Halo or skin in the excited states of some light mirror nuclei

The properties of three pairs of mirror nuclei ¹³N- ¹³C, ¹⁵N- ¹⁵O and ²¹Na- ²¹Ne (these mirror nuclei are all made of a good inert core plus an unpaired valence nucleon) are investigated by using the nonlinear relativistic mean-field (RMF) theory. It is found that the calculated binding energies with two different parameter sets are very close to the experimental ones for both the ground states and the excited states except for the large deformed nuclei. The calculations show that the 2s_1/2 excited states of ¹⁵N and of ²¹Na are both weakly bound with a proton halo and a proton skin (or a pigmy proton skin), respectively. In addition, the 1d_5/2 excited state of ¹³C and the 2s_1/2 excited state of ¹⁵O are also weakly bound with a neutron skin, respectively. The ratio of the valence nucleon radius to matter radius is deduced and it can be regarded as an additional criterion for the existence of exotic structure. The unbound 2s_1/2 and 1d_5/2 excited states of ¹³N are also discussed.     

Binding energies and modelling of nuclei in semiclassical simulations

We study the binding energies of spin–isospin saturated nuclei with nucleon number 8?A?100$8?A?100$ in semiclassical Monte Carlo many-body simulations. The model Hamiltonian consists of (i) nucleon kinetic energy, (ii) a nucleon–nucleon interaction potential, and (iii) an effective Pauli potential which depends on density. The basic ingredients of the nucleon–nucleon potential are a short-range repulsion, and a medium-range attraction. Our results demonstrate that one can always expect to obtain the empirical binding energies for a set of nuclei by introducing a proper density dependent Pauli potential in terms of a single variable, the nucleon number, A. The present work shows that in the suggested procedure there is a delicate counterbalance of kinetic and potential energetic contributions allowing a good reproduction of the experimental nuclear binding energies. This type of calculations may be of interest in further reproduction of other properties of nuclei such as radii and also exotic nuclei.     

q形变壳模型中奇A核的磁矩

将核磁矩算符定义为量子群SU_q(2)的一阶张量算符的形式.计算结果显示,q形变参数依赖于最后一个主壳层中的价核子数.在对满单j壳层外仅有一个价核子的奇A核磁矩值进行拟合后发现,在大多数情况下,较Schmidt值有所改进.     

Bounds to the size of halo nuclei

Inspired by the Bertlmann-Martin inequality relating the rms radius of the ground state wave function to the lowest dipole transition energy, we have proposed a dimensional relationship to be used in weakly bound two-body systems. In the present work, it is applied to halo nuclei. Lower and upper bounds to the size of halo nuclei are compared to values obtained from reaction cross sections. The case of the deuteron is also presented. Received: 18 September 1998     

Partial widths for the decays η:(1295) →γγ and η:(1440) →γγ

We discuss γγ partial widths of pseudoscalar/isoscalar mesons η:(M) in the mass region M∼ 1000–1500 MeV. The transition amplitudes η:(1295) →γγ and η:(1440) →γγ are studied within an assumption that the decaying mesons are the members of the first radial excitation nonet 2¹ S ₀qˉq. The calculations show that partial widths being of the order of 0.1 keV are dominantly due to the nˉn meson component while the contribution of the sˉs component is small. Received: 24 September 1999     

Isospin symmetry of odd-odd mirror nuclei: identification of excited states in N=Z-2 48Mn

Excited states have been observed in the N=Z-2 odd-odd nucleus 48Mn for the first time. Through comparison with the structure of 48V, a first high-spin study of an odd-odd mirror pair has been achieved. Differences between the T=1 analogue states in this pair have been interpreted in terms of Coulomb effects, with the aid of shell-model calculations in the full pf valence space. Unlike other mirror pairs, the energy differences have been interpreted almost entirely as due to a monopole effect associated with smooth changes in radius (or deformation) as a function of angular momentum. In addition, the large energy shift between analogue negative-parity states is interpreted in terms of the electromagnetic spin-orbit interaction in nuclei.     

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.     

