Quantitative conditions for the formation of p-wave neutron halos

With the experimental binding energies and configurations, the root-mean-square radii of p-wave valence neutron distributions for nuclei up to the second p-shell have been calculated in the framework of the single-particle potential model. By analyzing the relations between the radii and the binding energies, the scaling laws of p-wave valence neutron distributions are obtained. The quantitative conditions for the formation of p-wave neutron halos are deduced from these scaling laws. Based on the investigation on the probability of finding the valence nucleon outside the range of the interaction potential, a 2p_3/2 halo state in ⁴⁷S is anticipated for the first time. These obtained results might provide reference for searching for p-wave neutron halos in nuclei up to the second p-shell.     

Neutron Halos in the Excited States of Spherical Nuclei Near the β-Stable Line

The newly discovered neutron halos in the excited states of nuclei 12B, 13C, and 209pb are studied by therelativistic mean-field theory. The calculated binding energies are very close to the experimental ones. The experimentally extracted root-mean-square radii of the last neutron with different occupations in nuclei are well reproduced bycalculations. New candidates for the neutron halos in excited states are predicted and are useful for further search ofneutron halos in the excited states of stable nuclei.     

Neutron Halos in the Excited States of Spherical Nuclei Near the β-Stable Line

The newly discovered neutron halos in the excited states of nuclei ¹²B, ¹³C, and ²⁰⁹Pb are studied by the relativistic mean-field theory. The calculated binding energies are very close to the experimental ones. The experimentally extracted root-mean-square radii of the last neutron with different occupations in nuclei are well reproduced by calculations. New candidates for the neutron halos in excited states are predicted and are useful for further search of neutron halos in the excited states of stable nuclei.     

The neutron halo in heavy nuclei calculated with the Gogny force

The proton and neutron density distributions, one- and two-neutron separation energies and radii of nuclei for which neutron halos are experimentally observed, are calculated using the self-consistent Hartree-Fock-Bogoliubov method with the effective interaction of Gogny. Halo factors are evaluated assuming hydrogen-like antiproton wave functions. The factors agree well with experimental data. They are close to those obtained with Skyrme forces and with the relativistic mean-field approach.     

Binding energies of nuclei and their density distributions in a nonlocal extended Thomas-Fermi approximation

Basic properties of the ground states of spherical nuclei are investigated in a nonlocal extended Thomas-Fermi approximation under the assumption of Skyrme forces. It is shown that, for nuclei occurring near the β-stability line, the binding energies, the root-mean-square radii, and the density distributions found on this basis agree well with experimental data. Binding energies, root-mean-square radii, and density distributions are also calculated for the ground states of nuclei lying far off the β-stability line and for superheavy elements. For the proton, the neutron, and the total particle density, the thickness of the diffuse layer is investigated as a function of the number of neutrons in tin isotopes.     

Nuclear properties far from the stability line in the relativistic mean field theory

We study the nuclear properties far from the stability line in the relativistic mean field theory. We find that the parameter set NL 1 provides very good results on binding energies of unstable nuclei, while NL2 results are not good, although both parameter sets give equally good results on nuclear properties for stable nuclei. We discuss the neutron number dependence of the proton and the neutron root mean square radii of proton magic nuclei.     

Neutron density distributions deduced from antiprotonic atoms

The differences between neutron and proton density distributions at large nuclear radii in stable nuclei were determined. Two experimental methods were applied: nuclear spectroscopy analysis of the antiproton annihilation residues one mass unit lighter than the target mass and the measurements of strong-interaction effects on antiprotonic x rays. Assuming the validity of two-parameter Fermi neutron and proton distributions at these large radii, the conclusions are that the two experiments are consistent with each other and that for neutron rich nuclei it is mostly the neutron diffuseness which increases and not the half-density radius. The obtained neutron and proton rms radii differences are in agreement with previous results.     

