New neutron magic number <Emphasis Type="Italic">N</Emphasis> = 16 for neutron-rich nuclei

A survey of experimental results obtained at GANIL (Caen, France) on the study of the properties of very neutron-rich nuclei (Z=6–20, A=20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N=16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells, and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸O, they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behavior of the two-neutron separation energies S_2n derived from mass measurements gives very clear evidence for the existence of the new shell closure N=16 for Z=9 and 10 appearing between the 2s_1/2 and 1d_3/2 orbitals. This fact, strongly supported by the instability of C, N, and O isotopes with N>16, confirms the magic character of N=16 for the region from carbon up to neon, while the shell closure at N=20 tends to disappear for Z≤13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using in-beam γ-ray spectroscopy are also reported.     

The neutron drip line in the region of <Emphasis Type="Italic">N</Emphasis>=20 and <Emphasis Type="Italic">N</Emphasis>=28 closures

Experimental studies of neutron drip line nuclei are introduced. The neutron drip line in the oxygen-magnesium region has been explored by the projectile fragmentation of a ⁴⁸Ca beam. New neutron-rich isotopes, ³⁴Ne and ³⁷Na, have been observed together with some evidence for the particle instability of ³³Ne and ³⁶Na. Recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells, and together with the measurements of instability of doubly magic nuclide ²⁸O, they provide information on changes in neutron shell closures of very neutron-rich isotopes from carbon up to calcium. The conclusion about a rearrangement in neutron shell closures is given. The spectroscopic measurements can reveal details of the underlying microscopic structures; in-beam γ-ray spectroscopy is an effective tool to check for shell closures. The results on the γ-ray energies of the first 2⁺ level in even-even nuclei for the range N=12–32 are discussed. The strength of N=20 and N=28 shells is variable in the region from carbon up to magnesium.     

Single-particle properties of <Emphasis Type="Italic">N</Emphasis> = 12 to <Emphasis Type="Italic">N</Emphasis> = 20 silicon isotopes within the dispersive optical model

Experimental neutron and proton single-particle energies in N = 12 to N = 20 silicon isotopes and data on neutron and proton scattering by nuclei of the isotope ²⁸Si are analyzed on the basis of the dispersive optical model. Good agreement with available experimental data was attained. The occupation probabilities calculated for the single-particle states in question suggest a parallel-type filling of the 1d and 2s _1/2 neutron states in the isotopes ^{26,28,30,32,34}Si. The single-particle spectra being considered are indicative of the closure of the Z = 14 proton subshell in the isotopes ^30,32,34Si and the N = 20 neutron shell.     

Investigation of the neutron shell structure of the even-even isotopes <Superscript>40–56</Superscript>Ca within the dispersive optical model

Within the method of matching experimental data obtained in the neutron-stripping and neutron-pickup reactions on ^{40,42,44,46,48}Ca isotopes, the single-particle energies and probabilities that neutron states are filled are obtained for the even-even calcium isotopes. These data are analyzed within the dispersive optical model, and good agreement between the calculated and experimental values of the energies of states is obtained. The dispersive optical potential is extrapolated to the region of the unstable ^50,52,54,56Ca nuclei. The calculated single-particle energies of bound states in these isotopes are compared with the results of the calculations within the multiparticle shell model, the latter predicting a new magic number N = 34 for Z = 20 nuclei.     

α particle preformation and shell effect for heavy and superheavy nuclei

The α particle preformation factor is extracted within a generalized liquid drop model for Z = 84-92 isotopes and N = 126,128,152,162,176,184 isotones.The calculated results show clearly that the shell effects play a key role in α particle preformation.The closer the proton and neutron numbers are to the magic numbers,the more difficult the formation of the α cluster inside the mother nucleus is.The preformation factors of the isotopes reflect that N = 126 is a magic number for Po,Rn,Ra,and Th isotopes,but for U isotopes the weakening of the influence of the N =126 shell closure is evident.The trend of the factors for N = 126 and N = 128 isotones also support this conclusion.We extend the calculations for N = 152,162,176,184 isotones to explore the magic numbers for heavy and superheavy nuclei,which are probably present near Z = 108 to N = 152,162 isotones and Z = 116 to N = 176,184 isotones.The results also show that another subshell closure may exist after Z = 124 in the superheavy nuclei.This is useful for future experiments.     