Er，Yb和Hf同位素的基态占有率（英文）

应用严格求解的Nilsson 平均场加推广对力模型,在同时考虑质子-质子和中子-中子间对力相互作用的情况下,对稀土区的152-164Er,154-166Yb 和156-168Hf 核素的结合能、奇偶能差、低激发态转动惯量等基态性质进行系统的统一描述。通过计算结果与实验数值比较分析显示,对力相互作用在阐明以上核素能谱的基态性质中起到了关键的作用。应用拟合上述物理量所确定的模型参数,对156-162Yb 核素基态中价核子配成角动量J = 0,1,… ,12的价核子对占有率的计算结果显示,配成角动量为偶数价核子对的占有率远远高于配成角动量为奇数价核子对的占有率,其数值结果揭示了配成角动量为S,D和G的价核子对在所考虑的核素基态性质中占主导地位。The Nilsson mean-field plus extended-pairing model for deformed nuclei is applied to describe the ground-state properties of selected rare-earth nuclei. Binding energies, even-odd mass differences, moments of inertia for the ground-state band of 152-164Er, 154-166Yb, and 156-168Hf are calculated systematically in the model employing both proton-proton and neutron-neutron pairing interactions. In comparison with the corresponding experimental data, it is shown that for these rare-earth nuclei, pairing interaction is crucial in elucidating the properties of the ground state. With model parameters determined by fitting the energies of these states, ground-state occupation probabilities of valence nucleon pairs with angular momentum J =0,1, …,12 for even-even 156-162Yb are calculated. It is inferred that the occupation probabilities of valence nucleon pairs with even angular momenta are much higher than those of valence nucleon pairs with odd angular momenta. The results clearly indicate that S, D, and G valence nucleon pairs dominate in the ground state of these nuclei.     

Size of the proton emission region inp-C,d-C, α-C and C-C interactions at 4.2 GeV/c per incident nucleon from two-proton correlations

Correlations between secondary protons with small relative momenta have been studied in interactions of various light nuclei with the carbon target at 4.2 GeV/c per incident nucleon with the aim to determine the radius of the proton emission region. This radius is found to decrease with increasing momentum and transverse momentum of the proton pair, but it does not show any dependence on the mass of the projectile nucleus.     

Towards a new Gogny force parameterization: Impact of the neutron matter equation of state

A new parameterization of the effective nucleon–nucleon Gogny interaction is proposed. It reproduces the neutron matter equation of state much better than the commonly used D1S Gogny interaction and furthermore reduces the binding energies' drift for the major part of the isotopic chains. Other important nuclear properties related both to nuclear matter and finite nuclei are studied and shown to be of similar quality as with D1S.     

Finite Nuclei in a Relativistic mean—Field Theory with quadratic Couplings

A quadratic scalar and vector coupling model proposed recently has been applied to finite nuclei.The calculated results are compared with those of the derivative scalar couling(DSC) model and the nonlinear Walecka model,The results show that the spin-orbit splittings are improved considerably by quadratic ouplings in contrast to the DSC model,However,the binding energy per nucleon,rms charge radius,as well as the spin-orbit splittings in the quadratic model are still small compared with those given by the nonlinear Walecka model and the experimental data.     

核子质量、 半径及夸克凝聚的核物质密度依赖性

简要介绍核物质中核子的质量、 半径及夸克凝聚的密度依赖关系基于QCD模型和QCD有效场论研究的现状, 并具体介绍整体色对称模型（GCM）的研究结果. GCM研究表明, 在小于临界密度的情况下, 核物质中核子的质量随核物质密度的增大而减小, 核子的半径和夸克凝聚随核物质密度的增大而增大. 当达到临界密度时, 核子质量减小为零, 核子半径变为无限大, 夸克凝聚突变为零, 进而提出一个核物质中手征对称性恢复的新机制. The status of the investigations on the nucleon mass, nucleon radius and quark condensate in the framework of QCD inspired models and QCD effective field theories is briefly reviewed. The results in the global color symmetry model (GCM) are described a little detailedly. The calculated results indicate that, before the maximal density is reached, the mass of a nucleon in nuclear matter decreases, the radius of a nucleon and the quark condensate increase very slowly, with the increase of the nuclear matter density. As the maximal nuclear matter density is reached, the mass of the nucleon vanishes gradually. The radius becomes infinite and the quark condensate vanishes suddenly. A new mechanism for the chiral symmetry restoration in nuclear matter is proposed.     

