The exotic structures in the 2s_{1/2} states of five pairs of mirror nuclei ^{17}O-^{17}F, ^{26}Na-^{26}P, ^{27}Mg-^{27}P, ^{28}Al-^{28}P and ^{29}Si-^{29}P are investigated with the relativistic mean-field (RMF) theory and the single-particle model (SPM) to explore the role of the Coulomb effects on the proton halo formation. The present RMF calculations show that the exotic structure of the valence proton is more obvious than that of the valence neutron of its mirror nucleus, the difference of exotic size between each mirror nuclei becomes smaller with the increase of mass number A of the mirror nuclei and the ratios of the valence proton and valence neutron root-mean-square (RMS) radius to the matter radius in each pair of mirror nuclei all decrease linearly with the increase of A. In order to interpret these results, we analyze two opposite effects of Coulomb interaction on the exotic structure formation with SPM and find that the contribution of the energy level shift is more important than that of the Coulomb barrier for light nuclei. However, the hindrance of the Coulomb barrier becomes more obvious with the increase of A. When A is larger than 34, Coulomb effects on the exotic structure formation will almost become zero because its two effects counteract with each other.
We present analytic expressions of the Coulomb interaction between a spherical and a deformed nuclei which are valid for all separation distance. We demonstrate their significant deviations from commonly used formulae in the region inside the Coulomb radius, and show that they remove various shortcomings of the conventional formulae.
A comment on the importance of core polarization in halo nuclei. I point out that although core polarization is suppressed in neutron halos, it plays an essential role in their binding mechanism.
A lot of problems of atomic and nuclear physics depend on with high accuracy to the Coulomb potential. Therefore, it is very important to carefully and accurately calculate the Coulomb potential. In this study, a new analytical expression was obtained for calculating the Coulomb potential by choosing the Fermi distribution function, which is suitable for charge distribution in nuclei. The proposed formula guarantees an accurate and simple calculation of the Coulomb potential of nuclei. Using the analytical expression obtained, the Coulomb potentials for several spherical nuclei were calculated…
The density functional determining the Coulomb energy of nuclei is calculated to the first order in $e^2$. It is shown that the Coulomb energy includes three terms: the Hartree energy; the Fock energy; and the correlation Coulomb energy (CCE), which contributes considerably to the surface energy, the mass difference between mirror nuclei, and the single-particle spectrum. A CCE-based mechanism of a systematic shift of the single-particle spectrum is proposed. A dominant contribution to the CCE is shown to come from the surface region of nuclei. The CCE effect on the calculated proton drip line…
In this work, the Coulomb mixing and the isospin mixing in the ground states of even-even nuclei are evaluated in perturbation theory. The calculation of the isospin mixing is performed by using the connection to isovector monopole resonance properties. The uncertainty in the results that depends on different choices of the Skyrme interactions is shown. While Coulomb mixing turns out to be large in the ground states of heavy nuclei, isospin mixing is very small.
We develop the method for the calculation of the total reaction cross sections induced by the halo nuclei and stable nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energy. It is extended for nuclear reactions at low energy and intermediate energy by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with the 30 experimental data within 10 percent accuracy.The comparison be…
Corrections to the superallowed beta decay matrix elements are evaluated in perturbation theory using the notion of the isovector monopole resonance. The calculation avoids the separation into different contributions and thus presents a consistent, systematic and more transparent approach. Explicit expressions for the Coulomb correction as a function of mass number A, are given.
We set up a formalism to calculate the charge form factors of two-neutron halo nuclei with S-wave neutron-core interactions in the framework of the halo effective field theory. The method is applied to some known and suspected halo nuclei. In particular, we calculate the form factors and charge radii relative to the core to leading order in the halo EFT and compare to experiments where they are available. Moreover, we investigate the general dependence of the charge radius on the core mass and the one- and two-neutron separation energies.
Halo nuclei are characterized by a few weakly bound halo nucleons and a more tightly bound core. This separation of scales can be exploited in a few-body description of halo nuclei, since the detailed structure of the core is not resolved by the halo nucleons. We present an introduction to the effective (field) theory for low-energy properties of halo nuclei. The focus is on halos with S-wave interactions for which universal properties are most pronounced. The special role of the unitary limit is illustrated using the example of multineutron systems and the Efimov effect as a universal binding…
All possible dissociation cross sections for the loosely bound three-body halo nuclei $^6$He (n+n+$α$) and $^{11}$Li (n+n+$^{9}$Li) are computed as functions of target and beam energy. Both Coulomb and nuclear interactions are included in the same theoretical framework. The measurements agree with the calculations for energies above 100 Mev/nucleon. The largest cross sections correspond to final states with zero or three particles for heavy and with two neutrons for light targets.
