To explain the experimental facts that the fusion cross sections of proton-halo nucleus on heavy target nucleus is not enhanced as expected, the shielding supposition has been proposed. Namely, the proton-halo nucleus is polarized with the valence proton being shielded by the core. In this paper, within the frame of the Improved Quantum Molecular Dynamics model, the fusion reactions by $^{17}$F on $^{208}$Pb around Coulomb barrier have been simulated. The existence of shielding effect is verified by microscopic dynamics analysis and its influence on the effective interaction potential is also investigated.
In this study, for the first time, in particular to astrophysics and fusion studies, how atomic nuclei embedded in the plasma environment are affected by plasma are systematically analysed. The related interactions in plasma environments considered as Debye and quantum plasma are depicted by more general exponential cosine screened Coulomb (MGECSC) potential. The plasma effects on the change of nuclear energy levels are probed through computations performed within the nuclear shell-model framework. For this purpose, the single-particle energy (spe) values to be used in the calculations are obt…
In order to clear up the sensitivity of the nucleus-nucleus scattering to the nuclear matter distributions of exotic halo nuclei, we have calculated differential cross sections for elastic scattering of the $^6$He and $^{11}$Li nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon with different assumed nuclear density distributions in $^6$He and $^{11}$Li.
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\; \text…
According to the Schiff theorem an external electric field vanishes at atomic nucleus in a neutral atom, i.e. it is completely shielded by electrons. This makes a nuclear electric dipole moment (EDM) unobservable. In this paper an extension of the Schiff theorem to an oscillating electric field is considered. Such field can reach the nucleus and interact with the nuclear EDM. The enhancement effect appears if the field is in resonance with atomic or molecular transition. The shielding by electrons strongly affects low-energy nuclear electric dipole transition amplitudes in different nuclear re…
Some one-neutron halo nuclei can emit a proton in a beta decay of the halo neutron. The branching ratio towards this rare decay mode is calculated within a two-body potential model of the initial core+neutron bound state and final core+proton scattering states. The decay probability per second is evaluated for the $^{11}$Be, $^{19}$C and $^{31}$Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.
In order to clear up the sensitivity of the nucleus--nucleus reaction cross sections $σ_R$ to the nuclear matter distributions in exotic halo nuclei, we have calculated the values of $σ_R$ for scattering of $^6$He, $^{11}$Li, and $^{19}$C nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon. The calculations were performed in the "rigid target" approximation to the Glauber theory, different shapes of the nuclear density distributions in $^6$He, $^{11}$Li, and $^{19}$C being assumed.
With the help of a unified description of the nuclear structure and of the direct reaction mechanism we show that a recent 1H(11Li,9Li)3H experiment provides, for the first time in nuclear physics, direct evidence of phonon mediated pairing.
Using the Glauber theory, we calculate reaction cross sections for the deformed halo nucleus $^{31}$Ne. To this end, we assume that the $^{31}$Ne nucleus takes the $^{30}$Ne + $n$ structure. In order to take into account the rotational excitation of the core nucleus $^{30}$Ne, we employ the particle-rotor model (PRM). We compare the results to those in the adiabatic limit of PRM, that is, the Nilsson model, and show that the Nilsson model works reasonably well for the reaction cross sections of $^{31}$Ne. We also investigate the dependence of the reaction cross sections on the ground state pro…
Ab initio calculations of nuclei face the challenge of simultaneously describing strong short-range internucleon correlations and the long-range properties of weakly-bound halo nucleons. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which is better matched to the physical structure of the many-body wave function. We demonstrate that the use of natural orbitals significantly improves convergence for ab initio no-core configuration interaction calculations of the neutron halo nucleus 6He, relative to the traditional oscillator basis.
