Breakup Threshold Research Articles

The Movement of Efimov States in 2n Halo Nucleus: probing the roles of mass asymmetry and short range of interaction

This brief communication presents the results of our work to study the movement of Efimov states in 2-neutron halo nuclei. We discuss the emergence and evolution of Efimov states in to resonances beyond the two-body (n-Core) breakup threshold and also the movement of the Efimov state in a 2-neutron halo nucleus to the region of the so called, Thomas Collapse. We especially, probe the roles of mass asymmetry of the three-body system (n-n-core) and the short range of the n-core interaction in the movement of the Efimov states. The analysis has been carried out within the framework of a three-body model, assuming two-body, non-local, separable potentials for the binary sub-systems, namely, the n-n and n-core systems. The primary motivation has been to scan the parameter space of the range parameter and determine the value(s) for which the system can support the Efimov states. The analysis shows that the value of the range parameter $\beta$ = 5.2$\alpha$ ( $\alpha$ being the energy parameter given in terms of the deuteron binding energy ) produces the realistic three-body binding energy for $^{20}$C and also generates the excited Efimov states. However, as the value of $\beta$ is increased corresponding to decrease in the range of the two-body (n-core) interaction the ground and excited state binding energies increase drastically. In other words, as the range of the two-body interaction tends to zero the system enters the Thomas Collapse region away from the Efimov region.

Deuteron breakup effects on the d + 12C, 15N, 16O, 24Mg, 32S, 58Ni, and 70Ge elastic scattering angular distributions

Motivated by the well-known n + p cluster structure of deuterons, which appears at breakup threshold energy of 2.225 MeV, the angular distributions (ADs) for elastically scattered deuterons from various targets, namely, 12C, 15N, 16O, 24Mg, 32S, 58Ni, and 70Ge at different energies, are investigated microscopically within the continuum discretized coupled channel (CDCC) method as well as an effective potential (Ueff), considered as the sum of cluster folding and dynamical polarization potentials. The Ueff potentials were employed successfully to reproduce the elastic ADs data for the considered systems in a wide range of energies. The investigation gives evidence for the applicability of the Ueff in describing the ADs data for many nuclear systems.

Breakup prediction of oscillating droplets under turbulent flow

Droplet and bubble breakup phenomena under turbulent flow have been widely studied for over 70 years through theoretical, experimental and numerical approaches. Despite significant progress, the dynamics of breakup remains an active research topic. The present study considers a database of breakup events under turbulent conditions. The database contains neutrally buoyant droplets obtained for a single moderate turbulent Reynolds number and a Weber number near the critical Weber number of the droplets, allowing for long time evolution prior to droplet breakage. Each droplet in the database follows a consistent behavior: the droplet undergoes (1) an initial shape deformation, then (2) an extended oscillatory regime, until (3) a critical large deformation starts, leading to (4) a capillary-driven breakup. While the first two stages have been investigated in our previous work using spherical harmonics decomposition, this study focuses on the last two stages, describing them qualitatively and quantitatively by means of seven different shape parameters. These shape parameters are based on different information of the specific droplet such as its surface, its volume or its averaged mean curvature, and provide a multidimensional analysis of the droplet breakup. They are used to measure the time spent in the final two stages prior to breakup, as well as the transition between these stages. Additionally, we establish breakup thresholds for each shape parameter to predict neutrally buoyant droplet breakup under turbulent flow conditions.

Interplay of breakup and fusion in near-barrier collisions of weakly-bound nuclides

Light, weakly-bound nuclides such as 6,7Li and 9Be exhibit a diverse range of near-barrier reaction phenomena. Complete fusion is found to be suppressed by up to 35% with respect to barrier-passing model calculations. Their weak binding leads to significant breakup through excitation of the continuum, but also through production of weakly-bound or unbound neighbouring nuclides via nucleon transfer. Such systems also exhibit large yields of incomplete fusion, which is correlated empirically with cluster breakup thresholds for these stable nuclides. Disentangling these reaction phenomena and their complex interplay is one of the most interesting challenges in near-barrier reaction dynamics. Here we briefly review our recent progress in understanding the interplay between breakup and fusion. These results strongly suggest that the dominant mechanism leading to incomplete fusion and the suppression of complete fusion is direct capture of the projectile cluster constituents by the target nucleus, rather than requiring projectile breakup prior to fusion.

