Pairing effects in Sn isotopes

An extensive study of pairing effects in the Sn isotopes is carried out. The pairing Hamiltonian is treated by the chain-calculation method which provides practically exact solutions while involving less computational work than a complete-basis diagonalization. The coupling strength is fixed by reproducing the energy of the 9^? state in¹¹⁶Sn, while the single-particle energies have been determined by an analysis of the experimental low-energy spectra of the odd-A isotopes. A detailed comparison of the calculated results with experimental data evidences the importance of neutron pairing correlations in the 50–82 shell. The results of this paper complement those of our previous study of theN=82 isotones. It turns out that the role of pairing correlations is similar to a large extent in both cases.     

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).     

Single-neutron states in (101)Sn

The first data on the relative single-particle energies outside the doubly magic (100)Sn nucleus were obtained. A prompt 171.7(6) keV gamma-ray transition was correlated with protons emitted following the beta decay of (101)Sn and is interpreted as the transition between the single-neutron g(7/2) and d(5/2) orbitals in (101)Sn. This observation provides a stringent test of current nuclear structure models. The measured nug(7/2)-nud(5/2) energy splitting is compared with values calculated using mean-field nuclear potentials and is used to calculate low-energy excited states in light Sn isotopes in the framework of the shell model. The correlation technique used in this work offers possibilities for future, more extensive spectroscopy near (100)Sn.     

Reduced Shell Model Calculations of ^111Sb and ^112Sb

The low-lying states of the mid-heavy odd-even ^111Sb and odd-odd ^112Sb isotopes are calculated for the first time within the shell model framework. The shell model calculations have been carried out within the reduced model space including the single particle orbits ld5/2,097/2, ld3/2, 2Sl/2. We obtain the energy spectra for the ^111Sb and ^112Sb isotopes in the reduced model space by using CD-Bonn two-body effective nucleon-nucleon interaction. The energy spectra are compared to the experimental results to give some discussion about the low-lying states of ^111Sb and ^112Sb.     

Effect of 0h11/2 Level on Shell Model Calculations of ^105Sb and ^107Sb

The full and reduced shell model calculations have been carried out for the light odd-even ^105Sb and ^107Sb isotopes. The model space has been chosen as 1d5/2, 0g7/2, 1d3/2, 2s1/2, and 0h11/2 for the full calculations and excluded 0h11/2 for the reduced calculations. The reduced shell model calculations of ^105Sb and ^107Sb isotopes are presented for the first time. We obtain the energy spectra for the ^105Sb and ^107Sb isotopes in the full and reduced model space by using CD-Bonn two-body effective nucleon-nucleon interaction. The resulting energy spectra are compared to the experimental results to understand the effect of the 0h11/2 level on the shell model calculations. We draw conclusions about the right model space in the shell model calculations for the isotopes around the N =Z= 50 region of the periodic table.     

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.     

Global properties of nuclei from 100Sn to 132Sn

The paper presents the results of both microscopical and semi-empirical calculations of single-particle characteristics, nuclear binding, and one-nucleon separation energies of nuclei, as well as their root-mean-square radii, energy levels and transition rates in the long chain of Sn isotopes. We consider nuclei from the extremely neutron-deficient ¹⁰⁰Sn up to neutron excess ¹³⁶Sn, where the experimental information is available by now. The comprehensive comparison with the experimental data is carried out.     

Dispersive optical potential from an analysis of neutron single-particle energies in the Ti, Cr, and Fe isotopes featuring 20 to 50 neutrons

Neutron single-particle energies in unstable Ti, Cr, and Fe isotopes containing 20 to 26 neutrons were evaluated on the basis of experimental proton energies in the mirror-symmetric nuclei. The neutron single-particle energies in the 20 ? N ? 50 Ti, Cr, and Fe isotopes were calculated on the basis of the mean-field model with a dispersive optical potential, and the results were compared with available experimental data and with the results of estimations and calculations based on the relativistic mean-field model and on the multiparticle shell model with the GXPF1 interaction.     

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.     

