Neutron and proton densities in nuclei

A simple expression for nuclear densities which incorporates the correct asymptotic and central behaviour, gives quite accurate values for rms radii and surface thicknesses. It also brings out some important nuclear properties, (i) global constancy of neutron densities, (ii) equality of half-density radiiR for neutrons and protons, (iii) near constancy ofRN ^?1/3, (iv) larger surface thickness and rms radius for neutrons (v) shell effects on charge density.     

Thick skin in neutron/proton-rich sodium isotopes

Nucleon (both neutron and proton) density distributions of the chain of sodium isotopes are calculated using a semi-phenomenological model of nuclear density which incorporates correctly the asymptotic behaviour and the behaviour near the centre. The experimental charge root-mean-square radii and the single neutron and proton separation energies, required as input, are used. The calculated interaction cross-sections using these densities in the Glauber model agree well with the experiment. The calculated neutron rms radii r _n and the nuclear skin thickness ( r _n - r _p) closely agree with the corresponding experimental values and also are consistent with the Relativistic Hartree-Bogoliubov (RHB) calculations. Received: 24 April 2001 / Accepted: 28 June 2001     

Skyrme-Hartree-Fock Description of the Nuclear Structure in Ca Isotopes (Ⅰ)Binding Energy and Shell Effects,Radii and Density Distributions

The ground state properties of Ca isotopes far from stability line were systematically studied using the Skyrme Hartree Fock model.The shell effects on the binding energy and two neutron separation energy are discussed.The isospin dependency of the unclear radii and nucleon density distributions and the shell effects on these properties are also studied.It is shown that the neutron magic number affests the width of nuclear surface and the nucleon density distributions beyond the nuclear surface.The change of proton rms radii R_rms with neutron number excess I=(N-Z)/A follows R_rms=3/5(1+αI+βI²)r_pZ^1/3.The effect of the centrifugal potential on the nuclear density in the outer trach of nuclear surface is clearly shown.     

Isospin and density waves in asymmetric nuclear matter

The excitation of small density oscillations (zero sound) and isospin oscillations (isospin sound) in cold asymmetric nuclear matter (in the ground state ?⁰_n> ?⁰_p, ?⁰ = ?⁰_n+?⁰_p = 0.17 nucleons/fm³) is investigated within the framework of the Landau theory of normal Fermi liquids. There is only one undamped mode of excitation, which consists predominantly of isospin oscillations, with some admixture of density oscillations. The phase velocity of this undamped wave depends very weakly on the neutron excess and is close to that of a pure isospin wave (isospin sound) in symmetric nuclear matter of the same density. At the neutron excess corresponding to that existing in heavy nuclei the amplitude of the density oscillations constitutes about 30 % of the amplitude of the neutron excess density oscillations. Calculation with a suitably parametrized charge dependent quasiparticle interaction in asymmetric nuclear matter shows that for (?⁰_n??⁰_p)/?⁰ > 0.63 both zero sound and isospin sound are strongly damped.     

Evidence for a proton halo in 27P through measurements of reaction cross-sections at intermediate energies

Measurements of reaction cross-sections ( σ_R's) for some proton-rich nuclei ( N = 11–15 isotones) on carbon target at intermediate energies have been performed on RIBLL of HIRFL. A larger enhancement of the σ_R for ²⁷P has been observed than for its neighboring nuclei. A large difference between the proton and neutron density distributions (proton halo) is necessary to explain the enhanced cross-section for ²⁷P within the framework of the Glauber model. Density distributions with HO-type core plus Yukawa-square tail and rms radii for ²⁷P have been deduced from the measured σ_R data for the first time, which conform the long tail in its densities as predicted by RMF calculations. Received: 23 May 2001 / Accepted: 7 November 2001     

Probable Decay Modes at Limits of Nuclear Stability of the Superheavy Nuclei

The modes of decay for the even–even isotopes of superheavy nuclei of Z = 118 and 120 with neutron number 160 ≤ N ≤ 204 are investigated in the framework of the axially deformed relativistic mean field model. The asymmetry parameter η and the relative neutron–proton asymmetry of the surface to the center (R _η ) are estimated from the ground state density distributions of the nucleus. We analyze the resulting asymmetry parameter η and the relative neutron–proton asymmetry R _η of the density play a crucial role in the mode(s) of decay and its half-life. Moreover, the excess neutron richness on the surface, facets a superheavy nucleus for β^? decays.     