A relativistic mean-field study of magic numbers in light nuclei from neutron to proton drip-lines

In an axially deformed relativistic mean-field calculation of single-particle energy spectra ofN = 8 (Li-Mg) andN = 14,16 (C-Mg) isotonic chain and the one- and two-neutron separation energies of various isotopes of Li-Mg, new magic numbers are found to exist atN = 6 andN = 16 and/orN = 14, which are in addition to theN = 8 andN = 20 magic numbers. In neutron-rich nuclei, the shell gap atN = 6 is larger than atN = 8 and a large gap is observed forN = 16 or 14 for the neutron-rich andN = 14 for proton-rich nuclei. Large shell gaps are also found to exist atN = 14 and 16 orN = 16 alone for nuclei near theβ-stability line. The above results are independent of the parameter sets TM2, NL3 and NL-SH used here. Similarly, new large shell gaps are predicted atZ = 616 and/or 14 for protons.     

Pushing the limits of nuclear stability

Reaching the limits of nuclear stability offers unique opportunities to understand basic nuclear properties. New shell structures close to the driplines can change the existence of neutron-rich nuclei. A new search for ¹⁶Be confirmed the previous limit for particle stable Be isotopes at A=14. Single proton knock-out reactions offer the potential for more sensitive searches of very weakly bound nuclei. In order to extend the knowledge of the neutron dripline beyond Z=8 requires new accelerator developments. The proposed new rare isotope accelerator has the potential to push the limit of the neutron dripline to at least Z=25.     

Shell evolution in neutron-rich nuclei: the single particle perspective

The isospin dependence of spin-orbit(SO)splitting becomes increasingly important as N/Z increases in neutron-rich nuclei.Following the initial independent-particle strategy toward explaining the occurrence of magic numbers,we systematically investigated the isospin effect on the shell evolution in neutron-rich nuclei within the Woods-Saxon mean-field potential and the SO term.It is found that new magic numbers N=14 and N=16 may emerge in neutron-rich nuclei if one changes the sign of the isospin-dependent term in the SO coupling,whereas the traditional magic number,N=20,may disappear.The magic number N=28 is expected to be destroyed despite the sign choice of the isospin part in the SO splitting,corresponding to the strength of the SO coupling term.Meanwhile,the N=50 and 82 shells may persist within the single particle scheme,although there is a decreasing trend of their gaps toward extreme proton-deficient nuclei.Besides,an appreciable energy gap appears at N=32 and 34 in neutron-rich Ca isotopes.All these results are more consistent with those of the interacting shell model when enhancing the strength of the SO potential in the independent particle model.The present study may provide a more reasonable starting point than the existing one for not only the interacting shell model but also other nuclear many-body calculations toward the neutron-dripline of the Segrèchart.     

Emergence of new magic numbers,N = 16 and 32 by tensor interaction in Skyrme–Hartree–Fock theory

Melting of N = 20 shell and development of N = 16 and 32 shells for neutron-rich nuclei have been studied extensively by including tensor interaction in Skyrme–Hartree–Fock theory optimized to reproduce the splitting Δ1f shells of ^40,48Ca and ⁵⁶Ni nuclei. Evolution of gap generated by the energy difference of single-particle levels ν2s _1/2 and ν1d _3/2 has been found to be responsible for shell closure at N = 16. The splitting pattern of spin–orbit partners 2p shell model state in Ca, Ti, Cr, Fe and Ni isotopes indicates the formation of a new shell at N = 32 region.     

