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.     

Excitation functions of <Superscript>6</Superscript>Li incomplete fusion reactions with Pt nuclei

Experimentally determined excitation functions of the transfer reactions producing ^194–199Au and ^197m Hg isotopes during the interaction of ⁶Li with Pt nuclei are presented. An analysis of the experimental data as compared to EMPIRE-2.18 model calculations and experimental results on the d + ^natPt and α + ^natPt reactions allow determination of the interaction channels of d- and α-clusters in ⁶Li with the target nucleus. The results from model calculations of the reaction cross sections appear considerably lower than the experimental data. This discrepancy in describing the reactions with weakly bound nuclei is probably associated with the incomplete consideration of various interaction channels in the EMPERE-2.18 software. It is clear that a complete understanding of the interaction pattern in these processes requires consideration of the direct channels of ⁶Li nucleus cluster transfer during ⁶Li breakup near the Coulomb barrier.     

Peculiarities in total cross sections of reactions with weakly bound nuclei <Superscript>6</Superscript>He, <Superscript>9</Superscript>Li

The energy dependence of the total cross sections for the ⁶He + Si and ⁹Li + Si reactions was measured at beam energies between 5 and 20 MeV per nucleon. The results agree with experimental data published for the ⁶He + Si reaction. New data are obtained for the ⁹Li + Si reaction in the vicinity of a local enhancement of the total cross section. A theoretical analysis of the possible reasons behind the appearance of this peculiarity in the case of collisions of ⁶He and ⁹Li nuclei with silicon target nuclei is performed. In particular, the enhancement may owe its origin to the effect of loosely bound projectile nucleons.     

Study of fusion and nucleon transfer channels in the <Superscript>197</Superscript>Au + <Superscript>6</Superscript>He reaction in an energy range of <Superscript>6</Superscript>He to 20 Mev/A

New data on the cross sections of reactions occurring during the interaction of ⁶He nuclei with ¹⁹⁷Au at energies of ⁶He from 40 to 120 MeV are presented. The experiments were performed in the ACCULINNA secondary beam separator of the Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research. To identify the reaction products, the activation method for measuring the gamma activity of the target assembly of thin foils was used. The excitation functions for fusion reactions involving the evaporation of up to ten neutrons from the compound nucleus as well as reactions with the emission of charged particles and nucleon transfer in the investigated energy region are obtained. Data analysis was carried out using two codes: ALICE-MP and NRV. The cross sections for the (⁶He, xn) reactions occurring through the compound nucleus are mostly in agreement with the results of model calculations based on the statistical approach. It is shown that, up to the energies of 114 MeV, the cross-section drop in the complete fusion reactions is negligible. The experimental excitation functions of reactions leading to the formation of isotopes of mercury and gold (transfer reaction) indicate that the main contribution to their formation is made by direct processes and that evaporation reactions (⁶He, pxn) and (⁶He, αxn) play a minor role, as is evidenced by a comparison of the measured cross sections with the calculation results.     

Reactions involving loosely bound cluster nuclei: Heavy ions and new technologies

Experimental results on excitation functions for complete-fusion and transfer reactions in the interaction of ⁶He and ^6,8,9Li nuclei with various target nuclei are presented. Data on fusion-reaction cross sections in the case of ⁶He differ strongly from the predictions of the statistical model. A strong enhancement of the cross section at barrier energies is observed for this reaction channel. Also, an increase in the cross sections for neutron-transfer reactions (in the case of ⁶He and ^8,9Li beams) and deuteron-transfer reactions (in the case of ⁶Li) is observed in the deep-subbarrier energy region. The results are discussed from the point of view of the effect of the cluster structure of nuclei on the probability of interaction at barrier energies. The results of employing heavy-ion beams in new technologies are presented.     