We present a microscopic study of halo nuclei, starting from the Paris and Bonn potentials and employing a two-frequency shell model approach. It is found that the core-polarization effect is dramatically suppressed in such nuclei. Consequently the effective interaction for halo nucleons is almost entirely given by the bare G-matrix alone, which presently can be evaluated with a high degree of accuracy. The experimental pairing energies between the two halo neutrons in $^6$He and $^{11}$Li nuclei are satisfactorily reproduced by our calculation. It is suggested that the fundamental nucleon-nuc…
By means of the Furnstahl, Serot and Tang's model, the effects of surface tension and Coulomb interaction on the liquid-gas phase transition for finite nuclei are investigated. A limit pressure p-lim above which the liquid-gas phase transition cannot take place has been found. It is found that comparing to the Coulomb interaction, the contribution of surface tension is dominate in low temperature regions. The binodal surface is also addressed.
We investigate conditions for the occurrence of Efimov states in the recently discovered halo nuclei. These states could appear in systems, where one neutron is added to a pronounced one-neutron halo nucleus. Detailed calculations of the properties of the states are presented and promising candidates are discussed.
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 …
We investigate dissociation reactions of loosely bound and spatially extended three-body systems. We formulate a practical method for simultaneous treatment of long-range Coulomb and short-range nuclear interactions. We use $^6$He (n+n+$α$) and $^{11}$Li (n+n+$^{9}$Li) as examples and study the two-neutron separation cross sections as functions of target and beam energy. Individual Coulomb and nuclear as well as interference contributions are also extracted.
Isospin violation effects in nuclei are investigated within a microscopic approach which takes into account the influence of the residual strong interaction on the Coulomb interaction. The renormalization of the off-diagonal Coulomb field acting within a nucleus, by the residual strong interaction is calculated analytically in a simplified RPA. From the expression for the suppression coefficient of the isospin violating part of the Coulomb field, the isospin violating spreading widths of isobaric analog states are derived. The resulting reduction of the width is in agreement with the data on t…
We investigate the Coulomb excitation of low-lying states of unstable nuclei in intermediate energy collisions ($E_{lab}\sim10-500$ MeV/nucleon). It is shown that the cross sections for the $E1$ and $E2$ transitions are larger at lower energies, much less than 10 MeV/nucleon. Retardation effects and Coulomb distortion are found to be both relevant for energies as low as 10 MeV/nucleon and as high as 500 MeV/nucleon. Implications for studies at radioactive beam facilities are discussed.
The mechanism of the Coulomb breakup reactions of the nuclei with neutron-halo structure is investigated in detail. A time-dependent Schrödinger equation for the halo neutron is numerically solved by treating the Coulomb field of a target as an external field. The momentum distribution and the post-acceleration effect of the final fragments are discussed in a fully quantum mechanical way to clarify the limitation of the intuitive picture based on the classical mechanics. The theory is applied to the Coulomb breakup reaction of $^{11}$Be + $^{208}$Pb. The breakup mechanism is found to be differ…
The rapid Gaussian falloff of the oscillator functions at large radius makes them poorly suited for the description of the asymptotic properties of the nuclear wave function, a problem which becomes particularly acute for halo nuclei. We consider an alternative basis for ab initio no-core configuration interaction (NCCI) calculations, built from Coulomb-Sturmian radial functions, allowing for realistic exponential falloff. NCCI calculations are carried out for the neutron halo nuclei 6,8He, as well as the baseline case 4He, with the JISP16 nucleon-nucleon interaction. Estimates are made for th…
A study of the effect of deformation and pairing on the development of halo nuclei is presented. Exploratory three-body $core+n+n$ calculations show that both the NN interaction and the deformation/excitation of the core hinder the formation of the halo. Preliminary self-consistent mean-field calculations are used to search for regions in the nuclear chart where halos could potentially develop. These are also briefly discussed.
