Proton Halo Nuclei Research Articles

Nuclear structure and dynamics with light exotic beams

In this contribution some aspects of the reaction dynamics of collisions involving light exotic nuclei will be introduced. In particular the dynamics of proton-halo nuclei and the differences with neutron-halo induced reactions will be discussed. Moreover, the formation of quasi-molecular states in the scattering of light nuclei having a neutron skin with α-particles will be presented.

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

The 8B+64Zn reaction at 38.5 MeV has been studied at HIE-ISOLDE CERN to investigate proton halo effect on the reaction dynamics. For the first time it was used the only existing post-accelerated 8B beam. The measured elastic scattering angular distribution showed a small suppression of the Coulomb-nuclear interference peak, opposite to what observed for the one-neutron halo nucleus 11Be on the same target where a large suppression was observed instead. Inclusive angular and energy distributions of breakup fragments were also measured showing that, both, elastic and non-elastic breakup contribute. The presence of the additional Coulomb interactions halo-core and halo-target in 8B makes the reaction dynamics in this proton-halo nucleus different than the neutron-halo case.

Theoretical Study of Proton Halo Structure and Elastic Electron Scattering Form Factor for 23Al and 27P Nuclei by Using Full Correlation Functions (Tensor Force and Short Range)

The study of proton-rich nuclei's form factors, root-mean-square radius (rms), and nuclear density distributions is the focus of this work for nuclei (23Al and 27P), use two body charge density distributions (2BCDD's). With the effects of the strong tensor force and short range, the nucleon distribution function of the two oscillating harmonic particles in a two-frequency shell model operates with two different parameters: bc for the inner (core) orbits and bv for the outer (halo) orbitals. This work demonstrated the existence of proton halo nuclei for the nuclei (23Al and 27P) in the shell (2s1/2), and the computed proton, neutron, and matter density distributions for these nuclei both displayed the long tail of the performance. Using the Borne approximation of the plane wave, the elastic form factor of the electron scattering from the alien nucleus was calculated, this form factor is dependent on the difference in the proton density distribution of the last proton in the nucleus. The Fortran 95 power station program was used to calculate the neutrons, protons, matter density, elastic electron scattering form factor, and rms radii. The calculated outcomes for these exotic nuclei agree well with the experimental data.

Breakup of the proton halo nucleus 8B near barrier energies

The dynamics of a nuclear open quantum system could be revealed in the correlations between the breakup fragments of halo nuclei. The breakup mechanism of a proton halo nuclear system is of particular interest as the Coulomb polarization may play an important role, which, however, remains an open question. Here we use a highly efficient silicon detector array and measure the correlations between the breakup fragments of 8B incident on 120Sn at near-barrier energies. The energy and angular correlations can be explained by a fully quantum mechanical method based on the state-of-the-art continuum discretized coupled channel calculations. The results indicate that, compared to the neutron halo nucleus 6He, 8B presents distinctive reaction dynamics: the dominance of the elastic breakup. This breakup occurs mainly via the short-lived continuum states, almost exhausts the 7Be yield, indicating the effect of Coulomb polarization on the proton halo state. The correlation information reveals that the prompt breakup mechanism dominates, occurring predominantly on the outgoing trajectory. We also show that, as a large environment, the continuum of 8B breakup may not significantly influence elastic scattering and complete fusion.

Effect of different nucleon–nucleon interactions based on relativistic mean field theory on elastic scattering cross-sections of proton and neutron halo nuclei

Effect of different nucleon–nucleon interactions based on relativistic mean field theory on elastic scattering cross-sections of proton and neutron halo nuclei

