Evolution of the N = 20 and N = 28 shell closures in neutron-rich nuclei

The isospin dependence of shell closure phenomena is studied for light neutron-rich nuclei within a microscopic self-consistent approach using the Gogny force. Introducing configuration mixing, ³²Mg is found to be dynamically deformed, although the N = 20 spherical shell closure persists at the mean-field level for all N = 20 isotones. In contrast, the N = 28 spherical shell closure is found to disappear for N - Z≥ 10 whereas deformed shell closures are preserved and lead to shape coexistence in ⁴⁴ S. Configuration mixing shows that the ground state of this nucleus is triaxially deformed. The first 2⁺ excitation energy E_x = 1.46 MeV and the reduced transition probability B(E2;0⁺ _gs→ 2⁺ ₁)= 420 e ² fm ⁴ obtained with our approach are in good agreement with experimental data. Received: 26 July 2000 / Accepted: 30 August 2000     

Nuclear structure in the vicinity of the N = Z line in the A = 90-100 region

Neutron-deficient nuclei in the mass region A≈ 90-100 exhibit a large variety of phenomena. In this region the heaviest N = Z nuclei are identified and enhanced neutron-proton correlations are expected when protons and neutrons occupy identical orbitals. A variety of nuclear shapes are predicted and observed for A? 91, including superdeformed shapes. The nucleus ¹⁰⁰Sn is the heaviest N = Z doubly magic nucleus believed to be bound. Knowledge of the shell structure around ¹⁰⁰Sn is of utmost importance for understanding the nuclear shell model. New results on both the N = Z nucleus ⁸⁸Ru, superdeformed structures in A≈ 90 nuclei as well as the first result on the level structure in ¹⁰³Sn, and an extended level structure in ¹⁰²In are presented. The limitations of using stable beams and targets and the possibilities with new radioactive beams are briefly outlined. Received: 1 May 2001 / Accepted: 4 December 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     

Charge radius change in the heavy tin isotopes until A = 132 from laser spectroscopy

Laser spectroscopy measurements have been carried out on the very neutron-rich tin isotopes with the COMPLIS experimental setup. Using the 5s ²5p ²³ P ₀ → 5s ²5p6s ³ P ₁ optical transition, hyperfine spectra of ^126-132Sn and ^{125m, 127m, 129m-131m}Sn where recorded for the first time. The variation of the mean-square charge radius ( δ〈r ²〉) between these nuclei and nuclear moments of the isomers and the odd isotopes were thus measured. An odd-even staggering which inverts at A = 130 is clearly observed. This indicates a small appearance of a plateau on the δ〈r ²〉 which has to be confirmed by measuring the isotope shift beyond A = 132. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: leblanc@ipno.in2p3.fr     

On the liquid drop model mass formulae and charge radii

An adjustment to 782 ground-state nuclear charge radii for nuclei with N, Z 3 \ge8 leads to R₀ = 1.2257 A^1/3\ensuremath R_0 = 1.2257 A^{1/3} fm and s \sigma = 0.124 fm for the charge radius. Assuming such a Coulomb energy E_c = \frac35 e²Z²/1.2257 A^\frac13\ensuremath E_c = \frac{3}{5} e^2Z^2/1.2257 A^{\frac{1}{3}} , the coefficients of different possible mass formulae derived from the liquid drop model and including the shell and pairing energies have been determined from 2027 masses verifying N, Z 3 \ge8 and a mass uncertainty ￡ \le150 keV. These formulae take into account or do not the diffuseness correction ( Z²/A\ensuremath Z^2/A term), the charge exchange correction term ( Z^4/3/A^1/3\ensuremath Z^{4/3}/A^{1/3} term), the curvature energy, the Wigner terms and different powers of I = (N - Z)/A . The Coulomb diffuseness correction or the charge exchange correction term play the main role to improve the accuracy of the mass formulae. The different fits lead to a surface energy coefficient of around 17-18MeV. A possible more precise formula for the Coulomb radius is R₀ = 1.2332A^1/3 + 2.8961/A^2/3 - 0.18688A^1/3I\ensuremath R_0 = 1.2332A^{1/3} + 2.8961/A^{2/3} - 0.18688A^{1/3}I fm with s \sigma = 0.052 fm.     

