Measurement of interaction cross sections using isotope beams of Be and B and isospin dependence of the nuclear radii

Interaction radii for ^11,12,14Be and ^{8,12,13,14,15}B have been determined by the measurement of interaction cross sections at 790 MeV/nucleon. Effective root-mean-square (RMS) radii of nucleon distribution of these nuclei have been deduced using a Glauber-model calculation. Isospin dependence of nuclear radii are presented for isobars of mass numbers from 6 to 12, and compared with theoretical predictions by the droplet model and by a Hartree-Fock (HF) model. The HF model with the Skyrme-III potential, which includes a strong density-dependent force, reproduce the observed isospin dependence.     

Nuclear compression moduli and density-dependent forces

Density-dependent zero-range forces of the form of the modified delta interaction (MDI) are generalized (MDI3, MDI4) in order to yield reasonable values of the compression modulus in nuclear matter (K_N = 200 MeV). This low value can be fitted by introducing two terms with different density dependence in the force. The four free parameters of MDI3 are adjusted to reproduce the nuclear matter values of the binding energy, density and compression modulus, and to fulfil the condition that the total energy of ¹⁶O in harmonic oscillator wave functions has a minimum at the oscillator length b = 1.75 fm, corresponding to the correct rms radius. MDI4 contains in addition a two-body spin-orbit interaction. The five parameters of MDI4 are fitted to the above three nuclear matter data and by requiring that Hartree-Fock (HF) calculations in ²⁰⁸Pb yield the experimental charge rms radius and reasonable values of certain single-particle spin-orbit splittings. The quality of MDI4 is checked by comparing calculated rms radii, binding energies, and elastic electron scattering cross sections with available experimental data for doubly closed shell nuclei. As a test the energy levels and the nuclear monopole polarization of muonic ²⁰⁸Pb are calculated self-consistently yielding impressive agreement with experiment.     

Thermal neutron scattering parameters for light nuclei (A=12 to 27)

Neutron scattering lengths and free scattering cross sections were measured for isolated isotopes and natural elements in the mass region fromA=12 toA=27. By means of the Christiansen filter technique values for the coherent scattering lengths were obtained for the bound atoms of^12C,^13C,^14N,^15N,^16O,^17O,^18O, Mg and¹⁹F. Transmission experiments with neutrons of 0.51 meV, 1.26 eV and 5.19 eV yielded data for the free scattering cross sections of^19F,²³Na, Mg and¹⁹F. From all these results and with previous data the fundamental spin state scattering lengths for the concerned light nuclei have been deduced. The comparison of these values with resonance parameters has shown that the resonance data are complete. Therefore, values for the potential scattering radii could be obtained and discussed.     

Three-body structure of <Emphasis Type="Italic">A</Emphasis> = 9 isobars (Be,Li, and C) and elastic proton scattering

Density profiles and static features (radii, magnetic moments, and quadrupole moments) are calculated with the wave functions found for A = 9 isobars on the basis of the α + α + n three-body model for the ⁹Be nucleus, the ⁷Li + n + n three-body model for the ⁹Li nucleus, and the ⁷Be + p + p three-body model for the ⁹C nucleus. The differential cross sections and analyzing powers for elastic proton scattering on ⁹Be at E = 220 MeV and 1.0 GeV and on ⁹Li and ⁹C at E = 700 and 60 MeV/nucleon (in inverse kinematics) are calculated within Glauber diffraction theory. All of the results are compared with available experimental data and with the results of the calculations performed by other authors.     

