Cross Sections For Transfer Reactions Research Articles

The 50th anniversary of the coupled channels Born approximation (CCBA) and the coupled reaction channels (CRC) theories of nucleon transfer reactions (a unique interplay between theory, experiment and computer technology, conducted during the most tumultuous period in modern American society)

Nucleon transfer reactions have played a fundamental role in understanding the single-particle components, shell structure and collective properties of atomic nuclei. The conventional distorted wave Born approximation (DWBA) envisioned the nucleon transfer reaction as a one-step process, which proceeds directly from the ground state of the target nucleus to a state of the residual nucleus. The coupled channels Born approximation (CCBA) and coupled reaction channels (CRC) theories evolved because a number of nucleon transfer reaction cross sections could not be reconciled within the DWBA. These coupled channels models revealed that, in addition to the “one-step” process of the DWBA, “multi-step” nucleon transfer processes involving accessary pathways can participate in populating the final nuclear state. In the CCBA, the auxiliary pathways involved inelastic excitations of the target and/or residual nucleus, whereas, in the CRC, the pathways included sequential nucleon transfer passing through nuclear states of an intermediate partition. Coherent addition of contributions from one-step and multi-step nucleon transfer processes resulted in dramatic alterations in reaction cross sections, which were experimentally confirmed. The CCBA and CRC linked the structure of the nuclei participating in a reaction to modalities of nucleon transfer arising during the relative motion between the interacting ions. These complementary theories inexorably changed physicists’ interpretations of nucleon transfer reactions and, in doing so, heralded in the new field of direct heavy-ion reactions.

Dynamics in Nuclei

The nucleus is a complex many-body system with some remarkable emergent collective properties of multiple nucleons acting together. Bohr and Mottelson [1] provided a description of collective motion in nuclei based on geometrical shapes with superimposed oscillations around those shapes. Later, Lie algebras and symmetries were used to describe nuclear dynamics [2], followed by advances in the shell model approach [3] with new effective nucleon-nucleon two- and three-body interactions, and more recently with Hartree-Fock-Bogoliubov approximations within the extended generator coordinate method [4]. Yet, the underlying science question has remained the same. In nuclei, where there is explicit deformation in the ground state, “are the low-lying 0+ states collective vibrations built on the ground state or are they minima of a coexisting shape?” Ref. [4] has shown that for a significant percentage of K = 0+ excitations built on the deformed ground state (g.s.) should, in fact, be a collective vibration. The question has remained open due to sufficiently convincing experimental data with lifetimes, transfer reaction cross sections, and E0 transitions [5]. This paper summarizes the experimental situation regarding the lifetimes of 0+ states.

Effect of deformation dependence and mirror nucleus corrections energy on multinucleon transfer reaction cross sections

Multinucleon transfer reactions are currently a powerful way to synthesize neutron-rich nuclei. To explore the effect of nucleus deformation and mirror nucleus shell correction energy in the nucleus mass model on the calculation of multinucleon transfer reaction cross sections in the dinuclear system (DNS) model, three macroscopic microscopic mass models are selected and the transfer reaction cross sections are calculated for 136Xe+208Pb and 64Ni+238U by improved DNS model+GEMINI++, respectively. The mirror nucleus shell correction energy does not improve the accuracy of the cross section of the transfer reaction. The introduction of a different dependence of the Coulomb and surface energy on the deformation can improve the calculation of the transfer reaction cross section when the projectile and target nuclei are deformed nuclei.

Systematic study of global optical model potentials in (d, p) transfer reactions* *Supported by the National Natural Science Foundation of China (12035011, 11975167, 11535004, 11947211, 11905103, 11761161001, 11375086, 11565010, 11881240623, 11961141003), the National Key R&D Program of China (2018YFA0404403, 2016YFE0129300), the Science and Technology Development Fund of Macau (008/2017/AFJ) and the Fundamental Research Funds for the Central Universities (22120200101)

In the T-matrix form of the transfer reaction, the optical model potentials (OMPs) are used to compute the scattering wave function and transition operator. For most cases, the elastic scattering cross sections, normally used to generate the OMPs, are not directly given in the same experiment. Then, the global OMPs, which fit the experimental data over a broad mass and energy range, are widely used in the theoretical calculations. Different sets of global OMPs with different parameter sets can reproduce the scattering cross section equally well within the uncertainty. Here, we apply different global OMPs to calculate the (differential) cross sections of transfer reactions on the target nuclei , , , and at different energies. The results demonstrate that the effects of deuteron and nucleon global OMPs on transfer (differential) cross sections vary with energy and target mass. Furthermore, the influences of the spin-orbit coupling term of deuteron and nucleon global OMPs on the transfer cross sections are not negligible.

