Nuclear mean fields through self-consistent semiclassical calculations

Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density τ( r) and the spin-orbit density J( r) as functions of the local density ρ( r) are used to determine the central nuclear potentials V _n( r) and V _p( r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of the resulting semiclassical expansions for these potentials is fast and that they reproduce quite accurately the corresponding Hartree-Fock average fields. Received: 12 February 2000 / Accepted: 14 March 2002     

Magnetic moment and radius of the nucleon in a nonlocal model of meson-nucleon interaction

Magnetic moment and radius of the nucleon are calculated in a nonlocal extension of the chiral linear σ-model. Properties of the nonlocal model under the vector and axial transformations are considered. The conserved electromagnetic and vector currents, and partially conserved axial vector current are obtained. In the calculation of the nucleon electromagnetic vertex the π- and σ-loop diagrams are included. Contribution from vector mesons is added in the vector meson dominance model with a gauge-invariant photon-meson coupling. The nonlocality parameter associated with the πN interaction is fixed from the experimental magnetic moment of the neutron. Other parameters (nonlocality parameter for the σN interaction and the mass of the σ-meson) are constrained by the magnetic moment of the proton. The calculated electric and magnetic mean-square radii of the proton and neutron are in satisfactory agreement with experiment. Received: 12 February 2001 / Accepted: 4 September 2001     

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     

Rotational bands in 169Re

Based on the systematic investigation of the data available for nuclei with A≥ 40, a Z ^1/3-dependence for the nuclear charge radii is shown to be superior to the generally accepted A ^1/3 law. A delicate scattering of data around R _c/Z ^1/3 is inferred as owing to the isospin effect and a linear dependence of R _c/Z ^1/3 on N/Z (or (N - Z)/2) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. With the linear isospin dependence provided by the data and RCHB theory, a new isospin-dependent Z ^1/3 formula for the nuclear charge radii is proposed. Received: 23 September 2001 / Accepted: 21 January 2002     

Quasi-free Compton scattering and the polarizabilities of the neutron

Differential cross-sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz photon tagging spectrometer at the Mainz MAMI accelerator together with the Mainz [48]cm ;SPMOslash; × [64]cm NaI(Tl) photon detector and the G?ttingen SENECA recoil detector. The data cover photon energies ranging from [200]MeV to [400]MeV at θ^LAB _γ = 136.2^°. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction p(γ,π⁺ n). The “free” proton Compton scattering cross-sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross-section for free scattering from quasi-free data. Differential cross-sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron has been determined to be α_n - β_n = 9.8±3.6(stat)^+2.1 _-1.1(syst)±2.2(model) in units of [10^-4]fm ³. In combination with the polarizability sum α_n + β_n = 15.2±0.5 deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, α_n = 12.5±1.8(stat)^+1.1 _-0.6(syst)±1.1(model) and β_n = 2.7±1.8(stat)^+0.6 _-1.1(syst)±1.1(model) are obtained. The backward spin polarizability of the neutron was determined to be γ⁽ⁿ⁾ _π = (58.6±4.0)×10^-4 fm ⁴. Received: 21 August 2002 / Accepted: 16 October 2002 / Published online: 11 February 2003 RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="c" ID="c"Part of the Habilitation Thesis. RID="d" ID="d"e-mail: schumacher@physik2.uni-goettingen.de Communicated by Th. Walcher     

Quantum Monte Carlo calculations of light nuclei

Quantum Monte Carlo calculations using realistic two- and three-nucleon interactions are presented for nuclei with up to ten nucleons. Our Green's function Monte Carlo calculations are accurate to ∼1-2% for the binding energy. We have constructed Hamiltonians using the Argonne v₁₈ NN interaction and reasonable three-nucleon interactions that reproduce the energies of these nuclear states with only ∼500 keV rms error. Other predictions, such as form factors, decay rates, and spectroscopic factors also agree well with data. Some of these results are presented to show that ab initio calculations of light nuclei are now well in hand. Received: 1 May 2001 / Accepted: 4 December 2001     

Nucleon form factors from a covariant quark core: Limits in their description

In treating the relativistic 3-quark problem, a dressed-quark propagator parameterization is used which is compatible with recent lattice data and pion observables. Furthermore 2-quark correlations are modeled as a series of quark loops in the scalar and axialvector channel. The resulting reduced Faddeev equations are solved for nucleon and delta. Nucleon electromagnetic form factors are calculated in a fully covariant and gauge-invariant scheme. Whereas the proton electric form factor G _E and the nucleon magnetic moments are described correctly, the neutron electric form factor and the ratio G _E/G _M for the proton appear to be quenched. The influence of vector mesons on the form factors is investigated which amounts to a 25% modification of the electromagnetic proton radii within this framework. Received: 16 April 2002 / Accepted: 29 August 2002 / Published online: 17 January 2003 RID="a" ID="a"Supported by a Feodor-Lynen fellowship of the Alexander-von-Humboldt foundation and the Australian Research Council. RID="b" ID="b"Address after April 30: MPI für Metallforschung, Heisenbergstr. 1, 70569 Stuttgart, Germany. RID="c" ID="c"e-mail: Reinhard.Alkofer@uni-tuebingen.de Communicated by A. Sch?fer     

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.     

