The structure of neutron-rich calcium isotopes studied by the shell model with realistic effective interactions

We study the structure of neutron-rich calcium isotopes in the shell model with realistic interactions. The CD-Bonn and Kuo-Brown (KB) interactions are used. As these interactions do not include the three-body force, their direct use leads to poor results. We tested whether the adjustment of the single particle energies (SPEs) would be sufficient to include the three-body correlations empirically. It turns out that the CD-Bonn interaction, after the adjustment of SPEs, gives good agreement with the experimental data for the energies and spectroscopy. For the KB interaction, both the SPEs and monopole terms require adjustments. Thus, the monopole problem is less serious for modern realistic interactions which include perturbations up to the third order. We also tested the effect of the non-central force on the shell structure. It is found that the effect of the tensor force in the CD-Bonn interaction is weaker than in the KB interaction.     

Halo structure of (14)Be

The two-neutron halo nucleus (14)Be has been investigated in a kinematically complete measurement of the fragments ((12)Be and neutrons) produced in dissociation at 35 MeV/nucleon on C and Pb targets. Two-neutron removal cross sections, neutron angular distributions, and invariant mass spectra were measured, and the contributions from electromagnetic dissociation (EMD) were deduced. Comparison with three-body model calculations suggests that the halo wave function contains a large nu(2s(1/2))(2) admixture. The EMD invariant mass spectrum exhibited enhanced strength near threshold consistent with a nonresonant soft-dipole excitation.     

Rescattering effects in proton scattering on nuclei 6,8He and 8,9Li in the Glauber theory

The differential cross sections of elastic p^6,8He and p^8,9Li scattering are calculated within the Glauber diffraction theory at intermediate energies of 70 to 700 MeV/nucleon. The calculations are based on realistic three-body wave functions α-n-n (for ⁶He), α-2n-2n (for ⁸He), α-t-n (for ⁸Li), α-t-2n (for ⁹Li), obtained using current nuclear models, and the Glauber operator is expanded into a series of multiple scattering corresponding to the three-body nuclei configuration. The approach allows us to calculate the operator matrix elements with allowance for rescattering on all structural components of the investigated nuclei.     

Test of effective cluster interactions by pion scattering

The superposition of effective interactions is studied by a cluster approach to the pion-nucleus potential with particular emphasis on the treatment of the Pauli principle between the clusters. The model is based on the formalism of Kerman, McManus, and Thaler and constructs the pion-nucleus interaction by a superposition procedure of pion-cluster interactions in the framework of the fish-bone model. The second-order contribution due to excitations of the relative motion between the clusters has been taken into account as well as true absorption. A test calculation of ^+_20 scattering with the cluster approach reproduces the gross structure of the differential elastic cross section and the total non-elastic cross section of conventional calculations quite well. Furthermore, it is confirmed that the three-body Pauli interaction is negligible also in the case of a realistic and rather complicated pion-nucleus interaction thus justifying the usual folding approach. The rotational bands contribute about 10% to the cross sections.     

Realistic shell model study of nuclei around <Superscript>132</Superscript><Emphasis Type="Italic">Sn</Emphasis>

We have performed shell model calculations for ¹³⁴Te, ^130,134Sn, and ^132,134Sb using a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The calculated results are compared with the available experimental data. The main aim of this study was to put to a comprehensive test our realistic effective interaction in the A = 132 region. A very good agreement is obtained for all the five nuclei considered.Received: 12 November 2002, Published online: 2 March 2004PACS: 21.60.Cs Shell model - 21.30.Fe Forces in hadronic systems and effective interactions - 27.60. + j      

Green’s function calculations of light nuclei

The influence of short-range correlations in nuclei was investigated with realistic nuclear force. The nucleon-nucleon interaction was renormalized with V_lowk technique and applied to the Green’s function calculations. The Dyson equation was reformulated with algebraic diagrammatic constructions. We also analyzed the binding energy of ⁴He, calculated with chiral potential and CD-Bonn potential. The properties of Green’s function with realistic nuclear forces are also discussed.     

Nuclear matter equation of state and three-body forces

The energy per particle, symmetry energy, pressure, and free energy are calculated for symmetric nuclear matter using BHF approach with modern nucleon-nucleon CD-Bonn, Nijm1, Argonne v₁₈, and Reid 93 potentials. To obtain saturation in nuclear matter we add three-body interaction terms which are equivalent to a density-dependent two-nucleon interaction a la Skyrme force. Good agreement is obtained in comparison with previous theoretical estimates and experimental data.     