The repulsive Coulomb force poses severe challenges when describing $(d, p)$ reactions for highly charged nuclei as a three-body problem. Casting Faddeev-AGS equations in a Coulomb basis avoids introducing screening of the Coulomb force. However, momentum space partial-wave $t$-matrix elements need to be evaluated in this basis. When those $t$-matrices are separable, the evaluation requires the folding of a form factor, depending on one momentum variable, with a momentum space partial-wave Coulomb function, which has a singular behavior at the external momentum $q$. We developed an improved re…
The effect of continuum couplings in the fusion of the halo nucleus $^{11}$Be on $^{208}$Pb around the Coulomb barrier is studied using a three-body model within a coupled discretised continuum channels (CDCC) formalism. We investigate in particular the role of continuum-continuum couplings. These are found to hinder total, complete and incomplete fusion processes. Couplings to the projectile $1p_{1/2}$ bound excited state redistribute the complete and incomplete fusion cross sections, but the total fusion cross section remains nearly constant. Results show that continuum-continuum couplings e…
We investigate the formation cross sections of the deeply bound pionic atoms on halo nuclei theoretically. We consider one-neutron pick-up (d,3He) reaction for the pionic atom formation and find that the formation rate is significantly increased by the existence of the halo neutron with long tail of the wave function. This enhancement is expected to increase the experimental feasibility for the formation of the deeply bound pionic states on beta-unstable nuclei.
We study the influence of the Coulomb force on the Fermi beta-decays in nuclei. This work is composed of two main parts. In the first part, we calculate the Coulomb corrections to super-allowed beta decay. We use the notion of the isovector monopole state and the self-consistent charge-exchange Random Phase Approximation to compute the correction. In the second part of this work, we examine the influence of the anti-analog state on isospin mixing in the isobaric analog state and the correction to the beta-decay Fermi transition.
Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing important role in nuclear reactions, nuclear structure and nuclear astrophysics. In this paper the physical reasons of the Coulomb renormalization of the ANC are addressed. Using Pinkston-Satchler equation the ratio for the proton and neutron ANCs of mirror nuclei is obtained in terms of the Wronskians from the radial overlap functions and regular solutions of the two-body Schrödinger equation with the short-range interaction excluded. This ratio allows one to use microscopic overlap functions for mirror nuc…
The halo nuclei $^6$He and $^8$He are described in a consistent way in a microscopic multiconfiguration model, the refined resonating group method. The ground state properties have been calculated, and momentum distributions of fragments and neutrons have been determined in a simple reaction scenario, taking into account final-state interactions. The correlation of neutrons and fragments are investigated.
The influence of the Coulomb distortion for quasi-elastic (e,e') scattering on highly charged nuclei is investigated in distorted wave Born approximation for electrons. The Dirac equation is solved numerically in order to obtain exact electron continuum states in the electrostatic field generated by the charge distribution of an atomic nucleus. Different approximate models are used to describe the nucleon current in order to show that, at high electron energies and energy-momentum transfer, the influence of Coulomb distortions on (e,e') cross sections can be reliably described by the effective…
It is shown that the three-body non-Borromean halo nuclei like ^{12}Be, ^{18}C, ^{20}C have p-wave virtual states with energy of about 1.6 times the corresponding neutron-core binding energy. We use a renormalizable model that guarantees the general validity of our results in the context of short range interactions.
A systematic study of the root-mean-square distance between the constituents of weakly-bound nuclei consisting of two halo neutrons and a core is performed using a renormalized zero-range model. The radii are obtained from a universal scaling function that depends on the mass ratio of the neutron and the core, as well as on the nature of the subsystems, bound or virtual. Our calculations are qualitatively consistent with recent data for the neutron-neutron root-mean-square distance in the halo of $^{11}$Li and $^{14}$Be nuclei.
The even-Z odd-N neutron-halo nuclei, which are the possible lightest neutron-halo nuclei heavier than $^{37}$Mg, are explored by studying the shell-structure unique in weakly-bound neutrons for spherical or deformed shape. It is pointed out that due to the narrowed N=50 spherical energy-gap and a few resulting close-lying neutron one-particle levels, 1g$_{9/2}$, 3s$_{1/2}$, and 2d$_{5/2}$, for spherical shape, nuclei with some weakly-bound neutrons filling in those levels may be deformed and have a good chance to show deformed s-wave halo. Promising candidates are $^{71}_{24}$Cr$_{47}$, $^{73…
We exploit the separation of scales in weakly-bound nuclei to compute E2 transitions and electric form factors in a Halo EFT framework. The relevant degrees of freedom are the core and the halo neutron. The EFT expansion is carried out in powers of $R_{core}/R_{halo}$, where $R_{core}$ and $R_{halo}$ denote the length scales of the core and halo, respectively. We include the strong $s$-wave and $d$-wave interactions by introducing dimer fields. The dimer propagators are regulated by employing the power divergence subtraction scheme and matched to the effective range expansion in the respective…
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.
We study the nature of the low-lying dipole strength in neutron-rich nuclei, often associated to the Pygmy Dipole Resonance. The states are described within the Hartree-Fock plus RPA formalism, using different parametrizations of the Skyrme interaction. We show how the information from combined reactions processes involving the Coulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states.