Coulomb displacement energies and decay widths of isobaric analog states from Sm(3He,t) at θ = 0°

The ^{144,147,148,149,150,154}Sm(³He, t)^{144,147,148,149,150,152,154}Eu reactions leading to ground-state isobaric analog states (IAS) have been studied at θ = 0° and E(3He) = 45.9 MeV. The Coulomb displacement energies decrease more rapidly than $\text{A}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$. Approximately 110 keV of the total decrease of about 470 keV from A = 144 (spherical) to A = 154 (deformed) can be ascribed to deformation. No discontinuity is apparent at the transition from spherical to deformed shapes at N = 88–90. This is attributed to two effects: (i) rms radii increase with static deformations and with dynamical vibrations; (ii) Coulomb displacement energies depend on rms charge radii and on the rms radii of the neutron excess. The data suggest neutron deformations greater than proton deformations for A = 148 and 150 but smaller for A = 152 and 154. The IAS widths increase from ～30 keV to ～90 keV and can be attributed to mixing with the (T₀?1) component of a proposed isovector giant monopole resonance.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

An analysis of α-particle inelastic scattering using Hartree-Fock densities

Differential cross sections for the elastic and inelastic scattering of α-particles from ²⁰Ne and ²⁴Mg were calculated, using HF wave functions that had previously been used for (p, p') calculations. We do not use projected wave functions, but we do require consistency between the elastic and inelastic form factors. The result is that although the HF solutions are unable to fit the data, the discrepancy is significantly less than that found in (p, p') calculations.     

Exploratory coupled channels calculations for loosely bound carbon isotopes

We have investigated the loosely bound halo candidates ¹⁷C and ¹⁹C in a neutron+core coupling model. A deformed Woods-Saxon potential is used for the neutron-core interaction and the coupled channels equations are solved with Sturmian expansions of the relative motion wave functions for experimental one-neutron separation energies. The r.m.s. matter radii, longitudinal momentum distributions, E1 strength functions, neutron stripping cross sections and electromagnetic dissociation cross sections are calculated. Their sensitivity to the structural assumptions is explored. Available data does not allow final conclusions to be drawn for ¹⁹C but an assessment of the possible character of ¹⁷C and ¹⁹C is made, and in particular, of the role of s-orbital motion between halo-neutron and core.     

Nuclear matter sizes and isoscalar octupole transition rates of204,206,208Pb from 104 MeV α-particle scattering

Differential cross sections for elastic and inelastic scattering of 104 MeVα-particles from^204,206,208Pb were measured with high angular accuracy. The experimental results were analysed on the basis of a semimicroscopic folding model in order to determine the matter distributions at the nuclear surface and the transition densities. Using phenomenological parametrizations of the densities the analyses of elastic scattering yield rms radii of 〈r ²〉^1/2=5.55±0.06 (²⁰⁴Pb), 5.57±0.06 (²⁰⁶Pb), 5.63±0.05 (²⁰⁸Pb) fm. Various sensitivities affecting the results were studied. From the inelastic cross sections for the 3 ₁ ^? -states octupole transition probabilities and transition radii were derived by using different methods proposed in literature.     

Quadrupole core vibrations in the A = 211 isobars

States of the A = 211 isobars are described as three particles coupled to each other and to a vibrating ²⁰⁸Pb core. Model parameters are extracted from available data on A = 209, 210 isobars, but it is necessary to postulate a form for the two-body interaction to obtain all necessary matrix elements. Energy spectra and reduced transition probabilities are calculated and compared with experiment.     

Photodetachment of the positronium negative ion interacting with screened Coulomb (Yukawa) potentials

The effect of screened Coulomb (Yukawa) potentials on the photodetachment cross sections of the positronium negative ion is investigated by using the asymptotic form of the bound-state wave function and a plane wave form for the final-state wave function. The required normalization constant is determined from highly accurate, completely non-adiabatic wave functions for the three-particle systems. Photodetachment cross sections for the Ps^? ion are calculated for different Debye shielding lengths (D) ranging from infinite (pure Coulomb) to D = 1.81.     

