Borromean Nuclei Research Articles

Neutron-transfer induced breakup of the Borromean nucleus 9Be

We address the problem of evaluating neutron-transfer induced breakup cross sections caused by the Borromean nucleus 9Be, using the reaction 197Au(9Be,8Be)198Au as a test case. This reaction was recently measured over a wide range of incident energies around the Coulomb barrier. To deal with the high density of 198Au states that can be potentially populated in this reaction, we employ the Ichimura, Austern, Vicent model, in which the spectrum of physical states for this system is replaced by the solutions of a complex n+197Au potential, accounting effectively for the fragmentation of single-particle states into physical states. Furthermore, to account for the unbound nature of the emitted 8Be system, we employ a three-body model of 9Be. The calculated stripping cross sections are found to be in good agreement with existing data over a wide range of incident energies. The importance of taking into account the energy spread of the single-particle strength of the outgoing 8Be and the target-like residual nucleus is discussed.

Diverse mechanisms in proton knockout reactions from the Borromean nucleus ^{17}text {Ne}

Nucleon knockout experiments using beryllium or carbon targets reveal a strong dependence of the quenching factors, i.e., the ratio (hbox {R}_{textrm{s}}) of theoretical to the experimental spectroscopic factors (hbox {C}^2{textrm{S}}), on the proton-neutron asymmetry in the nucleus under study. However, this dependence is greatly reduced when a hydrogen target is used. To understand this phenomenon, exclusive ^{1}text {H}(^{17}text {Ne},2hbox {p}~^{16}text {F}) and inclusive ^{12}text {C}(^{17}text {Ne},2hbox {p}~^{16}text {F})hbox {X}, ^{12}text {C}(^{17}text {Ne},^{16}text {F})hbox {X} as well as ^{1}text {H}(^{17}text {Ne},^{16}text {F})hbox {X} (X-denotes undetected reaction products) reactions with ^{16}text {F} in the ground and excited states were analysed. The longitudinal momentum distribution of ^{16}{textrm{F}} and the correlations between the detached protons were studied. In the case of the carbon target, there is a significant deviation from the predictions of the eikonal model. The eikonal approximation was used to extract spectroscopic factor values hbox {C}^2{textrm{S}}. The experimental hbox {C}^2hbox {S} value obtained with C target is markedly lower than that for H target. This is interpreted as rescattering due to simultaneous nucleon knockout from both reaction partners, ^{17}text {Ne} and ^{12}text {C}.

Searching for universality of dineutron correlation at the surface of Borromean nuclei

The dineutron correlation is systematically studied in three different Borromean nuclei near the neutron dripline, 11Li, 14Be and 17B, via the (p,pn) knockout reaction measured at the RIBF facility in RIKEN. For the three nuclei, the correlation angle between the valence neutrons is found to be largest in the same range of intrinsic momenta, which can be associated to the nuclear surface. This result reinforces the prediction that the formation of the dineutron is universal in environments with low neutron density, such as the surface of neutron-rich Borromean nuclei.

Momentum-space structure of dineutrons in Borromean nuclei

A comparative study is made of the momentum-space structure of dineutrons in the Borromean nuclei $^{11}\mathrm{Li}$, $^{6}\mathrm{He}$, $^{22}\mathrm{C}$, and $^{19}\mathrm{B}$. The ground-state properties of these nuclei are well described by a three-body model using a newly constructed finite-range $nn$ interaction in momentum space. I clarify how the mean opening angle between momenta of valence neutrons and the opening-angle distribution reflect the two-neutron density of the Borromean nuclei. By indicating the similarities to the distributions for the correlation angle in the knockout-reaction experiments, I show that the angular correlations of halo neutrons can provide rich information for the characteristic structure of dineutrons in the Borromean nuclei.

Opening angle and dineutron correlations in knockout reactions with Borromean two-neutron halo nuclei

