Study of the structure of light,unstable nuclei and the mechanism of elastic proton scattering

The review presents calculations of elastic p ⁶He-, p ⁸Li-, p ⁹Li- and p ⁹C scattering in the framework of the Glauber theory of multiple diffraction scattering at intermediate energies of 70 and 700 MeV/nucleon. The most significant result of the calculations is that we have utilized realistic three-body wave functions obtained within modern nuclear models. The relation is found between differential cross sections and intercluster potentials, where the nuclear wave functions are calculated. Conclusions are made concerning the types of potentials which describe most realistically the available experimental data. The method for calculation of three-body wave functions in α-n-n-, α-t-n-, ⁷Be-p-p-, α-t-2n-, and ⁷Li-n-n models is described with discussion of inter-cluster potentials and the quantum-number configurations taken into consideration. It is revealed how the wave functions and the nuclear electromagnetic characteristics calculated using these wave functions depend on the choice of intercluster potentials. The derivation of matrix elements (amplitudes) of pA scattering in the framework of the Glauber approach with three-body wave functions is presented by an example of ⁶He nucleus. Discussing the results of calculation of differential cross sections and the analyzing power (A _y ), we established how the calculated characteristics depend on a wave-function structure and dynamics of the process determined by a Glauber operator of multiple scattering. The calculated differential cross sections and analyzing powers are compared with available experimental data and calculations by other authors performed for different formalisms, which allows us to make justified conclusions.     

Structure of light neutron-rich nuclei through coulomb dissociation

Coulomb breakup of neutron-rich nuclei around mass A ∼ 20 has been studied experimentally using secondary beams (∼ 500–600 MeV/u) of unstable nuclei produced at GSI. The spectroscopic factor deduced for the neutron occupying s _1/2 level in ¹⁵C ground state is consistent with the earlier reported value. The data analysis for Coulomb breakup of ¹⁷C shows that most of the cross section yields the ¹⁶C core in its excited state. For ^17–22O, the low-lying E1 strength amounts up to about 12% of the energy weighted dipole sum rule strength depending on neutron excess. The cluster sum rule limit with ¹⁶O as a core is almost exhausted for ^17,18O, while for more neutron rich isotopes the strength with respect to that limit decreases.     

Microscopic analysis of the elastic scattering of 11Li neutron-rich nuclei on protons

Amicroscopic optical potential is used to calculate cross sections for elastic ¹¹Li +p scattering at the energies of 62, 68.4, and 75 MeV per nucleon, and the results are compared with available experimental data. The potential used does not involve free parameters, but the depths of its real and imaginary parts are renormalized. The known trend in the energy dependence of the volume integrals of the optical potential is taken into account in analyzing experimental data. The role of spin-orbit interaction is studied, and the total reaction cross sections that are proposed to be measured in future experiments are calculated.     

Polarization phenomena in elastic proton scattering on odd nuclei

Polarization observables of elastic proton scattering on ¹³C and ¹³N nuclei are calculated by using the theory of multiple diffractive scattering and the α-cluster model with dispersion. The ¹³C and ¹³N nuclei are considered as those that consist of a deformed core and an additional cluster (nucleon) occurring with the highest probability inside the core. It is shown that this assumption on the structure of these nuclei makes it possible to match the calculated and measured observables without resort to adjustable parameters.     

Current topics on light neutron-rich nuclei

Highlights of RIKEN radioactive beam experiments are reviewed. In particular the phenomena of giant soft dipole excitation of halo nuclei are closely discussed.     

Rotational bands in light neutron-rich nuclei

A simple cluster model is used to describe rotational bands in light neutron-rich nuclei. It is concluded that bands observed earlier had a cluster structure.     

Structure of neutron-rich s-d shell nuclei

States in neutron-rich s-d shell nuclei were populated in the reaction of a ¹⁴C beam at E _lab=22 MeV on a ¹⁴C target. Coincidences between γ rays and either other γ rays or light charged particles were measured. γ rays in coincidence with protons established levels at 66.8, 1730, 1823, and 2219 keV in ²⁷Na. The states are compared with calculations based on the s-d shell model and the cranked Nilsson-Strutinsky model. A number of levels in ²⁴Ne were observed in both α-γ and α-γ-γ coincidences and are compared with shell-model calculations.     

A nonlocal optical potential with a Gaussian nonlocality for proton elastic scattering off light 1p-shell nuclei

The European Physical Journal A - Six cylindrical lead bismuth eutectic (LBE) targets having fixed diameter of 6 mm and varying lengths of 8–50 mm were irradiated with a 1.4 GeV proton beam...     

