Nuclear Matter Density Distributions Research Articles

Study of Matter Density Distributions, Elastic Electron Scattering Form factors and Root Mean Square Radii of 9C, 12N, 23Al, 11Be and 15C Exotic Nuclei

The ground state densities of neutron-rich (11Be,15C) and proton-rich (9C,12N,23Al) exotic nuclei are investigated using a two-body nucleon density distribution (2BNDD) with two frequency shells model (TFSM). The structure of the valence one-neutron of 11Be is in pure (1p1/2) and of 15C in pure (1d5/2) configuration, while the structure of valence one-proton configuration is in 9C,12N are to be in a pure (1p1/2) and 23Al in a pure (2s1/2) . For our studied nuclei, an efficient (2BNDD) operator for point nucleon system folded with two-body correlation operator's functions is used to investigate nuclear matter density distributions, elastic electron scattering form factors, and root-mean square (rms) radii. The effect of the strong tensor force (TC) in nucleon-nucleon forces is taken into account in the correlation. The wave functions of a single particle harmonic oscillator are used with two different oscillator size parameters, βc and βv, the former for core (inner) orbits and the latter for valence (halo) orbits. The measured matter density distributions of these nuclei clearly show the long tail results. The plane wave born approximation (PWBA) is used to investigate the elastic electron scattering form factors for these exotic nuclei.

Flow-plane decorrelations in heavy-ion collisions with multiple-plane cumulants

The azimuthal correlations between local flow planes at different (pseudo)rapidities ($\ensuremath{\eta}$) may reveal important details of the initial nuclear matter density distributions in heavy-ion collisions. Extensive experimental measurements of a factorization ratio (${r}_{2}$) and its derivative (${F}_{2}$) have shown evidence of the longitudinal flow-plane decorrelation. However, nonflow effects also affect this observable and prevent a quantitative understanding of the phenomenon. In this paper, to distinguish decorrelation and nonflow effects, we propose a new cumulant observable, ${T}_{2}$, which largely suppresses nonflow. The technique sensitivity to different initial-state scenarios and nonflow effects are tested with a simple Monte Carlo model, and in the end, the method is applied to events simulated by a multiphase transport model (AMPT) for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=200$ GeV. We also emphasize that a distinct decorrelation signal requires not only the right sign of an observable but also its proper dependence on the $\ensuremath{\eta}$ window of the reference flow plane to be consistent with the pertinent decorrelation picture.

Scission configuration in self-consistent calculations with neck constraints

The calculations of the potential energy surface are essential in the theoretical description of the fission process. In the constrained self-consistent approach, the smooth evolution of nuclear shape is described from the ground state until a very elongated one with a narrow neck. In all microscopic calculations, the rupture of the neck at scission is associated with a substantial change of nuclear matter density distribution and rapid energy decrease. In this paper, we show that there is no discontinuity of the potential energy surface at scission when multi-constrained calculations are applied with the neck constraint. An early rupture of the neck at lower quadrupole and octupole moments is discussed as competitive with the conventional fission path. We discuss the neck properties in the scission configuration. We find that the neck radius in the asymmetric fission mode cannot decrease below 2 fm, and the nuclear matter density cannot decrease below the saturation density. In the compact fission mode, nuclear density may go down to half of the saturation density before the rupture of the neck.

Matter Density Distributions, Root-mean Square Radii and Elastic Electron Scattering Form Factors of Some Exotic Nuclei (17B, 11Li, 8He)

The two-neutron halo-nuclei (17B, 11Li, 8He) was investigated using a two-body nucleon density distribution (2BNDD) with two frequency shell model (TFSM). The structure of valence two-neutron of 17B nucleus in a pure (1d5/2) state and in a pure (1p1/2) state for 11L and 8He nuclei. For our tested nucleus, an efficient (2BNDD's) operator for point nucleon system folded with two-body correlation operator's functions was used to investigate nuclear matter density distributions, root-mean square (rms) radii, and elastic electron scattering form factors. In the nucleon-nucleon forces the correlation took account of the effect for the strong tensor force (TC's). The wave functions of single particle harmonic oscillator are used with two different oscillator size parameters βc and βv, where the former is for the core (inner) orbits and the latter is for the valence (halo) orbits. The measured matter density distributions of these nuclei clearly showed long tail results. To investigate elastic electron scattering form factors the plane wave born approximation (PWBA) with two body nucleon density distribution (2BNDD's) was use.

Towards a systematic optical model potential for A = 8 projectiles

An optical model analysis of the available data for A = 8 ( $$^8$$ He, $$^8$$ Li and $$^8$$ B) projectiles on different targets with light, medium and heavy mass has been performed. A systematic potential set based on a Woods–Saxon Potential shape was obtained. This potential describes the elastic scattering angular distributions quite well. A more physical model within the framework of a semi-microscopic approach, where the nuclear matter density distributions of the $$^8$$ B, $$^8$$ Li and $$^8$$ He projectiles have been calculated by using a microscopic self-consistent relativistic mean field (RMF) theory, was also considered. The agreement of the calculated angular distributions with the data was reasonable. An improvement of the agreement could be achieved by changing the imaginary diffuseness parameter, which is a sensitive parameter in these calculations.