Hadron diffractive processes: the structure of soft pomeron and colour screening

On the basis of the experimental data on diffractive processes in πp, pp and pˉp collisions at intermediate, moderately high and high energies, we restore the scattering amplitude related to the t-channel exchange by vacuum quantum numbers by taking account of the diffractive s-channel rescatterings. At intermediate and moderately high energies, the t-channel exchange amplitude turns, with a good accuracy, into an effective pomeron which renders the results of the additive quark model. At superhigh energies the scattering amplitude provides a Froissart-type behaviour, with an asymptotic universality of cross sections such as σ^tot _πp/σ^tot _pp→ 1 at s→∞. The quark structure of hadrons being taken into account at the level of constituent quarks, the cross sections of pion and proton (antiproton) in the impact parameter space of quarks, σ_π(r _1⊥, r _2⊥; s) and σ_p(r _1⊥, r _2⊥, r _3⊥; s), are found as functions of s. These cross sections implicate the phenomenon of colour screening: they tend to zero at |r _i⊥−r _k⊥|→ 0. The effective colour screening radius for pion (proton) is found for different s. The predictions for the diffractive cross sections at superhigh energies are presented. Received: 15 December 1998     

Probing the structure of exotic nuclei by transfer reactions

Low energy single nucleon transfer reactions are proposed as a tool to investigate the structure of nuclei far off stability. Experimental concepts and conditions are discussed, in particular high resolution γ-ray spectroscopy after single nucleon pickup reactions. Nuclear structure is described by Skyrme Hartree-Fock calculations including pairing. As representative examples, binding energies, radii and wave functions for Mg and Sn isotopes are calculated. In the neutron deficient Mg isotopes a proton skin is found. At the neutron driplines the Mg and Sn isotopes develop extended neutron skins. The nuclear structure results are used in DWBA and EFR-DWBA transfer calculations. Single nucleon transfer reactions of ^32,36Mg and exotic Sn beams on targets ranging from ²H to ²⁴Mg in inverse kinematics are explored. The one-nucleon transfer cross sections decrease strongly for high-Z targets. An impact parameter analysis shows that the transfer process is selective on the tails of the wave functions. The largest cross sections are obtained for ²H and ⁹Be targets at incident energies of E _lab = 2-5 MeV/u. The energy-momentum dependence is closely related to the special properties of wave functions of weakly bound states. Two-neutron (p,t) stripping reactions are studied for a ⁶He projectile. A strong competition of sequential and direct processes is found at low energies. Received: 1 October 1997 / Revised version: 25 November 1997     

Measurement of the interaction cross-section and related topics

Recent experimental results concerning interaction cross-sections ( σ_I) are reviewed. The σ_I values were measured by a transmission method using the fragment separator at GSI. The σ_I values for B, C, N, O and F isotopes and the recently measured σ_I for Ar are presented. As related topics, an analysis by the recently developed Glauber model for a few-body system is introduced. By using this analysis, the effective density distributions for light neutron-rich nuclei can be deduced. The recently shown magic number N = 16 near to the neutron drip line is also discussed. Received: 1 May 2001 / Accepted: 4 December 2001     

Pion and kaon electromagnetic form factors in a SUL(3) ⊗ SUR(3) effective Lagrangian

A SU(2) effective Lagrangian is extended to a SU _L(3) ⊗SU _R(3) by including the vector and axial vector meson. With this effective Lagrangian, electromagnetic form factors of charged pion and kaon are calculated in both time- and space-like regions. The pseudoscalar meson loops are taken into account. Good agreement with experimental data is obtained for those form factors and charged pseudoscalar meson radii. Decay widths of ρ→ππ and φ→K ⁺ K ^- are also calculated and shown to agree with experimental data very well. Received: 20 December 1999 / Accepted: 12 October 2000     

Yrast level structure of the neutron-deficient N = 80 isotones 146Dy, 147Ho and 148Er up to high-spin values

High-spin level schemes of the N = 80 isotones ¹⁴⁶Dy, ¹⁴⁷Ho and ¹⁴⁸Er have been investigated by in-beam γ-ray spectroscopic methods using the NORDBALL Compton-suppressed multidetector array including proton and neutron selection. The projectile-target system ⁵⁸Ni + ⁹²Mo at 260 MeV beam energy has been used to produce the neutron-deficient N = 80 isotones. The previously known schemes have been extended to considerably higher spin and exitation energy, up to I = 23?, E _x≈ 8.9 MeV in ¹⁴⁶Dy, I = 53/2?, E _x≈ 8.7 MeV in ¹⁴⁷Ho and I = 23?, E _x≈ 9.6 MeV in ¹⁴⁸Er. The results are discussed in terms of the spherical shell model. Many of the levels can be described within this framework. Received: 12 January 2001 / Accepted: 11 April 2001     

