Nuclear Density Distribution Research Articles

Sensitivity of reaction cross sections to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus--nucleus reaction cross sections $\sigma_R$ to the nuclear matter distributions in exotic halo nuclei, we have calculated the values of $\sigma_R$ for scattering of $^6$He, $^{11}$Li, and $^{19}$C nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon. The calculations were performed in the "rigid target" approximation to the Glauber theory, different shapes of the nuclear density distributions in $^6$He, $^{11}$Li, and $^{19}$C being assumed.

Theoretical Exploration of the Isotopic Effect on Molecular High-Order Harmonic Generation

ABSTRACT The isotopic effect on the generation of the molecular high-order harmonics is studied by numerically solving the one-dimensional time-dependent Schrödinger equation when the model hydrogen molecule ions/hydrogen deuterium molecule ions are exposed to an intense laser pulse. To explain the effect more clearly, not only the ionization probabilities but also the electron–nuclear probability density distributions and time-frequency profiles are calculated. The results show that more intense harmonics are generated in the asymmetric diatomic molecule ions/hydrogen deuterium molecule ions than those of hydrogen molecule ions. Moreover, the interference minimum in the harmonic spectra is investigated by adjusting the laser intensity and the initial vibrational state. It is shown that the interference minimum is sensitive to the laser intensity and the initial vibrational level for hydrogen molecule ions; in contrast, it is only dependent on the initial vibrational level for hydrogen deuterium molecule ions.

Diffusion Path and Conduction Mechanism of Protons in Hydroxyapatite

Calcium hydroxyapatite (HAp, Ca10(PO4)6(OH)2) is the principal inorganic component of bone and teeth, one of the most important bioceramics, and a proton (H+) conductor with potential for energy conversion devices. The proton diffusion pathway in the HAp lattice is a key to understand the proton conduction mechanism and chemical reaction. Previous neutron-diffraction studies of HAp visualized the short-range proton diffusion pathway. In this work, we report the successful visualization of the long-range proton diffusion pathway in stoichiometric HAp at 923, 673, and 298 K through a combined technique of high-temperature neutron diffraction and bond valence method. We have visualized (1) one-dimensional proton diffusional pathways along the c-axis in the hexagonal channel and (2) two-dimensional proton migration pathway network on the ab-planes at z = 0 and 1/2. The proton diffusion and reorientation of hydroxide ions (OH–) are a complex sinusoidal process in the hexagonal channel along the c-axis, which is consistent with the anisotropic nuclear-density distribution of proton obtained by the neutron diffraction and maximum-entropy method.

An investigation of p+8He elastic scattering

The vector analyzing power and differential cross-section for the elastic scattering of 8 He 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 8 He nuclear structure has been tested through two different choices of the nuclear density distribution. It is concluded that the nucleus 8 He 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 8 He 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.

Effects of In-Medium Nucleon-Nucleon Cross Section and Nuclear Density Distribution on the Proton-Nucleus Total Reaction Cross Section

We present the proton-total reaction cross sections σR by comparing the experimental data with the Glauber model calculation using four sets of nucleon-nucleon cross sections used in literature (free nucleon-nucleon cross sections (NNCS), phenomenological NNCS, Bruckner-type NNCS and Pauli NNCS) and different nuclear densities for symmetric and asymmetric nuclei. For light symmetric target nuclei, the experimental σR data are well reproduced by the former three NNCS with the ground state density distributions of relativistic mean-field theory. On the other hand, for asymmetry heavier target nuclei, the calculations of the σR data depend significantly on the nuclear density distribution at large radius in the low energy region. The experimental σR of these nuclei are well reproduced by the empirical 3 pF density distribution and the in-medium NNCS. The neutron surface distributions are also discussed based on the 3 pF nuclear charge distributions.

Protonic conduction, crystal and electronic structures of La0.9Ba1.1Ga0.95Mg0.05O4−δ

Abstract We synthesize La 0.9 Ba 1.1 Ga 0.95 Mg 0.05 O 4 − δ and then investigate electrical conduction properties, crystal structure, and nuclear and electron density distributions. From conductivity measurements, it is demonstrated that this sample exhibits higher conductivity than La 0.9 Ba 1.1 GaO 4 − δ which is well-known as a protonic conductor. In addition, protonic conduction in La 0.9 Ba 1.1 Ga 0.95 Mg 0.05 O 4 − δ is confirmed by an H/D isotope effect on the conductivity. In order to clarify proton site in the specimen, we measure neutron diffraction and then perform the Rietveld and maximum entropy method analyses. As a result, it is indicated that protons coordinate oxygens at O3 site and form hydrogen bonds. It is also found that electronic states around oxygens are affected by the Ba and Mg substitutions.