晕核的标度定律

利用重叠函数的渐近归一化常数(ANC)计算了一系列核的价核子处于核外的几率及价核子密度分布的均方根半径〈r2〉1/2. 由于实验上抽取的核ANC近似与模型参数无关,因此由核ANC计算的核外几率和均方根半径是考察晕核的可靠且有效的观察量. 依价核子处于核外的几率大于50%为条件， 证实了一些核为晕核， 且给出了比较宽松的晕核出现的条件. 此外， 还用〈r2〉/R2≥1.5及〈r2〉1/2/rc≥2.0为判据考察了一系列晕核候选者. 最后， 利用r2算符在有限方势阱中的预期值给出了晕核的标度定律. We have extracted the probability for a valence particle being out the binding potential, as well as the root mean square radius of the probability distribution from the measured nuclear asymptotic normalization coefficients. According to the criterion of nuclear halo, i.e., the valence particle has larger than 50% probability being out of the nuclear binding potential, a number of halo nuclei have been confirmed. Based on these results, we have obtained a very relaxed condition for nuclear halo formation. In addition, a number of nuclear halo candidates have been analyzed with the criteria of 〈r2〉/R2≥1.5 and 〈r2〉1/2/rc≥2.0. Furthermore, we present the scaling laws for the dimensionless quantity 〈r2〉/R2 of the nuclear halo in terms of an analytical expressions of the expectation value for the operator r2 in a finite square well potential.     

Proton magic even-even isotopes and giant halos of Ca isotopes with relativistic continuum Hartree-Bogoliubov theory

We study the proton magic O, Ca, Ni, Zr, Sn, and Pb isotope chains from the proton drip line to the neutron drip line with the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Particulary, we study in detail the properties of even-even Ca isotopes due to the appearance of giant halos in neutron rich Ca nuclei near the neutron drip line. The RCHB theory is able to reproduce the experimental binding energiesE _b and two neutron separation energiesS _2n very well. The predicted neutron drip line nuclei are²⁸O,⁷²Ca,⁹⁸Ni,¹³⁶Zr,¹⁷⁶Sn, and²⁶⁶Pb. Halo and giant halo properties predicted in Ca isotopes withA>60 are investigated in detail through analysis of two neutron separation energies, nucleon density distributions, single particle energy levels, and the occupation probabilities of energy levels including continuum states. The spin-orbit splitting and the diffuseness of nuclear potential in these Ca isotopes, as well as the neighboring lighter isotopes in the drip line Ca region and find certain possibilities of giant halo nuclei in the Ne−Na−Mg drip line nuclei are also studied.     

Analysis of fissionability data at high excitation energies

A level density formula that takes into account the smoothed volume, surface and curvature dependence of the single particle level density at the Fermi surface using the results of Balian and Bloch, is shown to be compatible with the level spacings found in neutron resonance data if complemented by a simple Ansatz for shell effects (due to Ignatyuk) and pairing effects. The three parameters involved, a scaling parameter, a shell damping energy and a pairing energy shift are compatible, respectively, with known nuclear radii, microscopic level density calculations and odd-even mass fluctuations. At excitation energies on the order of the neutron binding energy no evidence for an absolute level density problem or a different behaviour of level densities (collective contributions) for deformed nuclei as opposed to spherical nuclei is found. The proposed level density formula allows to calculate a priori macroscopic ratios of level densities, e.g. at the groundstate and at the saddle point, removing this important parameter from the analysis of fissionability data. As a first application, the fissionability of a number of actinide nuclei at excitation energies a few MeV above the fission barrier is analysed.     

Finite-range effects in pionic atoms

Pionic atom data are refitted in terms of conventional π^? nuclear optical potentials, modified to allow for finite range in the underlying p-wave πN interaction. We find that level shifts and widths in light and medium-weight nuclei cannot distinguish between the various ranges tested. In heavy nuclei, and for reasonable choices of neutron radii, the data tend to exclude ranges of order 0.5 fm and larger.     

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     

Precision mass measurements of neutron halo nuclei using the TITAN Penning trap

Precise atomic mass determinations play a key role in various fields of physics, including nuclear physics, testing of fundamental symmetries and constants and atomic physics. Recently, the TITAN Penning trap measured the masses of several neutron halos. These exotic systems have an extended, diluted, matter distribution that can be modelled by considering a nuclear core surrounded by a halo formed by one or more of loosely bound neutrons. Combined with laser spectroscopy measurements of isotopic shifts precise masses can be used to obtain reliable charge radii and two-neutron-seperation energies for these halo nuclei. It is shown that these results can be used as stringent tests of nuclear models and potentials providing an important metric for our understanding of the interactions in all nuclei.     