If neutrons are progressively added to a normal nucleus, the Pauli principle forces them into states of higher momentum. When the core becomes neutron-saturated, the nucleus expels most of the wavefunction of the last neutrons outside to form a halo, which because of its large size can have lower momentum. It is an open question how nature stabilizes such a fragile system and provides the glue needed to bind the halo neutrons to the core. Here we show that this problem is similar to that of the instability of the normal state of an electron system at zero temperature solved by Cooper, solution…
Detailed analysis of the distribution of nuclear matter in the halo nucleus $^{11}$Be is performed within the microscopic approach based on the flexible variational basis of the functions of the "polarized" orbitals model. It is shown that the proposed approach reproduces, in agreement with the experiment, the most distinguishing features of the mass distribution in this system. Taking into account the results of specific calculations and the exceptionally high reliability of the experimental data on the nuclear density distribution in the "tail" of $^{11}$Be, we make a conclusion about the ex…
Theoretical investigation of two-proton halo-nucleus 17Ne has revealed that the valence protons are more likely to be positioned in the d-state than the s-state. In this study, this finding is clarified by calculation of the binding energy, it is found that the theoretical values for the d-state are closer to the experimental values, in contrast with those obtained for the s-state. The three-body model and MATLAB software are utilised to obtain theoretical values for the three-body-model 17Ne binding energy and matter radius. 17Ne has halo properties of a weakly bound valence proton, a binding…
We investigate the post-acceleration of the $^{10}$Be fragment in Coulomb breakup reaction of the halo nucleus $^{11}$Be, assuming that the excitation of the projectile is to states in the low energy continuum. The method used retains all finite-range effects associated with the interactions between the breakup fragments and can use realistic wave functions for the halo nuclei. We apply the method to compute the average momenta of the $^{10}$Be fragment at four different scattering angles following breakup of $^{11}$Be on a Au target at 42 MeV/nucleon beam energy. Our results, which are in qua…
We compute electromagnetic properties of the Be-11 nucleus using an effective field theory that exploits the separation of scales in this halo system. We fix the parameters of the EFT from measured data on levels and scattering lengths in the Be-10 plus neutron system. We then obtain predictions for the B(E1) strength of the 1/2^+ to 1/2^- transition in the Be-11 nucleus. We also compute the charge radius of the ground state of Be-11. Agreement with experiment within the expected accuracy of a leading-order computation in this EFT is obtained. We also indicate how higher-order corrections that…
Experimental data on Coulomb breakup and neutron removal indicate that 31Ne is one of the heaviest halo nuclei discovered so far. The possible ground state of 31Ne is either 3/2- coming from p-wave halo or 1/2+ from s-wave halo. In this work, we develop a treatable model to include deformed wave functions and a dynamical knockout formalism which includes the dependence on the nuclear orientation to study the neutron removal from 31Ne projectiles at energies around E=200 MeV/nucleon. A detailed account of the effects of deformation on cross sections and longitudinal momentum distributions is ma…
In a decade-and-a-half old experiment, Raabe et al.(Nature 431 (2004) 823), had studied fusion of an incoming beam of halo nucleus $^{6}He$ with the target nucleus $^{238}U$. We extract a new interpretation of the experiment, different from the one that has been inferred so far. We show that their experiment is actually able to discriminate between the structures of the target nucleus (behaving as standard nucleus with density distribution described with canonical RMS radius r = $r_0 A^{\frac{1}{3}}$ with $r_0$ = 1.2 fm), and the {\bf "core"} of the halo nucleus, which surprisingly, does not f…
The role of different continuum components in the weakly-bound nucleus $^6$He is studied by coupling unbound spd-waves of $^5$He by means of simple pairing contact-delta interaction. The results of our previous investigations in a model space containing only p-waves, showed the collective nature of the ground state and allowed the calculation of the electric quadrupole transitions. We extend this simple model by including also sd-continuum neutron states and we investigate the electric monopole, dipole and octupole response of the system for transitions to the continuum, discussing the contrib…
Role of different continuum components in the weakly bound nucleus 6He is studied by coupling unbound spd-waves of 5He by using simple pairing contact-delta interaction. The results show that 6He ground state $0^+$ displays collective nature by taking contribution from five different oscillating continuum states that sum up to give an exponentially decaying bound wavefunction emerging from five different possible configurations i.e. $(s_{1/2})^2$, $(p_{1/2})^2$, $(p_{3/2})^2$, $(d_{3/2})^2$ and $(d_{5/2})^2$. The ground state properties of 6He has been calculated.