Model of charge transfer collisions between C60 and slow ions.

A semiclassical model describing the charge transfer collisions of C60 fullerene with different slow ions has been developed to analyze available observations. These data reveal multiple Breit-Wigner-like peaks in the cross sections, with subsequent peaks of reactive cross sections decreasing in magnitude. Calculations of charge transfer probabilities, quasi-resonant cross sections, and cross sections for reactive collisions have been performed using semiempirical interaction potentials between fullerenes and ion projectiles. All computations have been carried out with realistic wave functions for C60's valence electrons derived from the simplified jellium model. The quality of these electron wave functions has been successfully verified by comparing theoretical calculations and experimental data on the small angle cross sections of resonant C60+C60 + collisions. Using the semiempirical potentials to describe resonant scattering phenomena in C60 collisions with ions and Landau-Zener charge transfer theory, we calculated theoretical cross sections for various C60 charge transfer and fragmentation reactions which agree with experiments.

Optimal condition for the production of heavy and superheavy neutron-rich isotopes with multinucleon transfer reaction

Production cross sections of multinucleon transfer reactions are systematically investigated in the framework of the improved DNS model combined with statistical GEMINI++ model. The calculated isotone distribution of final products in 20 reaction systems at collision energies above the Coulomb barrier are roughly in agreement with experimental data for a wide range of transfers, respectively, especially in the distribution trend. One founds that the combinations of actinide projectiles or larger neutron excess radioactive projectiles and 208Pb or 198Pt targets at energies near the Coulomb barrier can be considered for future experiments on the production of heavy neutron-rich nuclei.

Possibilities of synthesizing new proton-rich nuclei with 40 ≤ Z ≤ 60 using multinucleon transfer reactions * *Supported by the ational Natural Science Foundation of China (12175064, U2167203). Hunan Provincial Education Department (Key project 20A290)

Multinucleon transfer reactions near the Coulomb barrier are investigated based on the improved dinuclear system (DNS) model, and the deexcitation process of primary fragments are described using the statistical model GEMINI++. The production cross sections of Ca+ Sn and Ni+ Te based on the DNS model+GEMINI++ are calculated and compared with experimental data. The calculated results reproduce experimental data. The cross sections of fusion-evaporation, fragmentation, and multinucleon transfer reactions in the region are also provided in this paper. The results show that in the region, fusion-evaporation and fragmentation reactions have good results in the relatively proton-rich region, but in the extreme proton-deficient region, the MNT reaction is still promising for synthesizing proton-rich nuclei.

Determination of Asymptotic Normalization Coefficients by Analytic Continuation of Differential Cross Sections

A method is discussed for determining the asymptotic normalization coefficients (ANC) using the analytic continuation of experimental differential cross sections for nuclear transfer reactions to the pole point of the reaction amplitude with respect to the variable costheta, where theta is the scattering angle. Within the framework of this method, using experimental data on the differential cross section for the reaction {}^{12}textrm{C}(0^{+};0textrm{ MeV})(d,p){}^{13}textrm{C}(1/2^{+};3.09textrm{ MeV}) the ANC for the channel {}^{13}textrm{C}(1/2^{+};3.09textrm{ MeV})to{}^{12}textrm{C}(0^{+};0textrm{ MeV})+n was determined. When determining the ANC, the corrections caused by the Coulomb interaction in the initial, final and intermediate states of the reaction were taken into account. It is shown that these corrections significantly affect the extracted ANC value.