应用原子核的宏观－微观模型研究远离稳定线核的性质

应用原子核的宏观－微观模型研究远离稳定线核的性质，得到了一些结果，例如质子和中子滴线，质子和中子密度分布及其均方根半径和中子皮厚度随同位素位移的变化．对一些奇异核性质的计算结果同相对论平均场方法计算的结果作了比较，对质子滴线附近核的质子放射性也作了简要讨论．     

Deformed relativistic mean-field calculations on nuclei near Z = 50 with FSUGold

The ground-state properties of Sn, Te, Xe, and Ba isotopes have been systematically investigated in the framework of the deformed relativistic mean-field theory with the new parameter set FSUGold. The results show that FSUGold is as successful as NL3 ^* in reproducing the ground-state binding energies of the nuclei. The calculated two-neutron separation energies, quadrupole deformations, and root-mean-square (rms) charge radii are in good agreement with the experimental data. The parameter set FSUGold can successfully describe the shell effect of the neutron magic number N = 82 . Detailed discussions on the binding energies, two-neutron separation energies, quadrupole deformations, rms charge radii and “binding energies” of the last neutrons are given.     

Two-body and three-body halo nuclei

We have extracted the nuclear asymptotic normalization coefficients (ANC) for the virtual transitions B→A+N via some transfer reactions and the radioactive nuclear beam experiments. With these coefficients, root-mean-square (rms) radii for the valence particle in some possible halo nuclei have been calculated. The values of rms radii extracted with ANC approach are nearly model-independent, hence are a good quantity for the investigation of nuclear halo. In addition, we have also calculated the rms radii for the two valence neutrons in some three-body systems in terms of the relationship between the radii of valence particle, core nucleus and nuclear matter. With two conditions for nuclear halo formation, we have examined these extracted rms radii. The results show that 11Be(1/2+, g.s), 12B(1-, 2.621 MeV), 13C(1/2+, 3.089 MeV), 14C(0-, 6.903 MeV), 14C(1-, 6.094 MeV), 15C(1/2+, g.s) and 19C(1/2+, g.s) with the valence particle in the 2s ground or excited state are the neutron halo nuclei, whereas 17F(1/2+, 0.495 MeV) and 21Na(1/2+, 2.423 MeV) are the proton halo nuclei in the excited state. For three-body systems, except the well-established two-neutron halo nuclei 6He and 11Li, 14Be and 17B might be the two-neutron halo nuclei as well.     

Level inversion of N=9 isotones in the relativistic mean-field theory

We have studied the ground state properties of N=8 and N=9 isotones in the framework of the nonlinear relativistic mean-field (RMF) theory using force parameters NL-SH. Calculations show that the RMF theory can describe experimental data of binding energies and radii for these nuclei. The RMF theory can also reproduce the level inversion of N=9 isotones well if the ρ tensor coupling is included. One-neutron halos in ¹⁵C and ¹⁴B are predicted.     

Analysis of total reaction cross sections for deuterons on 1p-shell-nuclei

This study aims to analyze the differential cross sections(DCSs) of elastic scattering and total reaction cross sections(TRCSs) of the loosely-bound deuteron projectile impinging on 1 p-shell nuclei, such as9 Be,12 C, and16 O, at incident energies ranging between10.6 and 171 MeV using the continuum discretized coupled channel(CDCC) method. By fitting the experimental data for the DCSs and TRCSs, energy-dependent renormalization factors for the real and imaginary parts of the nucleon-nucleus opticalmodel potentials deduced from the studies proposed by Koning and Delaroche(KD02) and by Watson, Singh, and Segel(WSS),are obtained. It is found that with the WSS potential, which was obtained specifically for 1 p-shell nuclei, the CDCC calculations can simultaneously reproduce both the DCSs and the TRCSs. The results show that it is important to choose appropriate optical potentials to describe deuteron-induced reactions.