Study of Different Forms of Density Distributions in Proton–Nucleus Total Reaction Cross Section and the Effect of Phase in NN Amplitude

Proton total-reaction cross-section (σR), measurements for about five nuclei in the range 12C to 208Pb at beam energies spanning 40–800 MeV have been analyzed in a systematic way by using the optical limit approximation of the Coulomb-modified Glauber multiple scattering theory. Two different phenomenological nuclear density distributions of the target nucleus in addition to the realistic one have been used in the present analysis. By applying the energy dependence in the slope parameter of nucleon–nucleon (NN) scattering amplitude, it is found that in general, the predictions of σ R with the phenomenological Gambhir and Patil density distribution agree fairly well with the experimental data. The inclusion of phase in the NN amplitude improves the theoretical results. Our analysis shows that the calculated total reaction cross sections closely reproduce the measured data over the whole range of energy considered in this work. To validate our analyses, we have also obtained a fairly good representation of elastic p-nucleus differential scattering cross section data. The effect of a Coulomb energy shift in the proton beam has also been studied.

Nuclear and charge density distributions in ferroelectric PbTiO3: maximum entropy method analysis of neutron and X-ray diffraction data

We conducted in-situ high-temperature neutron and X-ray diffraction studies on tetragonal PbTiO3. Using a combination of Rietveld analysis and Maximum Entropy Method, the nuclear and charge density distributions were determined as a function of temperature up to 460 °C. The ionic states obtained from charge density distributions reveal that the covalency of Pb–O2 bonds gradually weakens with increasing temperature. The spontaneous polarizations calculated from the contributions of ionic state, ionic displacement, and nuclear polarization, are in good agreement with the experimental measurements. This method provides an effective approach to determine spontaneous polarizations in multiferroics with high-current leakage and low resistance.

Temperature of projectile like fragments in heavy ion collisions

A model in which a projectile like fragment can be simply regarded as a remnant after removal of some part of the projectile leads to an excited fragment. This excitation energy can be calculated with a Hamiltonian that gives correct nuclear matter binding, compressibility and density distribution in finite nuclei. In heavy ion collisions the model produces a dependence of excitation energy on impact parameter which appears to be correct but the magnitude of the excitation energy falls short. It is argued that dynamic effects left out in the model will increase this magnitude. The model can be directly extended to include dynamics but at the expense of increased computation. For many calculations for observables, a temperature is an easier tool to use rather than an excitation energy. Hence temperature dependences on impact parameter in heavy ion collisions are displayed.

Analysis of elastic scattering of pi-mesons by nuclei within the microscopic optical potential

Cross sections of inelastic scattering of π-mesons from Si, Ni, and Pb nuclei at energy T lab = 291 MeV are calculated using the distorted wave approximation. The microscopic direct and transition optical potentials are determined by specifying the pion-nucleon scattering amplitude and the nuclear density distribution, where we use the in-medium πN amplitude parameters obtained earlier by analyzing the elastic scattering data for the same nuclei. The cross sections are calculated on the basis of the relativistic wave equation. The deformation parameters of the nuclei are obtained by comparing inelastic scattering cross sections with the appropriate experimental data.

Crystal Structure and Oxide-Ion Diffusion of Nanocrystalline, Compositionally Homogeneous Ceria–Zirconia Ce0.5Zr0.5O2 up to 1176 K