Proton decays and neutron oscillations in the rishon model

We analyze proton decays and neutron oscillations in the rishon model. Proton decay is forbidden in lowest order of the compositeness scale Λ_H. In a one-generation rishon model, the leading proton decays violate B?L (e.g., p→νπ⁺). The lifetime is given by τ_p～Λ_H⁸/(U_R²m_p⁷), where U_R～M(W_R) is the mass scale of the right-handed W boson and m_p is the proton mass. For U_R～500 GeV, the obtained limit for the compositeness scale is Λ_H?10⁸ GeV. Neutron oscillations are also proportional to Λ_H⁸ and cannot be detected in the foreseeable future. All of these predictions may depend strongly on the understanding of higher generations of quarks and leptons within the model.     

Calculations of mass and moment of inertia for neutron stars

Masses and moments of inertia for slowly-rotating neutron stars are calculated from the Tolman-Oppenheimer-Volkoff equations and various equations of state for neutron-star matter. We have also obtained pressure and density as a function of the distance from the centre of the star. Generally, two different equations of state are applied for particle densities n > 0.47 fm^?3 and n < 0.47 fm^?3.The maximum mass is, in our calculations for all equations of state except for the unrealistic non-relativistic ideal Fermi gas, given by 1.50 M_⊙ < M < 1.82 M_⊙, which agrees very well with “experimental results”. Corresponding results for the maximum moment of inertia are 9.5 × 10⁴⁴ g · cm² < I < 1.58 × 10⁴⁵ g · cm², which also seem to agree very well with “experimental results”. The radius of the star corresponding to maximum mass and maximum moment of inertia is given by 8.2 km < R < 10.0 km, but a smaller central density ρ_c will give a larger radius.     

Large-pT protons from constituent diquark scattering

Recent data from the CERN ISR on the fractional proton yield in pp collisions are explained within the Stockholm diquark model. Describing the proton as a u(ud)₀ system, the observed high magnitude and fall-off _pT, θ and $\text{s}$ of the proton yield are natural consequences of constituent diquark elastic scattering. The _pT and θ dependence favour a value of around 10 GeV²/c² for the size parameter in the diquark form factor, corresponding to a diquark rms radius of around 0.2 fm. This is consistent with earlier results of the model applied to deep inelastic lepton-nucleon scattering and e⁺e^? annihilation.     

The harmonic oscillator energy level spacing for neutrons and protons in nuclei

Approximate expressions of?ω for neutrons and protons separately, as functions of the neutron numberN and the proton numberZ respectively, are derived. The dependence ?ω_n(?ω_p) on N(Z) is established using a rather recently proposed semi-phenomenological density distribution based on the separation energies of the last neutron or proton. The corresponding curves of?ω show “discontinuities in the slope” at the closed shells throughout the periodic table. The difference ?ω_n — {ie17-01} is also discussed.     

The size of the proton

The root-mean-square (rms) charge radius r _p of the proton has so far been known only with a surprisingly low precision of about 1% from both electron scattering and precision spectroscopy of hydrogen. We have recently determined r _p by means of laser spectroscopy of the Lamb shift in the exotic “muonic hydrogen” atom. Here, the muon, which is the 200 times heavier cousin of the electron, orbits the proton with a 200 times smaller Bohr radius. This enhances the sensitivity to the proton’s finite size tremendously. Our new value r _p?=?0.84184 (67) fm is ten times more precise than the generally accepted CODATA-value, but it differs by 5 standard deviations from it. A lively discussion about possible solutions to the “proton size puzzle” has started. Our measurement, together with precise measurements of the 1S–2S transition in regular hydrogen and deuterium, also yields improved values of the Rydberg constant, R _?∞??=?10,973,731.568160 (16) m^???1.     