Microscopic three-body force for asymmetric nuclear matter

Brueckner calculations including a microscopic three-body force have been extended to isospin-asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β = (N - Z)/A is fulfilled in the whole asymmetry range 0≤β≤1 up to high densities. The three-body force provides a strong enhancement of the symmetry energy which increases with density in good agreement with the predictions of relativistic approaches. The Lane's assumption that proton and neutron mean fields linearly vary vs. the isospin parameter is violated at high density due to the three-body force, while the momentum dependence of the mean fields turns out to be only weakly affected. Consequently, a linear isospin split of the neutron and proton effective masses is found for both cases with and without the three-body force. The isospin effects on multifragmentation events and collective flows in heavy-ion collisions are briefly discussed along with the conditions for direct URCA processes to occur in the neutron star cooling. Received: 18 February 2002 / Accepted: 16 May 2002     

Isoscalar and isovector nuclear matter properties and neutron skin thickness

Isoscalar and isovector nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and the isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. We also discovered that the correlations between the isovector properties and the incompressibility K show a singularity at the critical incompressibility K_c=306 MeV. It is shown that the neutron skin thickness gives crucial information about not only for the neutron EOS but also about the isovector nuclear matter properties and about the parameterization of Skyrme interaction. Charge exchange spin-dipole (SD) excitations are proposed to determine the neutron skin thickness model independently.     

Neutrons produced by 1.22 GeV antiproton interactions with nuclei

Inclusive neutron energy spectra were measured by time of flight using 1.22 GeV antiprotons from LEAR, CERN, as projectiles and targets from natural Al, Cu, Ag, Ho, Ta, Au, Pb, Bi, U. The sum of two Maxwellian distributions was fitted to the spectra obtained at several forward and backward angles yielding neutron multiplicities M_i and slope or temperature parameters T _i for the low-energy (evaporative, i=1) and high-energy (pre-equilibrium,i=2) parts, respectively. M ₁ increases with A, proportional to the nuclear volume, and M ₂ is growing with A , proportional to the nuclear radius. The T parameters are nearly independent of A. The results are compared with previous multiplicity measurements with a neutron detector, intranuclear cascade calculations and neutron spectra from stopped antiproton annihilation on nuclei. With the measured proton spectra also the ratio of emitted neutrons to protons was determined for Au. Received: 25 February 2000 / Accepted: 19 May 2000     

Neutron halos in hypernuclei

Properties of single- Λ and double- Λ hypernuclei for even-N Ca isotopes ranging from the proton dripline to the neutron dripline are studied using the relativistic continuum Hartree-Bogoliubov theory with a zero-range pairing interaction. Compared with ordinary nuclei, the addition of one or two Λ-hyperons lowers the Fermi level. The predicted neutron dripline nuclei are, respectively, ⁷⁵ _ΛCa and ⁷⁶ _2ΛCa, as the additional attractive force provided by the Λ-N interaction shifts nuclei from outside to inside the dripline. Therefore, the last bound hypernuclei have two more neutrons than the corresponding ordinary nuclei. Based on the analysis of two-neutron separation energies, neutron single-particle energy levels, the contribution of continuum and nucleon density distribution, giant halo phenomena due to the pairing correlation, and the contribution from the continuum are suggested to exist in Ca hypernuclei similar to those that appear in ordinary Ca isotopes. Received: 21 October 2002 / Accepted: 11 January 2003 / Published online: 8 April 2003     

Determination of the neutron electric form factor in the D(e,e′n)p reaction and the influence of nuclear binding

The electric form factor of the neutron G _E,n has been determined at the Mainz Microtron MAMI at the low momentum transfer Q ²= 0.15 (GeV/c)² in a measurement of the recoil polarisation ratio P _x/P_z in the quasifree reaction D(e,e′n)p. At this Q ² the influence of the nuclear binding is strong. A purely kinematical model is used to get some insight into the effect of the initial Fermi momentum distribution of the neutron. The influence of the final state interaction is determined quantitatively by a model of Arenh?vel et al.. After the corresponding corrections a value of G _E,n(0.15 (GeV/c)²) = 0.0481±0.0065_stat±0.0053_syst is obtained. Received: 12 April 1999     

Quenching of neutron E2 effective charge in neutron-rich nuclei and the ground-state spin-parity of 17C

The electric quadrupole moment of ¹⁷B and the g-factor of ¹⁷C were measured by using the fragmentation-induced nuclear polarization technique combined with the β-NMR method. The experimental quadrupole moment of ¹⁷B is found strikingly close to that of the neutron closed-shell isotope ¹³B, indicating a strong quenching of the neutron E2 core-polarization charge. From the result obtained for the ¹⁷C g-factor, we can conclude that the ground-state spin-parity of ¹⁷C is 3/2⁺. Received: 1 May 2001 / Accepted: 4 December 2001