Analysis of two-nucleon transfer reactions in the Ne20+Cd116 system at 306 MeV

Background: Heavy-ion induced two-nucleon transfer reactions are powerful tools to reveal peculiar aspects of the atomic nucleus, such as pairing correlations, single-particle and collective degrees of freedom, and more. Also, these processes are in competition with the direct meson exchange in the double charge exchange reactions, which have recently attracted great interest due to their possible connection to neutrinoless double-beta decay. In this framework, the exploration of two-nucleon transfer reactions in the 20Ne+116Cd collision at energies above the Coulomb barrier is particularly relevant since the 116Cd nucleus is a candidate for the double-beta decay. Methods: We measured the excitation energy spectra and absolute cross sections for the two reactions using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. We performed direct coupled reaction channels and sequential distorted wave Born approximation calculations using the double folding S\~ao Paulo potential to model the initial and final state interactions. The spectroscopic amplitudes for two- and singleparticle transitions were derived by different nuclear structure approaches: microscopic large-scale shell model, interacting boson model-2 and quasiparticle random phase approximation. Results: The calculations are able to reproduce the experimental cross sections for both two-neutron and twoproton transfer reactions. The role of couplings with the inelastic channels are found to be important in the two-proton transfer case. A competition between the direct and the sequential process is found in the reaction mechanism. For the two-proton transfer case, the inclusion of the 1g7/2 and 2d5/2 orbitals in the model space is crucial.

Asymptotic theory of charged particle transfer reactions at low energies and nuclear astrophysics

An asymptotic theory is proposed for the peripheral transfer [Formula: see text] reaction at low energies within the three-body ([Formula: see text], [Formula: see text] and [Formula: see text]) model by combining the dispersion theory and DWBA, where [Formula: see text], [Formula: see text] and [Formula: see text] is a transferred particle. The contribution of the three-body ([Formula: see text], [Formula: see text] and [Formula: see text]) Coulomb dynamics of the transfer mechanism both to the peripheral partial amplitudes for the partial wave [Formula: see text] and to the DWBA amplitude is investigated. The results of the analysis of the differential cross sections of the specific proton transfer reactions at above-barrier energies are presented. New estimates and their uncertainties are obtained for values of the asymptotic normalization coefficients for [Formula: see text] and [Formula: see text] as well as for the direct astrophysical [Formula: see text] factors at stellar energy of the radiative capture [Formula: see text] and [Formula: see text] reactions.

Cross Section of Transfer Reactions in $d+d$ Collisions at the Deuteron Beam Energy of 160 MeV

Cross Section of Transfer Reactions in $d+d$ Collisions at the Deuteron Beam Energy of 160 MeV

Studying the reactions of deuteron interaction with 9Be nuclei at low energies

Data on elastic and inelastic scattering, and the reactions of few-nucleon transfers in the interaction between the nuclei of deuteron and 9Be at energies of around 10 MeV/nucleon, are analyzed. A theoretical analysis is performed using the double-folding potential model with the wave function of the ground state of the 9Be nucleus, constructed in the three-cluster α + α + n-approximation. Calculations of the cross section of elastic scattering for the reaction d + 9Be using the calculated folding potential are preformed using the optical model. The resulting optical potential is used to analyze cross sections of transfer reactions and inelastic scattering in the context of the distorted waves method. A comparative analysis of the experimental data and theoretical calculations is performed.

TheMg30(t,p)Mg32“puzzle” reexamined

Author(s): Macchiavelli, AO; Crawford, HL; Campbell, CM; Clark, RM; Cromaz, M; Fallon, P; Jones, MD; Lee, IY; Salathe, M; Brown, BA; Poves, A | Abstract: Background: Competing interpretations of the results of a Mg30(t,p)Mg32 measurement populating the ground state and 02+ state in Mg32, both limited to a two-state mixing description, have left an open question regarding the nature of the Mg32 ground state. Purpose: Inspired by recent shell-model calculations, we explore the possibility of a consistent interpretation of the available data for the low-lying 0+ states in Mg32 by expanding the description from two-level to three-level mixing. Methods: A phenomenological three-level mixing model of unperturbed 0p0h, 2p2h, and 4p4h states is applied to describe both the excitation energies in Mg32 and the transfer reaction cross sections. Results: Within this approach, self-consistent solutions exist that provide good agreement with the available experimental information obtained from the Mg30(t,p)Mg32 reaction. Conclusion: The inclusion of the third state, namely the 4p4h configuration, resolves the puzzle that results from a two-levelmodel interpretation of the same data. In our analysis, the Mg32 ground state emerges naturally as dominated by intruder (2p2h and 4p4h) configurations, at the 95% level.

