Reaction cross sections and radii of A=17 and A=20 isobars

Reaction cross sections and root-mean-square (rms) radii of A=17 and A=20 isobars are calculated by using a simplified Glauber model and spherical and deformed Hartree-Fock (HF) wave functions. The small separation energy effect is discussed on the reaction cross sections of A=17 isobars and possible proton halo in ¹⁷Ne by using modified spherical HF wave functions. The calculated rms mass radii of A=20 isobars are increased appreciably by the deformation effect and show a similar irregular pattern as a function of the isospin to that of the observed radii.     

Charged particle multiplicities and inelastic cross sections in high energy nuclear collisions

Inelastic cross sections at 60 and 200 GeV/nucleon are determined in a streamer chamber for ¹⁶O on several nuclear targets. Charged particle multiplicity distributions for inelastic and central collisions are studied and compared with theoretical predictions. The inelastic cross section exhibit a geometrical dependence on nuclear radii. The multiplicity data are governed by the collision geometry. They are consistent with a picture of superposition of independent nucleon-nucleus interactions.     

Nucleon charge form factors and chiral quark models

Calculations of the proton and neutron charge form factors G_E^p,n(q²) are presented, based on chiral bag as well as confining Dirac potential models with chiral pion-quark coupling. Special emphasis is placed on a detailed treatment of the charged pion cloud contribution to the nucleon current. The role of a finite extension of the pion-quark vertex in truncating the summation over intermediate quark bag states is studied. Quark core radii (including recoil corrections) are constrained by a simultaneous calculation of the nucleon axial form factor. The proton charge form factor is well reproduced for $\text{|q}{}^2\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 0.7}\text{GeV}$ with quark core rms radii between 0.5–0.6 fm. About $\text{1}\text{3}$ of the proton charge is carried by the pion cloud in this model. The neutron charge form factor is obtained with the correct sign and overall q² dependence but needs further refinements, probably at the level of the isoscalar form factor.     

Generalized polarizabilities of the nucleon studied in the linear sigma model

The generalized polarizabilities of the nucleon have been calculated in the one-loop approximation of the linear sigma model in the limit of infinite sigma mass. In particular, we have investigated the spin-independent amplitude of virtual Compton scattering off the nucleon. The dependence of the polarizabilities on the momentum transferQ has been compared with two recent model calculations. It has been shown in the linear sigma model that only two of the three scalar polarizabilities are independent quantities. Particular attention has been paid to the real photon point (Q ²=0), where the results of the relativisitc chiral perturbation theory have been recovered.     

Generalized polarizabilities of the nucleon studied in the linear sigma model

The generalized polarizabilities of the nucleon have been calculated in the one-loop approximation of the linear sigma model in the limit of infinite sigma mass. In particular, we have investigated the spin-independent amplitude of virtual Compton scattering off the nucleon. The dependence of the polarizabilities on the momentum transfer Q has been compared with two recent model calculations. It has been shown in the linear sigma model that only two of the three scalar polarizabilities are independent quantities. Particular attention has been paid to the real photon point (Q² = 0), where the results of the relativistic chiral perturbation theory have been recovered.     

Transfer reactions of B with Ta

Excitation functions and mean recoil ranges are reported for the formation of ¹⁸²Os, ¹⁸³Re, ¹⁸²Re, ¹⁸¹Re and ¹⁸²Ta in ^{10, 11}B interactions with ¹⁸¹Ta. The stacked foil technique was used. The results are indicative of formation through a transfer reaction. We have considered a nucleon group transfer mechanism in a surface interaction followed by de-excitation via nucleon emission from the excited intermediate. Thus the energy dependence of recoils and cross sections of single nucleon and multinucleon transfer products have been calculated and found in good agreement with experimental results.     