Clustering in neutron-rich nuclei

Clustering in nuclei is discussed putting emphasis on the investigation of the role of nuclear clustering in neutron-rich nuclei. The subjects we discuss include clustering in neutron-rich Be, B and C isotopes, clustering in the island of inversion around N = 20, and clustering in the region with A ≈ 40. Be isotopes present us typical examples of clustering in neutron-rich nuclei not only in their ground band states but also in their excited band states, for which we show the analyses based on antisymmetrized molecular dynamics (AMD). Clustering in Be isotopes near neutron dripline is intimately related to the breaking of the neutron magic number N = 8. In this connection we report our study about the possible relation of the clustering with the breaking of the neutron magic number N = 20 in the island of inversion including ³²Mg and ³⁰Ne. Our discussion is not only about the positive parity states but also about negative parity states. Recently in the latter half of sd shell and in the pf shell many excited rotational bands with large deformation have been found to exist. Since the first excited K ^π = 0⁺ and K ^π = 0^- bands in ⁴⁰Ca have been regarded as constituting inversion doublet bands having the ³⁶Ar + α structure, and since the first excited K ^π = 0^- band in ⁴⁴Ti has been concluded to have ⁴⁰Ca + α structure through the α transfer reaction and by using the unique α optical potential on ⁴⁰Ca, it is important to investigate the role of α clustering in these newly-found rotational bands with large deformation. We will report the AMD study about this problem.     

Molecular structure of nuclei

Cluster structures of nuclei are discussed, with emphasis on nuclear clustering in unstable nuclei. The subjects we discuss are alpha condensed states, clustering in Be and B isotopes, and clustering in ³²Mg and ³⁰Ne. The subject of alpha cluster condensation comes from the clustering nature of dilute nuclear matter. We discuss that recent heavy-ion central collision experiments give us nice evidence of the clustering in dilute nuclear matter. We then present a new prediction of the existence of the “alpha cluster condensed states” in the self-conjugate 4n nuclei around the breakup threshold energy into n alpha-particles. As for the clustering in neutron-rich Be, we discuss the comparison between the antisymmetrized molecular-dynamics results and the recent experimental data, which shows that the clustering feature manifests itself very clearly in neutron-rich Be isotopes both in the ground and excited states. Clustering in Be isotopes near neutron dripline is intimately related to the breaking of the neutron magic number N = 8. We report our recent study about the possible relationship between the clustering and the breaking of the neutron magic number N = 20 in ³²Mg and ³⁰Ne. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: horiuchi@ruby.scphys.kyoto-u.ac.jp     

Shape transition in the neutron rich sodium isotopes

Mass spectrometer measurements of the neutron rich sodium isotopes show a sudden increase at ³¹Na in the values of the two-neutron separation energies. The spherical shell model naturally predicts a sudden decrease at ³²Na after the N = 20 shell closure. We propose that the explanation for this disagreement lies in the fact that sodium isotopes in this mass region are strongly deformed due to the filling of negative parity orbitais from the 1f_{$\text{7}\text{2}$} shell. Hartree-Fock calculations are presented in support of this conjecture.     

New magic number, N = 16, near the neutron drip line

We have surveyed the neutron separation energies (S(n)) and the interaction cross sections (sigma(I)) for the neutron-rich p-sd and the sd shell region. Very recently, both measurements reached up to the neutron drip line, or close to the drip line, for nuclei of Z/=3), which shows the creation of a new magic number. A neutron-number dependence of sigma(I) shows a large increase of sigma(I) for N = 15, which supports the new magic number. The origin of the new magic number is also discussed.     

Neutron single-particle characteristics of Ag isotopes in the dispersive optical model

The neutron dispersive optical potential for Ag isotopes is constructed for a wide range of variation in the N number. Good agreement with the experimental data on the scattering of neutrons by ¹⁰⁷Аg isotopes, and on single-particle energies and the probabilities of subshell occupation near the Fermi energy, is obtained for stable isotopes ^{107, 109}Ag using the dispersive optical model. Calculations that predict the evolution of the neutron single-particle energies up to the boundary of neutron stability are performed. It is shown that new magic number N = 56 (for Z = 40) disappears upon moving from Zr to Sn in an isotonic chain with N = 56, due to rapid deepening of level 1g _7/2.     