β-decay and isospin symmetry breaking

<p indent=0mm>The elegant concept of isospin symmetry is of fundamental importance in nuclear and elementary particle physics. As a β-decay process changes an up quark to a down quark or <italic>vice versa</italic>, studies of nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, can be a powerful means to probe isospin symmetry breaking. A series of β-decay experiments of sd-shell nuclei near the proton drip line produced by projectile fragmentation were performed at the Radioactive Ion Beam Line of the Heavy Ion Research Facility in Lanzhou (HIRFL-RIBLL1) using a silicon array with a high detection efficiency and a low detection threshold. The secondary ions were identified by the combination of Δ<italic>E</italic>-TOF and magnetic rigidity (<italic>Bρ</italic>) in which the time of flight (TOF) was measured by two plastic scintillators at the second and fourth focal planes of the RIBLL1 and the energy loss (Δ<italic>E</italic>) was measured by two silicon detectors in the front of the silicon array. Double-sided silicon strip detectors (DSSDs) in the center of the array served to measure the residual energies of secondary ions on an event-by-event basis and study their decay properties with an implantation-decay correlation. Several quadrant silicon detectors (QSDs) placed behind DSSDs were used for anticoincidences of the penetrating fragments and light particles coming along with the beam, and measurements of β particles and high-energy protons. The β-delayed proton peaks with known energies and their corresponding absolute intensities were used for the energy and detection efficiency calibrations of the DSSDs. The system allows us to measure protons with energies down to about <sc>200 keV</sc> without obvious β background in the proton spectrum and was successful to measure the energies, time, and positions of implanted ions and decay protons efficiently, supporting researchers to study the decay properties of nuclei towards the proton drip line. The β-decay data, together with the large-scale shell-model calculations, allows detailed investigations on the mirror-nuclei systems resulting in the systematic study of isospin symmetry breaking in the sd-shell nuclear region. It was found that the mirror asymmetry parameters become larger due to the smaller separation energies while approaching the proton drip line for the extremely proton-rich sulfur nuclei ^27,28,29S and the Coulomb forces and other isospin-symmetry nonconserving forces acting between protons would lead to extended proton wave functions and cause mirror asymmetries. The properties of ²²Si β-decay for the transitions to the low-lying states of ²²Al were measured, and the reduced transition probabilities were determined. Comparing with the data on the β-decay of the mirror nucleus ²²O, we found a mirror asymmetry of <italic>δ</italic>=209(96)% in the transition to the first 1⁺ excited state of the respective daughters. This is by far the largest value of <italic>δ</italic> observed in the low-lying states. Shell-model calculations with isospin-nonconserving forces, including the <italic>T</italic>=1,<italic> J</italic>=2, 3 interactions related to the s_1/2 orbit that introduces explicitly the isospin-symmetry breaking force and describes the loosely bound nature of the wave functions of the s_1/2 orbit, can reproduce the observed data well and demonstrate that this dramatically large mirror asymmetry is attributed to the significant proton occupation and loosely bound nature of the wave functions of the s_1/2 orbit, which suggests that ²²Al is a proton-halo nucleus.

Direct fusion measurement of the 8B proton-halo nucleus at near-barrier energies

Direct measurements of the total fusion cross section for B8+40Ar were achieved with the active target technique. The fusion excitation function was extracted at energies near the Coulomb barrier. The cross section is well described by a coupled reaction channels calculation. The data were compared with previous B8 fusion experiments on Si28 and Ni58 targets. No evidence of striking enhancement of the total fusion cross section at near the Coulomb barrier, that was previously reported for the B8+58Ni system, was observed in these direct measurements. The present data are systematically consistent with the results for B8+28Si at higher energies and with other weakly-bound systems at near-barrier energies.

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 cluster structures in nuclei through the ratio method

For one-neutron halo nuclei, the cross sections for elastic scattering and breakup at intermediate energy exhibit similar angular dependences. The Recoil Excitation and Breakup (REB) model of reactions elegantly explains this feature. It also leads to the idea of a new reaction observable to study the structure of loosely-bound nuclear systems: the Ratio. This observable consists of the ratio of angular distributions for different reaction channels, viz. elastic scattering and breakup, which cancels most of the dependence on the reaction mechanism; in particular it is insensitive to the choice of optical potentials that simulate the projectile-target interaction. This new observable is very sensitive to the structure of the projectile. In this article, we review a series of previous papers, which have introduced the Ratio Method and its extension to low beam energies and proton-halo nuclei.

A Study on the Emission of 1, 2 Proton Halo Nuclei from Parent with Z = 121–128 in the Superheavy Nuclei via Cluster Radioactivity

Probabilities for the emission of various one proton and two proton halo nuclei from parent superheavy (SH) isotopes with Z = 121–128 are studied with the Coulomb and proximity potential model (CPPM) as the interacting barrier. The half-lives and other characteristics for the emission of one proton halo nuclei, 8B, 11,12N, 17F, 23Al, 27,28P, and two proton halo nuclei, 9C, 17,18Ne, 20Mg, 29S from the SH parent isotopes are determined and plotted it as a function of neutron number of daughter nuclei. The shell closure effects of parent and daughter nuclei are evident from the plot of computed half-lives. The peaks in the plot of half-life show the shell closure of parent and dips in the half-life show the shell closure of daughter nuclei. In the SH region with Z = 121–128 and N = 147–194, we observed that neutron shell closure of parent occurs at N~184 and neutron shell closure of daughter nuclei at N~174–184. Moreover, the most probable proton halo nuclei emissions are also evident from the computed half-life values. We have also studied the Geiger-Nuttall plots of log10 (T1/2) vs. Q−1/2 and log10 (T1/2) vs. −ln(P) for all the selected proton halo nuclei emitting from the SH parent isotopes with Z = 121–128 and are found to be linear. From the linearity of these plots, we found that GN law is valid for the proton halo decay also.

