Narrow Results

We present a brief history of the structure study of ¹⁶O as a typical example in the development of the cluster model theory over 50 years.

This presentation focuses on some of the recent developments in low-energy nuclear structure theory, with emphasis on applications of coupled-cluster theory. We report on results for ground and excited states in ⁴He and ¹⁶O, and about extensions of coupled-cluster theory to treat three-body forces.

The total antisymmetric wave functions of the different states of nuclei with A = 5 are calculated by using the basis of the unitary scheme model corresponding to numbers of quanta of excitations N = 1, 2, 3, 4, 5, 6, and 7. The residual interactions used in these calculations are the Gogny et al. potential, the Doma et al. Potential, and an effective interaction which has been used successfully for the nucleus ⁶Li. The energy matrices for nuclei with A = 5 are diagonalized in terms of the oscillator parameter ℏω, which is varied in order to obtain the best fit to the spectra of these nuclei. The binding energy, the root mean-square radius, and the magnetic dipole moment of ⁵He are also calculated. Some new levels for these nuclei are obtained. The role of the three-body forces is also investigated for the nucleus ⁵He.

Two types of cluster–cluster potentials are obtained for the lithium nuclei. The first is an attractive one and the second is a superposition of repulsive and attractive Gaussian forces. The ground-state wave functions of the lithium nuclei ⁶Li, ⁷Li, ⁸Li, and ⁹Li are expanded in terms of products of two wave functions: the first represents the set of A-4 nucleons and the second represents the set of the last four nucleons. In the construction of these wave functions, we have used the basis functions of the translation-invariant shell model. The expansion coefficients of the factorizations of these wave functions are products of four-particle orbital and spin-isospin fractional parentage coefficients. Two least-square formulas for the cluster–cluster potentials, which depend on the mass number A, are fitted for the lithium nuclei.

The nonrelativistic wave functions of ³H and ³He nuclei have been obtained on the basis of the experimentally measured charge form factors. The differential cross section of the elastic ³He-nucleus scattering has been calculated with the help of the wave function derived. This cross section agrees with the experimental data on the elastic scattering of ³He by ⁹⁰Zr, ¹²⁰Sn, and ²⁰⁸Pb nuclei at 130 and 217 MeV. The integrated cross sections of various processes of ³H and ³He interaction with heavy nuclei have also been calculated.

The giant dipole resonance (GDR) in N = 28 isotones (⁴⁸Ca, ⁵⁰Ti, ⁵²Cr, ⁵⁴Fe) is analyzed in the framework of the Skyrme random-phase-approximation (RPA). Three Skyrme forces, SkM*, SLy6 and SV-bas, are used. The effects beyond RPA are simulated by the double folding procedure. We show that dipole strength exhibits a large collective shift, which testifies to a strong impact of the residual interaction and signals on considerable anharmonic effects. In ⁵²Cr, a significant pairing impact is found. For exception of ⁵⁰Ti, an acceptable agreement with the experiment data is obtained, which justifies the ability of Skyrme forces to describe GDR in light nuclei.

We present a systematic description of the exotic features in the ground states of light nuclei from the stable valley to the drip lines. A study with the even and odd isotopes of Ne, Mg, Si, S and Ar has been performed using theoretical formalisms (i) Relativistic mean-field plus state-dependent BCS approach and (ii) Macroscopic–Microscopic (MM) approach using the triaxially deformed Nilsson–Strutinsky Method. The computed binding energies and one- and two-neutron separation energies using both the theories show magic character of $N=14,20,28$ and 40. The neutron and proton radii and the neutron densities show a well-developed neutron skin in the neutron-rich isotopes. The exotic phenomena such as weakly bound structures and the central density depletion characterized as bubble effect are explored. Our calculations for the single particle levels, density profiles and the charge form factors indicate bubble-like structures. Few new candidates of bubble nuclei are identified. Most of the nuclei in this region are found deformed with mostly prolate shape and few triaxial shapes while many nuclei exhibit the phenomenon of shape coexistence. Our results display a reasonable agreement between both the theories and the available experimental data.

The advent of technology widened the study of shell closure for nuclei lying far away from the stability line. The classic shell closures are observed to be valid for nuclei near the stability line. The light exotic nuclei exhibit unique behavior compared to those of stable ones. The objective of this work is to study the shell closure in light nuclei near the neutron drip-line to the proton drip-line region. The systematics of two nucleon separation energy difference ($\mathrm{\Delta }S$) between calculated and experimental data are taken as a tool to study the shell closure of light nuclei. Nucleon separation energy is determined using the liquid drop model (LDM) expression with modified asymmetry and pairing energy terms. The light mass numbered isotopes and isotones as a function of even neutron and even proton numbers were considered for this work. The shell structure predicted by $\mathrm{\Delta }S$ systematics is compared with the first excitation energy $E(2^{+})$. The modified LDM is successful in identifying the shell structure properties of light nuclei in exotic region. The study supports the emergence of new shell closure and the disappearance of existing classic shell closure for both neutron and proton numbers. The shell structure predicted by $\mathrm{\Delta }S$ systematics for isotopes (isotones) of magic nucleon number $Z(N)=8,20$ was in agreement with the results of $E(2^{+})$ analysis.

This presentation focuses on some of the recent developments in low-energy nuclear structure theory, with emphasis on applications of coupled-cluster theory. We report on results for ground and excited states in ⁴He and ¹⁶O, and about extensions of coupled-cluster theory to treat three-body forces.

This proceedings article summarizes recent work presented at Chiral Dynamics 2006 on nuclear lattice simulations with chiral effective field theory for light nuclei. This work has been done in collaboration with , Evgeny Epelbaum, Hermann Krebs, and Ulf-G. Meißner.

Experiments confirm a variety of cluster structures in many light nuclei. The observation of nuclear halos at drip-lines has accentuated the question of the degrees of freedom for bound and low-lying continuum states. In these cases the many-body dynamics of nuclear structure may be well approximated by few-body cluster models that often suggest conceptually simple approaches explaining successfully many features of light nuclei. Thus few-body cluster models have been successfully used for description of the nuclear structure of weakly bound halo nuclei and their emergent cluster degrees of freedom. They have attractive features supplying in a most transparent way the asymptotic behavior and continuum properties of weakly bound systems. Such models assume a separation in internal cluster (core) degrees of freedom and the relative motion of few-body constituents. Such separation is only an approximation, and low-lying states appear where the core cannot be considered as inert system and additional degrees of freedom connected to excited core states have to be taken into account. For fixed total angular momentum a coupling to excited core states having different spins involves additional partial waves into the consideration. This allows to account for some emergent (collective) core degrees of freedom and gives a more realistic description of nuclear properties. It is an analogue to increasing the number of shells within the framework of shell-model approaches. Some examples from recent nuclear structure exploration within few-body halo cluster models are presented.