Exotic cluster structure in light neutron-rich nuclei

The cluster structure of C isotopes is investigated using a microscopic α+α+α+n+n… model based on the molecular orbit (MO) model. The stability of the linear chain of 3α with respect to the breathing mode and the bending mode for various neutron configurations is investigated. The combination of the valence neutrons in the π- and σ-orbits is promising to stabilize for these modes, and the excited states of ¹⁶C with the (3/2 _π ^- )²(1/2 _σ ^- )² configuration for the four valence neutrons are one of the most promising candidates for such structure. Furthermore, the equilateral-triangular shape of 3α surrounded by valence neutrons is suggested for ¹⁴C. The 3^-, 4^-, and 5^- members of this rotational band appear around the ¹⁰Be+α threshold, and these calculated states correspond to the experimentally observed 3^- state (9.80 MeV) and 4^- state (11.67 MeV). A positive-parity rotational band (0⁺, 2⁺, 4⁺) also arises around this threshold energy, and these results suggest that the picture of inversion doublet structure works also in neutron-rich nuclei.     

Haloes and clustering in light, neutron-rich nuclei

Clustering is a relatively widespread phenomenom which takes on many guises across the nuclear landscape. Selected topics concerning the study of halo systems and clustering in light, neutron-rich nuclei are discussed here through illustrative examples taken from the Be isotopic chain. The production and detection of multineutron clusters is also briefly presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: orr@caelav.in2p3.fr     

Microscopic study on proton elastic scattering of light exotic nuclei at energies below than 100 MeV/nucleon

The proton elastic scattering data on some light exotic nuclei, namely, ^{6, 8}He, ^{9, 11}Li, and ^{10, 11, 12}Be, at energies below than 100MeV/nucleon are analyzed using the single folding optical model. The real, imaginary, and spin-orbit parts of the optical potential (OP) are constructed only from the folded potentials and their derivatives using M3Y effective nucleon-nucleon interaction. These OP parts, their renormalization factors and their volume integrals are studied. The surface and spin-orbit potentials are important to fit the experimental data. Three model densities for halo nuclei are used and the sensitivity of the cross-sections to these densities is tested. The imaginary OP within high-energy approximation is used and compared with the single folding OP. This OP with few and limited fitting parameters, which have systematic behavior with incident energy, successfully describes the proton elastic scattering data with exotic nuclei.     

Coulomb breakup of neutron-rich isotopes of light nuclei

The effects of higher order multipole transitions, in particular, E2 and E1–E2 interference, in the Coulomb dissociation of neutron-rich nuclei ¹¹Be, ¹⁴B, ¹⁵C, and ¹⁹C on Pb targets at energies of 72, 86, 550, and 77 A MeV, respectively, within the framework of the eikonal-approximation approach are studied. The main steps involved in the derivation of the explicit expressions corresponding to dipole, quadrupole, and dipole-quadrupole-interference terms are outlined. The calculations reveal that the contribution of E2 transitions to the total cross section is finite but small, while that ofE1–E2 interference is nil.Nevertheless, the E1–E2 interference term introduces small distortions in the peak of the relative-energy spectrum. The calculated results are compared with the corresponding data and the comparison favors a value of 0.530 MeV as the ground-state binding energy of ¹⁹C. The text was submitted by the authors in English.     

Nuclear-matter distributions of halo nuclei from elastic proton scattering in inverse kinematics

Proton-nucleus elastic scattering at intermediate energies, a well-established method for probing nuclear-matter density distributions of stable nuclei, was applied for the first time to exotic nuclei. This method is demonstrated to be an effective means for obtaining accurate and detailed information on the size and radial shape of halo nuclei. Absolute differential cross-sections for small-angle scattering were measured at energies near 700 MeV/u for the neutron-rich helium isotopes ⁶He and ⁸He, and more recently for the lithium isotopes ⁶Li, ⁸Li, ⁹Li and ¹¹Li, using He and Li beams provided by the fragment separator FRS at GSI Darmstadt. Experiments were performed in inverse kinematics using the hydrogen-filled ionization chamber IKAR which served simultaneously as target and recoil-proton detector. For deducing nuclear-matter distributions, differential cross-sections calculated with the aid of the Glauber multiple-scattering theory, using various parametrizations for the nucleon density distributions as input, were fitted to the experimental cross-sections. The results on nuclear-matter radii and matter distributions are presented, and the significance of the data for a halo structure is discussed. Nuclear-matter distributions obtained for ⁶He and ⁸He conform with the concept that both nuclei compose of α-particle like cores and significant neutron halos. The matter distribution in ¹¹Li exhibits, as expected from previous reaction cross-section studies with nuclear targets, the by far most extended halo component of all nuclei being investigated. In addition the present data allow a quantitative comparison of the structure of the He and Li isobares of either the mass number A = 6 or A = 8. The measured differential cross-sections have also been used for probing density distributions as predicted from various microscopic calculations. A few examples are presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: p.egelhof@gsi.de     