Predicting the production of neutron-rich heavy nuclei in multinucleon transfer reactions using a semi-classical model including evaporation and fission competition, GRAZING-F

Background: Multi-nucleon transfer reactions have recently attracted attention as a possible path to the synthesis of new neutron-rich heavy nuclei. Purpose: We study transfer reactions involving massive nuclei with the intention of understanding if the semi-classical model GRAZING coupled to an evaporation and fission competition model can satisfactory reproduce experimental data on transfer reactions in which fission plays a role. Methods: We have taken the computer code GRAZING and have added fission competition to it (GRAZING-F) using our current understanding of $\Gamma_n/\Gamma_f$, fission barriers and level densities. Results: The code GRAZING-F seems to satisfactory reproduce experimental data for $+1p$, $+2p$ and $+3p$ transfers, but has limitations in reproducing measurements of larger above-target and below-target transfers. Nonetheless, we use GRAZING-F to estimate production rates of neutron-rich $N=126$ nuclei, actinides and transactinides. Conclusions: The GRAZING code, with appropriate modifications to account for fission decay as well as neutron emission by excited primary fragments, does not predict large cross sections for multi-nucleon transfer reactions leading to neutron-rich transactinide nuclei, but predicts opportunities to produce new neutron-rich actinide isotopes.

Fusion and transfer reactions in beams of light loosely bound nuclei at energies in the vicinity of the Coulomb barrier

Experiments devoted to studying cross sections for fusion and transfer reactions induced by the interaction of beams of halo-like (6He), cluster (6Li and 7Li), and loosely bound (3He) nuclei with nuclei of light and heavy elements are described. The cross sections obtained experimentally for such reactions are analyzed. Special features in the behavior of the cross sections for the formation of evaporation residues and products of transfer reactions at energies in the vicinity of the Coulomb barrier are revealed. In particular, an increase in the cross sections for fusion and transfer reactions involving halo-like nuclei and proceeding at energies in the subbarrier region is observed. The cross sections for neutron-transfer and light-cluster-transfer reactions reachmaximum values at an energy in the vicinity of the Coulomb barrier for the reaction being considered.

Cross sections of fusion and transfer reactions in interactions between 3He and Pt and 197Au nuclei in the subbarrier energy region

The reactions of complete and incomplete fusion, along with nucleon transfer reactions in the range of 3He energies from 10 to 24.5 MeV, are investigated by irradiating gold and platinum targets with an accelerated 3He ion beam on the U-120M cyclotron at the Institute of Nuclear Physics, Czech Academy of Sciences, Řež. Activation is used to determine the yield of nuclides resulting from nuclear reactions. The γ-activity induced in the targets is measured using a with high-resolution HPGe detector. Despite the low binding energy of 3He and the reactions with positive Q values, the measured cross sections of fusion reactions exhibit no specific features, compared to reactions conducted using beams of other light stable particles. Transfer neutron reactions in the subbarrier energy region have relatively high cross sections. These cross sections continue to grow as the energy of 3He rises. When a neutron is captured by a nucleus of 3He, the cross sections of these reactions reach their maximum values in the Coulomb barrier region.

