Two-neutron Transfer Reactions Research Articles

The quantification of pairing interaction in a two-neutron transfer through the intermediary continuum

An unbound intermediate system (A+1) with the presence of a resonance, can aid in the pairing enhancement in a two-neutron transfer reaction from a bound system A to another bound system (A+2). This enhancement is a consequence of the constructive interference via the several reaction channels available in the (A+1) system. We test this feature through our study in 6He, modeled as two neutrons in the orbitals of an intermediate 5He nucleus. Weighing up the natural case of an unbound 5He with a hypothetically bound 5He, we find that the inclusion of a properly modeled continuum favours the pairing correlations leading to enhanced two-neutron transfer cross-sections.

Analysis of two-particle transfer reaction in the 18O+40Ca and 20Ne+116Cd collisions

Two-neutron and two-proton transfer reactions have been analyzed in the present work. These kind of transfer reactions is an excellent tool to get insights into the short-range correlations on nucleons in a nuclear state. The direct and sequential two-particle transfer mechanisms, for which the valence particles can be transferred, were compared one with other to probe the populated nuclear states. Large-scale shell model calculations were performed to obtained the spectroscopic amplitudes for one and two valence particles.

Two-particle transfer processes as a signature of shape phase transition in Zirconium isotopes

We explore two-particle transfer reactions as a crucial probe of the occurrence of shape coexistence in shape phase transitions. The (t,p) reactions to the ground state and to excited 0+ states are calculated for the isotope chain of even-even Zirconium isotopes starting from stable nuclei up to beyond current experimental limits. Two-particle spectroscopic factors derived from Monte Carlo Shell Model calculations are used, together with the sequential description of the two-particle transfer reaction mechanism. The calculation shows a clear signature for a shape phase transition between 98Zr and 100Zr, which displays coexistence of a deformed ground state with an excited spherical 0+ state. Furthermore, we show that there is a qualitative difference with respect to the case of a normal shape phase transition that can be discriminated with two-neutron transfer reactions.

Збудження парних коливань у надплинних ядрах

Excitation of monopole pairing vibrations in superfluid nuclei in the two-neutron transfer reaction is studied within a kinetic model based on the semiclassical time-dependent Hartree - Fock - Bogolyubov theory. Using the anomalous (correlated) density response function, the monopole pairing mode and the amplitude of the dynamic variation of the pairing gap associated with this mode are obtained. It is shown that the pairing correlations give a coherent contribution to the spectroscopic factor for the excitation of monopole pairing vibrations in the two-neutron transfer reaction in superfluid nuclei. The contribution is determined by the distribution of neutron levels near the Fermi energy and does not exceed a few percent of the spectroscopic factor for the transfer of two neutrons to the ground state. This estimate is in agreement with experimental data for the ratio of the cross-section for excitation of the 0+-state in the (p, t)-reaction in the energy region of the monopole pairing mode, which is equal to the double pairing gap, to the cross section for excitation of the ground state in superfluid nuclei.

Investigation of γ softness: Lifetime measurements in Ru104,106

Lifetimes of the ${2}_{1}^{+}, {4}_{1}^{+}, {6}_{1}^{+}, {2}_{\ensuremath{\gamma}}^{+}$, and ${3}_{\ensuremath{\gamma}}^{+}$ states in $^{104,106}\mathrm{Ru}$ were measured by using the recoil-distance Doppler-shift technique and the Cologne Plunger device. Low-lying excited states in both nuclei were populated in a $^{104}\mathrm{Ru}(^{18}\mathrm{O},^{18}\mathrm{O})^{104}\mathrm{Ru}$* inelastic scattering and in a $^{104}\mathrm{Ru}(^{18}\mathrm{O},^{16}\mathrm{O})^{106}\mathrm{Ru}$ two-neutron transfer reaction using the Cologne FN Tandem accelerator. The experimental energy levels and deduced electromagnetic transition probabilities are compared in the context of $\ensuremath{\gamma}$ softness and the mapped interacting boson model with input from the microscopic self-consistent mean-field calculation using a Gogny interaction. The newly obtained results for the $\ensuremath{\gamma}$ band give a more detailed insight about the triaxial behavior of $^{104,106}\mathrm{Ru}$. The results will be discussed in the context of $\ensuremath{\gamma}$ soft and rigid triaxial behavior which is present in the neutron-rich Ru isotopes.