Fourier analysis of elastic light scattering spectrum of epithelial cell nuclei

<正>A new method for simultaneously determining the size and refractive index of epithelial cell nuclei is presented.The function of the modified elastic light scattering spectrum is regarded as a function of wave number factor,Q=2λ~(-1)sin(θ/2).The modified spectrum has a constant oscillation period with its frequency proportional to the average diameter of cell nuclei.To the same average diameter,the different relative refractive indexes of epithelial cell nuclei only induce the horizontal shift of the spectra.Both the oscillation frequency and the horizontal shift are quantified by the fast Fourier transform on the modified spectra.The average diameter can be figured out through the peak frequency divided by the value of the refractive index of the surrounding medium.The phase angle of the peak frequency has an approximate linear relationship with the relative refractive index of epithelial cell nuclei.     

Coexistence of different cluster configurations in light neutron-rich nuclei

On the basis of the algebraic version of the resonating-group method (RGM) and within the framework of the discrete representation in the Fock-Bargmann space, a microscopic theory of nuclear reactions with due regard for a coexistence of different cluster configurations in a compound nucleus is realized. Fundamental tenets of the algebraic version of the RGM are stated both for a single binary cluster configuration and for a compound system, where several cluster configurations coexist. Several examples of norm kernels, their eigenvalues, phase shifts, and effective cross sections are given for a number of binary cluster systems. The text was submitted by the authors in English.     

High-energy proton scattering on nuclei

We have studied high-energy proton scattering on Be, C, Cu and Pb targets using a single-arm spectrometer. The projectile momenta were 19 and 24 GeV/c, the square of the four-momentum transfer varied from t = 0.1 to t = 4.4 GeV². We have recorded momentum distributions of scattered protons in the high-momentum range. An application of multiple-scattering theory yielded agreement of calculation and experimental results to within a ± 30% uncertainty of the former.     

Isospin dependence of kinetic energies in light neutron-rich nuclei

Energy spectra andelectric dipole transitions ofN=7 isotones are studied by shell model calculations with isospin dependent kinetic energies for s-d shell orbits. The ground states of¹⁰Li and⁹He are predicted. Electric dipole transitions in¹³C and¹¹Be are studied by using the realistic single-particle wave functions in Woods-Saxon potential.JSPS Fellow for Japanese Junior Scientists.     

Investigating the neutron and proton density distributions in extremely neutron-rich nuclei

Manifestations of the neutron halo in extremely neutron-rich nuclei are investigated by the Hartree-Fock method using the Skyrme forces (SkM*, Ska, Sly4, SkI2) with allowance for axial deformation. The investigated nuclei, which lie beyond the theoretical neutron drip line (NDL), form peninsulas of nuclei stable with respect to one-neutron emission and belong to chains of isotones with the neutron number N = 32, 58, 82, 126, 184, and 258.     

Multichannel nuclear reactions involving light neutron-rich nuclei: Microscopic approach

The influence of the Pauli exclusion principle on the relative motion of light neutron-rich nuclei in their collision is investigated within the microscopicmethod using as an example ¹¹Be + n and ¹⁰Be + ² n nuclear reactions, as well as ³ n + n and ² n + ² n reactions. Antisymmetrization effects related to the kinetic and potential energy of the relative motion of colliding nuclei are analyzed. The influence of the Pauli exclusion principle on the kinetic energy of the relative motion of the ¹¹Be nucleus and a neutron is shown to result in their attraction. The same phenomenon is observed for the case of the ³ n + n cluster system. The strength of such attraction is high enough to ensure the existence of a bound state in the ¹²Be nucleus and a low-energy resonance in the tetraneutron. The conclusion is drawn that, for a resonance state in the ⁴ n system to exist, the value of the oscillator length must be large enough. It is shown also that increasing the oscillator length results in depression of the cluster-cluster potential. The text was submitted by the authors in English.