Neutron skin effect of some Mo isotopes in pre-equilibrium reactions

The neutron skin effect has been investigated for even isotopes of molybdenum at 25.6 MeV ^{94 − 100}Mo(p, xn) reaction using the geometry-dependent hybrid model of pre-equilibrium nuclear reactions. Here the initial neutron/proton exciton numbers were calculated from the neutron/ proton densities obtained from an effective nucleon–nucleon interaction of the Skyrme type. Initial exciton numbers from different radii of even Mo isotopes were used to obtain the corresponding neutron emission spectra. In this investigation the calculated results are compared with the experimental data as also with each other. The results using central densities in the geometry-dependent hybrid model are in better agreement with the experimental data.     

Study of isotope shifts,isotone shifts and nuclear compressibility from the analysis of muonic x-ray transitions

Muonic x-ray transitions in various spherical nuclei in the region 13?Z?83 have been analysed and the isotope and isotone shifts in charge radiusR are investigated. AssumingR=r ₀ A ^1/3, the isotopic and isotonic behaviour of the parameterr ₀ (=RA ^?1/3) is also studied. The variation ofr ₀ with mass numberA reveals the variation of average nucleon density, which in turn sheds light on the compressibility of nuclear matter. The isotope and isotone shifts inR exhibit the shell effects in the vicinity of magic neutron and proton numbers: 20, 28, 50, 82 and 126. The results indicate that neutron-proton interaction is maximum at the beginning of a major neutron shell and decreases gradually as the shell gets filled up. The behaviour of parameterr ₀ clearly suggests that low-Z nuclei are highly compressible while high-Z nuclei are more or less incompressible. The parameterr ₀ too is observed to exhibit profound shell effects.     

Deuterium–tritium catalytic reaction in fast ignition: Optimum parameters approach

One of the main concerns about the current working on nuclear power reactors is the potential hazard of their radioactive waste. There is hope that this issue will be reduced in next generation nuclear fusion power reactors. Reactors will release nuclear energy through microexplosions that occur in a mixture of hydrogen isotopes of deuterium and tritium. However, there exist radiological hazards due to the accumulation of tritium in the blanket layer. A catalytic fusion reaction of DT _x mixture may stand between DD and an equimolar DT approach in which the fusion process continues with a small amount of tritium seed. In this paper, we investigate the possibility of DT_x reaction in the fast ignition (FI) scheme. The kinematic study of the main mechanism of the energy gain–loss term, which may disturb the ignition and burn process, was performed in FI and the optimum values of precompressed fuel and proton beam driver were derived. The recommended values of fuel parameters are: areal density ρ R ≥ 5g · cm^?2 and initial tritium fraction x ≤ 0.025. For the proton beam, the corresponding optimum interval values are proton average energy 3 ≤ E _p ≤ 10 MeV, pulse duration 5 ≤ t _p ≤ 15 ps and power 5 ≤ W _p ≤ 12 × 10²² (keV·cm³ · ps^?1). It was proved that under the above conditions, a fast ignition DT _x reaction stays in the catalytic regime.     

Nuclear matter distributions for 16,17,18O from a microscopic analysis of elastic proton scattering

An analysis of 65 MeV elastic proton scattering by ^16,17,18O has been made in terms of a reformulated optical model. Matter distributions for ¹⁷O and ¹⁸O have been obtained relative to ¹⁶O. The results for the rms matter radii are R₁₇?R₁₆ = 0.04±0.03 fm and R₁₈?R₁₆ = 0.35± 0.07 fm.     