We try to explain the differences in the 6He dipole strength function in refs. [1] and [2]. We perform the full basis calculation of the strength function with the same renormalized interaction as in [1] and show that the size of the basis, needed for converged calculations of the 6He continuum spectrum, is much larger than that for the discrete spectrum. The renormalized interaction of [1] therefore cannot be used for the continuum spectrum calculations with the same basis as for the ground state.
This work addresses the question of precisely what features of few body models of halo nuclei are probed by elastic scattering on protons at high centre-of-mass energies. Our treatment is based on a multiple scattering expansion of the proton-projectile transition amplitude in a form which is well adapted to the weakly bound cluster picture of halo nuclei. In the specific case of $^{11}$Li scattering from protons at 800 MeV/u we show that because core recoil effects are significant, scattering crosssections can not, in general, be deduced from knowledge of the total matter density alone. We ad…
The 11Be break-up is calculated using a non perturbative time-dependent quantum calculation. The evolution of the neutron halo wave function shows an emission of neutron at large angles for grazing impact parameters and at forward angles for large impact parameters. The neutron angular distribution is deduced for the different targets and compared to experimental data. We emphasize the diversity of diffraction mechanisms, in particular we discuss the interplay of the nuclear effects such as the towing mode and the Coulomb break-up. A good agreement is found with experimental data.
A new two-dimensional procedure for extrapolation of the values of matter, neutron, and proton radii obtained in no-core shell model (NCSM) calculations to infinite size of its basis is proposed. A relationship between the radii is used as an additional test. Together with the JISP16 potential, which is frequently used in NCSM calculations of the radii, the Daejeon16 potential is applied for these purposes for the first time. Halo nucleus 6He is the object of studies. The small spread of radii values, successful testing using relationship between the values of these three radii, and reasonable…
The unusual structure of Li11, the first halo nucleus found, is analyzed by the Preparata model of nuclear structure. By applying Coherent Nucleus Theory, we obtain an interaction potential for the halo-neutrons that rightly reproduces the fundamental state of the system.
We combine Halo/Cluster Effective Field Theory (H/CEFT) and the Gamow Shell Model (GSM) to describe the $0^+$ ground state of $\rm{^6He}$ as a three-body halo system. We use two-body interactions for the neutron-alpha particle and two-neutron pairs obtained from H/CEFT at leading order, with parameters determined from scattering in the p$_{3/2}$ and s$_0$ channels, respectively. The three-body dynamics of the system is solved using the GSM formalism, where the continuum states are incorporated in the shell model valence space. We find that in the absence of three-body forces the system collaps…
We solve the Faddeev equations for 11Li (n+n+9Li) using hyperspherical coordinates and analytical expressions for distances much larger than the effective ranges of the interactions. The lowest resonances are found at 0.65 MeV (1/2+, 3/2+, 5/2+) and 0.89 MeV (3/2+, 3/2-) with widths of about 0.35 MeV. A number of higher-lying broader resonances are also obtained and related to the Efimov effect. The dipole strength function and the Coulomb dissociation cross section are also calculated. PACS numbers: 21.45.+v, 11.80.Jy, 21.60.Gx
We study the energy dependence of the cross sections for nucleon removal of 8B projectiles. It is shown that the Glauber model calculations with nucleon-nucleon t-matrix reproduce well the energy dependence of the breakup cross sections of 8B. A DWBA model for the breakup cross section is also proposed and results are compared with those of the Glauber model. We show that to obtain an agreement between the DWBA calculations, the Glauber formalism, and the experimental data, it is necessary to modify the energy behavior of the effective interaction. In particular, the breakup potential has a qu…
Reaction and elastic differential cross sections are calculated for light nuclei in the framework of the Glauber theory. The optical phase-shift function is evaluated by Monte Carlo integration. This enables us to use the most accurate wave functions and calculate the phase-shift functions without approximation. Examples of proton nucleus (e.g. p-$^6$He, p-$^6$Li) and nucleus-nucleus (e.g. $^6$He$-^{12}$C) scatterings illustrate the effectiveness of the method. This approach gives us a possibility of a more stringent analysis of the high-energy reactions of halo nuclei.