Magic numbers in superheavy elements

The energy density method is used to study the magic character of neutron and proton numbers corresponding to N > 126 and Z > 82. It is found that N = 184 and N = 228 are the next neutron magic numbers. For the protons, however, no sign of a shell closure appears for 82 < Z ? 130. Some simple criteria for the β^? - and α-stability of N = 184 and N = 228 isotones are also discussed.     

TITAN: An ion trap facility for on-line mass measurement experiments

Precision determinations of ground state or even isomeric state masses reveal fingerprints of nuclear structure. In particular, at the limits of existence for very neutron-rich or -deficient isotopes, one can extract detailed information about nuclear structure from separation energies or binding energies. Mass measurements are important to uncover new phenomena, to test new theoretical predictions, or to refine model approaches. For example, the N?=?28 shell has proven more stable than previously expected; however, the predicted new “magic” number at N?=?34 in the K and Ca isotopes has yet to be confirmed experimentally. For these neutron-rich nuclei, the inclusion of three-body forces leads to significantly better predictions of the ground-state mass. Similarly, halo nuclei present an excellent application for ab-initio theory, where ground state properties, like masses and radii, test our understanding of nuclear structure. Precision mass determinations at TRIUMF are carried out with the TITAN (TRIUMF’s Ion Traps for Atomic and Nuclear science) facility. It is an ion-trap setup coupled to the on-line facility ISAC. TITAN has measured masses of isotopes as short-lived as 9 ms (almost an order of magnitude shorter-lived than any other Penning trap system), and it is the only one with charge breeding capabilities, which allow us to boost the precision by almost 2 orders of magnitude. We recently made use of this feature by measuring short-lived, proton-rich Rb-isotopes, up to ⁷⁴Rb while reaching the 12?+ charge state, which together with other improvements led to an increase in precision by a factor 36.     

Decay spectroscopy of neutron-rich nuclei with A ≃ 100

We review structure data obtained by decay spectroscopy of neutron-rich nuclei of mass close to 100. Emphasis is put on the contribution of experiments at IGISOL in the nineties. They confirmed the earlier postulated shape coexistence in the fast shape-transition region between N = 58 (spherical ground states and low collectivity) and N = 60 (strong axial deformation). A detailed spectroscopic study of the A = 99 chain established the upper-Z limit of the N = 56 shell closure region with ⁹⁹Nb, owing to striking similarities with ⁹⁷Y. A consequence of the N = 56 closure is that the s _1/2 odd-neutron becomes the ground state of the most neutron-rich N = 57 isotones, starting with ⁹⁹Mo, instead of the degenerated d _5/2 and g _7/2 subshells familiar in the tin region. Consequences on the change of spin on astrophysical r-process calculations are briefly discussed. Finally, we say a few words about neutron-rich rhodium and palladium isotopes near the neutron midshell where regular and intruder states coexist very close to each other.     

放射性核束的库仑激发

综述了利用中、高能放射性核束的库仑激发方法研究位于N＝20和28主壳隙附近的丰中子核结构所取得的进展．系统的实验结果清晰地表明,在离开β稳定线区域时N＝20兰壳隙突然消失和N＝28主壳隙的减弱过程．提出了利用兰州放射性束流线开展双幻核Ni50附近核素的低位能级核结构研究的构想． The study of coulomb excitation of the neutron-rich nuclei around N=20 and 28 shell closure with radioactive ion beam at intermediate energy is reviewed. The systematics of the measured energy of the 2+1 state shows that the N=20 shell closure in neutron-rich isotopes with Z≤12 disappears suddenly and N=28 shell elosure appears to be weak for 44S.The coulomb excitation studies of the exotic nuclei around the double magic 7828Ni50 at RIBLL are proposed.