Background: Knockout reactions with proton targets provide an invaluable tool to access the properties of two-neutron halo nuclei. Recently, experimental results for the average opening angle as a function of the intrinsic neutron momentum in $^{11}\mathrm{Li}$ have shown a localization of dineutron correlations on the nucleus surface.Purpose: Study the model dependence and the effect of distortion and absorption on the opening angle distributions to assess the reliability of this observable to extract properties of Borromean two-neutron halo nuclei.Method: A quasifree sudden model is used to describe the knockout process, where absorption effects are modeled by the eikonal $S$ matrix between the proton target and the core of the Borromean nucleus. Final states in momentum space are built within a three-body model for the projectile, which enables the description of momenta and opening angle distributions.Results: A strong dependence on absorption effects is found for the opening angle at large intrinsic momenta, while the region of lower momenta is mostly insensitive to them. Reasonable agreement with the available data is obtained for $^{11}\mathrm{Li}$ at low momenta with weights for $s$ and $p$ waves different from those previously reported, showing a model dependence in their extraction. For $^{19}\mathrm{B}$, test calculations show marked sensitivity to small $p$-wave components.Conclusions: The opening angle for $(p,pn)$ knockout reactions on Borromean nuclei at small intrinsic momenta is a reliable observable mostly sensitive to the structure of the Borromean nucleus. For larger momenta, the reaction mechanism leads to a larger distortion of the distribution. In the case of nuclei with small components of opposite parity to the dominant ones, this observable can be used to explore them. The relation between dineutron in coordinate space and opening angle in momentum space is found to be model dependent.

Quasifree Neutron Knockout Reaction Reveals a Small s-Orbital Component in the Borromean Nucleus ^{17}B.

A kinematically complete quasifree (p,pn) experiment in inverse kinematics was performed to study the structure of the Borromean nucleus ^{17}B, which had long been considered to have a neutron halo. By analyzing the momentum distributions and exclusive cross sections, we obtained the spectroscopic factors for 1s_{1/2} and 0d_{5/2} orbitals, and a surprisingly small percentage of 9(2)% was determined for 1s_{1/2}. Our finding of such a small 1s_{1/2} component and the halo features reported in prior experiments can be explained by the deformed relativistic Hartree-Bogoliubov theory in continuum, revealing a definite but not dominant neutron halo in ^{17}B. The present work gives the smallest s- or p-orbital component among known nuclei exhibiting halo features and implies that the dominant occupation of s or p orbitals is not a prerequisite for the occurrence of a neutron halo.

Proton inelastic scattering in inverse kinematics as a mean for determining decay rates in continuum: The 9Be + p case

In this work we investigate whether it is feasible with proton inelastic scattering in inverse kinematics to quantify breakup decay rates, by observing the proton recoil in a full kinematics approach. Taking as example the 2.43 MeV excited state of 9Be, we perform an exclusive breakup measurement of 9Be incident on a proton target at an energy of 51 MeV. Two of the three cluster constituents (α and α) as well as the proton target recoil are recorded in a triple coincidence mode. As in other methods we have determined relative α−α and α−n, Q-value and 9Be excitation spectra, energy spectra for all fragments observed and non observed, reconstructed in a full kinematics approach. Additionally to that, we have obtained and concentrated on energy spectra of the proton recoil. The signature of the 9Be configurations were identified in bi-dimensional ΔE−E spectra (proton contour) and decay rates were determined for all three configurations He5+α, Be8+n and α+α+n. Finally a breakup cross section was deduced as σbreak=(142±20)mb. We conclude that proton inelastic excitation to continuum of Borromean light nuclei in inverse kinematics, may provide the mean for probing in the proton recoil spectra the decay rates through all cluster configurations. This involves extensive simulations with the implementation of the experimental conditions and of calculations describing the physics in continuum.

Global descriptions and decay rates for continuum excitation of weakly bound nuclei

In this work we will present an overview of our global studies on continuum excitations induced by protons, for the weakly bound nuclei $$^6\hbox {Li}$$ , $$^7\hbox {Li}$$ and $$^9\hbox {Be}$$ , presenting strong clustering modes. Measurements are made in inverse kinematics and extensive simulations have been developed, to corroborate the analysis and interpretation of the results. The focus of the measurements is on the breakup reaction, but simultaneously this research is complemented by the study of all involved reaction channels, including elastic scattering. In this respect our theoretical interpretation in a Continuum Discretized Coupled Channel approach can be fully validated. Between our sound conclusions we can underline the following: the non reciprocity between the strengths of the breakup probability and the coupling to continuum; the experimental validation of a continuum discretization for three body Continuum Discretized Coupled Channel theories; and last but not least the unique possibility for deducing continuum decay rates of borromean nuclei in proton induced studies, by considering the kinematics of the target recoil. Other specific conclusions for each system will be discussed.