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     

Studies with one- and two-proton drip line nuclei

In recent experiments at GANIL, we studied nuclei at the one- and two-proton drip line. The production rates allowed to search for direct 2p emission in the drip line nuclei ⁴²Cr, ⁴⁵Fe, and ⁴⁹Ni. No evidence for this decay mode was found in ⁴²Cr and ⁴⁹Ni, whereas the situation stays unclear for ⁴⁵Fe due to the limited statistics. In the medium-mass region ( A = 50-70), the half-life was measured for all proton-rich nuclei in the range T _z = 0 to T _z = - 1 between Z = 27 and Z = 36. First half-lives were determined for ⁶⁰Ga, ⁶²Ge, ⁶⁴As and ⁶⁶Se. Finally, β-decay studies of the 0⁺ → 0⁺ decay of ⁶²Ga have been performed at IGISOL in Jyv?skyl?. Non-analog transitions have been observed and are compared to theoretical predictions. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: blank@cenbg.in2p3.fr     

Influence of the spin-orbit couplingon nuclear superfluidity along the N = Z line

We show that the spin-orbit potential of the nuclear mean field destroys isoscalar superfluid correlations in self-conjugate nuclei. Using group theory and boson mapping techniques on a Hamiltonian including single particle splittings and a SO _ST(8) pairing interaction, we give analytical expressions for the spin-orbit dependence of some N = Z properties such as the relative position of T = 0 and T = 1 states in odd-odd systems or double binding-energy differences of even-even nuclei. Received: 12 April 2000 / Accepted: 25 May 2000     

Gamow-Teller transitions from 58Ni to discrete states of 58Cu

Under the assumption that isospin is a good quantum number, symmetry is expected for the transitions from the ground states of T = 1, T _z = ±1 nuclei to the common excited states of the T _z = 0 nucleus situated between the two nuclei. The symmetry can be studied by comparing the strengths of Gamow-Teller (GT) transitions obtained from a (p, n)-type charge-exchange reaction on a target nucleus with T _z = 1 with those from the β-decay of the T _z = - 1 nucleus. The A = 58 system is the heaviest for which such a comparison is possible. As a part of the symmetry study, we measured the GT transitions from ⁵⁸Ni (T _z = 1) to ⁵⁸Cu (T _z = 0) by using the zero-degree (³ He, t) reaction at 150 MeV/nucleon. With the achieved resolution of 50 keV, many hitherto unresolved GT states have been identified. The GT transition strengths were obtained for states up to 8 MeV excitation, i.e., near to the Q window limitation ( Q _EC = 9.37 MeV) of the β-decay from ⁵⁸Zn (T _z = - 1) to ⁵⁸Cu. The strength distribution is compared with that from shell-model calculations. Received: 24 November 2001 / Accepted: 30 January 2002     

Crossing of the πd<Subscript>5/2</Subscript> and πg<Subscript>7/2</Subscript> orbitals in the <Subscript>51</Subscript>Sb isotopes

Self-consistent calculations using the D1S Gogny force have been performed in order to study the mechanism involved in the crossing of the πd _5/2 and πg _7/2 orbitals in the Sb isotopes. This inversion is well predicted by the HFB + blocking calculations with spherical symmetry performed for the odd-A Sb isotopes. In addition, several HFB and HF calculations have been performed for even-even nuclei of the five neighbouring isotopic chains (Z = 46 to 54, from the proton dripline to N = 82). The results obtained for the binding energies of the two proton orbitals indicate that the radii of the systems play an important role in the crossing, even though some particular πν interactions also give a contribution. The spin-orbit interaction, which is known to be concentrated mainly at the nuclear surface, is proposed to be the main responsible of the crossing.     

Nuclear-matter distributions of halo nuclei from elastic proton scattering in inverse kinematics

Proton-nucleus elastic scattering at intermediate energies, a well-established method for probing nuclear-matter density distributions of stable nuclei, was applied for the first time to exotic nuclei. This method is demonstrated to be an effective means for obtaining accurate and detailed information on the size and radial shape of halo nuclei. Absolute differential cross-sections for small-angle scattering were measured at energies near 700 MeV/u for the neutron-rich helium isotopes ⁶He and ⁸He, and more recently for the lithium isotopes ⁶Li, ⁸Li, ⁹Li and ¹¹Li, using He and Li beams provided by the fragment separator FRS at GSI Darmstadt. Experiments were performed in inverse kinematics using the hydrogen-filled ionization chamber IKAR which served simultaneously as target and recoil-proton detector. For deducing nuclear-matter distributions, differential cross-sections calculated with the aid of the Glauber multiple-scattering theory, using various parametrizations for the nucleon density distributions as input, were fitted to the experimental cross-sections. The results on nuclear-matter radii and matter distributions are presented, and the significance of the data for a halo structure is discussed. Nuclear-matter distributions obtained for ⁶He and ⁸He conform with the concept that both nuclei compose of α-particle like cores and significant neutron halos. The matter distribution in ¹¹Li exhibits, as expected from previous reaction cross-section studies with nuclear targets, the by far most extended halo component of all nuclei being investigated. In addition the present data allow a quantitative comparison of the structure of the He and Li isobares of either the mass number A = 6 or A = 8. The measured differential cross-sections have also been used for probing density distributions as predicted from various microscopic calculations. A few examples are presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: p.egelhof@gsi.de     