Microscopic calculations for upper-fp,g<Subscript>9/2</Subscript> shell nuclei: Ge &; Se

Shell-model calculations for isotopes of Ge and Se are reported where valence nucleons beyond the N = 28 = Z core occupy levels of the normal parity upper-fp shell (f_5/2,p_3/2,p_1/2) and the unique parity g_9/2 intruder configuration. Results are given for realistic interactions of the Kuo-Brown-3 type with various model space truncations that key in on the number of nucleon pairs allowed to occupy the intruder level. Electromagnetic (E2 & M1) rates as well as decay probabilities are calculated, some of which are key in determining the structure of “waiting point” nuclei that regulate certain nucleo-astrosynthesis processes. The role of the intruder level, which is treated on an equal footing with the normal parity levels, is shown to be important for reproducing structural details. The levels of the upper-fp shell are handled within the framework of a normal ls-coupled basis as well as its pseudo-SU(3) counterpart, and respectively, the g_9/2 as a single level and as a member for the complete gds shell. The second of these two approaches, namely, the SU(3) picture, allows one to better probe the effect of deformation.     

Transition from spherical to deformed shapes of nuclei in the Monte Carlo shell model

The transition from spherical to deformed shapes is studied in terms of large-scale shell-model calculations for Ba isotopes as a function of valence nucleon number with fixed single-particle space and Hamiltonian. A new version of the Monte Carlo shell model is introduced so as to incorporate pairing correlations efficiently, by utilizing condensed pair bases. The energy levels and electromagnetic matrix elements are described in agreement with experiments throughout the transitional region. The orbital M1 sum rule is calculated as a measure of the deformation evolution, and the Q-phonon picture is shown to be reasonable from spherical to deformed nuclei.     

A Hartree-Fock nuclear mass formula

We recall the main features of the recently published mass formula, HFBCS-1, based on the Hartree-Fock-BCS method, and compare its extrapolations out to the neutron drip line with those given by the fine-range droplet model. A new Hartree-Fock-Bogolyubov mass formula, HFB-1, is described: the rms error of the fit to 1888 masses is 0.766 MeV, compared with 0 .738 MeV for HFBCS-1, but there are no substantial changes in the predictions relevant to the r-process. After a critical examination of various questions relating to the effective nucleon mass and to the requirements of the relativistic mean-field theory, we conclude that the greatest remaining ambiguity concerns the nature of the pairing force. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: pearson@lps.umontreal.ca     

Investigation of phase-equivalent potentials by a halo transfer reaction

Using the supersymmetric quantum mechanics, we investigate the wave function-sensitive properties of the supersymmetric potentials which have received a lot of attention in the literature recently. We show that a superdeep potential and its phase-equivalent shallow-partner potential give very similar rms radius values for the weakly bound systems such as the deuteron and ¹¹Be nuclei. Although the corresponding eigenstates differ in the node-number, our investigation on the ¹¹Be(p, d )¹⁰Be single nucleon halo transfer reaction at 35 MeV show that also other physical quantities such as the cross-section angular distributions calculated using these wave functions reflect the nodal structure rather weakly. This lends support to two nearly equivalent treatments of the Pauli principle. Received: 15 May 2000 / Accepted: 14 September 2000     

Binding energies of proton-rich nuclei determined from their mirror pairs

In addition to the Coulomb displacement energy, the residual differences between the binding energies of mirror nuclei (a pair of nuclei with the same mass number plus interchanged proton and neutron numbers) contribute to the shell effect via the valence scheme in this study. To this end, one linear combining type of valence nucleon number, namely, \begin{document}$ \alpha N_p+\beta N_n $\end{document}, is chosen to tackle this shell correction, in which \begin{document}$ N_p $\end{document} and \begin{document}$ N_n $\end{document} are the valence proton and neutron numbers with respect to the nearest shell closure, respectively. The mass differences of mirror nuclei, as the sum of the empirical Coulomb displacement energy and shell effect correction, are then used to obtain the binding energies of proton-rich nuclei through the available data of their mirror partners to explore the proton dripline of the nuclear chart.