Halo Nuclei Research Articles

Application of Supersymmetric Quantum Mechanics to Calculate Resonance Energy and Wave Function of $$^{19}$$C Halo Nucleus

Application of Supersymmetric Quantum Mechanics to Calculate Resonance Energy and Wave Function of $$^{19}$$C Halo Nucleus

Rotating deformed halo nuclei and shape decoupling effects

To explore the rotational excitation of deformed halo nuclei, the angular momentum projection (AMP) has been implemented in the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), in which both the mean field and collective wave functions are expanded in terms of Dirac Woods-Saxon basis. The DRHBc + AMP approach self-consistently describes the coupling between single particle bound states and the continuum not only in the ground state but also in rotational states. The rotational modes of deformed halos in 42,44Mg are investigated by studying properties of rotational states such as the excitation energy, configuration, and density distribution. Our study demonstrates that the deformed halo structure persists from the ground state in the intrinsic frame to collective states. Especially, the typical behavior of shape decoupling effects in rotating deformed halo nuclei is revealed.

Probing proton halo effects in the 8B+64Zn collision around the Coulomb barrier

Proton halo effects in the 8B+64Zn reaction at an energy around 1.5 times the Coulomb barrier have been studied at HIE-ISOLDE CERN using, for the first time, the only existing postaccelerated 8B beam. This, together with the use of a high granularity and large solid angle detection system, allowed for a careful mapping of the elastic angular distribution, especially in the Coulomb-nuclear interference region. Contrary to what is observed for the one-neutron halo nucleus 11Be on the same target in a similar energy range, the analysis of the elastic scattering angular distribution shows only a modest suppression of the Coulomb-nuclear interference peak, with no remarkable enhancement of the total reaction cross-section. Inclusive angular and energy distributions of 7Be produced in direct reaction processes have also been measured. The comparison of these data with the results of theoretical calculations for the elastic and non-elastic breakup contributions indicate that both processes are important. Overall, the experimental data suggest a 8B collision dynamics at the barrier very different from the one of neutron halo nuclei, showing only modest effects of coupling to continuum. This behaviour can be interpreted as due to the presence of the additional Coulomb interactions halo-core and halo-target together with the presence of the centrifugal barrier felt by the valence proton of 8B.

Detailed study of the eikonal reaction theory for the breakup of one-neutron halo nuclei

Background: One-neutron removal reactions are used to study the single-particle structure of unstable nuclei, and in particular the exotic halo nuclei. The Eikonal Reaction Theory (ERT) has been developed by Yahiro, Ogata and Minomo in Prog. Theor. Phys. 126, 167 (2011) to include dynamical effects, which are missing in the usual eikonal description of these reactions. Encouraging results have been obtained for total breakup cross sections in comparison to more elaborate reaction models. Purpose: We extend these comparisons to more differential breakup cross sections expressed as functions of the relative energy or parallel momentum between the core and halo neutron. Method: ERT predictions of these cross sections are compared to state-of-the-art calculations. Results: The hypotheses upon which the ERT is based are confirmed and their range of validity is made clearer. The actual ordering of the evolution operators {affects ERT differential} cross sections and a specific choice leads to excellent agreement with the reference calculation. Dynamical effects in the treatment of the neutron-target interaction can be significant in the parallel-momentum observable. Conclusions: The role of the different interactions in the dynamics of breakup reactions of one-neutron halo nuclei are better understood and improvements to the ERT are suggested.

PROPERTIES OF LIGHT NUCLEI 6He AND 6Be IN THE FRAMEWORK OF THE THREE-CLUSTER MODEL

This scientific work is the study of the structure of light nuclei 6He and 6Be in the framework of the three-cluster α+2n-model. The calculation methods have been based on the variational solution of the stationary Schrödinger equation for the relative motion of three clusters in 6He and 6Be nuclei, respectively. The realistic Reid potential has been chosen as the nucleon-nucleon interaction potential, and the potential with even-odd wave splitting has been used for the interaction of the alpha-particle and nucleons. Realistic wave functions of the relative motion of the alpha particle and nucleons in these nuclei and low-lying energy levels have been calculated. The static observables of the 0+ ground state of 6He and 6Be nuclei, in particular, the root-mean-square charge and material radii and binding energies, have been determined. The obtained values of the root-mean-square charge and material radii of the 6He nucleus confirm the hypothesis of the presence of a neutron halo structure of this nucleus.