Proton-neutron interaction near closed shells

Odd-odd nuclei around double shell closures are a direct source of information on the proton-neutron interaction between valence nucleons. We have performed shell-model calculations for doubly odd nuclei close to ²⁰⁸Pb, ¹³²Sn, and ¹⁰⁰Sn using realistic effective interactions derived from the CD-Bonn nucleon-nucleon potential. The calculated results are compared with the available experimental data, attention being focused on particle-hole and particle-particle multiplets. While good agreement is obtained for all the nuclei considered, a detailed analysis of the matrix elements of the effective interaction shows that a stronger core-polarization contribution seems to be needed in the particle-particle case.     

Study of the structure of light,unstable nuclei and the mechanism of elastic proton scattering

The review presents calculations of elastic p ⁶He-, p ⁸Li-, p ⁹Li- and p ⁹C scattering in the framework of the Glauber theory of multiple diffraction scattering at intermediate energies of 70 and 700 MeV/nucleon. The most significant result of the calculations is that we have utilized realistic three-body wave functions obtained within modern nuclear models. The relation is found between differential cross sections and intercluster potentials, where the nuclear wave functions are calculated. Conclusions are made concerning the types of potentials which describe most realistically the available experimental data. The method for calculation of three-body wave functions in α-n-n-, α-t-n-, ⁷Be-p-p-, α-t-2n-, and ⁷Li-n-n models is described with discussion of inter-cluster potentials and the quantum-number configurations taken into consideration. It is revealed how the wave functions and the nuclear electromagnetic characteristics calculated using these wave functions depend on the choice of intercluster potentials. The derivation of matrix elements (amplitudes) of pA scattering in the framework of the Glauber approach with three-body wave functions is presented by an example of ⁶He nucleus. Discussing the results of calculation of differential cross sections and the analyzing power (A _y ), we established how the calculated characteristics depend on a wave-function structure and dynamics of the process determined by a Glauber operator of multiple scattering. The calculated differential cross sections and analyzing powers are compared with available experimental data and calculations by other authors performed for different formalisms, which allows us to make justified conclusions.     

Ab initio shell model calculations with three-body effective interactions for p-shell nuclei

We present a qualitative improvement of the ab initio no-core shell model (NCSM) approach by implementing three-body interaction capability for p-shell nuclei. We report the first calculations using three-body effective interactions derived from realistic nucleon-nucleon potentials for 6Li, 8Be, and 10B and demonstrate that the use of three-body effective interactions speeds up the convergence of the NCSM approach. For 10B, we predict JpiT = 1(+)0 ground state, contrary to the experimental observation of 3(+)0, when the AV8(') potential is used, indicating the need for true three-body forces.     

Nuclear level densities below 40 MeV excitation energy in the mass regionA ≃ 50

Consistent pre-equilibrium emission and statistical model calculations of fast neutron induced reaction cross sections are used to validate nuclear level densities for excitation energies up to 40 MeV in the mass regionA ?50. A “composed” level density approach has been employed by using the back-shifted Fermi gas model for excitation energies lower than 12 MeV and a realistic analytical formula for higher excitations. In the transition region from the BSFG model range to that of full applicability of the realistic formula, an interpolation between the predictions of the two models is adopted. The interpolation rule, suggested by microscopic level density calculations, has been validated through the comparison of the calculated and experimental cross sections.     

Significance of Deuteron Breakup in Halo Transfer

 We discuss the quasi-adiabatic approximations to the three-body wave-function in breakup processes and clarify the assumptions underlying the model. This suggests alternative approximation schemes. Using different theoretical three-body models, calculated angular distributions of differential cross sections for the ¹¹Be(p,d) reaction are presented, for which new preliminary data have been reported at 35 MeV. We show that calculations are sensitive to the inclusion of deuteron breakup and to the breakup model used, particularly if absolute spectroscopic information on the 0⁺ and 2^{+ 10}Be core-state parentages is deduced. There is also considerable sensitivity to the model employed in calculations of the relative cross sections of the two states. Received January 19, 1999; revised April 16, 1999; accepted for publication February 28, 2000     

Subthreshold and near-threshold K +-meson photoproduction on nuclei

The inclusive K ⁺-meson production in photon-induced reactions in the near-threshold and subthreshold energy regimes is analyzed for the one-step (γN → K ⁺ Y, Y=Λ, Σ) incoherent production processes on the basis of an appropriate new folding model that takes properly into account the struck-target nucleonremoval energy and the internal momentum distribution (nucleon spectral function), extracted from recent quasielastic-electron-scattering experiments and from many-body calculations based on realistic models of NN interaction. Simple parametrizations of the total and differential cross sections for K ⁺ production in photon-nucleon collisions are presented. A comparison of the model calculations of the K ⁺ differential cross sections for γ¹²C interactions in the threshold region with existing experimental data is given, which displays the contributions to K ⁺ production at considered incident energies from the use of the single-particle part, as well as high momentum and high removal energy part, of the nucleon spectral function. Detailed predictions for the K ⁺ total and differential cross sections for γ²H, γ¹²C, and γ²⁰⁸Pb interactions at subthreshold and near-threshold energies are provided. The effect of the uncertainties in the elementary K ⁺-production cross sections on the K ⁺ yield is explored.     