We study the exotic deformed nucleus $^{31}$Ne using an approach that combines self-consistent structure and reaction theory. We utilize the fully-relativistic, microscopic deformed Hartree-Bogoliubov theory in continuum (DRHBc) to demonstrate that deformation and pairing correlations give rise to a halo structure with large-amplitude $p$-wave configuration in $^{31}$Ne. We then use the valence nucleon wave functions and angle-averaged density distributions of $^{30}$Ne from this model as input for a Glauber reaction model to study the observables of neutron-rich Neon isotopes and search for h…
In order to study the bound-state structure of the Helium halo nuclei, the 8-nucleon Yakubovsky formalism has been implemented for 8He in a 5-body sub-cluster model, i.e. alpha+n+n+n+n. In this case, the 8-nucleon Yakubovsky equations has been obtained in the form of two coupled equations, based on the two independent components. In addition, by removing the contribution interactions of the 8 and 7s bound nucleons in the formalism, the obtained equations explicitly reduce to the 6-nucleon Yakubovsky equations for 6He, in the case of effective 3-body model, i.e. alpha+n+n. In view of the expect…
Is $^{40}$Mg a Borromean halo nucleus? A case built on the electric-dipole response
The University of Manchester（曼彻斯特大学）；Akal University（阿卡尔大学）；Research Center for Nuclear Physics (RCNP), Osaka University（大阪大学核物理研究中心）；Universidad de Sevilla（塞维利亚大学）；Osaka Metropolitan University（大阪公立大学）；RIKEN Nishina Center（理化学研究所西村中心）；Hokkaido University（北海道大学）；University of Warsaw（华沙大学）
We discuss the spin-dependence of the effective two-body interactions appropriate for three-body computations. The only reasonable choice seems to be the fine and hyperfine interactions known for atomic electrons interacting with the nucleus. One exception is the nucleon-nucleon interaction imposing a different type of symmetry. We use the two-neutron halo nucleus 11Li as illustration. We demonstrate that models with the wrong spin-dependence are basically without predictive power. The Pauli forbidden core and valence states must be consistently treated.
Data for the scattering of 6He, 8He, 9Li, and 11Li from hydrogen are analyzed within a fully microscopic folding model of proton-nucleus scattering. Current data suggest that of these only 11Li has a noticeable halo. For 6He, we have also analysed the complementary reaction 6Li(gamma,pi)6He(gs). The available data for that reaction support the hypothesis that 6He may not be a halo nucleus. However, those data are scarce and there is clearly a need for more to elicit the microscopic structure of 6He.
The universal properties and structure of halo nuclei composed of two neutrons (2n) and a core are investigated within an effective quantum mechanics framework. We construct an effective interaction potential that exploits the separation of scales in halo nuclei and treat the nucleus as an effective three-body system. The uncertainty from higher orders in the expansion is quantified through theoretical error bands. First, we investigate the possibility to observe excited Efimov states in 2n halo nuclei. Based on the experimental data, 20C is the only halo nucleus candidate to possibly have an …
A dripline nucleus $^{22}$C is studied in a Borromean three-body model of $^{20}$C+$n$+$n$. The valence neutrons, interacting via a realistic potential, are constrained to be orthogonal to the occupied orbits in $^{20}$C. We obtain ample results supporting that $^{22}$C is an ideal $S$-wave two-neutron halo nucleus: The ground state is bound by 390-570 keV, the root mean square neutron and proton radii are 4.0 and 2.4 fm, and the two neutrons are predominantly in $(s_{1/2})^2$ orbits. The binding mechanism of $^{22}$C is discussed. One- and two-body density distributions elucidate the halo cha…
