Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48. Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square （rms） radii of charge and neutron, and shell gaps have been calculated. The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42. The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43. The evolution of shell gaps with proton number Z can be clearly observed. Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region. In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.     

Nuclear properties of Z=114 isotopes and shell structure of ~(298)114

The two-neutron separation energies(S_(2n)) and α-decay energies(Q_α) of the Z=114 isotopes are calculated by the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB) approach with the SLy5,T22,T32 and T43 interactions.It is found that the tensor force effect on the bulk properties is weak and the shell closure at N=184 is seen evidently with these interactions by analyzing the S_(2n) and Q_α evolutions with neutron number N.Meanwhile,the single-particle energy spectra of ~(298)114 are studied using the spherical SHFB approach with these interactions to furthermore examine the shell structure of the magic nucleus ~(298)114.It is shown that the shell structure is almost not changed by the inclusion of the tensor force in the Skyrme interactions.Finally,by examining the energy splitting of the three pairs of pseudospin partners for the protons and neutrons of ~(298)114,it is concluded that the pseudospin symmetry of the neutron states is preserved better than that of the proton states and not all of the pseudospin symmetries of the proton and neutron states are influenced by the tensor force.     

Spurious Shell Closures in the Relativistic Mean Field Model

Following a previous systematic theoretical study of the ground-state properties of over 7000 nuclei from the proton drip line to the neutron drip line in the relativistic mean field model [Prog. Theor. Phys. 113 （2005） 785], which is in fair agreement with existing experimental data, we observe a few spurious shell closures, i.e. proton shell closures at Z = 58 and Z = 92. These spurious shell closures are found to persist in all the effective forces of the relativistic mean field model, e.g. TMA, NL3, PKDD and DD-ME2.     

Basic characteristics of nuclear landscape by improved Weizs?cker-Skyrmetype nuclear mass model

Atomic Mass Evaluation(AME2016) has replenished the latest nuclear binding energy data. Other physical observables, such as the separated energies, decay energies, and the pairing gaps, were evaluated based on the new mass table. An improved Weizs?cker-Skyrme-type(WS-type) nuclear mass model with only 13 parameters was presented, including the correction from two combinatorial radial basis functions(RBFs), where shell and pairing effects are simultaneously dealt with using a Strutinsky-like method. The RBFs code had 2267 updated experimental binding energies as inputs, and their correspondent root-mean square(rms) deviations dropped to 149 keV. For the training of other mass models by RBFs correction, rms deviations are clustered between 100 keV to 200 keV. Compared with other experimental quantities, the rms deviations calculated within the improved WS-type model falls between 100 keV and 250 keV. We extrapolate the binding energies to 12435 nuclei, which covers the ranges 8 ≤ Z ≤ 128 and 8 ≤ N ≤ 251 in the framework of the WS-type model with RBFs correction. Simultaneously, the ground state deformations β_(2,4,6) and all parts in the WS-type mass formula are presented in this paper. Finally, we tabulated all calculated characteristics within the improved formula and linked them to https://github.com/lukeronger/Nuclear Data-LZU: nuclear binding energies, one-nucleon and two-nucleon separation energies(S_(n,p,2n,2p)), and β-decay energies( Q_α and Q_(β-,β+,EC)), and the pairing gap ?_n and ?_p.     

Global α-decay study based on the mass table of the relativistic continuum Hartree-Bogoliubov theory

The α-decay energies(Qα) are systematically investigated with the nuclear masses for 10 Z 120 isotopes obtained by the relativistic continuum Hartree-Bogoliubov(RCHB) theory with the covariant density functional PC-PK1, and compared with available experimental values. It is found that the α-decay energies deduced from the RCHB results present a similar pattern to those from available experiments. Owing to the large predicted Qαvalues( 4 Me V), many undiscovered heavy nuclei in the proton-rich side and super-heavy nuclei may have large possibilities for α-decay. The influence of nuclear shell structure on α-decay energies is also analysed.     

Signatures of shell evolution in alpha decay across the N=126 shell closure

Within the alpha-cluster model, we particularly investigate the alpha decay of exotic nuclei in the vicinity of the N = 126 neutron shell plus the Z = 82 proton shell. The systematics of alpha-preformation probability(P_α),as an indicator of the shell effect, is deduced from the ratio of the experimental decay width to the calculated one.Through the comparative analysis of the P_α trend in the N = 124-130 isotonic chain, the N = 126 and Z = 82 shell closures are believed to strongly affect the formation of the alpha particle before its penetration. Additionally, the P_α variety in Po and Rn isotopes is presented as another proof for such an influence. More importantly, it may be concluded that the expected neutron(or proton) shell effect gradually fades away along with the increasing valence proton(or neutron) number. The odd-even staggering presented in the P_α value is also discussed.     

