ultra-high vacuum of 10−8 mbar to prevent carbon built-up and gamma charged-particle timing in the order of nanoseconds sufficient to separate proton and alpha particles.

Characterizing the astrophysical S factor for C12+C12 fusion with wave-packet dynamics

A quantitative study of the astrophysically important sub-barrier fusion of $^{12}$C+$^{12}$C 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.

Essentials of the macroscopic-microscopic folded-Yukawa approach and examples of its record in providing nuclear-structure data for simulations

The macroscopic-microscopic model based on the folded-Yukawa singleparticle potential and a “finite-range” macroscopic model is probably the approach that has provided the most reliable predictions of a large number of nuclear-structure properties for all nuclei between the proton and neutron drip lines. I will describe some basic features of the model and the development philosophy that may be the reason for its success. Examples of quantities modeled within the same model framework are, nuclear masses, ground-state level structure, including spins, ground-state shapes, fission barriers, heavy-ion fusion barriers, sub-barrier fusion cross sections, β-decay half-lives and delayed neutron emission probabilities, shape coexistence, and α-decay Qα energies to name a few. I will show how well it predicted various properties measured after published results. Rather than giving an incomplete model description here I will give a timeline of model development and provide references to typical applications and references that are sufficiently complete that several individuals have written computer codes based on these references, codes whose results have excellent agreement with ours.