Effect of the continuum on pairing enhancement in a two-neutron transfer process

Enhancement, due to constructive interference through the many possible reaction channels, occurs in two-neutron transfer reactions from a bound system A to a weakly-bound system (A+2), whenever the intermediate system is unbound and consists of a continuum with a resonant state. We elucidate this phenomenon in the case of 6He, modeled as two neutrons in the orbitals of an intermediate 5He nucleus, comparing the realistic case of an unbound (A+1) system with an artificially bound case. A properly modeled continuum in these calculations is found to be crucial and leads to significant enhancement due to pairing correlations.

Two-neutron transfer as a tool to study pairing correlations in nuclei

A feasibility study of two-neutron transfer reactions, using 12C and 19F targets, was performed. In this experiment, a 6He beam at 20 MeV incident energy was delivered by the RIBRAS facility. The main goal of this work was to test the RIBRAS system, operated in a single-solenoid mode, to investigate (6He,α) reactions in light nuclei. The excitation function of the 14C nucleus, populated by the 12C(6He,α) reaction, was extracted from the data. Evidence of nn-transfer reactions populating the ground state and the first state in 14C were observed. However, the present spectrum might have contribution from other reaction channels such as the 6He breakup. Future experiments with the RIBRAS dual-solenoid mode will improve the quality of the data by reducing a significant amount of background.

Lifetime measurements to investigate γ softness and shape coexistence in Mo102

Lifetimes of low-spin excited states in $^{102}\mathrm{Mo}$ populated in a $^{100}\mathrm{Mo}(^{18}\mathrm{O},\phantom{\rule{0.16em}{0ex}}^{16}\mathrm{O})^{102}\mathrm{Mo}$ two-neutron transfer reaction were measured using the recoil-distance Doppler-shift technique at the Cologne FN Tandem accelerator. Lifetimes of the ${2}_{1}^{+}$, ${4}_{1}^{+}$, ${6}_{1}^{+}$, ${0}_{2}^{+}$, ${2}_{\ensuremath{\gamma}}^{+}$, ${3}_{\ensuremath{\gamma}}^{+}$ states and one upper limit for the lifetime of the ${4}_{\ensuremath{\gamma}}^{+}$ state were obtained. The energy levels and deduced electromagnetic transition probabilities are compared with those obtained within the mapped interacting boson model framework with microscopic input from Gogny mean-field calculations. With the newly obtained signatures a more detailed insight in the $\ensuremath{\gamma}$ softness and shape coexistence in $^{102}\mathrm{Mo}$ is possible and discussed in the context of the $Z\ensuremath{\approx}40$ and $N\ensuremath{\approx}60$ region. The nucleus of $^{102}\mathrm{Mo}$ follows the $\ensuremath{\gamma}$ soft trend of the Mo isotopes. The properties of the ${0}_{2}^{+}$ state indicate, in contrast with the microscopic predictions, shape coexistence which also occurs in other $N=60$ isotones.

Halo effects in the Li11(p,t)Li9 reaction

I investigate the $^{11}\mathrm{Li}(p,t)^{9}\mathrm{Li}$ two-neutron transfer reaction at ${E}_{\mathrm{lab}}=33$ MeV within the distorted wave Born approximation (DWBA). The $^{11}\mathrm{Li}$ and $^{3}\mathrm{H}$ nuclei are described in the hyperspherical formalism, as $^{9}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}n+n$ and $p+n+n$ configurations, respectively. The calculation of the cross section is shown to be much more complicated than in one-neutron transfer reactions, owing to the three-body structure of $^{11}\mathrm{Li}$. The $^{11}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}p$ and $^{9}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}t$ scattering wave functions are determined with the continuum discretized coupled channel (CDCC) method. Approximations derived from equivalent local potentials are used to compute the transfer cross section at the DWBA. The model reproduces experimental data reasonably well, considering that there is no adjustable parameter. I show that the cross section is fairly sensitive to the long-range part of the $^{11}\mathrm{Li}$ wave function, and therefore to its halo structure.

Investigation of pair-correlated 0+ states in Ba134 via the Ba136(p,t) reaction

We performed a high resolution study of ${0}^{+}$ states in $^{134}\mathrm{Ba}$ using the $^{136}\mathrm{Ba}(p,t)$ two-neutron transfer reaction. Our experiment shows a significant portion of the $L=0$ pair-transfer strength concentrated at excited ${0}^{+}$ levels in $^{134}\mathrm{Ba}$. Potential implications in the context of $^{136}\mathrm{Xe}\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}^{136}\mathrm{Ba}$ neutrinoless double beta decay matrix element calculations are briefly discussed.