Properties of nuclear matter andN=Z closed-shell nuclei

A simple three-parameter density dependent effective interaction is used to study the properties of nuclear matter, neutron matter and some bulk properties such as ground state energies and rms charge radii of three double-closed shell nuclei⁴He,¹⁶O and⁴⁰Ca. The three parameters of the effective interaction are determined by requiring to fit the binding energy and density of infinite nuclear matter at saturation density as well as ground state energy of¹⁶O in the first order perturbation theory. This interaction gives correct saturation in nuclear matter with a value of 283 MeV for compressibility. The symmetry coefficienta _T atk _F=1·36 fm^–1 is 28·58 MeV. The energy per particle in neutron matter is calculated in the range of nuclear matter densities and it compares well with those ofNemeth andSprung. Groundstate energies and rms charge radii of⁴He,¹⁶O and⁴⁰Ca are calculated using oscillator eigen functions as single particle wave functions. Results for ground state energies are in good agreement with empirical values and rms charge radii are slightly better than those obtained byMoszkowski with the MDI.The authors are thankful to the Computer Centre, Utkal University, Bhubaneswar for providing computational facilities for this work.     

The single-particle characteristics of Pb isotopes near the drip lines calculated within the dispersive optical model

The neutron and proton dispersive optical potential for the ²⁰⁸Pb nucleus has been determined for the energy region from–70 to +60 MeV and used to calculate the differential elastic scattering, the total interaction and reaction cross sections, as well as the single-particle characteristics, the neutron and charge densities, rms radii, and the thickness of the nucleus skin. The calculated results are in good agreement with the experimental data. The proton dispersive optical model potential for the spherical and close to spherical Pb isotopes within the neutron and proton drip lines has been obtained by a similar method. The calculation predicts a trend towards the growth of the proton particle-hole gap, which corresponds to Z = 82 shell closure as Z approaches the proton drip line.     

Influence of relativistic effects on electron-loss cross sections of heavy and superheavy ions colliding with neutral atoms

The influence of relativistic effects, such as relativistic interaction and relativistic wave functions, on the electron-loss cross sections of heavy and superheavy atoms and ions (atomic number Z ? 92) colliding with neutral atoms is investigated using a newly created RICODE-M computer program. It is found that the use of relativistic wave functions changes the electron-loss cross section values by about 20–30% around the cross-section maximum compared to those calculated with nonrelativistic wave functions. At relativistic energies E ≥ 200 MeV/u, the relativistic interaction between colliding particles leads to a quasiconstant behavior of the loss cross sections σ _EL ^rel ～ const, to be compared with the Born asymptotic law σ _EL ^B ～ lnE/E.     

On the basic properties of the A = 48 isobars

Binding energies of the A = 48 isobars and their charge radii are defined on the basis of self-consistent calculations and using the concept of isobaric symmetry in nuclei. The text was submitted by the authors in English.     

Characteristics of elastic proton scattering from <Emphasis Type="Italic">A</Emphasis> = 9 Li,Be, and C isobars

Differential cross sections and analyzing powers (A _y ) for elastic proton scattering from ⁹Be at 220 MeV and 1.0 GeV and from ⁹Li and ⁹C at 60 and 700 MeV/nucleon are calculated in the context of the Glauber diffraction theory with the three-body wave functions for the ⁹Be, ⁹Li, and ⁹C nuclei described by the α + α + n, ⁷Li + n + n, and ⁷Be + p + p models. Comparison with the available experimental data is made, which allows some conclusions about the quality of the model wave functions.     

Inclusive fragment production in84Kr +197Au atE/A=35 MeV

Inclusive cross sections of intermediate mass fragments from the reaction⁸⁴Kr+¹⁹⁷Au atE/A=35 MeV were measured over the range 8°≦Θ _lab≦70° with a low detection threshold. A moving-source parameterization was used to fit the double-differential cross sections. The integrated cross section for fragment production exceeds the total reaction cross section thus indicating a large probability for multi-fragment processes. The deduced large temperature parameters can be explained by assuming emission from a rotating source. From the comparison to reactions with¹²C and⁴⁰Ar projectiles at E/A=30 MeV a systematics of inclusive fragment production as a function of the projectile mass is obtained.