Deformed two-neutron halo in B19

Ground state properties of $^{19}\mathrm{B}$ are studied by using the deformed relativistic Hartree-Bogoliubov theory in continuum. The calculations with the density functional PK1 show that $^{19}\mathrm{B}$ is a deformed two-neutron ($2n$) halo nucleus. By examining the evolution of single neutron levels, it is found that the valence levels, which are weakly bound or embedded in the continuum due to pairing, contain considerable $s$-wave components with the probability amplitude of 0.359 and lead to the formation of the halo. Strong quadrupole correlations mix $sd$ orbitals and drive $^{19}\mathrm{B}$ to be prolate. The calculated density of the neutron core presents a prolate shape while the neutron halo is oblate, meaning $^{19}\mathrm{B}$ is a $2n$ halo candidate with shape decoupling effects.

Influence of halo single-neutron transfer on near barrier ^{15}C + ^{12}C total fusion

A recent comparison of the average fusion cross section, leftlangle sigma _mathrm {F}rightrangle , for energies just above the Coulomb barrier for the ^{12-15}C + ^{12}C systems found that the behaviour as a function of projectile neutron excess could not be satisfactorily explained by static barrier penetration model calculations and suggested that the neutron dynamics plays an important rôle. In this work we demonstrate that the (^{15}C,^{14}C) single neutron transfer has a significant influence on the above barrier ^{15}C + ^{12}C total fusion, although not quite in the way expected since it leads to a reduction in the cross section, contrary to the trend in the measured leftlangle sigma _mathrm {F}rightrangle . However, this result underlines the danger of ignoring the effect of neutron transfer reactions on fusion in systems involving neutron halo nuclei.

Stable15N and Neutron Halo 16N Nuclei Structure Study by Elastic Electron Scattering Form Factors and Nucleon Momentum Distributions

In this manuscript, the elastic electron scattering form factors and the nucleon momentum distributions (NMD) for stable 15N and neutron halo 16N at the ground state were reported. This was accomplished by utilizing the well-known Coherent Density Fluctuation Model (CDFM) via the employment of fluctuation function (|F(q)|2) which is coupled with the density distributions nuclei. The long-tail performance in the NMD at high momentum region was further determined via experimental and theoretical fluctuation functions. The evaluated elastic electron scattering form factors were evaluated on the bases of the density distributions as well as the root mean square (RMS) radii for each measured nucleon. The proposed study provides a robust correlation between the theoretical formation factors and the practical results of 15N and 16N nuclei.

Experimental study of the F17+C12 fusion reaction and its implications for fusion of proton-halo systems

The halo nature of the low-lying $1/2$+ first excited state of the exotic weakly-bound proton drip-line nucleus $^{17}$F has long been hypothesized. The structure of such a halo nucleus would imply special nuclear properties including, possibly, an enhancement in its fusion cross section above the barrier. The total fusion cross section of $^{17}$F + $^{12}$C near the Coulomb barrier was studied using the newly developed "Encore" active-target detector at Florida State University. Total fusion cross sections for the stable counterpart systems $^{16}$O + $^{12}$C and $^{19}$F + $^{12}$C were also measured to enable a systematic comparison. No influence of the halo nature of the $^{17}$F $1/2$+ first excited state on its fusion excitation function was observed when compared with the stable counterpart systems.

Prediction of the analyzing power for p⃗+He6 elastic scattering at 200 MeV from p⃗+He4 elastic scattering at 200 MeV

We apply the cluster-folding (CF) model for $\vec{p}+^{6}$He scattering at 200 MeV, where the potential between $\vec{p}$ and $^{4}$He is fitted to data on $\vec{p}+^{4}$He scattering at 200 MeV. For $\vec{p}+^{6}$He scattering at 200 MeV, the CF model reproduces measured differential cross section with no free parameter, We then predict the analyzing power $A_y(q)$ with the CF model, where $q$ is the transfer momentum. Johnson, Al-Khalili and Tostevin construct a theory for one-neutron halo scattering, taking (1) the adiabatic approximation and (2) neglecting the interaction between a valence neutron and a target, and yield a simple relationship between the elastic scattering of a halo nucleus and of its core under certain conditions. We improve their theory with (3) the eikonal approximation in order to determine $A_y(q)$ for $^{6}$He from the data on $A_y(q)$ for $^{4}$He. The improved theory is accurate, when approximation (1)--(3) are good. Among the three approximations, approximation (2) is most essential. The CF model shows that approximation (2) is good in $0.9 < q < 2.4$ fm$^{-1}$. In the improved theory, the $A_y(q)$ for $^{6}$He is the same as that for $^{4}$He. In $0.9 < q < 2.4$ fm$^{-1}$, we then predict $A_y(q)$ for $\vec{p}+^{6}$He scattering at 200 MeV from measured $A_y(q)$ for $\vec{p}+^{4}$He scattering at 200 MeV. We thus predict $A_y(q)$ with the model-dependent and the model-independent prescription. The ratio of differential cross sections measured for $^{6}$He to that for $^{4}$He is related to the wave function of $^{6}$He. We then determine the radius between $^{4}$He and the center-of-mass of valence two neutrons in $^{6}$He. The radius is 5.77 fm.