Nuclear matter distributions in the neutron-rich carbon isotopes 14−17C from intermediate-energy proton elastic scattering in inverse kinematics

The absolute differential cross sections for small-angle proton elastic scattering off the nuclei 12,14−17C have been measured in inverse kinematics at energies near 700 MeV/u at GSI Darmstadt. The hydrogen-filled ionization chamber IKAR served simultaneously as a gas target and a detector for the recoil protons. The projectile scattering angles were measured with multi-wire tracking detectors. The radial nuclear matter density distributions and the root-mean-square nuclear matter radii were deduced from the measured cross sections using the Glauber multiple-scattering theory. A possible neutron halo structure in 15C, 16C and 17C is discussed. The obtained data show evidence for a halo structure in the 15C nucleus.

Theoretical Study on Carbon Isotopes

This work is devoted to develop nuclear matter density distribution form for the heavy ions valid for the stable and halo nuclei. In this study we consider the neutron halo nuclei (15,17,19C) and (16,22C). The first group has a 1n-halo while the second has a 2n-halo. Based on the developed densities, the elastic scattering cross section data of C-isotopes on target of 12C, at incident energies 70.8, 78 and 106.9 MeV/N, have been analyzed within the energy density functional theory. A consistent structural study of the neutron drip–line 22 C nucleus is done.

Theoretical Study of Nuclear Density Distributions and Elastic Electron Scattering Form Factors of Some Proton Halo Nuclei (17Ne and 8B)

Theoretical investigation of proton halo-nucleus (8B and 17Ne) has revealed that the valence protons are to be in pure (1p1/2)1 orbit for 8B and (1d3/2)2 orbit for 17Ne. The nuclear matter density distributions, the elastic electron scattering form factors and (proton, charge, neutron and matter) root-mean square (rms) are studied for our tested nuclei, through an effective two-body density operator for point nucleon system folded with two-body full correlation operator's functions. The full correlation (FC's ) takes account of the effect for the strong short range repulsion (SRC's) and the strong tensor force (TC's) in the nucleon-nucleon forces. The effective two-body density operator is produced and used to derive an explicit form for ground state two-body nucleon density distributions (2BNDD's) applicable for proton – rich halo nuclei and Fortran 95 programs are utilized to obtain theoretical values of our calculation. The effect of the TC's and SRC's on the ground state also calculated. 2BNDD's obtained within the two- frequency shell model (TFSM) approach, the elastic charge scattering form factors F(q)'s of proton halo nuclei are studied through Plane Wave Born Approximation (PWBA) .

Theoretical Study of Nuclear Density Distributions and Elastic Electron Scattering form Factors for Some Halo Nuclei

The nuclear matter density distributions, elastic electron scattering charge formfactors and root-mean square (rms) proton, charge, neutron and matter radii arestudied for neutron-rich 6,8He and 19C nuclei and proton-rich 8B and 17Ne nuclei. Thelocal scale transformation (LST) are used to improve the performance radial wavefunction of harmonic-oscillator wave function in order to generate the long tailbehavior appeared in matter density distribution at high . A good agreement resultsare obtained for aforementioned quantities in the used model.

Puzzle of the folding potential on the nuclear halo reactions

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 11 Be and 6 He , 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 12 C .

Nuclear reactions of 19,20C on a liquid hydrogen target measured with the superconducting TOF spectrometer

Reaction cross sections with various kinds of breakup channels for neutron-rich carbon isotopes 18–20C and for 9Be impinging on a liquid hydrogen target were investigated at 40 MeV/nucleon. The nuclides of interest were produced via projectile fragmentation from a 63 MeV/nucleon 40Ar beam and were separated in flight at the RIKEN projectile fragment separator (RIPS). The combination of the large-acceptance superconducting TOF spectrometer, TOMBEE (TOF Mass analyzer for exotic BEam Experiment), with a liquid hydrogen target, CRYPTA (CRYogenic ProTon and Alpha target system), enables simultaneous measurements of several reaction channels: the reaction cross sections (σR), individual elemental fragmentation cross sections (σΔZ), charge-changing cross sections (σcc), neutron-removal cross sections (σ−xn), and charge-pickup cross sections (σΔZ+1) for 19,20C; σΔZ, σ−xn, and σΔZ+1 for 18C; and σR for 9Be. The present σR of 9Be on proton, σR=397±23 mb, measured in the inverse kinematics, was consistent with the previous measurements using proton beams at different laboratories. The σR of 19C and 20C on proton were determined to be σR=754±22 mb and σR=791±34 mb, respectively. Taking into account the beam energy and target dependence of σR, the present σR are found to be considerably enhanced compared with those measured at around 1 GeV/nucleon. The σΔZ+1 appears to increase with the mass number of the projectiles, and it significantly contributes to σR in the present energy range. The finite-range optical-limit and few-body Glauber model analyses were performed for σR to study the nuclear matter density distributions and to derive the relative strength of the s-wave components of the valence neutrons in 19C and 20C. A neutron halo structure of 19C is confirmed with an s-wave dominance of the valence neutron when the effect of the charge-pickup reaction is taken into account. The large σ−n of 19C and σ−2n of 20C also support the decoupled structures of 18C +n and 18C+2n, respectively. The σcc of 19C and 20C agree with each other within their experimental uncertainties, which might indicate a similar proton density distribution in 19C and 20C. The σΔZ decreases monotonically without the even–odd effect as the number of removed protons increases.