Total interaction and proton-removal cross-section measurements for the proton-rich isotopes 7Be, 8B,and 9C

In an experiment performed at the FRS of GSI, we measured total interaction cross sections for ⁷Be, ⁸B, and ⁹C, one-proton-removal cross sections for ⁸B and ⁹C as well as two-proton-removal cross sections for ⁹C on targets ranging from carbon to lead at an energy of 285 MeV/nucleon. In addition, we performed measurements at 142 MeV/nucleon for ⁸B. The experimental results are compared to different calculations. Glauber-type calculations with different model·density distributions show that, down to incident energies of about 50 MeV/nucleon, total interaction cross-section measurements with light targets are not sensitive to an extended proton distribution in ⁸B. However, at lower incident energies, a tail in the proton density distribution is needed to explain the total interaction cross sections. Total interaction cross-section measurements with high-Z targets in the present experiment show a significant increase of the cross sections due to low-lying electromagnetic strength.     

Elastic electron scattering from 3He and 4He

The cross sections for elastic electron scattering from ³He and ⁴He were measured for the momentum transfer range from 0.45–2.0 fm^?1. The cross sections were separated into their longitudinal (charge) and transverse (magnetic) contributions using the Rosenbluth formula. The charge and magnetic form factors were obtained model-independently.The rms charge radii were found to be 1.671 (14) fm for ⁴He and 1.976 (15) fm for ³He, and the magnetic rms radius of ³He is 1.99 (6) fm. The mis charge radius for ⁴He is in excellent agreement with the latest muonic data.Comparison of the form factors was made with Faddeev three-body calculations using realistic two-body NN interactions. At present the theoretical calculation is not able to reproduce the experimental data.     

Fusion cross sections for 10,11B+12C at sub-Coulomb energies

Total fusion cross sections for the ¹⁰B + ¹²C and ¹¹B + ¹²C reactions have been determined over a 5 MeV (c.m.) energy range extending to ≈ 3 MeV below the Coulomb barrier. Absolute γ-ray yields for specific transitions in the de-excitation of the heavy products following compound nucleus decay were measured using a Ge(Li) detector. Statistical model calculations of the decay modes of the compound nucleus have been used to deduce, from the γ-ray data, cross sections for single proton, neutron and α-particle emission, and to determine total cross sections for compound nucleus formation. No evidence has been found for sub-Coulomb resonances in either reaction. The total reaction cross sections are compared with optical model calculations using different parameter sets and the observed trend in the very low energy cross sections is discussed relative to other reactions in the same mass region.     

Dispersion theory of nucleon transfer reactions induced by heavy ions

A new approach, the distorted wave pole approximation (DWPA) with the three-body Coulomb effects, is developed by combining the dispersion method and DWBA to analyse the heavy ion-induced neutron transfer reactions. The influence of the three-body Coulomb dynamics on the peripheral partial wave amplitudes is investigated. Differential cross sections of the neutron transfer reactions are calculated to compare the proposed model with the conventional DWBA. The values of nuclear vertex constants for virtual separation of neutron from various nuclei are obtained. The results of the calculations show that DWPA can be applied to analyse the heavy ion-induced neutron transfer reactions and that the three-body Coulomb effects are taken into account with acceptable accuracy in DWBA.     

Model Calculation of n 6Li Reactions Below 20 MeV

Based on the unified Hauser-Feshbach and exciton model for light nuclei, the calculations of reaction cross sections and the double-differential cross sections for n 6Li are performed. Since all of the first-particle emissions are from the compound nucleus to the discrete levels, the angular momentum coupling effect in pre-equilibrium mechanism must be taken into account. The fitting of the measured data indicates that the three-body break-up process needs to be involved, and the pre-equilibrium reaction mechanism dominates the reaction processes. In light nucleus reactions the recoil effect must be taken into account.``     

Absorption effects in halo-nucleus core or nucleon stripping reactions

Inclusive halo-nucleus core or nucleon stripping reactions are considered on the basis of a potential three-body model using the eikonal and adiabatic approximations. Clear analytical expressions for the cross sections of these reactions are obtained, and numerical calculations for ¹¹Be halo nucleus are performed. Constituent absorption by the target nucleus substantially influences the integral and differential (with respect to longitudinal momentum) nucleon stripping cross section. It is demonstrated that the differential core stripping cross section contains more complete information on the unperturbed wave function of the halo nucleus.