In simple models of the nuclear charge operator, measurements of the Coulomb sum and the charge form factor of a nucleus directly determine the proton-proton correlations. We examine experimental results obtained for few-body nuclei at Bates and Saclay using models of the charge operator that include both one- and two-body terms. Previous analyses using one-body terms only have failed to reproduce experimental results. However, we find that the same operators which have been used to successfully describe the charge form factors also produce substantial agreement with measurements of the Coulom…
The sensitive correlations between the low-density halo structure and the high-density properties of the nuclear equation of state (EOS) are constructed in light kaonic nuclei with the relativistic mean-field theory. More specifically, the $1p_{1/2}$ halo spreads out linearly with increasing the pressure and sound velocity square at supra-normal densities and quadratically with decreasing the incompressibility at saturation density. These results suggest that the novel halo in light kaonic nuclei can serve as a sensitive indicator of the nuclear EOS of symmetric matter at supra-normal densitie…
We investigate how the Coulomb interaction affects the energy $E$ and width $Γ$ of resonance states in mirror nuclei. We employ a three-cluster microscopic model to determine position of resonance states in two- and three-body continua. Two parameters are introduced to quantify effects of the Coulomb interactions. As the energy and width of the corresponding resonance states of mirror nuclei are displayed on an $E$-$Γ$ plane, these parameters determine a rotation and a dilatation. With the help of these parameters we found resonance states with strong, small and medium effects of the Coulomb i…
Three-body calculations of (d,p) and (p,d) reactions involving one-neutron halo nuclei 11Be and 15C are performed using the framework of Faddeev-type scattering equations. Important effects of the optical potential nonlocality are found improving the description of the experimental data. The obtained values for the neutron spectroscopic factor are consistent with estimations from other approaches.
A relativistic coupled-channels theory for the calculation of dissociation cross sections of halo nuclei is developed. A comparison with non-relativistic models is done for the dissociation of $^{8}$B projectiles. It is shown that neglecting relativistic effects leads to seizable inaccuracies in the extraction of the astrophysical S-factor for the proton+beryllium radiative capture reaction.
We investigate the use of elastic and inelastic scatterings with secondary beams of radioactive nuclei as a mean to obtain information on ground state properties and transition matrix elements to continuum states. An eikonal model is developed for this purpose by using the folding potential. In particular we discuss possible signatures of halo wavefunctions in elastic and inelastic scattering experiments.
We investigate the role of higher multipole excitations in the electromagnetic dissociation of one-neutron halo nuclei within two different theoretical models -- a finite range distorted wave Born approximation and another in a more analytical method with a finite range potential. We also show, within a simple picture, how the presence of a weakly bound state affects the breakup cross section.
Fusion reactions of neutron-halo nuclei are investigated theoretically with a three-body model. The time-dependent wave-packet method is used to solve the three-body Schrodinger equation. The halo neutron behaves as a spectator during the Coulomb dissociation process of the projectile. The fusion cross sections of 11Be-209Bi and 6He-238U are calculated and are compared with measurements. Our calculation indicates that the fusion cross section is slightly hindered by the presence of weakly bound neutrons.
The neutron skin and halo distributions in medium and heavy nuclei are calculated within the extended Thomas-Fermi approximation. Calculations are carried out for the effective Skyrme-like forces using the direct variational method. The analytical expression for the isovector shift of the rms radii $Δr_{np}$ as a sum of skin- and halo-like terms is obtained. The contribution of halo and skin terms to $Δr_{np}$ are found to be approximately equal.
An unified shell model scheme to evaluate simultaneously the contribution of antibound states and Gamow resonances to the nuclear halos is presented. The calculations, performed in the complex energy plane, are applied to the case of $^{11}$Li. It is found that $^{11}$Li may develop a resonant state excitation near the breakup threshold.
The proton and neutron density distributions, one- and two-neutron separation energies and radii of nuclei for which neutron halos are experimentally observed, are calculated using the self-consistent Hartree-Fock-Bogoliubov method with the effective interaction of Gogny. Halo factors are evaluated assuming hydrogen-like antiproton wave functions. The factors agree well with experimental data. They are close to those obtained with Skyrme forces and with the relativistic mean field approach.