原子核基态性质的系统研究

在Skyrme-Hartree-Fock-Bogoliubov（SHFB）理论框架下,利用SkOP1,SkOP2,SKC和SKD 4套新的Skyrme相互作用参数系统地研究了Ca,Ni,Sn和Pb同位素链上原子核的结合能、电荷半径等基态性质,并重点讨论了丰中子Ca核的新中子幻数以及Pb的同位素位移现象。通过与实验数据和SLy5相互作用参数的结果对比,发现这4套相互作用参数都能很好地再现结合能的实验数据,其预言精度比SLy5要高。对于丰中子Ca核,只有SKC和SKD相互作用参数能够再现N=28处的壳效应,而对于实验上发现的新幻数N=32和34,所有的相互作用参数均不能再现这一结果。对于电荷半径,发现所有的相互作用参数均不能很好地预言Ca同位素链电荷半径的演化规律以及Pb的同位素位移现象。另外,还将这些相互作用参数推广至远离β稳定线原子核的单粒子能级结构研究,发现其不适用于描述其随同位旋的演化行为。因此,为了更好地描述远离β稳定线原子核的宏观性质及单粒子能级,建议在拟合Skyrme相互作用参数时,除自旋-轨道耦合项包括合理的同位旋依赖外,还要考虑张量力成分。The nuclear ground state properties of Ca, Ni, Sn and Pb isotopes, such as the binding energies, the charge radii, are studied systematically by 4 sets of new Skyrme parametrizations SKC, SKD, SkOP1 and SkOP2 in the framework of the Skyrme-Hartree-Fock-Bogoliubov (SHFB) method. The new magic numbers of neutronrich Ca isotopes and the isotopic shift of Pb isotopes are discussed emphatically. By the comparisons between the calculations and the experimental data and results from the SLy5 interaction parametrization, it is found that the experimental binding energies can be reproduced accurately by all parametrizations. The calculated accuracies of SKC, SKD SkOP1 and SkOP2 parametrizations are higher than the ones of SLy5 parametrization. For the neutron-rich Ca nuclei, the shell effect of N=28 can be reproduced by the SKC and SKD parametrizations, but the magic numbers at N=32 and 34 are not found by the calculations of all the parametrizations. For the charge radii, the experimental evolution tendency of Ca isotopes and isotopic shift of Pb isotopes can not be reproduced by all the parametrizations. In addition, all Skyrme parametrizations are extended to study the structure of the nuclei far from the β stability line, it is shown that the single-particle energy evolutions with the isospin are not suitable for being studied by these parametrizations. Thus the tensor force component should be considered besides the isospin dependence in spin-orbit coupling term when the Skyrme interaction parametrizations are fitted.     

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.     

Analysis of the neutron single-particle energies of Zn, Ge, and Se isotopes within a mean field model with dispersive optical potential

The parameters of the neutron dispersive optical potential of even-even Zn, Ge, and Se isotopes (both stable and unstable) are determined from an analysis of experimental and estimated neutron single-particle energies. The imaginary part of the potential depends on the shell structure of the isotopes. The calculated energies are found to be in good agreement with the experimental and estimated energies.     

Generalized hybrid derivative coupling model for finite nuclei

The generalized hybrid derivative coupling model has been applied to explore various ground state properties of different nuclei. In this work we have confined our calculation only to the model characterized by the hybridization parameter α = 1/4 which gives better results than the other models of the same class, as we have seen earlier, for nuclear matter calculations. The binding energy, single-particle energy spectra, density and charge radii of different doubly closed nuclei like ¹⁶O, ⁴⁰Ca, ⁴⁸Ca, ⁹⁰Zr, ¹³²Sn, ²⁰⁸Pb have been studied. The success of this model, in describing the doubly closed nuclei, motivates us to extend this calculation further in the case of open shell nuclei after incorporating the pairing interaction and using a BCS transformation. We have calculated the binding energy for such nuclei. We have also studied the isotopic shift for different Pb isotopes with respect to ²⁰⁸Pb. We have compared our results with the other standard theoretical results as well as with the experimental values. Received: 18 August 2000 / Accepted: 13 April 2001     

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.     