Soft-core Interaction for the <Superscript>4,6</Superscript>He + <Superscript>64</Superscript>Zn Fusion Reactions

In this paper, the cross section of the ⁴He + ⁶⁴Zn and ⁶He + ⁶⁴Zn reactions, at bombarding energies above and below the fusion barrier, has been investigated. Soft-core nucleon-nucleon interaction and the Monte Carlo method have been employed for studying the nuclear potential of the projectile-target system. One adjustable parameter has been chosen in this study. This parameter can change the depth of the soft-core potential. It has to be adjusted so that the calculated elastic scattering and fusion cross sections are in acceptable agreement with experimental data. Our results indicate that an increase in energy decreases the depth parameter of the soft-core nucleon-nucleon potential obtained from careful analysis the ⁴He + ⁶⁴Zn and ⁶He + ⁶⁴Zn reactions. Likewise, by comparing the results obtained from both reactions, one can observe that the calculated depth parameter for the reaction related to ⁶He is larger than that for ⁴He at the same energy, in particular at the sub-barrier energies. We try to explain this behavior.     

Semiclassical description of the <Superscript>6</Superscript>He+<Superscript>12</Superscript>C elastic scattering

The results of the elastic scattering of ⁶He+¹²C systemat E _Lab = 18 MeV by using the barrier and internal wave decomposition of the S-matrix element within the framework of the WKB method are presented. This is the first detailed study for the interaction of the exotic ⁶He nucleus on different stable nuclei by using a semiclassicalmethod. In this paper, we show that in order to obtain the elastic scattering cross section of the ⁶He+¹²C systemat energies close to the Coulomb barrier, it is vitally important to take into account the inner complex turning points in the calculations and the tunneling effects play a crucial role to explain the experimental data. The semiclassical results are compared with the experimental data as well as the quantum-mechanical one.     

Inverse Quasifission in <Superscript>156,160</Superscript>Gd + <Superscript>186</Superscript>W Reactions

To investigate the impact shell effects have in the formation of neutron-rich fragments in multinucleon transfer reactions, a series of experiments to explore the binary channel in ^156,160Gd + ¹⁸⁶W reactions at energies near and above the Coulomb barrier is performed at the Flerov Laboratory’s U-400 accelerator using the CORSET setup. These experiments are aimed mainly at obtaining the production cross sections of leadlike fragments in the process of inverse quasifission. The mass, energy, and angular distributions of the binary reaction products are measured at energies of 860 and 935 MeV of ¹⁶⁰Gd ions and 878MeV in the case of ¹⁵⁶Gd ions. The excitation energies of primary fragments are estimated using their measured mass–energy distributions. Enhanced yields of products with masses of 200–215 amu are observed for both reactions. At energies above the barrier for side-to-side collisions (935 MeV), the yield of lead-like fragments is an order of magnitude larger than at energies near the Coulomb barrier, due possibly to the influence of orientation effects. The enhancement observed in the yield of reaction products with masses heavier than the target mass confirms that multinucleon transfer reactions can be used to obtain new neutron-rich isotopes, and to synthesize new superheavy elements.     

Near-barrier neutron transfer in reactions <Superscript>6</Superscript>He + <Superscript>45</Superscript>Sc, <Superscript>64</Superscript>Zn,and <Superscript>197</Superscript>Au

Experimental cross sections of formation of isotopes ⁴⁶Sc (in reaction ⁶He + ⁴⁵Sc), ^196,198Au (in reaction ⁶He + ¹⁹⁷Au), and ⁶⁵Zn (in reaction ⁶He + ⁶⁴Zn) are analyzed. The time-dependent Schrödinger equation for the outer neutrons of ⁶He and ¹⁹⁷Au nuclei is solved numerically to calculate the probability of neutron transfer and transfer cross sections. In reaction ⁶He + ¹⁹⁷Au, the contribution of fusion and subsequent evaporation to experimental data can be neglected, while the corresponding contributions to reactions ⁶He + ⁴⁵Sc and ⁶He + ⁶⁴Zn are considerable. Fusion–evaporation is taken into account using the computational code of the NRV knowledge base. The results of calculations are in satisfactory agreement with the experimental data.     

Taking into Account the Centre-of-Mass Correlations in the Cross Sections for Elastic Scattering of Intermediate Energy Protons on the Exotic Nuclei <Superscript>6</Superscript>He and <Superscript>8</Superscript>He

We calculate the differential cross sections for proton elastic scattering on the exotic halo nuclei ⁶He and ⁸He at energies around ~0.7 GeV at the momentum transfers squared up to 0.30 (GeV/c)² and investigate the influence of the nucleon centre-of-mass correlations on the calculated cross sections. In particular, we show that the approximate account of the centre-of-mass correlations used previously considerably overestimates the cross sections at high values of the momentum transfer.     

