Two-neutron Transfer Reactions Research Articles

How to Study Efimov States in Exotic Nuclei?

The existence of Efimov states in atomic nuclei has been predicted by several authors considering 3-body systems of the form Core–neutron–neutron. While these states appear elusive and very challenging experimentally, we discuss possible reactions that can be used to produce and study them in exotic (weakly-bound) nuclei. Following simple arguments, we show that cross-sections relative to the ground states should scale with the parameter \({\lambda_0}\), which is the same scale factor for binding energies and radii. We derive back of the envelope estimates for: one- and two-neutron transfer reactions, and inelastic scattering. The (d, p) reaction appears as the most promising approach and we discuss in more detail some experimental considerations using the example of \({^{19}C(d, p)^{20}C}\). These initial estimates could serve as a starting point for more refined and realistic calculations, which will be required for careful experimental planning and further analysis.

Development of a measurement system for the determination of ([formula omitted]) cross-sections using multi-nucleon transfer reactions

We have installed a new experimental apparatus to measure γ-rays from highly excited states populated by the multi-nucleon transfer reactions with heavy-ion projectiles to determine the (n, γ) cross-sections by means of the surrogate reaction method. An apparatus consists of two anti-Compton LaBr3(Ce) spectrometers to measure the γ-rays and a Si ΔE–E detector system to detect outgoing projectile-like particles. Reactions of 153-MeV 18O beams with 155Gd and 157Gd targets were used to study the performance of apparatus. By using the LaBr3(Ce) scintillators with relatively large volume (101.6mm in diameter and 127mm in length), we have successfully measured γ-rays from the compound nuclei, which have excitation energy above neutron separation energy, populated by 155Gd(18O, 16O)157Gd and 157Gd(18O, 16O)159Gd two-neutron transfer reactions. To measure in-beam γ-rays through heavy-ion-induced transfer reaction, it is important to assign the reaction channel clearly, since the cross-sections of the transfer reactions are much smaller than those of competing reactions such as Coulomb excitation and fusion reactions. The Si ΔE–E detector system was used to separate outgoing particles. The present study has demonstrated high capability of apparatus to measure the de-excitation γ-rays in the compound nuclei produced by the multi-nucleon transfer reactions for determination of the (n, γ) cross-sections by using the surrogate reaction method.

Understanding the two neutron transfer reaction mechanism in 206Pb(18O,16O)208Pb

The absolute cross sections for elastic scattering and two-neutron transfer reaction for 18O + 206Pb system have been measured at an incident energy near the Coulomb barrier. Detailed coupled reaction channel calculations have been carried out for description of the measured angular distributions for the elastic scattering and transfer reactions simultaneously. The two-neutron transfer reaction 206Pb(18O, 16O)208Pb in the g.s. → g.s. transition is analyzed in (i) extreme cluster model assuming a di-neutron transfer, (ii) two-step successive transfer, and (iii) microscopic approach (independent coordinate scheme) of simultaneous transfer of two neutrons. The relative importance of one step simultaneous transfer versus two-step successive transfer has been studied. Present analysis suggests dominance of cluster transfer of a di-neutron. The contribution from the two-step sequential processes is less significant, however, the combined “two-step plus simultaneous (microscopic)” calculations give a reasonably good agreement with the measurement. The possibility of multi-step route via projectile and target excitations and contribution from such indirect transfer paths to the present two-neutron transfer cross section has been investigated.

Exploring the 12C(18O,16O)14C two-neutron transfer reaction at energies far above the Coulomb barrier

The 12C(18O,16O)14C two-neutron transfer reaction has been studied at an incident energy of 275 MeV and the ejectiles have been momentum analysed at forward angles by the MAGNEX spectrometer. The identification of the 16O ejectiles was obtained by combining a standard ΔE-E technique with the simultaneous measurement of the angle and the position at the focal plane. The 14C excitation energy spectra have been obtained and several known bound and resonant states of the residual nuclei have been identified. The results have been compared to a previous measurement of the same reaction at 84 MeV incident energy.

Probing the pairing interaction through two-neutron transfer reactions

We analyze two-neutron transfers in nuclei within a mean-field approach. We first show that the response associated with pairing excitations can be affected by the surface/volume localization of the employed effective pairing interaction. Then, ground-state-to-ground-state transitions are studied and some improvements on the currently used theoretical formulas are discussed. Finally, Cr isotopes at the drip line are analyzed. The analysis of pair-transfer reactions in these nuclei may improve our understanding of two aspects: the spatial distibution of pairing correlations in nuclei and the debated question of the persistence of pairing at the drip lines.