Tests of collectivity in Zr98 by absolute transition rates

Lifetimes of low-spin excited states in $^{98}$Zr were measured using the recoil-distance Doppler-shift technique and the Doppler-shift attenuation method. The nucleus of interest was populated in a $^{96}$Zr($^{18}$O,$^{16}$O)$^{98}$Zr two-neutron transfer reaction at the Cologne FN Tandem accelerator. Lifetimes of six low-spin excited states, of which four are unknown, were measured. The deduced $B(E2)$ values were compared with Monte Carlo shell model and interacting boson model with configuration mixing calculations. Both approaches reproduce well most of the data but leave challenging questions regarding the structure of some low lying states.

Reaction Channel selection techniques and γ – γ fast-timing spectroscopy using the ν-Ball Spectrometer

The reaction of a pulsed 18O beam on a self-supporting and gold-backed isotopically-enriched 164Dy target of thickness 6.3 mg/cm2 at separate primary beam energies of 71, 76 and 80 MeV was studied at the accelerator at the ALTO facility of the IPN Orsay. The γ rays produced were detected using the newly-constructed ν-Ball spectrometer which comprised of HPGe and LaBr3(Ce) detectors. This conference paper describes the methodology and effectiveness of multiplicity/sum-energy gating, for channel selection between fusion evaporation events and lower multiplicity/energy events from inelastic nuclear scattering and Coulomb excitation of the target, and from two-neutron transfer reactions to 166Dy.

Investigation of 0+ strength in 150Sm using the (p,t) reaction

The aim of this investigation is to reveal the structure of 150Sm by measuring for the first time a rather complete set of energy levels of this nucleus up to 4 MeV and determine the total angular momentum of the states. The study was carried out at the 14 MV Tandem Accelerator of the Munich universities by measuring complete angular distributions for states up to 4 MeV excited in the direct two-neutron transfer reaction 152Sm(p,t)150Sm at an incident energy of 22 MeV. Emphasis was put on determining the 0+ excited states, which are some of the most important excitations in the rare-earth region. Up to now only three 0+ levels are known in 150Sm, and investigating the distribution of energy and intensity of these excited states also at higher excitation energy might reveal the main contributions in the wave functions of this nucleus.

Transfer to the continuum of 11Be with the application of ab-initio S-matrix

The 9Be(18O,16O)11Be two-neutron transfer reaction at 84 MeV is measured at forward angles to explore the continuum of 11Be nucleus. Transfer-to-the-continuum (TC) reaction calculations are applied using for the first time an ab-initio S-matrix. It is derived from the ab-initio no-core shell model with continuum (NCSMC) method, recently used to describe the bound and continuum spectrum of 11Be. Previously known levels are confirmed and theoretical and experimental evidence for a 9/2+ state at Ex = 5.8 MeV is given, whose configuration is thought to be 10Be(2+) + n(d5/2).

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.

Two-neutron transfer reactions as a tool to study the interplay between shape coexistence and quantum phase transitions * *This work has been partially supported by the Ministerio de Ciencia e Innovación (Spain) under projects number FIS2017-88410-P, PID2019-104002GB-C21 and PID2019-104002GB-C22, by the Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (Spain) under Group FQM-160 (JMA) and FQM-370

The atomic mass table presents zones where the structure of the states changes rapidly as a function of the neutron or proton number. Among them, notable examples are the A ≈ 100 Zr region, the Pb region around the neutron midshell (N = 104), and the N ≈ 90 rare-earth region. The observed phenomena can be understood in terms of either shape coexistence or quantum phase transitions. The objective of this study is to find an observable that can distinguish between both shape coexistence and quantum phase transitions. As an observable to be analyzed, we selected the two-neutron transfer intensity between the 0+ states in the parent and daughter nuclei. The framework used for this study is the Interacting Boson Model (IBM), including its version with configuration mixing (IBM-CM). To generate wave functions of isotope chains of interest needed for calculating transfer intensities, previous systematic studies using IBM and IBM-CM were used without changing the parameters. The results of two-neutron transfer intensities are presented for Zr, Hg, and Pt isotopic chains using IBM-CM. Moreover, for Zr, Pt, and Sm isotopic chains, the results are presented using IBM with only a single configuration, i.e., without using configuration mixing. For Zr, the two-neutron transfer intensities between the ground states provide a clear observable, indicating that normal and intruder configurations coexist in the low-lying spectrum and cross at A = 98 → 100. This can help clarify whether shape coexistence induces a given quantum phase transition. For Pt, in which shape coexistence is present and the regular and intruder configurations cross for the ground state, there is almost no impact on the value of the two-neutron transfer intensity. Similar is the situation with Hg, where the ground state always has a regular nature. For the Sm isotope chain, which is one of the quantum phase transition paradigms, the value of the two-neutron transfer intensity is affected strongly.