Effect of nuclear-reaction mechanisms on the population of excited nuclear states and isomeric ratios

Experimental data on the cross sections for channels of fusion and transfer reactions induced by beams of radioactive halo nuclei and clustered and stable loosely bound nuclei were analyzed, and the results of this analysis were summarized. The interplay of the excitation of single-particle states in reaction-product nuclei and direct reaction channels was established for transfer reactions. Respective experiments were performed in stable (⁶Li) and radioactive (⁶Не) beams of the DRIBs accelerator complex at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, and in deuteron and ³Не beams of the U-120M cyclotron at the Nuclear Physics Institute, Academy Sciences of Czech Republic (?e? and Prague, Czech Republic). Data on subbarrier and near-barrier fusion reactions involving clustered and loosely bound light nuclei (⁶Li and ³He) can be described quite reliably within simple evaporation models with allowance for different reaction Q-values and couple channels. In reactions involving halo nuclei, their structure manifests itself most strongly in the region of energies below the Coulomb barrier. Neutron transfer occurs with a high probability in the interactions of all loosely bound nuclei with light and heavy stable nuclei at positive Q-values. The cross sections for such reactions and the respective isomeric ratios differ drastically for nucleon stripping and nucleon pickup mechanisms. This is due to the difference in the population probabilities for excited single-particle states.     

Manifestation of the cluster structure of the <Superscript>9</Superscript>Be nucleus in direct nuclear reactions

Specific features of ⁴He interaction with light ⁹Be nuclei are studied. The potential of ⁴He–⁹Be interaction is calculated within the framework of the double folding model using the wave function of the ground state of the ⁹Be nucleus constructed in the three-cluster α + α + n approximation. The differential cross sections of elastic and inelastic ⁴He–⁹Be scattering and single-nucleon transfer in the intermediate range of energies are calculated. Comparative analysis of experimental and calculated results demonstrate their good agreement, indicating that the model assumptions on the cluster structure of ⁹Be nucleus are valid.     

Analyzing the p(<Superscript>6</Superscript>He,n gamma)<Superscript>6</Superscript>Li reaction

The differential cross section of the charge-exchange reaction p(⁶He, n)⁶Li(0⁺, 3.56 MeV) is calculated within the context of direct mechanisms: the stripping of a heavy ⁵He cluster, replacing a virtual neutron with a proton in the 5He cluster field, and the mechanism of consecutive transfer of a neutron and an α particle. The spatial structure of initial and final nucleus is determined from the dependence of various direct mechanisms contributions from spatial configurations.     

Dynamic polarization potentials for <Superscript>6</Superscript>He + <Superscript>209</Superscript>Bi and <Superscript>11</Superscript>Li + <Superscript>208</Superscript>Pb systems at near-barrier energies

The Coulomb dipole induced dynamic polarization potentials for ⁶He + ²⁰⁹Bi and ¹¹Li + ²⁰⁸Pb systems within the framework of Feshbach’s formalism with a motive to ascertain the presence or absence of threshold anomaly have been studied. As a result of this study, the threshold anomaly has been found to be present for both systems. It has also been found that at deep sub-barrier energies the imaginary part either starts increasing or at least remains unchanged which indicates the presence of the breakup threshold anomaly. In addition, the Coulomb breakup transmission factors for both systems have been found to have maximum value below and near-barrier energies, but at very high energies due to closure of the breakup channel the breakup transmission coefficients quickly becomes zero.     

Diffractive scattering of <Superscript>7</Superscript>Be and <Superscript>8</Superscript>B nuclei by <Superscript>12</Superscript>C nuclei

A theory of the diffractive scattering of loosely bound three-cluster nuclei by nuclei was developed with allowance for Coulomb interaction. The differential cross sections for the scattering of projectile exotic nuclei ⁷Be and ⁸B by ¹²C nuclei at an energy of 40 MeV per nucleon were calculated within the proposed formalism. The results describe satisfactorily relevant experimental data.     