Systematic study of fusion suppression and its dependency on projectile breakup threshold energy

Measurements of the excitation function (EF) of the observed evaporation residues (ERs) populated in the 20Ne + 93Nb reaction at E lab ≈ 91−145 MeV are carried out to explore the systematic of fusion suppression and its dependency on projectile breakup threshold energy, by employing the offline γ-ray detection method. The EF of the observed ERs populated through complete and/or incomplete fusion processes are analysed in the framework of statistical mode code PACE4. The fusion function, derived from the experimentally measured fusion cross section data, is compared with the universal fusion function (UFF) to estimate the degree of fusion incompleteness. Based on the observed results, an empirical formula is proposed to interrelate the degree of fusion suppression and breakup threshold energy of the incident projectile.

Investigation of the fusion mechanism in the Li6 -induced reaction on Nb93

We attempt to put forth the competing reaction mechanisms through residual cross section measurement in $^{6}\mathrm{Li}$ fusion with $^{93}\mathrm{Nb}$. The measured residual cross sections in the 24--43 MeV energy range are analyzed with the theoretical estimations from pace4, empire3.2.2, and alice23 statistical model codes. The replication of major $xn$-channel cross sections by empire with enhanced generalized superfluid model (EGSM) level density confirms that the population of $xn$-channel residues is through the complete fusion (CF) mechanism. The preequilibrium (PEQ) emission signatures were witnessed in the case of $^{97}\mathrm{Ru}$ residue populated via the $2n$ channel. Amplification of major experimental $p$- and $\ensuremath{\alpha}$-channel cross sections relative to the optimal theory was interpreted by considering the possibility of an incomplete fusion (ICF) process in addition to CF, owing to the low breakup threshold of the $^{6}\mathrm{Li}$ projectile. Thus, the ICF strength fraction $({F}_{\mathrm{ICF}})$ was estimated. The ${F}_{\mathrm{ICF}}$ turned out to be $\ensuremath{\approx}8--20%$ with an increasing trend and is found to be thoroughly higher than the deduced ${F}_{\mathrm{ICF}}$ for $^{7}\mathrm{Li}$ reaction on $^{93}\mathrm{Nb}$ target. In the case of weakly bound $^{6,7}\mathrm{Li}$-induced reactions, the first attempt is made to understand the influence of entrance channel parameters such as bombarding energy, $\ensuremath{\alpha}$-separation energy, Coulomb factor, mass asymmetry, neutron skin thickness, angular momentum, etc., on ${F}_{\mathrm{ICF}}$. The observed trend of the isomeric cross section ratios from the relative population of isomeric and ground states of $^{96,94}\mathrm{Tc}$ radionuclides is also discussed.

S matrices of elastic α−C12 scattering at low energies in effective field theory

The elastic $\ensuremath{\alpha}\text{\ensuremath{-}}^{12}\mathrm{C}$ scattering at low energies for $l=0,1,2,3,4,5,6$ is studied in effective field theory. I discuss the construction of the $S$ matrices of elastic $\ensuremath{\alpha}\text{\ensuremath{-}}^{12}\mathrm{C}$ scattering in terms of the amplitudes of subthreshold bound and resonant states of $^{16}\mathrm{O}$, which are calculated from the effective Lagrangian. The parameters appearing in the $S$ matrices are fitted to the phase shift data below the $p\text{\ensuremath{-}}^{15}\mathrm{N}$ breakup threshold energy, and one finds that the phase shifts are well described within the theory.

Analysis of elastic scattering of 6Li by 90Zr near Coulomb barrier

We use a phenomenological optical potential constructed in consideration of a versatile potential developed by Joseph N. Ginocchio. The optical potential uses less number of energy-dependent parameters to analyse nuclear scattering data. We study the ratios of elastic to Rutherford differential scattering cross sections of the system 6Li + 90Zr at various energies, namely, 10.19, 11.11, 12.07, 13.95, 15.84, 17.71, 19.60, 23.36, 28.05 and 31.87 MeV in the centre-of-mass system. The study of angular distributions is performed in a wide angular range. Our theoretical calculations explain the experimental results and follow breakup threshold anomaly phenomenon near the Coulomb barrier. We discuss the variation of reflection function |S l | with ‘l’ for each contributing partial wave and calculate reaction cross section for the system against the projectile energy 31.87 MeV with permissible error.