Halo phenomena in deformed nuclei are investigated within a deformed relativistic Hartree Bogoliubov (DRHB) theory. These weakly bound quantum systems present interesting examples for the study of the interdependence between the deformation of the core and the particles in the halo. Contributions of the halo, deformation effects, and large spatial extensions of these systems are described in a fully self-consistent way by the DRHB equations in a spherical Woods-Saxon basis with the proper asymptotic behavior at large distance from the nuclear center. Magnesium and neon isotopes are studied and…
Although the neutron (n) does not carry a total electric charge, its charge and magnetization distributions represented in momentum space by the electromagnetic form factors, $F_1^{(n)} (q^2)$ and $F_2^{(n)} (q^2)$, lead to an electromagnetic potential of the neutron. Using this fact, we calculate the electromagnetic corrections to the binding energy, $B_d$, of the deuteron and a one neutron halo nucleus (11Be), by evaluating the neutron-proton and the neutron-charged core (10Be) potential, respectively. The correction to $B_d$ (~9 keV) is comparable to that arising due to the inclusion of the…
The recently observed large cross sections for the Coulomb dissociation of $^{31}$Ne nucleus indicate that this nucleus takes a halo structure in the ground state. We analyse these experimental data using the particle-rotor model, that takes into account the rotational excitation of the core nucleus $^{30}$Ne. We show that the experimental data can be well reproduced when the quadrupole deformation parameter of $^{30}$Ne is around $β_2=0.2\sim0.3$, at which the ground state takes the spin and parity of $I^π$=3/2$^-$. This state corresponds to the Nilsson level [330 1/2] in the adiabatic limit …
We investigate fusion cross section of a nucleus with a valence neutron, using the time-dependent wave-packet method. For a stable projectile, in which the valence neutron is tightly bound (e_n < -3 MeV), the neutron could enhance the fusion probability when the matching condition of orbital energies are satisfied. In contrast, for a halo nucleus, in which the binding energy of the neutron is very small (e_n>-1 MeV), the fusion probability is hindered by the presence of the weakly bound neutron.
We study the two-neutron correlations in the ground state of the weakly-bound two-neutron halo nucleus $^{22}$C sitting at the edge of the neutron-drip line and also in the unbound nucleus $^{26}$O sitting beyond the neutron dripline. For the present study, we employ a three-body (core$+n+n$) structure model designed for describing the two-neutron halo system by explicit inclusion of unbound continuum states of the subsystem (core$+n$). We use either a density-independent or a density-dependent contact-delta interaction to describe the neutron-neutron interaction and its strength is varied to …
The neutron-rich $^{11}$Li halo nucleus is unique among nuclei with known separation energies by its ability to emit a proton and a neutron in a $β$ decay process. The branching ratio towards this rare decay mode is evaluated within a three-body model for the initial bound state and with Coulomb three-body final scattering states. The branching ratio should be comprised between two extreme cases, i.e.\ a lower bound $6 \times 10^{-12}$ obtained with a pure Coulomb wave and an upper bound $5 \times 10^{-10}$ obtained with a plane wave. A simple model with modified Coulomb waves provides plausib…
We demonstrate that there is no appreciable enhancement of the anapole moment of $^{11}$Be. The effect of small energy intervals is compensated for by a small overlap of the halo neutron wave function with core.
We perform a detailed analysis for the structure of 31F, which is a candidate of the halo nucleus. We calculate the radius and reaction cross-section using a three-body model of 29F+n+n and discuss how the competition between the neutron-pairing and the single-particle energy induces structural changes of 31F. The present analysis further clarifies a new aspect of the anti-halo efect that suppresses the halo structure.