Fusion reaction of a weakly bound nucleus with a deformed target

We discuss the role of deformation of the target nucleus in the fusion reaction of the $^{15}\mathrm{C}+^{232}\mathrm{Th}$ system at energies around the Coulomb barrier, in which $^{15}\mathrm{C}$ is a well-known one-neutron halo nucleus. To this end, we construct the potential between $^{15}\mathrm{C}$ and $^{232}\mathrm{Th}$ with the double folding procedure, assuming that the projectile nucleus is composed of the core nucleus, $^{14}\mathrm{C}$, and a valence neutron. In addition, we also take into account the coupling to the one-neutron transfer process to the $^{14}\mathrm{C}+^{233}\mathrm{Th}$ configuration. We show that such calculation simultaneously reproduces the fusion cross sections for the $^{14}\mathrm{C}+^{232}\mathrm{Th}$ and the $^{15}\mathrm{C}+^{232}\mathrm{Th}$ systems, implying an important role of the transfer coupling in fusion of neutron-rich nuclei.

Density distribution investigation through the geometrical structure for the 27S halo nucleus

27S was predicted as a proton halo nucleus in the 2s1/2 state due to the abnormally large protons root mean square radius. The presence of weakly bound (S2n = 0.90(20) MeV) two valence protons in the 27S nucleus strongly supported this prediction. The core density, matter density, and halo density for this nucleus (27S) have been investigated in this study. The geometrical halo structure has been used for different parameter calculations to investigate these density distributions since sufficient experimental data are not available for this 27S nucleus. The parameters’ values were calculated easily following this geometrical structure. Gaussian-Gaussian (GG) distribution has been applied to investigate these densities. In our present study, the 27S nucleus was investigated as a 2-p halo nucleus due to its low valence two-protons separation energy (0.90 MeV). The 2-p halo 27S nucleus was described having (25Si) + p + p configuration. These measured parameters’ values were then used to investigate the Gaussian-Gaussian (GG) density distributions. MATLAB computational software was also used for these distribution investigations. From these density distributions, a maximum density of 1.042%, 1.001%, and 0.4789% at the centre of the nucleus was obtained for the core density (ρc ), matter density (ρm ), and halo density (ρh ), respectively. The presence of longer tails on the halo and matter distributions also support the prediction as a two-proton halo nucleus.

Study of the proton halo structure of nuclei 23Al and 27P using the binary cluster model

The neutron, proton, and matter densities of the ground state of the proton-rich 23Al and 27P exotic nuclei were analyzed using the binary cluster model (BCM). Two density parameterizations were used in BCM calculations namely; Gaussian (GS) and harmonic oscillator (HO) parameterizations. According to the calculated results, it found that the BCM gives a good description of the nuclear structure for above proton-rich exotic nuclei. The elastic form factors of the unstable 23Al and 27P exotic nuclei and those of their stable isotopes 27Al and 31P are studied by the plane-wave Born approximation. The main difference between the elastic form factors of unstable nuclei and their stable isotopes is caused by the variation in the proton density distributions, especially the details of the outer part. Moreover, the Glauber model is used to calculate the matter rms radii and reaction cross-section of these exotic nuclei. The calculated results of the mentioned nuclei give a good accordance with the experimental data.

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.

Elastic scattering angular distributions of neutron halo nucleus $$^{11}$$Be studied via dynamic polarization potentials

Cluster aspects of the nuclear structure manifest themselves in, among many other types of nuclear reactions, the breakup reactions of weakly-bound nuclei and their couplings with the other reaction channels. In the present work we analyzed the breakup coupling effects to the elastic scattering angular distributions of $$^{11}$$ Be with a $$^{208}$$ Pb target at an incident energy of 140 MeV. Weighted mean local polarization potentials (WMLPPs), which mimic the dynamic polarization potentials (DPPs) induced by the breakup coupling effects to the elastic scattering channel, were obtained from continuum discretized coupled channel (CDCC) calculations. Suppression of the Coulomb-nuclear interference peaks (CNIPs) of the elastic scattering angular distributions is found to be caused by the destructive interference between the Coulomb and the Coulomb-distorted nuclear amplitude due to the WMLPPs. Comparisons between the WMLPPs and the theoretically calculated Coulomb dipole polarization potentials (CDPPs) suggest that the breakup coupling effect of the $$^{11}$$ Be+ $$^{208}$$ Pb system cannot be represented by the CDPPs alone.