Probing the pairing interaction through two-neutron transfer reactions

The treatment of the pairing interaction in mean-field-based models is addressed. In particular, the possibility to use pair transfers as a tool to better constrain this interaction is discussed. First, pairing inter- actions with various density dependencies (surface/volume mixing) are used in the microscopic Hartree-Fock- Bogoliubov + quasiparticle random-phase approximation model to generate the form factors to be used in reac- tion calculations. Cross sections for (p,t) two-neutron transfer reactions are calculated in the one-step zero-range distorted-wave Born approximation for some Tin isotopes and for incident proton energies from 15 to 35 MeV. Three different surface/volume mixings of a zero-range density-dependent pairing interaction are employed in the microscopic calculations and the sensitivity of the cross sections to the different mixings is analyzed. Differences among the three different theoretical predictions are found espacially for the nucleus 136 Sn and they are more important at the incident proton energy of 15 MeV. We thus indicate (p,t) two-neutron transfer reactions with very neutron-rich Sn isotopes and at proton energies around 15 MeV as good experimental cases where the sur- face/volume mixing of the pairing interaction may be probed. In the second part of the manuscript, ground-state to ground-state transitions are investigated. Approximations made to estimate two-nucleon transfer probabilities in ground-state to ground-state transitions and the physical interpretation of these probabilities are discussed. Probabilities are often calculated by approximating both ground states of the initial nucleus A and of the final nucleus A ±2 by the same quasiparticle vacuum. We analyze two improvements of this approach. First, the effect of using two different ground states with average numbers of particles A and A ±2 is quantified. Second, by using projection techniques, the role of particle number restoration is analyzed. Our analysis shows that the improved treatment plays a role close to magicity, leading to an enhancement of the pair-transfer probability. In midshell regions, part of the error made by approximating the initial and final ground states by a single vacuum is com- pensated by projecting onto a good particle number. Surface effects are analyzed by using pairing interactions with a different volume/surface mixing. Finally, a simple expression of the pair-transfer probability is given in terms of occupation probabilities in the canonical basis. We show that, in the canonical basis formulation, surface effects that are visible in the transfer probability are related to the fragmentation of single-particle occupancies close to the Fermi energy. This provides a complementary interpretation with respect to the standard quasiparti- cle representation where surface effects are generated by the integrated radial profiles of the contributing wave functions.

Dyson treatment of NFT medium polarization processes in superfluid nuclei

We discuss the solution of the Dyson equation (also known as the Nambu-Gor'kov equation) for the case of medium polarization Nuclear Field Theory (NFT) processes in nuclei, and apply it to the nucleus 120Sn. Starting from a mean field obtained with the Sly4 effective nucleon-nucleon force, (mk = 0.7), we renormalize the single-particle states and the pairing interaction through the coupling to collective vibrations of the system, obtaining a detailed description of the fragmentation of the quasiparticle strength and of the state-dependent pairing gap. These quantities are calculated in term of one- and two-particle spectroscopic amplitudes, amplitudes which can be used to calculate both one- and two-nucleon absolute transfer reaction cross sections to be directly confronted with the experimental findings.

Probing the pairing interaction through two-neutron transfer reactions

Cross sections for ($p,t$) two-neutron transfer reactions are calculated in the one-step zero-range distorted-wave Born approximation for the tin isotopes $^{124}$Sn and $^{136}$Sn and for incident proton energies from 15 to 35 MeV. Microscopic quasiparticle random-phase approximation form factors are provided for the reaction calculation and phenomenological optical potentials are used in both the entrance and the exit channels. Three different surface/volume mixings of a zero-range density-dependent pairing interaction are employed in the microscopic calculations and the sensitivity of the cross sections to the different mixings is analyzed. Since absolute cross sections cannot be obtained within our model, we compare the positions of the diffraction minima and the shapes of the angular distributions. No differences are found in the position of the diffraction minima for the reaction $^{124}$Sn($p,t$)$^{122}$Sn. On the other side, the angular distributions obtained for the reaction $^{136}$Sn($p,t$)$^{134}$Sn with surface and mixed interactions differ at large angles for some values of the incident proton energy. For this reaction, we compare the ratios of the cross sections associated to the ground state and the first excited state transitions. Differences among the three different theoretical predictions are found and they are more important at the incident proton energy of 15 MeV. As a conclusion, we indicate ($p,t$) two-neutron transfer reactions with very neutron-rich Sn isotopes and at proton energies around 15 MeV as good experimental cases where the surface/volume mixing of the pairing interaction may be probed.

Effects of the valence neutron of the lithium isotopes in6,7,8Li+208Pb systems

Using the measured experimental data for 6,7,8 Li+208 Pb system, we investigated the relation between the interaction distance and the lowest threshold separation energy of the projectiles. Although 6 Li can be considered more weakly bound projectile than 8 Li, the lithium isotope with the largest interaction distance is not 6 Li but 8 Li. Also, we can infer that the difference of the semiexperimental direct reaction (DR) cross sections and the total breakup / transfer reaction cross sections comes from α and 7 Li capture. Finally, the barrier height, VB , of 8 Li + 208 Pb system compared with 7 Li + 208 Pb system are reduced about 3MeV. This is the rise of flux from exp the elastic into the reaction channel, which tends to enhance σ R exp . As a result, we can deduce that the valence neutron play a role as the lowering of the barrier height.