Nuclear-level densities around Z = 50 from neutron evaporation spectra in (p, n) reactions

Neutron excitation functions, spectra, and angular distributions in the (p, n) reactions on the isotopes ¹¹⁶Sn, ¹¹⁸Sn, ¹²²Sn, and ¹²⁴Sn were measured in the proton-energy range 7–11 MeV. The measurements were performed by the time-of-flight method with the aid of a fast-neutron spectrometer at the EGP-15 pulsed tandem accelerator of the Institute of Physics and Power Engineering (Obninsk). A high resolution (about 0.6 ns/m) and a high stability of the time-of-flight spectrometer made it possible to identify reliably low-lying levels along with the continuous section of the neutron spectra. The data obtained in this way were analyzed on the basis of the statistical equilibrium and preequilibrium models of nuclear reactions. The respective calculations were performed with the aid of the precise Hauser-Feshbach formalism of statistical theory. The nuclear-level densities in the isotopes ¹¹⁶Sb, ¹¹⁸Sb, ¹²²Sb, and ¹²⁴Sb were determined, along with their energy dependences and model parameters. In the excitation-energy range 0–2 MeV, the energy dependence of the nuclear-level densities exhibits a structure that is associated with the shell inhomogeneities of the spectrum of single-particle states near filled shells. The isotopic dependence of the nuclear-level density is discovered and explained. It is also shown that the data obtained here for the nuclear-level density differ markedly from the predictions of model systematics of nuclear-level densities.     

Ground State Properties of Ds Isotopes Within the Relativistic Mean Field Theory

The ground state properties of Ds (Z=110) isotopes (N=151-195) are studied in the framework of the relativistic mean field (RMF) theory with the effective interaction NL-Z2.The pairing correlation is treated within the conventional BCS approximation.The calculated binding energies are consistent with the results from finite-range droplet model (FRDM) and Macroscopic-microscopic method (MMM).The quadrupole deformation,α-decay energy,α-decay half-live,charge radius,two-neutron separation energy and single-particle spectra are analyzed for Ds isotopes to find new characteristics of superheavy nuclei (SHN).Among the calculated results it is rather distinct that the isotopic shift appears evidently at neutron number N=184.     

Influence of an enlargement of the model space on number projected quasiparticle calculations

Results of number projected quasiparticle calculations for Sn isotopes in large and in small model spaces are compared when the force strengths and single-particle energies are determined consistently within each model space. When extending the model space, one observes that the model parameters extracted from the odd nuclei become more satisfactory. For even nuclei the collective states are not lowered in energy although electromagnetic transition rates increase considerably. Spectroscopic factors for one-nucleon transfer reactions change noticeably only for shells close to the Fermi level. Two-nucleon transfer cross-sections are strongly increased for ground state to ground state transitions only. We criticize a usual approximation formula for theL=0 two-nucleon transfer cross-section.     

Influence of an enlargement of the model space on number projected quasiparticle calculations

Results of number projected quasiparticle calculations for Sn isotopes in large and in small model spaces are compared when the force strengths and single-particle energies are determined consistently within each model space. When extending the model space, one observes that the model parameters extracted from the odd nuclei become more satisfactory. For even nuclei the collective states are not lowered in energy although electromagnetic transition rates increase considerably. Spectroscopic factors for one-nucleon transfer reactions change noticeably only for shells close to the Fermi level. Two-nucleon transfer cross-sections are strongly increased for ground state to ground state transitions only. We criticize a usual approximation formula for theL=0 two-nucleon transfer cross-section.     

The FBCS model and the inverse gap equations applied to the tin isotopes

The FBCS model for odd nuclei and the inverse gap equations are applied to a whole sequence of tin isotopes,viz.^111–125Sn. From spectroscopic data on the odd isotopes, the single-particle energies and interaction strengths are obtained. With these parameters the lowest states of the even isotopes are calculated by a number-projected two-quasiparticle diagonalization and by the usual BCS one. This is done with two Gaussian interactions and the SDI. In the case of the Gaussian forces the experimental energies are well reproduced by the number-projected treatment. Effective charges for Eλ transitions, which are required to reproduce the experimental transition rates, are rather constant for the whole series of isotopes, in case of the number-projected treatment. In addition a number of spectroscopic factors for one-nucleon transfer reactions are calculated and good agreement with experiments is observed.