Study of the threshold anomaly in the elastic scattering of d+ 197Au

Measurements of the elastic scattering angular distribution for the d+ 197Au system were carried out covering deuteron incident energies in the range from 5 to 16 MeV, i.e. approximately 50% below and above the Coulomb barrier. A critical interaction distance of d I = 2.49 fm was determined from these distributions, which is comparable to that of the radioactive halo nucleus 6He. The experimental angular distributions were systematically analyzed using two alternative models: the semi-microscopic São Paulo and the effective Woods–Saxon optical potentials, for which the best-fitting parameters were determined. These potentials, integrated with the vicinity of the sensitivity radius, were calculated for each energy. For both models, the energy dependence of these integrals presented the breakup threshold anomaly around the coulomb barrier, a typical signature of weakly bound nuclei.

Probing reaction mechanisms through residual cross section measurement for 7Li+Zn system

Though the picture remains incoherent to draw a concrete conclusion, especially with weakly bound particles, prolific efforts have been devoted to unfolding the reaction mechanisms at energies below 10 MeV/u. The dearth of extensive data and ambiguous findings in the light to medium mass region galvanizes the exploration of the entire mass domain. In the course of discerning the underlying reaction mechanisms in 7Li fusion with natural Zn, the excitation function (EF) analysis has been reported within the energy range of 21–43 MeV. Residual cross sections have been measured employing the stacked foil activation technique followed by offline γ-spectroscopy. Subsequently, the measured EFs have been compared with theoretical predictions from statistical model codes PACE4 and EMPIRE3.2.2. EF analysis affirms the dominance of the complete fusion (CF) mechanism as revealed through the gross satisfaction of measured data from the n-emitting channels by both the model codes. The observed enhancement in subsequent channels relative to theory has been implicitly interpreted as the role of other mechanisms like breakup fusion and/or direct cluster transfer in populating residues owing to the low breakup threshold of weakly bound 7Li. A critical piece of experimental evidence concerning the discrepancy in the branching intensity of 93.31 keV γ-peak from the decay of 67Ga residue reported in various nuclear databases has been witnessed. Thus, the revised estimated intensity value has been reported, along with a discussion on the optimized production of Ga isotopes for medicinal applications.

Cluster folding model analysis of the 7Be+28Si elastic scattering in the near-barrier

In the framework of the optical model, the elastic scattering of the radioactive projectile 7Be on the 28Si target at four energies near the Coulomb barrier has been analyzed. The cluster folding model is used to determine the real part of the nuclear optical potential. For comparison, two microscopic optical potentials have been generated using the DDM3Y effective NN interaction based upon two different forms for 7Be density distribution. All the obtained real potentials, in conjunction with phenomenological Woods-Saxon imaginary parts, have successfully reproduced the elastic scattering angular distributions over the measured angular range. The energy dependence of the real and imaginary strengths that are produced by the best-fit of the experimental data was examined. Neither the usual threshold anomaly nor the breakup threshold anomaly can be observed at the considered energy range. The obtained cross sections have been reduced and compared with earlier theoretical and experimental data of 7Li on the same target near the Coulomb barrier.

Cluster structure of C11 investigated with a breakup reaction

The excitation spectra above the breakup threshold of C11 were measured using the invariant mass method with a 25.0-MeV/nucleon beam bombarding a carbon target for the first time. This measurement was performed with a zero-degree double-sided silicon strip detector together with four CsI(Tl) detectors, which could detect breakup fragments with low relative kinetic energy. Some resonances in C11 were clearly observed in the excitation energy range of 8–14 MeV proceeding through the Be7 + α channel. Among them, a resonance with the largest yield was observed around 8.10 MeV. We assign it as the head of the Kπ=3/2− rotational band, and suggest the 9.38-MeV state as the second member of this band.1 MoreReceived 3 May 2022Revised 16 September 2022Accepted 11 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.014320©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBreakup reactionsNuclear structure & decaysProperties6 ≤ A ≤ 19Nuclear Physics