Properties of $$^{8-11}$$Be isotopes with isospin-dependent spin–orbit potential in a cluster approach

The nonlocalized clustering approach is generalized to $$^{8-11}$$ Be isotopes with isospin dependent spin–orbit potential. A new form of the Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave function is introduced to provide a correct description for the $$\sigma $$ -binding neutron in $$^{11}$$ Be. Systematic calculations for $$^{8-11}$$ Be isotopes are performed and results fit well with experimental values. The low energy spectrum of $$^{11}$$ Be is also obtained, especially the correct spin-parity $$1/2^{+}$$ is reproduced for the intruder ground state. The exotic neutron halo structure of $$^{11}$$ Be is studied by calculations of root-mean-square radii and density distribution. The spectroscopic factor is also calculated and discussed for the $$1/2^+$$ ground state of $${}^{11}$$ Be.

Nuclear matter distributions in the neutron-rich carbon isotopes 14−17C from intermediate-energy proton elastic scattering in inverse kinematics

The absolute differential cross sections for small-angle proton elastic scattering off the nuclei 12,14−17C have been measured in inverse kinematics at energies near 700 MeV/u at GSI Darmstadt. The hydrogen-filled ionization chamber IKAR served simultaneously as a gas target and a detector for the recoil protons. The projectile scattering angles were measured with multi-wire tracking detectors. The radial nuclear matter density distributions and the root-mean-square nuclear matter radii were deduced from the measured cross sections using the Glauber multiple-scattering theory. A possible neutron halo structure in 15C, 16C and 17C is discussed. The obtained data show evidence for a halo structure in the 15C nucleus.

Three-body breakup of 6He and its halo structure

The Borromean halo nucleus 6He has been studied by a kinematically complete measurement of Coulomb and nuclear breakup into α + 2n on Pb and C targets at 70 MeV/nucleon. Fully quantum-mechanical four-body breakup calculations reproduce the energy and angular differential cross sections below Erel∼1 MeV for both targets. The model used here reproduces the 6He ground-state properties as well as α-n and n-n scattering data and predicts an average opening angle 〈θnn〉 of 68∘ between the two halo neutrons. However, the model underestimates the breakup cross sections for higher Erel, indicating a possible contribution from the inelastic breakup. Alternatively, we examine the empirically modified calculations that reproduce the energy-differential cross sections for a wide range of scattering angles for both targets. The extracted B(E1) peaks at Erel∼1.4 MeV and amounts to 1.6(2) e2fm2 for Erel ≤ 20 MeV, resulting 〈θnn〉 = 56−10+9 degrees. In either interpretation, the current results show evidence of the dineutron spatial correlation in 6He.

Role of continuum in nuclear direct reactions with one-neutron halo nuclei: A one-dimensional model

We study the evolution of a single-particle wave function during the collision of a one dimensional potential well by another well, which can be regarded as a simple model for the problem of the scattering of a one-neutron halo nucleus by another nucleus. This constitutes an effective three-body problem, whose solution in three dimensions can be extremely complicated, particularly when breakup and rearrangement channels are to be considered. Our one-dimensional model provides the essential three-body nature of this problem, and allows for a much simpler application and assessment of different methods of solution. To simplify further the problem, we assume that the potential well representing the projectile moves according to a predetermined classical trajectory, although the internal motion of the "valence" particle is treated fully quantum-mechanically. This corresponds to a semiclassical approach of the scattering problem. Different approaches are investigated to understand the dynamics involving one-body halo-like systems: the "exact" time-dependent solution of the Schr\"odinger equation is compared to a numerical continuum-discretized coupled-channels (CC) calculation presenting various model cases including different reaction channels. This framework allows us to discuss the reaction mechanism and the role of continuum, whose inclusion in the CC calculation results to be crucial to reproduce the "exact" solution, even when the initial and final states are well bound. We also link each dynamical situation with analogous problem solved in a three dimensional (3D) CC framework, discussing the main challenges experienced in the usual 3D models.

Halo EFT calculation of charge form factor for two-neutron $${}^{6}\text {He}$$ halo nucleus: two-body resonant P-wave interaction

We take a new look at $^{6}\textrm{He}$ halo nucleus and set up a halo effective field theory at low energies to calculate the charge form factor of ${}^{6}\textrm{He}$ system with resonant P-wave interaction. P-wave Lagrangian has been introduced and the charge form factor of ${}^{6}\textrm{He}$ halo nucleus has been obtained at Leading-Order. In this study, the mean-square charge radius of ${}^{6}\textrm{He}$ nucleus relative to ${}^{4}\textrm{He}$ core and the root-mean-square (r.m.s) charge radius of ${}^{6}\textrm{He}$ nucleus have been estimated as $\langle r_{E}^{2}\rangle=1.408\; \textrm{fm}^{2}$ and $\langle r_{E}^{2}\rangle_{{}^{6}He}^{\frac{1}{2}}=2.058 \;\textrm{fm}$, respectively. We have compared our results with the other available theoretical and experimental data.