Neutron halos in the excited states for N=127 isotones

Properties of the ground states and the excited states of N=127 isotones are investigated by using the nonlinear relativistic mean field theory with the interactions PK1. By analyzing the rms of proton and neutron, the single particle energies of valence nucleon and the density distributions of neutron, proton and the last neutron, it can be found that there exists a neutron halo in the excited states of 3d5/2, 4s1/2 and 3d3/2 in 209Pb. It is also predicted that there exists a neutron halo in the excited states of 3d5/2, 4s1/2 and 3d3/2 in 207Hg, 208Tl, 210Bi and 211Po.     

Doubly magic properties in superheavy nuclei

A systematic study of global properties of superheavy nuclei in the framework of the Liquid Drop Model and the Strutinsky shell correction method is performed. The evolution equilibrium deformations, TRS graphs and α-decay energies are calculated using the TRS model. The analysis covers a wide range of even-even superheavy nuclei from Z=102 to 122. Magic numbers and their observable influence occurring in this region have been investigated. Shell closures appear at proton number Z=114 and at neutron number N=184.     

Doubly magic properties in superheavy nuclei

A systematic study of global properties of superheavy nuclei in the framework of the Liquid Drop Model and the Strutinsky shell correction method is performed. The evolution equilibrium deformations, TRS graphs and α-decay energies are calculated using the TRS model. The analysis covers a wide range of even-even superheavy nuclei from Z =102 to 122. Magic numbers and their observable influence occurring in this region have been investigated. Shell closures appear at proton number Z =114 and at neutron number N =184.     

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.     

Determination of the N=16 shell closure at the oxygen drip line

The neutron unbound ground state of (25)O (Z=8, N=17) was observed for the first time in a proton knockout reaction from a (26)F beam. A single resonance was found in the invariant mass spectrum corresponding to a neutron decay energy of 770_+20(-10) keV with a total width of 172(30) keV. The N=16 shell gap was established to be 4.86(13) MeV by the energy difference between the nu1s(1/2) and nu0d(3/2) orbitals. The neutron separation energies for (25)O agree with the calculations of the universal sd shell model interaction. This interaction incorrectly predicts an (26)O ground state that is bound to two-neutron decay by 1 MeV, leading to a discrepancy between the theoretical calculations and experiment as to the particle stability of (26)O. The observed decay width was found to be on the order of a factor of 2 larger than the calculated single-particle width using a Woods-Saxon potential.     

Electromagnetic properties of neutron-rich Ge isotopes

The electric quadrupole moment Q and the magnetic momentp(or the g factor) of low-lying states in even-even nuclei ~(72-80)Ge and odd-mass nuclei ~(75-79) Ge are studied in the framework of the nucleon pair approximation(NPA) of the shell model,assuming the monopole and quadrupole pairing plus quadrupole-quadrupole interaction.HA H.Our calculations reproduce well the experimental values of Q(2_1~+) and g(2_1~+) for ~(72,74,76) Ge,as well as the yrast energy levels of these isotopes.The structure of the 2_1~+ states and the contributions of the proton and neutron components in Q(2_1~+) and g(2_1~+) are discussed in the SD-pair truncated shell-model subspace.The overall trend of Q(2_1~+) and g(2_1~+)as a function of the mass number A,as well as their signs,are found to originate essentially from the proton contribution.The negative value of Q(2_1~+) in ~(72,74)Ge is suggested to be due to the enhanced quadrupole-quadrupole correlation and configuration mixing.     

Isoscalar giant monopole resonance for drip-line and super heavy nuclei in the framework of relativistic mean field formalism with scaling calculation

We study the isoscalar giant monopole resonance for drip-lines and super heavy nuclei in the framework of relativistic mean field theory with a scaling approach. The well known extended Thomas-Fermi approximation in the nonlinear σ-ω model is used to estimate the giant monopole excitation energy for some selected light spherical nuclei starting from the region of proton to neutron drip-lines. The application is extended to the super heavy region for Z=114 and 120, which are predicted by several models as the next proton magic numbers beyond Z=82. We compared the excitation energy obtained by four successful force parameters NL1, NL3, NL3*, and FSUGold. The monopole energy decreases toward the proton and neutron drip-lines in an isotopic chain for lighter mass nuclei, in contrast to a monotonic decrease for super heavy isotopes. The maximum and minimum monopole excitation energies are obtained for nuclei with minimum and maximum isospin in an isotopic chain, respectively.     