Neutron-pair structure in the continuum spectrum of O26

The structure of $^{26}$O is currently being investigated on both theoretical and experimental fronts. It is well established that it is unbound and the resonance parameters are fairly well-known. The theoretical analysis may involved two- and three-body interactions, as well as correlations with the continuum spectrum of energy. In order to properly assess the structure of the ground and excited states, it is imperative to include a large single particle representation with the right asymptotic behavior. The purpose of this work is to provide details of the single particle continuum configurations of the ground and excited $0^+$ states. We use a large complex energy single particle basis, formed by resonances and complex energy scattering states, the so called Berggren basis, and a separable interaction, which is convenient to solve in a large model space. Three $0^+$ states were found in the complex energy plane. Changes of the resonant parameters, i.e. energy and width, were analyzed as a function of strength of the residual interaction. It is shown how a subtle difference in the interaction could change the unbound character of $^{26}$O into a Borromean nucleus. Only one of the two excited states can be considered as a candidate for a physical meaningful resonance. The calculated occupation probabilities are in agreement with other theoretical approaches although the calculated half live is three-order of magnitude smaller than the experimental one.

Be9+p breakup at 5.67A MeV in a full kinematics approach

The exclusive breakup of the Borromean nucleus Be9 incident on a proton target at 5.67 MeV/nucleon was studied with a triple coincidence requirement between the two breakup α fragments and the recoiling proton. The analysis was performed using an event-by-event code in a full kinematics approach, and Q-value spectra, relative spectra, and energy spectra of all reaction products were determined. Clear signatures of the three breakup modes: α+α+n, Be8+n, and He5+He4 were observed in the recoiling proton spectra and the rates of these modes were quantified.Received 3 May 2019Revised 18 December 2019Accepted 22 January 2020DOI:https://doi.org/10.1103/PhysRevC.101.024602©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBreakup reactionsNuclear reactionsUnstable nuclei induced nuclear reactionsProperties6 ≤ A ≤ 19Nuclear Physics

Ab initio Gamow in-medium similarity renormalization group with resonance and continuum

We have developed a novel ab initio Gamow in-medium similarity renormalization group (Gamow IMSRG) in the complex-energy Berggren framework. The advanced Gamow IMSRG is capable of describing the resonance and nonresonant continuum properties of weakly bound and unbound nuclear many-body systems. As test grounds, carbon and oxygen isotopes have been calculated with chiral two- and three-nucleon forces from the effective field theory. Resonant states observed in the neutron-dripline 24O are well reproduced. The halo structure of the known heaviest Borromean nucleus 22C is clearly seen by calculating the density distribution in which the continuum s channel plays a crucial role. Furthermore, we predict low-lying resonant excited states in 22C. The Gamow IMSRG provides tractable ab initio calculations of weakly bound and unbound open quantum systems.

Two-Neutron Correlations in a Borromean $$\varvec{^{20}\mathrm{C}+n+n}$$ System: Sensitivity of Unbound Subsystems

The structure of $^{22}$C plays a vital role in the new physics at subshell closure of $N=16$ in the neutron-rich region. We study the two-neutron correlations in the ground state of the weakly-bound Borromean nucleus $^{22}$C sitting at the edge of the neutron-drip line and its sensitivity to ${\rm core}$-$n$ potential. For the present study, we employ a three-body (${\rm core}+n+n$) structure model designed for describing the Borromean system by explicit coupling of unbound continuum states of the subsystem (${\rm core}+n$). We use a density-independent contact-delta interaction to describe the neutron-neutron interaction and its strength is varied to fix the binding energy. Along with the ground-state properties of $^{22}$C, we investigate its electric-dipole and monopole responses, discussing the contribution of various configurations. Our results indicate more configuration mixing as compared to the previous studies in the ground state of $^{22}$C. However, they strongly depend upon the choice of the $^{20}{\rm C}$-$n$ potential as well as the binding energy of $^{22}$C, which call for new precise measurements for the low-lying continuum structure of the binary system ($^{20}{\rm C}+n$) and the mass of $^{22}$C. These measurements will be essential to understand the Borromean three-body system $^{22}$C with more accuracy.