The eikonal description of breakup reactions diverges because of the Coulomb interaction between the projectile and the target. This divergence is due to the adiabatic, or sudden, approximation usually made, which is incompatible with the infinite range of the Coulomb interaction. A correction for this divergence is analysed by comparison with the Dynamical Eikonal Approximation, which is derived without the adiabatic approximation. The correction consists in replacing the first-order term of the eikonal Coulomb phase by the first-order of the perturbation theory. This allows taking into accou…
The Coulomb-nuclear interference is studied as a function of the projectile ground-state binding energy in the 8Li + 12C and 8Li + 208Pb breakup reactions, by considering an arbitrary range for the 8Li ground-state binding energies εb, varying from the experimental one 2.03 MeV down to 0.01 MeV. Regardless the target mass, we first show that the Coulomb breakup cross section is stronger dependent on εb than the nuclear breakup cross section, due to the long-range nature of the Coulomb forces and to the electromagnetic transition matrix elements. For example, in case of 8Li + 208Pb reaction at …
Nuclei at both the neutron- and proton-drip lines are studied. In the cluster-core model, the halo-structure of all the observed and proposed cases of neutron- or proton-halos is investigated in terms of simple potential energy surfaces calculated as the sum of binding energies, Coulomb repulsion, nuclear proximity attraction and the centrifugal potential for all the possible cluster+core configurations of a nucleus. The clusters of neutrons and protons are taken to be unbound, with additional Coulomb energy added for proton-clusters. The model predictions agree with the available experimental…
Effects of the relativistic correction of the Coulomb interaction on doubly-magic nuclei are discussed with Skyrme Hartree--Fock calculations. The relativistic correction is treated by using the local density approximation. It is found that the correction to the total energy is about $ 2.4 \, \mathrm{MeV} $ for $ {}^{208} \mathrm{Pb} $, while proton and neutron radii do not change significantly. This difference is larger than the difference of the Coulomb exchange (Fock) energy calculated with the local density (Hartree--Fock--Slater) approximation and that with the exact treatment and the neu…
We consider the Parity Nonconserving (PNC) mixing in the ground state of exotic (halo) nuclei caused by the PNC weak interaction between outer neutron and nucleons within nuclear interior. For the nucleus $^{11}Be$ as an example of typical nucleus with neutron halo, we use analytical model for the external neutron wave functions to estimate the scale of the PNC mixing. The amplitude of the PNC mixing in halo state is found to be an order of magnitude bigger than that of typical PNC mixing between the ``normal'' nuclear states in nearby nuclei. The enhanced PNC mixing in halo cloud is proportio…
Our understanding of halo nuclei has so far relied on high-energy scattering and reactions, but a number of uncertainties remain. I discuss in general terms the new range of observables which will be measured by experiments around the Coulomb barrier, and how some details of the reaction mechanisms still need to be clarified.
We calculate, in a systematic way, the enhancement effect on antiproton-proton and antiproton-nucleus annihilation cross sections at low energy due to the initial state electrostatic interaction between the projectile and the target nucleus. This calculation is aimed at future comparisons between antineutron and antiproton annihilation rates on different targets, for the extraction of pure isospin channels.
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…
We investigate effects of the Coulomb force on the nuclear pairing properties by performing the Gogny Hartree-Fock-Bogolyubov calculations for the $N=20$, $28$, $50$, $82$ and $126$ nuclei. The Coulomb force reduces the proton pair energy and the even-odd mass difference by about 25%, except for nuclei at and around the proton shell or subshell closure. We then propose a renormalization scheme via a reduction factor $γ_p$ for the proton pairing channel. It is found that a single value of $γ_p(=0.90)$ well takes account of the Coulombic effect, for nuclei covering wide range of the mass number …
Nuclear many-body theory is used to study nuclear matter and finite nuclei at extreme isospin. In-medium interactions in asymmetric nuclear matter are obtained from (Dirac-) Brueckner theory. Neutron skin formation in Ni and Sn isotopes is investigated by relativistic mean-field calculations in DDRH theory with density dependent meson-nucleon vertices. Applications to light nuclei are discussed with special emphasis on pairing and core polarization in weakly bound nuclei. Approaches accounting for continuum coupling in dripline pairing and core polarization are presented. Calculations for the …
The formalism to describe electron scattering reactions on two-neutron halo nuclei is developed. The halo nucleus is described as a three-body system (core+n+n), and the wave function is obtained by solving the Faddeev equations in coordinate space. We discuss elastic and quasielastic scattering using the impulse approximation to describe the reaction mechanism. We apply the method to investigate the case of electron scattering on $^6$He. Spectral functions, response functions, and differential cross sections are calculated for both neutron knockout and $α$ knockout by the electron.
An analytical model is developed to study the spectra of electromagnetic dissociation of two-neutron halo nuclei without precise knowledge about initial and final states. Phenomenological three-cluster bound state wave functions, reproducing the most relevant features of these nuclei, are used along with no interaction final states. The 6-He nucleus is considered as a test case, and a good agreement with experimental data concerning the shape of the spectrum and the magnitude of the strength function is found.