FOLDING MODEL ANALYSIS OF 6He + 12C ELASTIC SCATTERING

Elastic scattering of the two-neutron halo nucleus, 6 He , on 12 C 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 6 He . 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 determination of the Coulomb energy of a nuclear system at the scission point upon fission

The dependence of the Coulomb energy of deformed nuclei on the shape and the nuclear matter density distribution is considered. For an ellipsoidal shape of the nucleus and a homogeneous distribution of nuclear matter, the result was obtained in a simple analytical form convenient for further use. Separate attention was paid to the consideration of a Fermi-like distribution of nuclear matter using different shapes of the nucleus that reflect several different kinds of collective motions. After these considerations, the dependence of the Coulomb energy of the fission products at the scission point of binary fission reactions on configurations, shapes and nuclear matter distributions was investigated. Calculation of the dependence of the shape of the nuclei deformation parameters at the scission point from their total kinetic energies was made in detail. Finally, the influence of shell effects on the mass yield of fission products is discussed.

Nuclear structure studies on halo nuclei by direct reactions with radioactive beams

The investigation of direct reactions with exotic beams in inverse kinematics gives access to a wide field of nuclear structure studies in the region far off stability. The basic concept and the methods involved are briefly discussed. The present contribution will focus on the investigation of light neutron-rich halo nuclei. Such nuclei reveal a new type of nuclear structure, namely an extended neutron distribution surrounding a nuclear core. An overview on this phenomenon, and on the various methods which gave first evidence and qualitative confirmation of our present picture of halo nuclei, is given. To obtain more quantitative information on the radial shape of halo nuclei, elastic proton scattering on neutron-rich light nuclei at intermediate energies was recently investigated for the first time. This method is demonstrated to be an effective means for studying the nuclear matter distributions of such nuclei. The results on the nuclear matter radii of 6He and 8He, the deduced nuclear matter density distributions, and the significance of the data on the halo structure is discussed. The present data allow also a sensitive test of theoretical model calculations on the structure of neutron-rich helium isotopes. A few examples are presented. The investigation of few-nucleon transfer reactions in inverse kinematics may provide new and complementary information on nuclear structure, as well as astrophysical questions. The physics motivation and the experimental concept for such experiments, to be performed due to momentum matching reasons at low incident energies around 5–20 MeV/u at the new generation low energy radioactive beam facilities SPIRAL, PIAFE, etc., is briefly discussed.

Folding model analysis of α-particle elastic scattering with a semirealistic density-dependent effective interaction

Differential cross sections for the elastic scattering of α-particles from 40Ca, 46,48,50Ti, 58Ni, 90Zr and 208Pb at 140 MeV and from 58,60,62,64Ni at 172 MeV are analysed using a double-folding model with a semirealistic density-dependent effective interaction based on the M3Y interaction for the real potential and various phenomenological imaginary potentials. Very good fits with consistent parameters of the model have been obtained. The application of the folding model analyses of α-particle elastic scattering to the determination of the nuclear matter density distribution is critically examined.

Nuclear-structure dependence of the fusion cross section for heavy ions

The energy dependence of the fusion cross section and its maximum value are well predicted, for a wide range of nuclei and energies, by introducing information on the nuclear matter density distribution into a simple formula.

Tests of proton-nucleus elastic scattering theory

Many numerical applications of the multiple scattering theories of Glauber and Kerman, McManus and Thaler have in the last few years been applied to proton elastic scattering at intermediate energies for the purpose of studying nuclear matter density distributions. The desire to describe more complicated reactions microscopically is also in evidence. Thus, the need for tests of the accuracy of the multiple scattering theories and the various approximations employed in numerical analyses is of paramount importance. Several such tests are proposed and some recent results are reviewed.

Optical-model analysis of elastic scattering and polarization of 49.5 MeV protons on 148Sm

Abstract The measurement and optical-model analysis of polarized and unpolarized proton elastic scattering data from 148 Sm at 49.5 MeV are presented as a preliminary to coupled channels calculations for all the even Sm isotopes. The differential cross-section and polarization measurements extend over an angular range of 10° to 118° c.m. Analysis has been made in terms of the simple optical model and also the recent reformulation of Greenlees, Pyle and Tang using nuclear-matter density distributions and a realistic two-body force.