The crystal structure, phase stability, and oxide-ion diffusion of nanocrystalline ceria–zirconia materials are unresolved important issues, in particular at high temperatures, where the ceria–zirconia catalysts work efficiently. Here, we report a high-temperature neutron diffraction study of nanocrystalline [10.1(7) nm], compositionally homogeneous, tetragonal Ce0.5Zr0.5O2. Contrary to the previous work, we have observed no tetragonal-to-cubic phase transition in the nanocrystalline Ce0.5Zr0.5O2 up to 1176 K. The axial ratio c/aF and oxygen displacement along the c-axis from the fluorite regular 8c 1/4,1/4,1/4 position of the nanocrystalline Ce0.5Zr0.5O2 are almost independent of temperature. It was found that the c/aF ratio and oxygen displacement in nanocrystalline Ce0.5Zr0.5O2 are smaller than those of the bulk sample. It was shown that the refined atomic displacement parameter and spatial (maximum entropy method nuclear density) distribution of oxygen atom in nanocrystalline Ce0.5Zr0.5O2 are larger than those in nanocrystalline CeO2, which are factors of the high bulk oxygen diffusivity and catalytic activity in nanocrystalline Ce0.5Zr0.5O2. Possible diffusion pathways of oxide ions along the fluorite ⟨100⟩ and ⟨110⟩ directions were visualized in the spatial distribution of bond valence sums calculated using the present refined crystal structure of nanocrystalline Ce0.5Zr0.5O2 at 1023 K. The diffusion path is not straight but curved and forms a three-dimensional network.

Sensitivity of cross sections for elastic nucleus-nucleus scattering to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus-nucleus scattering to the nuclear matter distributions of exotic halo nuclei, we have calculated differential cross sections for elastic scattering of the $^6$He and $^{11}$Li nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon with different assumed nuclear density distributions in $^6$He and $^{11}$Li.

Role of Ga3+ and Cu2+ in the High Interstitial Oxide-Ion Diffusivity of Pr2NiO4-Based Oxides: Design Concept of Interstitial Ion Conductors through the Higher-Valence d10 Dopant and Jahn–Teller Effect

We have investigated the crystal structure, nuclear- and electron-density distributions, electronic structure, and oxygen permeation rate of three K2NiF4-type oxides of Pr2(Ni0.75Cu0.25)0.95Ga0.05O4+δ, Pr2Ni0.75Cu0.25O4+δ, and Sr2Ti0.9Co0.1O4–e, in order to study the role of d10 Ga3+, Jahn–Teller Cu2+, and interstitial oxygen O3 in the high oxygen diffusivity of Pr2(Ni0.75Cu0.25)0.95Ga0.05O4+δ. The composition Pr2(Ni0.75Cu0.25)0.95Ga0.05O4+δ has a larger amount of interstitial oxygen O3 atoms (δ = 0.31 at room temperature (RT)) compared with Pr2Ni0.75Cu0.25O4+δ (δ = 0.19 at RT) and the oxygen deficient Sr2Ti0.9Co0.1O4–e (e = 0.02 at RT). The interstitial O3 atom is stabilized by (1) the substitution of (Ni,Cu)2+ by higher valence Ga3+, (2) static atomic displacements of the apical O2 oxygen, and (3) local relaxation near d10 Ga3+. Nuclear-density distributions of Pr2(Ni0.75Cu0.25)0.95Ga0.05O4+δ and Pr2Ni0.75Cu0.25O4+δ at high temperatures have visualized the −O2–O3–O2– diffusional pathway of oxide ions, w...

STRUCTURE AND REACTIONS OF NEUTRON-RICH OXYGEN ISOTOPES

The structure of 16-26 O is investigated within the relativistic mean field (RMF) as well as high-energy nuclear collisions. The reaction cross-sections of 16-24 O +12 C around 1 GeV are calculated within the multiple scattering theory, where the multiple integrals are evaluated by Monte Carlo method as well as by the optical limit approximation of the Glauber model. In-medium effects are investigated within the optical limit, where it is found to be important in order to get reliable information about nuclear radii and density distributions. The reaction cross-sections indicate to a halo structure for 23 O . This neutron halo is also found in the rms matter radii and nuclear densities especially when Fermi shape is used in the optical limit, including in-medium effects, in extracting the parameters of the density distributions from the experimental reaction cross-sections.