Shielding effects in fusion reactions with a proton-halo nucleus * * Supported by National Natural Science Foundation of China (11965004, U1867212, 11711540016, 11847317, 11947413), Natural Science Foundation of Guangxi province (2016GXNSFFA380001, 2017GXNSFGA198001), Foundation of Guangxi innovative team and distinguished scholar in institutions of higher education, and Innovation project of Guangxi Graduate Education (XYCSZ2018051)

To explain the experimental observation that the fusion cross-section of a proton-halo nucleus with a heavy target nucleus is not enhanced as expected, the shielding hypothesis was proposed, where the proton-halo nucleus is polarized and the valence proton shielded by the core. In the frame of the improved quantum molecular dynamics model, the fusion reaction 17F on 208Pb around the Coulomb barrier is simulated. The existence of the shielding effect is verified by the microscopic dynamics simulations. Its influence on the effective interaction potential is also investigated.

The effect of temperature on fusion cross-sections of the 8 B proton halo nucleus

The effect of temperature on fusion cross-sections of the 8 B proton halo nucleus

Extension of the ratio method to proton-rich nuclei

The ratio method has been developed to improve the study of one-neutron halo nuclei through reactions. By taking the ratio of angular distributions for two processes, viz. breakup and elastic scattering, this new observable is nearly independent of the reaction mechanism and hence much more sensitive to the projectile structure than the cross sections for each single process. We study the extension of the ratio method to proton-rich nuclei and also explore the optimum experimental conditions for measuring this new observable. We compare accurate dynamical calculations of reactions for proton-rich projectiles to the prediction of the ratio method. We use the dynamical eikonal approximation that provides good results for this kind of reaction at intermediate energy. Our tests for 8B, an archetypical one-proton halo nucleus, on Pb, Ni, and C targets at 44 MeV/nucleon show that, the ratio works less well than for neutron halos due to the non-negligible Coulomb interaction between the valence proton and the target. Nevertheless, thanks to its strong sensitivity to the single-particle structure of the projectile, the ratio method still provides pertinent information about nuclear structure on the proton-rich side of the valley of stability. To account for the lower quality of the method applied to charged systems, we suggest variations in its application from the original idea. Interestingly the method is not affected if energy ranges—or bins—are considered in the projectile continuum. This makes the ratio easier to measure experimentally by increasing the breakup cross section. We also extend our analysis to 17F, 25Al, and 27P, whose study is of interest to both nuclear astrophysics and nuclear structure. We show that, albeit less precise than for one-neutron halo nuclei, nuclear-structure information can be inferred from the ratio method applied to exotic proton-rich nuclei. For nuclei in which the valence proton is deeply bound and/or sits in an l ≥ 2 orbital, the method provides only estimates of nuclear-structure features, like the one-proton separation energy or the orbital angular momentum of the valence proton in the ground state. When the valence proton is loosely bound in an s or p orbital, viz. for proton halo nuclei, more detailed structure information can be obtained through this new reaction observable.

Proton- and neutron-halo breakups: Similarities and differences

It is shown in this paper that the decrease of the projectile ground state binding energy in a neutron-halo nucleus and the removal of the Coulomb barrier in the proton-halo nucleus, produce a similar qualitative effect on the elastic scattering cross sections. The variation of the binding energy produces opposite effects on elastic scattering and breakup cross sections. A strongly destructive Coulomb-nuclear interference owing to the decrease of the binding energy is also obtained.

Density distributions and form factors of the exotic 8B nucleus

Results of charge, neutron and matter densities and related form factors for one- proton halo nucleus 8B are presented using a two- frequency shell model approach. We choose a model space for the core of 7Be different from that of the extra one valence proton. One configuration is assumed for the outer proton to be in 1p1/2 - shell. The results of the matter density distributions are compared with those fitted to the experimental data. The calculated proton and matter density distributions of this exotic nucleus exhibit a long tail behavior, which is considered as a distinctive feature of halo nuclei. Elastic electron scattering form factors of this exotic nucleus are also studied. The effects of the proton halo on the electron scattering form factors are analyzed. The form factors of the exotic unstable 8B nucleus are compared with those of the stable 10B nucleus. The differences between the results of unstable 8B and stable 10B nuclei come from the long tail in the density distribution of the last proton.