Experimental study of the 2n-transfer reaction 138Ba(18O,16O)140Ba in the projectile energy range 61–67 MeV

Two-neutron transfer reactions serve as an important tool for nuclear-structure studies in the neutron-rich part of the nuclear chart. In this paper, we report on the first experimental attempt to populate the excited states of140Ba employing the 2n-transfer reaction138Ba(18O,16O)140Ba. 140Ba is highly important, as it is placed on the onset of octupole correlations and the lifetimes of its excited states are completely unknown, with the sole exception of the first state. The experiment was carried out at the Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN–HH) in Magurele, Romania. Lower limits on the lifetimes of the ground state band up to the state are reported. Furthermore, relative cross-sections regarding the 2n-transfer reaction with respect to the fusion and the total inelastic reaction channels have been deduced. Further investigation directions of the nuclear structure of 140Ba are also discussed.

Two-neutron transfer reactions and the quantum chaos measure of nuclear spectra

A new statistical interpretation of the nuclear collective states is suggested and applied recently in rare earths and actinide nuclei by the two-neutron transfer reactions in terms of the nearest neighbor-spacing distributions (NNSDs). Experimental NNSDs were obtained by using the complete and pure sequences of the collective states through an unfolding procedure. The two-neutron transfer reactions allow to obtain such a sequence of the collective states that meets the requirements for a statistical analysis. Their theoretical analysis is based on the linear approximation of a repulsion level density within the Wigner-Dyson theory. This approximation is successful to evaluate separately the Wigner chaos and Poisson order contributions. We found an intermediate behavior of NNSDs between the Wigner and Poisson limits. NNSDs turn out to be shifted from a chaos to order with increasing the length of spectra and the angular momentum of collective states. Perspectives for the statistical analysis of the symmetry breaking of states with the fixed projection of angular momenta $K$ are discussed.

Microscopic structure of coexisting 0+ states in Ni68 probed via two-neutron transfer

The structure of low-spin states originating from shape-coexisting configurations in $^{68}_{40}$Ni$_{28}$ was directly probed via the two-neutron transfer reaction $^{66}$Ni$(t,p)^{68}$Ni in inverse kinematics using a radioactive ion beam on a radioactive target. The direct feeding to the first excited 0$^+$ state was measured for center-of-mass angles 4°–16° and amounts to an integral of 4.2(16)% relative to the ground state. The observed difference in feeding of the 0$^+$ states is explained by the transfer of neutrons, mainly in the $pf$ shell below $N=40$ for the ground state, and across $N=40$ in the $g_{9/2}$ orbital for the 0$_2^+$, based on second-order distorted-wave Born approximation calculations combined with state-of-the-art shell-model two-nucleon amplitudes. However, the direct feeding to the 2$_1^+$ state [29(3)%] is incompatible with these calculations.

Two-neutron transfer reactions and shape phase transitions in the microscopically formulated interacting boson model

Two-neutron transfer reactions are studied within the interacting boson model based on the nuclear energy density functional theory. Constrained self-consistent mean-field calculations with the Skyrme energy density functional are performed to provide microscopic input to completely determine the Hamiltonian of the IBM. Spectroscopic properties are calculated only from the nucleonic degrees of freedom. This method is applied to study the $(t,p)$ and $(p,t)$ transfer reactions in the assorted set of rare-earth nuclei $^{146-158}$Sm, $^{148-160}$Gd, and $^{150-162}$Dy, where spherical-to-axially-deformed shape phase transition is suggested to occur at the neutron number $N\approx 90$. The results are compared with those from the purely phenomenological IBM calculations, as well as with the available experimental data. The calculated $(t,p)$ and $(p,t)$ transfer reaction intensities, from both the microscopic and phenomenological IBM frameworks, signal the rapid nuclear structural change at particular nucleon numbers.