Excitation functions for complete-fusion and transfer reactions in <Superscript>4</Superscript>He interaction with <Superscript>197</Superscript>Au nuclei

Excitation functions are measured for the fusion reactions ¹⁹⁷Au(⁴He, xn)^201?xn Tl that are induced by alpha-particle interaction with gold nuclei in the energy range 14–36 MeV and in which x neutrons (0 ≤ x ≤ 3) are evaporated. The stack-activation technique was used to record and separate reaction products. Experimental data on the fusion reactions followed by evaporation of one to three neutrons agree with results of previous studies. For the radiative-capture reaction ¹⁹⁷Au(⁴He,γ)²⁰¹Tl, the upper limit on the cross section proved to be much lower. The excitation functions for the reactions subjected to measurements are compared with the results of calculations based on the statistical model and with the results of an experiment performed previously in a ⁶He beam.     

Diffractive dissociation of deuterons and exotic nuclei <Superscript>6</Superscript>He and <Superscript>19</Superscript>C

A theory is developed for describing the diffractive dissociation of loosely bound two-cluster nuclei in the nuclear and Coulomb fields of nuclei having a diffuse boundary. The energy spectra of charged products of the breakup of ²H, ⁶He, and ¹⁹C nuclei are calculated on the basis of the proposed approach, and the results are found to be rather sensitive to nuclear structure. For some angles of neutron and proton emission from the reaction ¹²C(d, np)¹²C, the calculated cross sections are in satisfactory agreement with the results of kinematically complete experiments performed recently to study the breakup of intermediate-energy deuterons.     

The excitation functions of complete and incomplete fusion reactions of 6Li with Pt nuclei

Experimental results from measuring the energy dependences of cross sections of fusion and transfer reactions for ⁶Li beams and Pt targets are presented. The experiments were performed using the MSP-144 magnetic analyzer; stacks of platinum foils were installed at the focal plane of this analyzer. In the energy range 22.5–42.5 MeV, the energy resolution of the beam hitting the target stack was not worse than 0.25 MeV and that of the transmitted beam was not worse than 0.40 MeV. The yields of products of neutron and deuteron transfer reaction on target nuclei were measured using the γ activity induced in the platinum targets. Thus, excitation functions for transfer reactions were obtained in a wide energy range, including near the Coulomb barrier. It was shown that the basic reaction channel is the deuteron capture from ⁶Li. In this case, the maximum of the excitation function for ⁶Li breakup and subsequent deuteron capture lies near the Coulomb barrier of the reaction.     

Effect of the Structure of Light Loosely Bound Nuclei on the Mechanisms of Nuclear Reactions

The results of experiments devoted to studying fusion and transfer reactions in beams of loosely bound (³He) and cluster (⁶Li, ⁷Li) nuclei, as well as nuclei that have a halo structure (⁶He and ⁸He), with nuclei of light and heavy elements are generalized. Special features in the behavior of cross sections for the formation of evaporation residues and transfer-reaction products at energies near the barrier are revealed. The behavior of cross sections for nucleon- and cluster-transfer reactions leads to different populations of single-particle and collective states in target-like nuclei. The effect of various channels of nuclear reactions involving light nuclei on the population of the ^195mHg and ^197mHg(13/2⁺), ^198mTl and ^196mTl(7⁺), and ^196mAu and ^198mAu(12⁻) pairs of isomeric states is considered. The values of the isomeric ratios (σ_m/σ_g) for reaction products originating from fusion reactions followed by particle evaporation and from nucleon-and cluster-transfer reactions are explained.

     

Measurement of the excitation function for the <Superscript>7</Superscript>Li(t,p)<Superscript>9</Superscript>Li reaction using detection of delayed neutrons

The excitation function for the ⁷Li(t, p)⁹Li reaction is measured at the EGP-10 electrostatic tandem accelerator (VNIIEF) at the incident triton energies E _t = 5–11.3 MeV. The measurements were based on detection of delayed neutrons resulting from the decay of ⁹Li nuclei. The neutrons were detected by the 4π detector consisting of ³He counters enclosed in a polyethylene moderator. A pulsed mode was used for irradiating the LiF target (210 μg cm^?2) of natural isotopic composition on the tantalum backing. Absolutization of the excitation function was performed against the ⁷Li(p, n) reaction cross sections.