Core polarization and neutron halos

The effects of core polarization on the structure of Li and Be halos and their consequences on one-and two-neutron transfer reactions are discussed.

Selectivity of the 12C(18O, 16O)14C reaction

A study about the 12C(18O, 16O)14C two-neutron transfer reaction was performed at the Catania INFN-LNS laboratory at 84 MeV incident energy. The 16O ejectiles produced in the reactions were momentum analyzed and identified by the MAGNEX spectrometer. The Q-value spectrum of 14C shows several known bound and resonant states, in particular states with 2p-4h configuration respect to the 16O core. The integrated cross sections show an enhanced yield for the two-neutron transfer compared to the one-neutron transfer. These results are some experimental evidences that the (18O, 16O) reaction proceeds mainly by the direct transfer of the neutron pair, instead of a second order process.

The (18O,16O) reaction: a bridge from direct to dissipative dynamics

A study of the (18O,16O) two-neutron transfer reaction at 84 MeV incident energy was pursued at the Catania INFN-LNS laboratory on several targets. In the energy spectra obtained from the light targets, several known low lying and resonant states of the product nuclei are observed. Instead, the spectra from the heavier targets are dominated by the appearance of a broad bump, indicating that more dissipative processes are contributing. In this case, calculations based on semi-classical transport theories seem to indicate the possible occurrence of dissipative reaction mechanisms.

Two-neutron transfer reaction mechanisms in12C(6He,4He)14C using a realistic three-body6He model

The reaction mechanisms of the two-neutron transfer reaction $^{12}$C($^6$He,$^4$He) have been studied at 30 MeV at the TRIUMF ISAC-II facility using the SHARC charged-particle detector array. Optical potential parameters have been extracted from the analysis of the elastic scattering angular distribution. The new potential has been applied to the study of the transfer angular distribution to the 2$^+_2$ 8.32 MeV state in $^{14}$C, using a realistic 3-body $^6$He model and advanced shell model calculations for the carbon structure, allowing to calculate the relative contributions of the simultaneous and sequential two-neutron transfer. The reaction model provides a good description of the 30 MeV data set and shows that the simultaneous process is the dominant transfer mechanism. Sensitivity tests of optical potential parameters show that the final results can be considerably affected by the choice of optical potentials. A reanalysis of data measured previously at 18 MeV however, is not as well described by the same reaction model, suggesting that one needs to include higher order effects in the reaction mechanism.

New structures in the continuum of light nuclei populated by two-neutron transfer reactions

The 12 C( 18 O, 16 O) 14 C reaction has been studied at 84 MeV incident energy. The ejectiles have been momentum analysed at forward angles by the MAGNEX magnetic spectrometer. The energy spectra were obtained up to about 20 MeV excitation energy. Calculations based on the removal of two uncorrelated neutrons from the projectile describe a significant part of the continuum observed in the energy spectra. In particular, a resonance of the residual nucleus dominates the region near the two-neutron emission threshold.

Natural Parity States Excited via ($^{18}$O,$^{16}$O) Two-neutron Transfer Reaction

Natural Parity States Excited via ($^{18}$O,$^{16}$O) Two-neutron Transfer Reaction

The Continuum of $^{11}$Be Populated by the ($^{18}$O,$^{16}$O) Two-neutron Transfer Reaction

The Continuum of $^{11}$Be Populated by the ($^{18}$O,$^{16}$O) Two-neutron Transfer Reaction

Correlation investigations of the low-energy 10He spectrum

The spectrum of low-lying states in the 10He nucleus is investigated for the two-neutron transfer reaction 3H(8He, p)10He. The secondary beam of 8He nuclei with the energy 21.5 MeV/nucleon and a cryogenic tritium target are used in the experiment. The 10He ground state is observed in the missing mass spectrum at the energy of 2.1 MeV (Γ ∼ 2 MeV) above the decay threshold. Analysis of the angular correlations of the 10He decay products yields the spin and parity of two excited 10He states, Jπ = 1− in the energy range from 4 to 6 MeV and Jπ = 2+ at energies above 6 MeV.