Measurements of the spin rotation parameter A in the elastic pion-proton scattering in the D13(1700) resonance region

The spin rotation parameters A and R were measured for the elastic pion-proton scattering by the PNPI-ITEP collaboration in the D₁₃(1700) resonance region. The main goal of the experimental program is to resolve the current partial-wave analyses (PWA) uncertainties. Simultaneously with A and R the polarization parameter P was measured with the purpose to improve the experimental database and estimate systematic errors. The constraint which demands a smooth energy dependence of all π^- p transverse amplitude zeros in the complex plane together with the new experimental data on A parameter can lead to the conclusion that the Barrelet branch of “zero trajectories" is chosen improperly in PWA of the Carnegie-Mellon-Lawrence-Berkely-Laboratory groups at the range of the pion beam momentum near 1.0 GeV/c. The setup included a longitudinally polarized proton target with superconductive magnet, multiwire spark chambers and carbon polarimeter with thick filter. The experiment was performed at the ITEP proton synchrotron, Moscow. Received: 17 August 2001 / Accepted: 13 September 2001     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

Charge Radii of Argon Isotopes in the f7/2 Shell and Radii Systematics in the Ca-Region

Changes in mean square (ms) nuclear charge radii of Ar isotopes across the 1f_7/2 shell are studied by fast-beam collinear laser spectroscopy using an ultra-sensitive detection method based on optical pumping and state-selective collisional ionization. The new data set on Ar, in combination with the known charge radii of K, Ca and Ti in the ν1f_7/2 shell, offers an opportunity to obtain a more complete overview of nuclear radii trends around the proton shell closure Z = 20 and between the neutron shell closures N = 20 and N = 28.     

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     

Structure of neutron-rich Λ hypernuclei

Properties of light neutron-rich Λ hypernuclei (¹⁶ _ΛC, ¹² _ΛBe, and ¹¹ _ΛLi) are calculated within the Skyrme-Hartree-Fock approach. Interplay between hypernuclear interaction features and properties of these hypernuclei is studied. Response of weakly bound neutron states to hyperon addition depends generally on core distortion by hyperon, and it is essentially different for the different states. This response is especially sensitive to details of the ΛN interaction for 1p _1/2 states. Implications of the nuclear spin-orbit potential and nuclear incompressibility in the neutron-rich system properties are inferred. Dependence of the Λ binding energies in hypernuclei on Z at fixed A is discussed. Received: 16 December 1998     

Probing the interactions of charmed mesons with nuclei in ¯p-induced reactions

We study the perspectives of resonant and nonresonant charmed-meson production in ˉp + A reactions within the Multiple Scattering Monte Carlo (MSMC) approach. We calculate the production of the resonances Ψ(3770),Ψ(4040) and Ψ(4160) on various nuclei, their propagation and decay to D,ˉD, D ^*,ˉD^*, D _s,ˉD_s in the medium and vacuum, respectively. The modifications of the open charm vector mesons in the nuclear medium are found to be rather moderate or even small such that dilepton spectroscopy will require an invariant mass resolution of a few MeV. Furthermore, the elastic and inelastic interactions of the open charm mesons in the medium are taken into account, which can be related to (u, d )-, s- or c-quark exchange with nucleons. It is found that by studying the D/ˉD ratio for low momenta in the laboratory ( ? 2 - 2.2 GeV/c) as a function of the target mass A stringent constraints on the c-quark exchange cross-section can be obtained. On the other hand, the ratios D ^- _s/D ⁺ _s as well as D/D ^- _s and D/D ⁺ _s at low momenta as a function of A will permit to fix independently the strength of the s-quark exchange reaction in D ^- _s N scattering. Received: 1 March 2002 / Accepted: 21 March 2002     

Charge-independent effective interactions for shell-model studies in the 0g9/2-1p1/2 space

The matrix elements of the effective Hamiltonian in the 0g _9/2-1p _1/2 space are determined by a least-square fit to the energies of 477 levels of nuclei with 38≤Z≤50 and 47≤N≤50. The results of the calculation are found to be in better agreement with experiment than those obtained with previously determined interactions. Received: 31 May 2001 / Accepted: 14 June 2001     

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