Disentangling fractional momentum transfer in the F19+Sm154 system

Forward recoil range distributions of evaporation residues produced in the system $^{19}\mathrm{F}+^{154}\mathrm{Sm}$ were measured at projectile energy $\ensuremath{\approx}107$ MeV using the offline $\ensuremath{\gamma}$-ray activation technique. The entire and fractional linear momentum transfers inferred from these recoil range distributions were used to identify the evaporation residues formed by complete and incomplete fusion mechanisms. The forward recoil range distributions of measured evaporation residues populated through $x\mathrm{n}/\mathrm{p}x\mathrm{n}$ channels were found to be consisting of a single peak only while the evaporation residues populated through $\ensuremath{\alpha}$ emitting channel had contributions from incomplete fusion also. The observed incomplete fusion process in the population of $\ensuremath{\alpha}$ emitting channel residues is explained through the breakup fusion model. The results indicate the occurrence of incomplete fusion involving the breakup of $^{19}\mathrm{F}$ into $^{4}\mathrm{He}+^{15}\mathrm{N}$ and/or $^{8}\mathrm{Be}+^{11}\mathrm{B}$ followed by fusion of one of the fragments with target nucleus $^{154}\mathrm{Sm}$. From these measurements, the relative contributions of complete and incomplete fusion were separated out. The forward recoil range distributions data show that the incomplete fusion contribution in the fusion of fragment $^{15}\mathrm{N}$ is more dominant as compared to the fusion of fragment $^{11}\mathrm{B}$ with $^{154}\mathrm{Sm}$ target due to the smaller value of $\ensuremath{\alpha}$ breakup threshold energy $({E}_{\mathrm{B}.\mathrm{U}.}^{\ensuremath{\alpha}})$. The measured forward recoil range distributions of evaporation residues produced through $\ensuremath{\alpha}$ emitting channels provide experimental signature of strong clustering in $^{19}\mathrm{F}$ projectile as $\ensuremath{\alpha}$ and $^{15}\mathrm{N}$. The incomplete fusion strength function has also been deduced from the measured recoil range distributions and found to be compatible with those deduced from the measured excitation functions for the same system and beam energy.

Positronium collisions with polar molecules

We calculate elastic and positronium (Ps) break-up cross sections for collisions of Ps with the polar molecules CO, HCl, and LiF in the fixed-nuclei approximation. We incorporate electron exchange and correlation for these processes by using the free-electron-gas model developed earlier for Ps scattering by rare-gas atoms, ${\mathrm{N}}_{2}$, ${\mathrm{O}}_{2}$, and ${\mathrm{CO}}_{2}$ molecules. The present target molecules provide a range of dipole moments from the weakly polar CO to the strongly polar LiF. We find that Ps scattering is similar to electron scattering when the cross sections are plotted as a function of projectile velocity for the targets with smaller dipole moments (CO, HCl). However, we do not see such a similarity for LiF which has a large dipole moment. Below the Ps break-up threshold we observe resonance structures similar to those obtained earlier for the other molecular targets that we have studied.

Microscopic description of the H(α,γ)2Li6 radiative capture reaction

The $^{2}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma})^{6}\mathrm{Li}$ radiative capture responsible for the $^{6}\mathrm{Li}$ production during the big-bang nucleosynthesis is comprehensively studied within a microscopic approach. The approach implements microscopically clustering aspects of nuclear structure and dynamics in an oscillator-basis representation. The total astrophysical $S$ factor of the reaction is calculated. All allowed partial electric quadrupole and magnetic dipole transitions between the $^{4}\mathrm{He}+^{2}\mathrm{H}$ continuum and the $^{6}\mathrm{Li}$ ground state are considered in the standard long-wavelength limit. Isospin-forbidden electric dipole transitions are taken into account in two ways. The first method is based on the expression for the electric dipole operator at the leading order of the long-wavelength approximation with the usage of the exact-mass prescription. In the second method, this operator is written at the first order beyond the leading-order approximation. Contributions of the transitions are compared to each other. The $^{4}\mathrm{He}+^{2}\mathrm{H}$ nuclear phase shifts for the initial channels of the considered reaction are computed. Important properties of the $^{6}\mathrm{Li}$ nucleus, such as the breakup threshold, the asymptotic normalization constants, and the electric quadrupole moment are also described. Deformation effects and their manifestations in $^{6}\mathrm{Li}$ are discussed. The obtained results are shown to be in good agreement with a large set of experimental data.

All-charm tetraquark in front form dynamics

We study all-charm tetraquarks in the front form of Hamiltonian dynamics using the many-body basis function approach known as basis light-front quantization. The model Hamiltonian contains transverse and longitudinal confining potentials and a one-gluon-exchange effective potential. We calculate masses of two-charm-two-anticharm states focusing on the lowest state. We also calculate two-quark and four-quark estimates of meson-meson breakup threshold. The results suggest that the lowest two-charm-two-anticharm state is not a tightly bound tetraquark. We discuss implications of the cluster decomposition principle for theories formulated on the light front and present our treatment of identical particles together with color-singlet restrictions on the space of quantum states.