The (18O,16O) two-neutron transfer reaction at 84 MeV

The (18O,16O) two-neutron transfer reaction has been studied at 84 MeV incident energy on different targets. The charged ejectiles produced in the reactions have been momentum analyzed and identified by the MAGNEX spectrometer. Q-value spectra have been extracted with a remarkable energy resolution (FWHM = 160 keV) and several known bound and resonant states have been identified. 15C excitation energy spectra populated by the 13C(18O,16O)15C reaction show excited states with well known dominant 2p-4h configuration, similarly to the spectra populated by (p,t) reactions. This demonstrates the clear selectivity of (18O,16O) reactions. Two unknown structures at 10.5 MeV and 13.6 MeV have been observed. Calculations based on the removal of two uncorrelated neutrons from the 18O projectile describe the structure at 10.5 MeV as a resonance of 15C near the 13C+n+n threshold, while the second bump at 13.6 MeV is not described with such calculations. This model does not account neither for the strong population of the narrow resonances with known 2p-3h configuration observed between Sn and S2n, because of the lack of n-n correlations. This indicates that also the second bump can have a structure dominated by n-n correlations.

Neutron pair correlations inA=100nuclei involved in neutrinoless double-βdecay

The pairing properties of the neutrinoless double beta decay $(0\nu2\beta)$ candidate $^{100}$Mo have been studied, along with its daughter $^{100}$Ru, to provide input for nuclear matrix element calculations relevant to the decay. The $(p,t)$ two-neutron transfer reaction was measured on nuclei of $^{102,100}$Ru and $^{100,98}$Mo. The experiment was designed to have particular sensitivity to $0^{+}$ states up to excitation energies of $\sim 3$ MeV with high energy resolution. Measurements were made at two angles and L=0 transitions identified by the ratio of yields between the two angles. For the reactions leading to and from $^{100}$Ru, greater than 95% of the L=0 $(p,t)$ strength was in the ground state, but in $^{100}$Mo about 20% was in excited $0^{+}$ states. The measured $(p,t)$ data, together with existing $(t,p)$ data, suggest that $^{100}$Mo is a shape-transitional nucleus while $^{100}$Ru is closer to the spherical side of that transition. Theoretical calculations of the $0\nu2\beta$ nuclear matrix element may be complicated by this difference in shape.

States of 14C and 15C via the (18O,16O) two-neutron transfer reaction at 84 MeV

A study of the 14C and 15C states was pursued at the Catania INFN-LNS laboratory by the 12C(18O,16O)14C and 13C(18O,16O)15C reactions at 84 MeV incident energy. The 16O ejectiles were detected at forward angles by the MAGNEX magnetic spectrometer. Exploiting the large momentum acceptance (20%) and solid angle (50 msr) of the spectrometer, energy spectra were obtained with a relevant yield up to 20 MeV excitation energy. The application of the powerful trajectory reconstruction technique did allow to get energy spectra and angular distributions with resolution of about 160 keV and 0.3°. In the energy spectra several known low lying states of 14C and 15C have been observed and some unknown resonant structures at about 10.5 and 13.6 MeV in 15C and 16 MeV in 14C appear.

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.

Recent results related to excited states of6Be and10He

The 1H(6Li,6Be)n charge-exchange reaction and the 3H(8He, p)10He two-neutron transfer reaction were recently carried out at the ACCULINNA fragment separator (FLNR, Dubna) to populate the ground and excited states of 6Be and 10He nuclei, respectively. The 6Be ET spectrum (ET is the 6Be energy above its 4He+p+p decay threshold) was obtained with high statistics and described by the well-known 0+ ground state of 6Be at ET = 1.37 MeV, the 2+ state at ET = 3.05 MeV and a broad structure extending from 4 to 16 MeV which could be interpreted as the isovector soft dipole mode associated with the 6Li ground state. In the 10He case the 0+ ground state was found at about 2.1(2) MeV (T ∼ 2 MeV) above the 8He+n+n breakup threshold. Angular correlations observed for 10He decay products show prominent interference patterns allowing to draw conclusions about the structure of low-energy excited states: 1- (E T ∼ 5 MeV) and 2+ (ET > 6 MeV).

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.

Shell evolution in light nuclei inferred from transfer reactions

Recent results on shell evolution in light exotic nuclei obtained through experiments performed at GANIL using the MUST2 particle array are reported. The one-nucleon transfer reactions 20O(d,t) was investigated using a setup combining the MUST2 and TIARA particle arrays, together with EXOGAM germanium detectors. Preliminary results on the populated states as well as comparison with calculated spectroscopic factors are presented. In a second study, the Z = 8 shell closure was investigated by means of the two-neutron transfer reaction 14O(p,t) using a set of MUST2 telescopes. A newly observed state at low excitation energy in the unbound 12O points to the Z = 8 shell quenching, analogously to the established case at N = 8 in the neutron-rich mirror nucleus 12Be.