Analysis of 8B Proton Halo Nucleus Scattered from 12C and 58Ni at Different Energies

Angular distributions in the elastic scattering of 8B from 12C and 58Ni targets at different energies have been analyzed in the framework of the double-folding (DF) optical model. The real central part of the nuclear optical potential is obtained by folding the M3Y effective interaction with the cluster density distribution of the 8B nucleus. The experimental angular distributions have been successfully reproduced. This confirms the validity of the cluster structure of the 8B nucleus.

Theoretical Study of Nuclear Density Distributions and Elastic Electron Scattering Form Factors of Some Proton Halo Nuclei (17Ne and 8B)

Theoretical investigation of proton halo-nucleus (8B and 17Ne) has revealed that the valence protons are to be in pure (1p1/2)1 orbit for 8B and (1d3/2)2 orbit for 17Ne. The nuclear matter density distributions, the elastic electron scattering form factors and (proton, charge, neutron and matter) root-mean square (rms) are studied for our tested nuclei, through an effective two-body density operator for point nucleon system folded with two-body full correlation operator's functions. The full correlation (FC's ) takes account of the effect for the strong short range repulsion (SRC's) and the strong tensor force (TC's) in the nucleon-nucleon forces. The effective two-body density operator is produced and used to derive an explicit form for ground state two-body nucleon density distributions (2BNDD's) applicable for proton – rich halo nuclei and Fortran 95 programs are utilized to obtain theoretical values of our calculation. The effect of the TC's and SRC's on the ground state also calculated. 2BNDD's obtained within the two- frequency shell model (TFSM) approach, the elastic charge scattering form factors F(q)'s of proton halo nuclei are studied through Plane Wave Born Approximation (PWBA) .

Charge radius of the 13N* proton halo nucleus with Halo Effective Field Theory

We evaluated the charge radius of the first excited state of 13N with halo Effective Field Theory (hEFT) at the low energies. The halo effective field theory without pion is used to examine the halo nucleus bound state with a large S-wave scattering length. We built Lagrangian from the effective core and the valence proton of the fields and obtained the charge form factor at Leading–Order (LO). The charge radius at leading order for the first excited state of the proton halo nucleus, 13N, has been estimated as rc= 2.52 fm. This result is without any finite-size contributions included from the core and the proton. If we consider the contributions of the charge radius of the proton and the core, the result will be [rC]13N*= 5.85 fm.

Cross section and astrophysical S-factor for [formula omitted] reaction with Halo Effective Field Theory at low-energies

We considered one of the proton halo nuclei candidates, 13N* nucleus, and calculated the cross section and astrophysical S-factor for 12C(p, γ)13N* reaction using halo effective field theory without pion (hEFT¬π). The halo effective field theory is used to examine the halo nucleus bound state with a large S-wave scattering length. We calculated the radiative proton capture cross section and the astrophysical S-factor from the fields of the core and the valence proton at the Leading-Order (LO). We showed that there is a good agreement among the our results for cross section and astrophysical S-factor of the 12C(p, γ)13N* reaction and the experimental data. The astrophysical S-factor that has been estimated at the zero energy (Ecm=0) by using a theoretical calculation of the cross section for direct radiative capture and an extrapolation of this calculation obtained S(0)=1.883×10−3 MeV-b.

B8+Al27 scattering at low energies

We present $^{8}\mathrm{B}+^{27}\mathrm{Al}$ elastic scattering angular distributions for the proton-halo nucleus $^{8}\mathrm{B}$ at two energies above the Coulomb barrier, namely ${E}_{\mathrm{lab}}=15.3$ and 21.7 MeV. The experiments were performed in the Radioactive Ion Beams in Brasil facility (RIBRAS) in S\~ao Paulo, and in the TwinSol facility at the University of Notre Dame, USA. The angular distributions were measured in the angular range of 15--80 degrees. Optical model and continuum discretized coupled channels calculations were performed, and the total reaction cross sections were derived. A comparison of the $^{8}\mathrm{B}+^{27}\mathrm{Al}$ total reaction cross sections with similar systems including exotic, weakly bound, and tightly bound projectiles impinging on the same target is presented.