Symmetry dependence of rms Charge Radii

The nucleon number dependence of rms charge radii is often approximated by some simple formula containing the mass number only, R(A)=r(A)A^1/3, where r(A) is a slowly varying function of A. However, for nuclei off the stability line, the mass number A=N + Z is not enough to characterise the dependence of the R(Z, N) radius surface on the nucleon numbers Z and N. In the present work, an additional term has been included, depending on the symmetry parameter I=(N ? Z)/A. Several parametrisations were tried, using weighted least-squares procedures for the fit to a present-day data base. The best fit (with χ²/ń=17) was found for R(A, I)=r(A)A^1/3 + b_I/(I ? I_stab), where I_stab=(N_stab ? Z_stab)/A is the value of the symmetry parameter of the stable isobar with mass number A, and b_I=?0.83 fm. The formula R(A, I)=[r(A) + a_I(I ? I_stab)]A^1/3 is only slightly inferior to the previous one, moreover, it is supported by simple model calculations; here a_I=?0.20 fm (χ²/ń=20). The difficulty in determining the right parametrisation is caused by the fact that the surface R_exp(A, I) is not smooth: there are strong shell and deformation effects. To avoid the distorting effect of these deviations on the parameter values, more than half of the original data had to be omitted.     

Mass yield distributions of target fragments from the reactions of iron with 135 MeV/nucleon 12C and 80 MeV/nucleon 16O ions

Cross sections for the production of target fragments in the reactions of iron with 135 MeV/nucleon ¹²C and 80 MeV/nucleon ¹⁶O ions have been measured by off-line γ-ray spectroscopy. Through these data, the mass yield distributions have been obtained. The result of the experiment for the reaction with 135 MeV/nucleon ¹²C ions is compared with theoretical calculations using the fusion-fragmentation model and the GEMINI code for sequential binary decay, following a calculation with the fireball model. Reveived: 24 March 1999 / Revised version: 16 July 1999     

Nuclear radii: A critique of the droplet model

Equivalent sharp radii of a number of nuclei are calculated with the droplet model, using parameters that have been determined by the Hartree-Fock (HF) method with a given force (Gogny). They are found to be systematically smaller than the sharp radii given by direct HF calculations on the nucleus in question with the same force. This is shown to be a result of nuclear matter being squeezed by the surface tension much more in the droplet model than in the HF method. Inclusion of higher-order terms in the droplet model's expansion in powers of $\text{A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$ in no way helps to remove the anomaly, and in fact serious questions concerning the convergence of this expansion arise.     

Nuclear symmetry energy effects in finite nuclei and neutron star

Within a relativistic mean-field model with nonlinear isoscalar–isovector coupling, we explore the possibility of constraining the density dependence of nuclear symmetry energy from a systematic study of the neutron skin thickness of finite nuclei and neutron star properties. We find the present skin data supports a rather stiff symmetry energy at subsaturation densities that corresponds to a soft symmetry energy at supranormal densities. Correlation between the skin of ²⁰⁸Pb and the neutron star masses and radii with kaon condensation has been studied. We find that ²⁰⁸Pb skin estimate suggest star radii that reveals considerable model dependence. Thus precise measurements of neutron star radii in conjunction with skin thickness of heavy nuclei could provide significant constraint on the density dependence of symmetry energy.     

Density-dependent Brueckner-Hartree-Fock approach in deformed nuclei

Recently a method has been developed which includes into the Brueckner-Hartree-Fock (BHF) approach in a finite nucleus those terms which produce the density dependence of the effective interaction between nucleons. This method is extended to the deformed open shell nuclei ¹²C and ²⁰Ne. The results indicate that it is possible to describe these nuclei starting from a bare realistic nucleon-nucleon interaction (Reid soft-core potential). Binding energies, quadrupole moments, root mean square radii are improved compared to the usual BHF approach with the same force or the HF approach with a phenomenological effective force.     

Self-consistent description of finite nuclei based on a relativistic quark model

Relativistic Hartree equations for spherical nuclei have been derived from a relativistic quark model of the structure of bound nucleons which interact through the (self-consistent) exchange of scalar (σ) and vector (ω and ϱ) mesons. The coupling constants and the mass of the σ-meson are determined from the properties of symmetric nuclear matter and the rms charge radius in ⁴⁰Ca. Calculated properties of static, closed-shell nuclei from ¹⁶O to ²⁰⁸Pb are compared with experimental data and with results of Quantum Hadrodynamics (QHD). The dependence of the results on the nucleon size and the quark mass is investigated. Several possible extensions of the model are also discussed.     