As a model of a neutron halo nucleus we consider a neutron bound to an inert core by a zero range force. We study the breakup of this simple nucleus in the Coulomb field of a target nucleus. In the post-form DWBA (or, in our simple model CWBA (``Coulomb Wave Born Approximation'')) an analytic solution for the T-matrix is known. We study limiting cases of this T-matrix. As it should be, we recover the Born approximation for weak Coulomb fields (i.e., for the relevant Coulomb parameters much smaller than 1). For strong Coulomb fields, high beam energies, and scattering to the forward region we f…
Halo nuclei projectiles can undergo into a fragmentation process when scattered by a nucleus target. The corresponding core from exotic nuclei is usually observed while the others fragments of the reaction are not. We use the recently proposed theory by [Phys. Lett. B767, 53 (2017)] with a four-body description of the inclusive breakup reaction where the projectile is 20C described like a two-neutron halo nucleus. The momentum of both neutrons are integrated out giving a generic description of the core angular distribution. In this preliminary study we perform an analysis of the inclusive inel…
Rotational Feshbach resonances in the deformed halo nucleus $^{31}$Ne
National Institute of Technology (KOSEN), Gifu College（岐阜工业高等专门学校）；RIKEN Nishina Center（理化学研究所仁科加速器中心）；Department of Physics, Kyushu University（九州大学物理学系）；Research Center for Nuclear Physics (RCNP), Osaka University（大阪大学核物理研究中心）
A microscopic self-consistent triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc), which simultaneously takes into account the triaxiality and pairing correlations as well as continuum effects, is established and applied to explore the novel halo phenomenon in aluminum isotopes. The experimental proton drip line and the available data of neutron separation energies and charge radii are reproduced well without any free parameters. The neutron-richest odd-odd aluminum isotope observed so far, 42Al, is predicted to be triaxially deformed with beta=0.35 and gamma=42. Its one-neutr…
We investgate the breakup of one-neutron halo nuclei in the Coulomb field of a target nucleus. In the post-form distorted wave Born approximation theory of this reaction, with only Coulomb distortions in the entrance and the outgoing channels, an analytic solution for the breakup $T$-matrix is known. We study this $T$-matrix and the corresponding cross-sections numerically. This formula can be related to the first order semiclassical treatment of the electromagnetic dissociation. This theory contains the electromagnetic interaction between the core and the target nucleus to all orders. We show…
Halo nuclei are excellent examples of few-body systems consisting of a core and weakly-bound halo nucleons. Where there is only one nucleon in the halo, as in 11Be, the many-body problem can be reduced to a two-body problem. The contribution of the 1s1/2 orbital to the ground state configuration in 11Be, characterized by the spectroscopic factor, S, has been extracted from direct reaction data by many groups over the past five decades with discrepant results. An experiment was performed at the Holifield Radioactive Ion Beam Facility using a 10Be primary beam at four different energies with the…
We have investigated the implications of the neutron halo configuration, observed in the ground-state of some neutron-rich light nuclei, on neutron radiative transition processes. In particular, we have studied the influence of the neutron halo on the direct radiative capture (DRC) process. The energy dependence as well as the strength of E1 emission due to incident p-wave neutrons is strongly influenced by the halo configuration of the residual nucleus capturing state. We have compared the calculated 10Be(n,gamma)11Be DRC cross section with that derived from the experiment in the inverse kine…
The breakup cross section (BUX) of 22C by 12C at 250 MeV/nucleon is evaluated by the continuum-discretized coupled-channels method incorporating the cluster-orbital shell model (COSM) wave functions. Contributions of the low-lying 0+_2 and 2+_1 resonances predicted by COSM to the BUX are investigated. The 2+_1 resonance gives a narrow peak in the BUX, as in usual resonant reactions, whereas the 0+_2 resonant cross section has a peculiar shape due to the coupling to the nonresonant continuum, i.e., the Fano effect. By changing the scattering angle of 22C after the breakup, a variety of shapes o…
We prove that the corner angle distributions in the bound three-body system AAB, which consists of two particles of type A and one particle of type B, approach universal form if the pair AA has a virtual state at zero energy and the binding energy of AAB goes to zero. We derive explicit expressions for the universal corner angle distributions in terms of elementary functions, which depend solely on the mass ratio m(A)/m(B) and do not depend on pair interactions. On the basis of experimental data and calculations we demonstrate that such systems as the asymmetric Helium trimer $^3$He$^4$He$_2$ …
We discuss the effect of the coupling to the break-up channel on the total fusion involving a halo nucleus with a heavy target. We show that there is a competition between the hindrance arising from this coupling, mostly at above barrier energies, and the enhancement which ensues at sub-barrier energies owing to the static effect of the extended matter distribution and the coupling to the soft modes.
We discuss the role of deformation of the target nucleus in the fusion reaction of the $^{15}$C + $^{232}$Th system at energies around the Coulomb barrier, for which $^{15}$C is a well-known one-neutron halo nucleus. To this end, we construct the potential between $^{15}$C and $^{232}$Th with the double folding procedure, assuming that the projectile nucleus is composed of the core nucleus, $^{14}$C, and a valance neutron. By taking into account the halo nature of the projectile nucleus as well as the deformation of the target nucleus, we simultaneously reproduce the fusion cross sections for …