Realistic Gamow shell-model calculations for neutron-rich carbon isotopes

The weakly bound nuclei near the drip-line have many interesting properties which have been the hot spot for current nuclear physics research. Carbon isotopes can reach a high neutron to proton ratio and could be a good example to investigate the weakly bound and unbound nuclei. The drip-line nucleus 22C is the heaviest Borromean nucleus that people have observed and corresponds to a sub-shell at neutron number N =16 which is also observed in nitrogen and oxygen isotopes. For nuclei close to drip-line, the coupling of bound-, resonant- and continuum states becomes particularly important. But the traditional shell models with harmonic-oscillator basis are difficult to describe the resonant- and continuum states because the harmonic-oscillator potential always has a localized wave function and bound-eigenstates. One of the ways to include the continuum effects is employing the Berggren basis which is generated by finite potential like Woods-Saxon potential. With Berggren basis, the Schrodinger equation is expanded to complex-momentum space and the bound-, resonant- and continuum states could be taken into account on an equal footing. In addition, the necessity of chiral three-body forces has been shown in many ab-initio calculations like the reproducing of oxygen drip-line and low-lying spectrum of beryllium and boron isotopes. So it is meaningful to have a theoretical research of the carbon isotopes with considering both continuum effects and three-body forces. In this paper, we calculate the neutron-rich carbon isotopes with realistic Gamow shell model which starts from chiral N3LO two-body and chiral N2LO three-body forces. The three-body forces are included by normal-ordering approach. We use Woods-Saxon potential with 14C as a core to generate the Berggren basis. The parameters of Woods-Saxon potential are chosen to reproduce the single-particle energies close to experimental data. In Berggren basis, the continuum states are lying on the integral contour within the fourth quarter of complex-momentum space and discretized by Gauss-Legendre quadrature method for the further calculations. The effective interactions are built by Q ^ -box folded-diagram method within the model space of {1s1/2-bound, 0d5/2-bound, 0d3/2-resonance, d3/2-continuum, s1/2-continuum}. In order to deal with the large dimensions caused by the introducing of continuum states, we take an approximation that only two or less particles are allowed to occupy the continuum states. The ground states energies and the first 2+ excitation energies are calculated for even-mass carbon isotopes from A =16 to A =24 and achieve a good agreement with the experimental data. With our calculations, the 22C is shown to be the last bound even- A carbon isotope. In addition, by investigating the evolution of the first 2+ states, our results agree with the experiment that the sub-shell at N =14 in oxygen isotopes is observed to disappear in carbon isotopes, meanwhile the sub-shell at N =16 is reproduced by our calculations. Furthermore, we compare the ground states energies calculated with and without three-body forces and find out that the three-body forces will make the results more weakly bound and more consistent with experimental values especially for 22C and 24C. Meanwhile, the resonance widths which are calculated self-consistently by realistic Gamow shell model become broader. So our calculations give a support that the three-body forces will introduce a repulsive effect in neutron rich carbon isotopes and play a key role when describing the nuclear drip-line.

Observation of excited states in Mg20 sheds light on nuclear forces and shell evolution

The exotic Borromean nucleus $^{20}$Mg with $N$ = 8, located at the proton drip-line provides a unique testing ground for nuclear forces and the evolution of shell structure in the neutron-deficient region. We report on the first observation of proton unbound resonances together with bound states in $^{20}$Mg from the $^{20}$Mg($d$,$d'$) reaction performed at TRIUMF. Phenomenological shell-model calculations offer a reasonable description. However, our experimental results present a challenge for current first-principles nuclear structure approaches and point to the need for improved chiral forces and {\it ab initio} calculations. Furthermore, the differential cross section of the first excited state is compared with distorted-wave Born approximation calculations to deduce a neutron quadrupole deformation parameter of $\beta_n$=0.46$\pm$0.21. This provides the first indication of a possible weakening of the $N$ = 8 shell closure at the proton drip-line.

On three-cluster disintegration of 9Be

We study a process of the photodisintegration of some Borromean light nuclei into three clusters. Thisstudy is performed within a three-cluster microscopic model. In Reference [1] this model was applied toobtain parameters of resonance states in 9Be and 9B and to establish their nature. Main aim of the presentinvestigations is to describe the dipole transition probability from the ground state of 9Be to the states ofthree-cluster α+α+n continuum by using the same model. That model exploits the hypersphericalharmonics basis (HHB) and thus reduces many-channel Schrödinger equation to the algebraic matrix(AM) form. The dipole transitions from the ground 3/2- state to the 1/2+ states of three-cluster continuumwere studied in detail. The role of resonance states in three-cluster continuum to this process isinvestigated in detail. The dominant channels with the maximal dipole strength due to the couplingbetween the ground and scattering states are discovered

Two-proton capture on the 68Se nucleus with a new self-consistent cluster model

We investigate the two-proton capture reaction of the prominent rapid proton capture waiting point nucleus, 68Se, that produces the borromean nucleus 70Kr (Se68+p+p). We apply a recently formulated general model where the core nucleus, 68Se, is treated in the mean-field approximation and the three-body problem of the two valence protons and the core is solved exactly. We compare using two popular Skyrme interactions, SLy4 and SkM*. We calculate E2 electromagnetic two-proton dissociation and capture cross sections, and derive the temperature dependent capture rates. We vary the unknown 2+ resonance energy without changing any of the structures computed self-consistently for both core and valence particles. We find rates increasing quickly with temperature below 2–4 GK after which we find rates varying by about a factor of two independent of 2+ resonance energy. The capture mechanism is sequential through the f5/2 proton-core resonance, but the continuum background contributes significantly.

