Narrow Results

We exploit the possibility of new configurations in three-body halo nuclei, Samba type (the neutron-core form a bound system) as a doorway to Borromean systems. The nuclei ¹²Be, ¹⁵B, ²³N and ²⁷F are of such nature, in particular ²³N with a half-life of 37.7 s and a halo radius of 6.07 fm is an excellent example of Samba-halo configuration. The fusion below the barrier of the Samba halo nuclei with heavy targets could reveal the so far elusive enhancement and a dominance of one-neutron over two-neutron transfers, in contrast to what was found recently for the Borromean halo nucleus ⁶He+²³⁸U.

A candidate of a neutron-halo nucleus, ³¹Ne, contains a single neutron in the pf shell. Within Glauber and eikonal models, we analyze reactions used to study ³¹Ne. We show in a ³⁰Ne+n model that the magnitudes of the total reaction and above all of the one-neutron removal cross sections of ³¹Ne on ¹²C and ²⁰⁸Pb targets strongly depend on the orbital angular momentum of the valence neutron, thereby providing efficient ways to determine the structure of ³¹Ne ground state. We also show that elastic-breakup observables exhibit a strong dependence upon the orbital of the valence neutron.

We investigate the three-body Coulomb breakup of a two-neutron halo nucleus, ⁶He. The three-body scattering states of ⁶He are described by using the Complex-scaled solutions of the Lippmann-Schwinger equation. We calculate the breakup cross section and the invariant mass spectra, and discuss the relations between the structures in these observables and the n-n and α-n correlations of ⁶He.

The radial sensitivity of the elastic scattering of the weakly-bound ⁶Li and halo ⁶He nuclei on medium-mass ⁶⁴Zn target and heavy target ²⁰⁸Pb is examined around the Coulomb barrier energies. We present that very good agreement between theoretical and experimental results have been obtained with small χ²/N values. The fusion cross-section and volume integrals of the potentials have been deduced from the theoretical calculations for all studied systems at relevant energies. We have also analyzed the elastic scattering of the ⁶He+²⁰⁸Pb system at E_lab = 14, 16, 18, 22, 27 MeV in order to investigate whether there is a dispersion relation between the real and imaginary parts of the optical potential.

We have studied the fusion of ¹¹Be with ²⁰⁹Bi and ¹⁵C with ²³²Th in the energy region around the barrier within the framework of quantum diffusion approach and have found enhancement in fusion cross-section in deep sub-barrier region and a very minor suppression in the above barrier energy region with respect to the corresponding experimental observations. The fusion cross-section is found to be slightly increased for reactions involving ¹¹Be and ¹⁵C nuclei in comparison to those involving the stable ¹⁰Be and ¹²C isotopes, respectively.

In a decade-and-a-half old experiment, Raabe et al. [Nature 431, 823 (2004)], had studied fusion of an incoming beam of halo nucleus ⁶He 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 “core” of the halo nucleus, which surprisingly, does not follow the standard density distribution with the above RMS radius. In fact, the core has the structure of a tennis-ball (bubble)-like nucleus, with a “hole” at the center of the density distribution. This novel interpretation of the fusion experiment provides an unambiguous support to an almost two decades old model [A. Abbas, Mod. Phys. Lett. A16, 755 (2001)], of the halo nuclei. This Quantum Chromodynamics based model succeeds in identifying all known halo nuclei and makes clear-cut and unique predictions for new and heavier halo nuclei. This model supports the existence of tennis-ball (bubble)-like core, of even the giant-neutron halo nuclei. This should prove beneficial to the experimentalists, to go forward more confidently, in their study of exotic nuclei.

Analysis of the fusion reactions of halo nuclei is one of the important subjects of nuclear physics. In addition, temperature-dependent analysis of fusion cross-sections of these nuclei is a deficient topic in the literature. In order to overcome this deficiency, the fusion cross-sections of ⁶He, ⁸He and ${}^{11}$Li which are the most important halo nuclei are analyzed by using both temperature-independent potential and temperature-dependent potential. All the theoretical results are compared with each other as well as the experimental data. It is seen that the results of temperature-independent potential are in good agreement with the data while the temperature-dependent potential has a significant impact on the fusion cross-sections. Finally, the changes with the temperature of both real and nuclear potentials of all the reactions are investigated.

The differential elastic cross-sections of ${}^{12}$C–${}^{12}$C and ${}^{11}$Li–${}^{12}$C nuclei are calculated in the complete Glauber theory. The role of the possible correlations connected to the shell effects in ${}^{11}$Li nucleus is considered.

The complete Glauber calculation of the differential cross-sections of ${}^{12}\mathrm{\text{C}}$–${}^{12}\mathrm{\text{C}}$ and halo nuclei on ${}^{12}\mathrm{\text{C}}$ scattering was performed using the previously proposed in Y. M. Shabelski and A. G. Shuvaev [Phys. Rev. C 104, 064607 (2021); Mod. Phys. Lett. A 37, 2250081 (2022)] method of generating function. The results are different as compared with the similar calculations in the optical model and the rigid target approximation. The halo nuclei radii extracted from the scattering data via the complete Glauber analysis come out to be larger than those obtained in the approximate approaches.

Elastic scattering of the two-neutron halo nucleus, ⁶He, on ¹²C target at 38.3 and 41.6 MeV/nucleon has been analyzed in the framework of the double-folding optical model. Real double-folded potentials based on the realistic density-dependent DDM3Y and JLM effective nucleon–nucleon interactions are generated using different forms of the nuclear matter density distribution of ⁶He. The imaginary optical potentials are taken in the conventional Woods–Saxon form. The bare (unnormalized) real folded potentials derived from the JLM interaction are more successful in reproducing the data at both energies than those derived from the DDM3Y interaction. The effect of contribution of the dynamic polarization potential is also studied. A semimicroscopic approximation is proposed to simulate this potential by introducing a repulsive real part extracted from the generated folded potential. Fits to data have been slightly improved by considering this approximation.