Relativistic Hartree-Bogoliubov description of deformed light nuclei

The Relativistic Hartree-Bogoliubov model is applied in the analysis of ground-state properties of Be, B, C, N, F, Ne and Na isotopes. The model uses the NL3 effective interaction in the mean-field Lagrangian, and describes pairing correlations by the pairing part of the finite-range Gogny interaction D1S. Neutron separation energies, quadrupole deformations, nuclear matter radii, and differences in radii of proton and neutron distributions are compared with recent experimental data.Received: 27 August 2003, Revised: 12 March 2004, Published online: 19 October 2004PACS:   21.60.Jz Hartree-Fock and random-phase approximations - 21.10.Gv Mass and neutron distributions - 27.20. + n - 27.30. + t      

On (n,p) cross sections for 14 MeV neutrons

Using older compilations and recent data the (n, p) cross sections for neutron energies between 14 and 15 MeV have been collected and revised critically. The experimental data can be represented phenomenologically by the formula $$\log _{10} ({{\sigma _{np} } \mathord{\left/ {\vphantom {{\sigma _{np} } {mb}}} \right. \kern-\nulldelimiterspace} {mb}}) = 0.2 + 0.4A^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - 4.6{{(N - Z)} \mathord{\left/ {\vphantom {{(N - Z)} {A^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} }}} \right. \kern-\nulldelimiterspace} {A^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} }}$$ . The compound part of the (n, p) reactions is described by a statistical model; the direct reactions are taken into account semiempirically.     

Is the nuclear spin-orbit interaction changing with neutron excess?

The difference in the energies of the lowest states corresponding to the two nodeless single-particle orbitals outside the Z=50 closed proton shell, h(11/2) and g(7/2), increases with neutron excess. We have measured the Sn(alpha,t) reaction for all seven stable even Sn isotopes and found that the spectroscopic factors are constant for these two states, confirming their characterization as single-particle states. The trend in energies is consistent with a decrease in the nuclear spin-orbit interaction. A similar trend, also suggesting a decreasing spin-orbit splitting, is seen in the energies of the neutron single-particle states outside the N=82 core, i(13/2) and h(9/2).     

Setup for studying quasi-free neutron-neutron scattering in the energy range of 20–60 MeV

A setup installed on the RADEX neutron beam channel (Institute for Nuclear Research, Russian Academy of Sciences) and designed to study quasi-free nn scattering in the n + d → p + n + n reaction is described. The setup is a two-arm time-of-flight spectrometer composed of scintillation neutron hodoscope (in the left arm), a scintillation neutron detector (in the right arm), and an active scintillation deuterated target for detecting protons. Secondary neutrons are detected at angles corresponding to the kinematic conditions of quasi-free nn scattering. Events are selected at low energies of the outgoing proton spectator. It is shown that data on neutron-neutron quasi-free scattering can be obtained in a wide range of primary-neutron energies.     

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.     

Highly accurate coupled-cluster singlet and triplet pair energies from explicitly correlated calculations in comparison with extrapolation techniques

Coupled-cluster singles and doubles (CCSD) valence shell correlation energies of the systems CH₂ (<¹A₁ state), H₂O, HF, N₂, CO, Ne, and F₂ are computed by means of standard calculations with correlation-consistent basis sets of the type cc-pVxZ (x = D, T, Q, 5, 6) and by means of explicitly correlated coupled-cluster calculations (CCSD-R12/B) with large uncontracted basis sets of the type 19s14p8d6f4g3h for C, N, O, F, and Ne and 9s6p4d3f for H. These CCSD-R12/B calculations provide reference values for the basis set limit of CCSD theory. The computed correlation energies are decomposed into singlet and triplet pair energies. It is established that the singlet pair energies converge as X^?3 and the triplet pair energies as X^?5 with the cardinal number of the correlation-consistent basis sets, and an extrapolation technique is proposed that takes into account their different convergence behaviour. Applied to the cc-pV5Z and cc-pV6Z results, this new extrapolation yields pair energies with a mean absolute deviation of 0.02 mE_h from the CCSD-R12/B reference values. For the seven systems under study, the extrapolated total valence shell correlation energies agree to within 0.2 mE_h with the CCSD-R12/B benchmark data.