Linking structure and dynamics in (p,pn) reactions with Borromean nuclei: The 11Li(p,pn)10Li case

One-neutron removal (p,pn) reactions induced by two-neutron Borromean nuclei are studied within a Transfer-to-the-Continuum (TC) reaction framework, which incorporates the three-body character of the incident nucleus. The relative energy distribution of the residual unbound two-body subsystem, which is assumed to retain information on the structure of the original three-body projectile, is computed by evaluating the transition amplitude for different neutron-core final states in the continuum. These transition amplitudes depend on the overlaps between the original three-body ground-state wave function and the two-body continuum states populated in the reaction, thus ensuring a consistent description of the incident and final nuclei. By comparing different 11Li three-body models, it is found that the 11Li(p,pn)10Li relative energy spectrum is very sensitive to the position of the p1/2 and s1/2 states in 10Li and to the partial wave content of these configurations within the 11Li ground-state wave function. The possible presence of a low-lying d5/2 resonance is discussed. The coupling of the single particle configurations with the non-zero spin of the 9Li core, which produces a spin-spin splitting of the states, is also studied. Among the considered models, the best agreement with the available data is obtained with a 11Li model that incorporates the actual spin of the core and contains ∼31% of p1/2-wave content in the n-9Li subsystem, in accord with our previous findings for the 11Li(p,d)10Li transfer reaction, and a near-threshold virtual state.

Inclusive breakup of Borromean nuclei

We derive the inclusive breakup cross section of a three-fragment projectile nuclei, a = b + x1 +x2, in the spectator model. The resulting four-body cross section for observing b, is composed of the elastic breakup cross section which contains information about the correlation between the two participant fragments, and the inclusive non-elastic breakup cross section. This latter cross section is found to be a non-trivial four-body generalization of the Austern formula [1], which is proportional to a matrix element of the form, . The new feature here is the three-body absorption, represented by the imaginary potential, W3b. We analyze this type of absorption and supply ideas of how to calculate its contribution.

Inclusive breakup of three-fragment weakly bound nuclei

The inclusive breakup of three-fragment projectiles is discussed within a four-body spectator model. Both the elastic breakup and the non-elastic breakup are obtained in a unified framework. Originally developed in the 80's for two-fragment projectiles such as the deuteron, in this paper the theory is successfully generalized to three-fragment projectiles. The expression obtained for the inclusive cross section allows the extraction of the incomplete fusion cross section, and accordingly generalizes the surrogate method to cases such as (t,p) and (t,n) reactions. It is found that two-fragment correlations inside the projectile affect in a conspicuous way the elastic breakup cross section. The inclusive non-elastic breakup cross section is calculated and is found to contain the contribution of a three-body absorption term that is also strongly influenced by the two-fragment correlations. This latter cross section contains the so-called incomplete fusion where more than one compound nuclei are formed. Our theory describes both stable weakly bound three-fragment projectiles and unstable ones such as the Borromean nuclei.

Cooper pairs in the Borromean nuclei 6He and 11Li using continuum single particle level density

A Borromean nucleus is a bound three-body system which is pairwise unbound because none of the two-body subsystem interactions are strong enough to bind them in pairs. As a consequence, the single-particle spectrum of a neutron in the core of a Borromean nucleus is purely continuum, similarly to the spectrum of a free neutron, but two valence neutrons are bound up in such a core. Most of the usual approaches do not use the true continuum to solve the three-body problem but use a discrete basis, like for example, wave functions in a finite box. In this paper the proper continuum is used to solve the pairing Hamiltonian in the continuum spectrum of energy by using the single particle level density devoid of the free gas. It is shown that the density defined in this way modulates the pairing in the continuum. The partial-wave occupation probabilities for the Borromean nuclei 6He and 11Li are calculated as a function of the pairing strength. While at the threshold strength the (s1/2)2 and (p3/2)2 configurations are equally important in 6He, the (s1/2)2 configuration is the main one in 11Li. For very small strength the (s1/2)2 configuration becomes the dominant in both Borromean nuclei. At the physical strength, the calculated wave function amplitudes show a good agreement with other methods and experimental data which indicates that this simple model grasps the essence of the pairing in the continuum.