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     

Elastic scattering of35Cl from27Al,58, 62Ni,116, 120, 124Sn and141Pr

Elastic scattering angular distributions for³⁵Cl from²⁷Al,^{58, 62}Ni,^{116, 120, 124}Sn and¹⁴¹Pr have been measured at energies between 100 and 170 MeV. Optical model analyses have been performed to determine reaction cross sections, strong absorption radii and grazing angular momenta. The results are compared with the corresponding quantities extracted by means of the Fresnel scattering model. Near the interaction barrier the quarter point method yields reaction cross sections systematically smaller than the optical model results. The interaction radii, however, do not show significant differences or energy dependencies. These radii are compared with trend formulae for interaction radii, and comparisons with fusion radii are made.     

Real part of the optical potential for composite particles

The optical potential for a composite particle is most simply approximated by the sum of the optical potentials of the constituent nucleons. Restricting ourselves to the real parts of the potentials we use this model as a first approximation in a calculation of the potentials for d, ³He, α and ¹²C. We add corrections for (i) the energy dependence of the nucleon potentials, (ii) three-body terms, (iii) the Pauli principle. All corrections can be important and that for the Pauli principle can be very large. We obtain a good explanation of the following phenomena: (a) the deuteron potential is nearly the sum of the neutron and proton potentials, (b) the potential for ³He is about 20 % less than the sum of the potentials of the nucleons in the ³He projectile, (c) the volume integral of the potential for ³He falls at both high and low energies in the energy range 20–100 MeV, (d) shallow potentials with large radii are found for low energy (30 MeV) scattering of α-particles, (e) deeper potentials are found for higher energy α-particle scattering. We predict shallow potentials for ¹²C scattering from light targets but deeper potentials for heavier targets.     

Electromagnetic form factors of3He and3H

The electric and magnetic form factors of³He and³H are calculated with 3-nucleon wave functions obtained from the solution of Schrödinger equation with separable potentials of two different shapes which have already been employed in the coulomb energy calculation. The effect of important meson exchange corrections is evaluated and their dependence on the wave function studied. The form factors can depend rather sensitively on the nucleon form factors as well, and this dependence is studied by using two different parametrisations for the latter.     

Chiral condensate and chemical freeze-out

We consider a chemical freeze-out mechanism which is based on a strong medium dependence of the rates for inelastic flavor-equilibrating collisions based on the delocalization of hadronic wave functions and growing hadronic radii when approaching the chiral restoration. We investigate the role of mesonic (pion) and baryonic (nucleon) fluctuations for melting the chiral condensate in the phase diagram in the (T, μ)-plane. We apply the PNJL model beyond mean-field and present an effective generalization of the chiral perturbation theory result which accounts for the medium dependence of the pion decay constant while preserving the GMOR relation. We demonstrate within a schematic resonance gas model consisting of a variable number of pionic and nucleonic degrees of freedom that within the above model a quantitative explanation of the hadonic freeze-out curve and its phenomenological conditions can be given.     

Electromagnetic radii of nucleon and pion

A new determination of the spectral functions of nucleon form factors according to the Frazer-Fulco method leads to reliable results up to t ?1GeV² and to improved values for the radii.     

Nuclear mass form factors from coherent photoproduction of πmesons

Data for coherent photoproduction of π⁰ mesons from nuclei ( ¹²C, ⁴⁰Ca, ⁹³Nb, ^natPb), recently measured with the TAPS detector at the Mainz MAMI accelerator, have been analyzed in view of the mass form factors of the nuclei. The form factors have been extracted in plane-wave approximation of the A(γ,π⁰)A reaction and corrected for final-state interaction effects with the help of distorted-wave impulse approximations. Nuclear mass rms radii have been calculated from the slope of the form factors for q² → 0. Furthermore, the Helm model (hard-sphere form factor folded with Gaussian) was used to extract diffraction radii from the zeroes of the form factor and skin thicknesses from the position and height of its first maximum. The diffraction radii from the Helm model agree with the corresponding charge radii obtained from electron scattering experiments within their uncertainties of a few per cent. The rms radii from the slope of the form factors are systematically lower by up to 5% for PWIA and up to 10% for DWIA. Also the skin thicknesses extracted from the Helm model are systematically smaller than their charge counterparts.