The halo structures in some light nuclei are investigated systemically with the nuclear asymptotic normalization coefficient (ANC) method and the relativistic mean-field (RMF) theory. Some important results about the halo structures in mirror nuclei are obtained, and some qualitative analyses are made to explore the role of Coulomb effects on the formation of proton halo nuclei.

Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π/2 (ρ→∞ and r is too small except 0) in the configuration space. The derived asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (nnα) wave function for ⁶He nucleus obtained by other authors on the basis of multicluster stochastic variational method using the two forms of the αN-potential. The ranges of r (or ρ) from the asymptotical regions are determined for which the agreement between the calculated wave function and the asymptotics formulae is reached. Information about the values of the three-body asymptotic normalization factors is extracted.

We have used a novel theoretical technique to calculate the resonance state of ¹¹Be using a two-body model (¹⁰Be+n). The effective two-body potential for the system has a shallow well followed by a low and very wide barrier causing numerical difficulties in the calculation of low-lying resonances. Using supersymmetric quantum mechanics (SSQM), one can construct an isospectral potential with a bound state in the continuum (BIC). This isospectral potential has a deep well and high barrier which can effectively trap the system giving rise to a BIC. Our calculated resonance energy of the state of ¹¹Be matches extremely well with the experimental value. Calculated width of the resonance also agrees within the computational error bars.

Total reaction cross-sections of the two neutron halo nuclei ¹¹Li and ²²C elastic scattering from ¹²C target at E = 30–1000 MeV/nucleon have been analyzed using the eikonal phase shift based, for the first time, on the semi-phenomenological nucleon density. The obtained results reasonably agree with those of previous theoretical calculations as well as the corresponding experimental data.

The general properties of exotic carbon systems, considered as a core with a two-neutron (n - n) halo, are described within a renormalized zero-range three-body model. In particular, it is addressed the cases with a core of ¹⁸C and ²⁰C. In such a three-body framework, ²⁰C has a bound subsystem (¹⁹C), whereas ²²C has a Borromean structure with all subsystems unbound. ²²C is also known as the heaviest carbon halo nucleus discovered. The spatial distributions of such weakly-bound three-body systems are studied in terms of a universal scaling function, which depends on the mass ratio of the particles, as well as on the nature of the subsystems.

The two-neutron halo nucleus ¹¹Li has been investigated in this work. Jacobi coordinates is used to describe the three-body system, using two configurations that are the T-configuration and Y-configuration. The calculations have been calculated based on a cluster model. The ¹¹Li nucleus is considered as three-body system core (⁹Li)+n+n. The core here has been considered as a deformed core. The calculations confirmed that the core has some deformation and has an oblate shape which in turn has effects on the structure of three-body system.

The vector analyzing power and differential cross-section for the elastic scattering of ⁸He nucleus from polarized protons at 71 MeV/nucleon have been analyzed in the framework of the optical model potentials. Microscopic single folding (SF) optical potentials (OP) have been constructed based upon two different effective nucleon–nucleon (NN) interactions, namely Jeukenne–Lejeune–Mahaux (JLM) and BDM3Y1 effective interactions. The effect of ⁸He nuclear structure has been tested through two different choices of the nuclear density distribution. It is concluded that the nucleus ⁸He may be considered as a thick skin exotic nucleus. In order to investigate the vector analyzing power data, besides the Thomas phenomenological representation, three different forms of the spin–orbit (SO) part of the OP have been considered. These forms are based directly or indirectly upon the density distribution of ⁸He nucleus. It is found that SO potentials of larger root mean square radii are able to successfully describe the vector analyzing power data more than those of shorter radii.

Folding potentials of the elastic scattering drip-line nuclei at various incident energies is one method to study nuclear matter density distributions and nuclear radii. The nuclei with density distributions consisting of a bulk (core) and an outer layer (halo), dilute and spatially extended are called the halo nuclei caused for the weak particle binding. Several halo nuclei are studied and many potential candidates are identified. All the cross-sections of the elastic scattering for the drip-line nuclei ¹¹Be and ⁶He, are calculated to understand the exotic properties of these nuclei starting from its structure, extended radius, nuclear size till the large total reaction cross-sections for these nuclei when it interact with a stable target ¹²C.

In the framework of the optical limit approximation (OLA), the reaction cross-section for halo nucleus — stable nucleus collision at intermediate energy, has been studied. The projectile nuclei are taken to be one-neutron halo (1NHP) and two-neutron halo (2NHP). The calculations are carried out for Gaussian–Gaussian (GG), Gaussian-Oscillator (GO), and Gaussian-2S (G2S) densities for each considered projectile. As a target, the stable nuclei in the range 4–28 of the mass number are used. An analytic expression of the phase shift function has been derived. The zero range approximation is considered in the calculations. Also, the in-medium effect is studied. The obtained results are analyzed and compared with the geometrical reaction cross-section and the available experimental data.

Few-body systems, such as cold atoms and halo nuclei, share universal features at low energies, which are insensitive to the underlying inter-particle interactions at short ranges. These low-energy properties can be investigated in the framework of effective field theory with two-body and three-body contact interactions. I review the effective-field-theory studies of universal physics in three-body systems, focusing on the application in cold atoms and halo nuclei.