Glauber-model analysis of total reaction cross sections for Ne, Mg, Si, and S isotopes with Skyrme-Hartree-Fock densities

A systematic analysis is made on the total reaction cross sections for Ne, Mg, Si, and S isotopes. The high-energy nucleus-nucleus collision is described based on the Glauber model. Using the Skyrme-Hartree-Fock method in the three-dimensional grid-space representation, we determine the nuclear density distribution for a wide range of nuclei self-consistently without assuming any spatial symmetry. The calculated total reaction cross sections consistently agree with the recent cross section data on Ne$+^{12}$C collision at 240$A$\,MeV, which makes it possible to discuss the radius and deformation of the isotopes. The total reaction cross sections for Mg$+^{12}$C, Si$+^{12}$C and S$+^{12}$C cases are predicted for future measurements. We also find that the high-energy cross section data for O, Ne, and Mg isotopes on a $^{12}$C target at around 1000\,$A$MeV can not be reproduced consistently with the corresponding data at 240\,$A$MeV.

Structure and nuclear density distribution in the cheralite—CaTh(PO4)2: studies of its behaviour under high pressure (36 GPa)

The crystal structure of the cheralite—CaTh(PO4)2—has been revisited by neutron diffraction and its behaviour under high pressure investigated by X-ray diffraction up to 36 GPa. The neutron diffraction data at ambient pressure gave a more accurate determination of the Ca/Th cation position than previous XRD data, taking advantage that the neutron scattering lengths of calcium and thorium are of same order of magnitude. The nuclear density distribution was also determined using the maximum entropy method (MEM) confirming that the two cations are not located at the same position in the unit cell but are slightly displaced from one another along a specific direction in order to minimize the electrostatic repulsion with the surrounding phosphorus atoms. At high pressure, the compound did not show any phase transition or amorphization. From the evolution of the unit-cell volume as a function of the pressure, the zero-pressure bulk modulus B0 and its pressure derivative B0 ′ have been determined by fitting the experimental compressibility curve to the Birch–Murnaghan equation of state. The results are B0 = 140(2) GPa and B 0 ′ = 4.4(4) GPa.

Theoretical study of the central depression of nuclear charge density distribution by electron scattering

The charge form factors of elastic electron scattering for isotones with N = 20 and N = 28 are calculated using the phase-shift analysis method, with corresponding charge density distributions from relativistic mean-field theory. The results show that there are sharp variations at the inner parts of charge distributions with the proton number decreasing. The corresponding charge form factors are divided into two groups because of the unique properties of the s-states wave functions, though the proton numbers change uniformly in two isotonic chains. Meanwhile, the shift regularities of the minima are also discussed, and we give a clear relation between the minima of the charge form factors and the corresponding charge radii. This relation is caused by the diffraction effect of the electron. Under this conclusion, we calculate the charge density distributions and the charge form factors of the A = 44 nuclei chain. The results are also useful for studying the central depression in light exotic nuclei.

Experimental visualization of lithium conduction pathways in garnet-type Li7La3Zr2O12

The evolution of the Li-ion displacements in the 3D interstitial pathways of the cubic garnet-type Li(7)La(3)Zr(2)O(12), cubic Li(7)La(3)Zr(2)O(12), was investigated with high-temperature neutron diffraction (HTND) from RT to 600 °C; the maximum-entropy method (MEM) was applied to estimate the Li nuclear-density distribution. Temperature-driven Li displacements were observed; the displacements indicate that the conduction pathways in the garnet framework are restricted to diffusion through the tetrahedral sites of the interstitial space.

Experimental Visualization of Chemical Bonding and Structural Disorder in Hydroxyapatite through Charge and Nuclear-Density Analysis

Calcium hydroxyapatite (HAp, Ca10(PO4)6(OH)2) is the principal inorganic component of bone and teeth, bioactive material, and proton (H+) conductor. However, the chemical bonding and structural disorder of HAp are unclear. Here we report precise charge- and nuclear-density distributions of HAp at 298 and 673 K. The present results clearly demonstrate the covalent P–O and O–H bonds, more ionic Ca–O bonds, and the charge transfers from P to O atoms and from H to O atoms in HAp. This work shows that the hexagonal–monoclinic phase transition of HAp is accompanied by the occupational and orientational ordering of OH– ions, the tilting of the PO4 tetrahedron, and the Ca displacements. Diffusion paths of proton are visualized along the c-axis in hexagonal HAp. We anticipate that the visualization of chemical bonding and structural disorder of HAp will contribute greatly to our understanding of biominerals, reactions, biological organisms, and the diffusion process in HAp-based proton conductors.

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.