Variational calculations of asymmetric nuclear matter

We report on variational calculations of the energy E(ρ, β) of asymmetric nuclear matter having ? = ?_n + ?_p = 0.05 to 0.35 fm^?3, and β = (?_n ? ?_p/g9 = 0 to 1. The nuclear h used in this work consists of a realistic two-nucleon interaction, called v₁₄, that fits the available nucleon-nucleon scattering data up to 425 MeV, and a phenomenological three nucleon interaction adjusted to reproduce the empirical properties of symmetric nuclear matter. The variational many-body theory of symmetric nuclear matter is extended to treat matter with neutron excess. Numerical and analytic studies of the β-dependence of various contributions to the nuclear matter energy show that at ? < 0.35 fm^?3 the β⁴ terms are very small, and that the interaction energy EI(ρ, β) defined as E(ρ, β) ? T_F(ρ, β), where T_F is the Fermi-gas energy, is well approximated by EI₀(?) + β²EI₂(ρ). The calculated symmetry energy at equilibrium density is 30 MeV and it increases from 15 to 38 MeV as ? increases from 0.05 to 0.35 fm^?3.     

Possibility of a phase transition to a pion condensate in neutron stars

We consider the possibility that a pion condensate may arise in an infinite nuclear medium as a consequence of the modification of the pion propagator due to isobar-hole and nucleon-hole excitations, This does not seem likely in a system with N = Z at densities of less than 0.17 fm^?3, but does seem likely to occur at the densities encountered in the interior of neutron stars. We estimate a necessary neutron density of ? 0.38 fm^?3 and a condensate energy density of ? ? 0.25 MeV fm^?3.     

Symmetry energy impact in simulations of core-collapse supernovae

In this work we study the effect of the symmetry energy on several properties of neutron stars. First, we discuss its effect on the density, proton fraction and pressure of the neutron star crust-core transition. We show that whereas the first two quantities present a clear correlation with the slope parameter L of the symmetry energy, no satisfactory correlation is seen between the transition pressure and L . However, a linear combination of the slope and curvature parameters at ρ = 0.1 fm^?3 is well correlated with the transition pressure. In the second part we analyze the effect of the symmetry energy on the pasta phase. It is shown that the size of the pasta clusters, number of nucleons and the cluster proton fraction depend on the density dependence of the symmetry energy: a small L gives rise to larger clusters. The influence of the equation of state at subsaturation densities on the extension of the inner crust of the neutron star is also discussed. Finally, the effect of the density dependence of the symmetry energy on the strangeness content of neutron stars is studied in the last part of the work. It is found that charged (neutral) hyperons appear at smaller (larger) densities for smaller values of the slope parameter L. A linear correlation between the radius and the strangeness content of a star with a fixed mass is also found.     

The effect of the initial exciton numbers on <Superscript>54,56</Superscript>Fe(<Emphasis Type="Italic">p,xp</Emphasis>) Pre-Equilibrium Reactions

In pre-equilibrium nuclear reactions, the geometry-dependent hybrid model is applied with the use of the neutron and proton densities to investigate the effect of initial exciton numbers on the nucleon emission spectra. The initial exciton numbers calculated with the theoretical neutron and proton densities have been obtained within the Skryme-Hartree-Fock method with SKM* and SLy4 forces on target nuclei in the ^54,56Fe(p, xp) reaction at 61.5-MeV incident proton energy by using a new calculationmethod of Tel et al. Also, the differences between the initial exciton numbers for protons and neutrons as a function of nuclear radius, focusing on systematic discrepancies correlated to differences in the proton and neutron densities have been investigated.     

Structure of 10C and 11C from elastic and inelastic scattering on a proton target

We measured elastic and inelastic scattering to the low-lying states of ¹⁰C and ¹¹C isotopes on a proton target with respective incident energies 45.3 and 40.6 A MeV. Data are analyzed with a microscopic complex potential. Elastic data are sensitive to the rms matter radius, which has been deduced for both isotopes. The moment of the neutron transition density was deduced for ¹⁰C from inelastic scattering.