Bound and resonance states near the critical charge region in two-electron atoms

The critical nuclear charge ${Z}_{c}$ of the two-electron atoms below which the ground state transforms into a shape resonance and the critical stability of the system around ${Z}_{c}$ have been well established. However, the behavior of the shape resonance below ${Z}_{c}$ is still a mystery. By employing the complex-scaling method using Hylleraas configuration-interaction basis functions, we trace the trajectory of the shape resonance from ${Z}_{c}$ down to a very small nuclear charge. It is shown that at specific values of $Z$ far below ${Z}_{c}$ the resonance crosses over higher-lying one-electron thresholds, and when $Z$ is decreased below 0.316, the shape resonance lies above the three-body breakup threshold. We finally show that the imaginary part of the resonance energy at small nuclear charges can be modeled by the dispersion relation with a high-order Pad\'e approximant correction.

Reanalysis of 6Li+90Zr angular distributions using different nuclear potentials

The experimental angular distributions for 6Li elastically scattered from a 90Zr target in the energy range 14.89–240 MeV are theoretically reanalyzed using phenomenological and semi-microscopic potentials. The phenomenon of the break-up threshold anomaly (BTA) is well represented in the various used potentials. In analyzing nuclear systems induced by weakly bound projectiles such as 6Li, the well-known reduction in the strength of the real part of potential generated based on double folding (DF) and cluster folding (CF) models is also observed. The Sao Paulo potential (SPP) is used to perform double folding calculations. In order to fit the data fairly, a reduction of ∼ 42% and 45% in the strength of the microscopic real part of potential constructed using SPP and CFM, respectively, is found to be required. By including an additional dynamical polarization potential, the data are also reproduced without renormalizing the real cluster folding potential.

Systematic study of fusion suppression for tightly bound projectiles at above-barrier energies

The present work aims to explore the effects of projectile breakup on fusion cross section at energies near the Coulomb barrier to well above it. The complete fusion cross section for the strongly bound non-$\ensuremath{\alpha}$-cluster projectile $^{14}\mathrm{N}$ in interaction with a $^{181}\mathrm{Ta}$ target was obtained by summing the experimentally measured channel-by-channel cross section data of evaporated residues. The obtained total fusion cross section was compared with the theoretical code ccfull and the results were found to be consistent with each other. Further, the experimental fusion function data on $^{181}\mathrm{Ta}$ target with $^{14}\mathrm{N}$ projectile were deduced and compared with those obtained for other strongly bound projectiles, viz., $^{12,13}\mathrm{C}$, $^{16}\mathrm{O}$, and $^{19}\mathrm{F}$, in order to get some systematics in fusion reactions. The analysis of experimental fusion functions was performed within the framework of a benchmark curve called the universal fusion function (UFF). A suppression of about 5--25% with respect to UFF was observed for the presently studied systems at energies above the Coulomb barrier, indicating that the suppression is essentially due to the prompt breakup of the projectiles and is a strong function of breakup threshold of projectiles. The magnitude of such suppression was found to be lower for $^{14}\mathrm{N}$ projectile as compared to other strongly bound projectiles. Moreover, an interesting exponential relation between the experimentally deduced suppression factor and the breakup threshold of the projectile was obtained.

Simultaneous analysis of elastic scattering and fusion in He6+Zn64 : A transition in direct reaction mechanisms, striking threshold anomalies, and halo effects

Using the extended optical model, a simultaneous analysis is carried out of elastic scattering and fusion reactions induced by the neutron halo $^{6}\mathrm{He}$ projectile on a $^{64}\mathrm{Zn}$ target. Dynamic polarization potentials ${U}_{F}$, ${U}_{D}$ are introduced which can be associated to fusion and direct couplings, respectively. Appropriate fitting parameters leading to dispersive potentials are found which provide a good simultaneous description of the data. An unexpected local maximum is uncovered in the energy dependence of the total reaction cross sections, indicating a transition in the involved direct reaction processes, and a possible underlying mechanism is discussed. ${U}_{F}$ is found to follow the normal threshold anomaly but with an unusually large threshold energy. ${U}_{D}$, on the other hand, exhibits a breakup threshold anomaly, but with a strikingly high value of the peak energy, which can be associated to the above-mentioned transition. The results also are discussed within the context of possible halo effects.