Description of nuclear moments and nuclear spectra in the particle-rotor model

The particle-rotor model using strong coupling basis functions is briefly reviewed. Recent developments are discussed. For example, a formalism for odd-odd nuclei (and negative parity states in even nuclei) is presented. With a standard neutron-proton interaction, measured spins and moments of transitional and deformed Ho nuclei are used to extract their main configurations. Total energy calculations in the (ε, ψ)-plane based on the particle-rotor model are presented for¹⁸⁵Au.     

Relation of photonuclear reactions to π-meson photoproduction process

Neutron-proton pair knocking-out by photons from iron (Fe⁵⁶) nuclei is studied by measuring induced gamma activity of Mn⁵⁴ isotope. Experiments are performed in a synchrotron beam at two maximum photon energies, 150 and 650 MeV. It was found that the yield of the reaction under study at the maximum energy of 150 MeV is almost zero, whereas a significant yield of gamma active Mn⁵⁴ nuclei is measured at the energy of 650 MeV. The cross section of the neutron-proton pair production reaction on Fe⁵⁶ at an energy of 650 MeV is estimated as 4 · 10^?27 cm².     

On the origin of the Wigner energy

Surfaces of experimental masses of even-even and odd-odd nuclei exhibit a sharp slope discontinuity at N = Z. This cusp (Wigner energy), reflecting an additional binding in nuclei with neutrons and protons occupying the same shell model orbitals, is usually attributed to neutron-proton pairing correlations. A method is developed to extract the Wigner term from experimental data. Both empirical arguments and shell-model calculations suggest that the Wigner term can be traced back to the isospin T = 0 part of nuclear interaction. The structure of the Wigner energy is analyzed in terms of neutron-proton pairs of a given angular momentum and isospin. In particular, we find that the Wigner term cannot be solely explained in terms of correlations between the neutron-proton J = 1, T = 0 (deuteron-like) pairs.     

Isotopic dependence of the shape of Se nuclei in the collective-model representation

The energy structure of low-lying excited states in the nuclei of even selenium isotopes is considered on the basis of a soft-nucleus model. The nuclei are treated as nonaxial rotors, longitudinal and transverse vibrations of their surface being taken into account in the quadrupole-deformation approximation featuring an admixture of an octupole deformation. The parameters of a phenomenological collective model for the ^{72,74,76,78,80,82}Se nuclei are found both in the case of β vibrations (longitudinal vibrations) and in the presence of additional γ vibrations (transverse vibrations) of the nuclear surface.     

中子晕核引起核反应中的同位旋效应

利用同位旋相关的量子分子动力学(IQMD)对中子晕核，⁸He和¹⁰He引起核反应中重要的同位旋效应和松散的中子晕结构影响的平均特征进行了研究.因为IQMD中的互作用势和介质中核子-核子碰撞截面灵敏地依赖于碰撞系统的密度分布.而扩展的中子晕密度分布包含了中子晕核的同位旋效应和松散的中子晕结构的平均特征，从而将这些信息通过动力学碰撞带入到反应机理中. 为了清楚地鉴别中子晕核带入反应机理重要的同位旋效应和松散中子晕结构的影响，通过比较中子晕核和相等质量稳定弹核在相同入射道条件下，所得物理观测量之间的差别加以确定.计算结果确实发现具有初始晕核信息的中子扩展密度分布将重要的同位旋效应和松散中子晕结构带入到各种物理观测量中.例如与相等质量稳定相比，中子晕核的晕特征引起了原子核阻止的降低；并明显地增加了核子发射中子-质子比和同位旋分馏比. 关键词： 中子晕核 原子核阻止 核子发射中子-质子比 同位旋分馏比     

Neutron hole states in theN=81 nuclei

The energy spectra of theN=81 nuclei have been calculated by coupling the neutron single-hole motion to the quadrupole vibrations of the nuclear surface. The wave functions are used to calculateM1 andE2 moments. Gamma-ray branching ratios are extensively discussed and compared with the many experimental data on ₅₄ ¹³⁵ Xe₈₁, ₅₈ ¹³⁹ Ce₈₁ and ₆₀ ¹⁴¹ Nd₈₁. Also spectroscopic factors for (p,d) reactions have been calculated and compared to experimental single-neutron pick-up reactions. The excitation energy and the lifetime of the isomeric stateπ ^π, decaying by anM4 transition, are studied, in particular in their dependence on the number of extra protons. The behaviour of the centroid of the neutron single-hole energies as a function of the number of extra protons is calculated with a delta force for the neutron-proton interaction.     

Mass-surface predictions near the doubly magic nuclide 78Ni

The mass surface of nuclei close to the doubly magic nuclide ⁷⁸Ni is calculated by two methods. The first relies on the multiparticle shell model based on an effective interaction and a mean nuclear potential. The second employs the concept of so-called “magic crosses” and enables us to determine the masses of odd-odd nuclei close to ⁷⁸Ni by using similarity of the shell structure and neutron-proton interaction in the region of nuclei under consideration and in the region of heavy magic nuclides. The energies of the separation of one and two neutrons from nuclei close to ⁷⁸Ni and the energies of the β decay of these nuclei—recall that these quantities of astrophysical interest—are presented.     

Analysis of209Bi and238U photofission cross section in the quasi-deuteron region of photonuclear absorption

An analysis of the photofission reactions in the quasi-deuteron energy range of photonuclear absorption (30–140 MeV) has been performed for²⁰⁹Bi and²³⁸U nuclei. Experimental cross section data available in the literature have been compared with calculated values obtained from a model in which the incoming photon is assumed to be absorbed by a neutron-proton pair (Levinger's quasi-deuteron photoabsorption), followed by a mechanism of evaporation-fission competition for the excited residual nuclei. The model has been shown to reproduce the main experimental features of²⁰⁹Bi and²³⁸U photofission cross section, although unexplained differences still remain in the case of²³⁸U-fission by 30– 50 MeV incident photons.     

New perspectives on the level density of compound resonances

The level density of compound resonances observed at neutron separation energy is subject of closer investigation and interpretation. The structures in the level density parameter as a function of the mass number allow the determination of the hierarchy of the compound states and the definition of a base line which represents the level density parameter of spherical nuclei with no residual interaction and no shell effects. Using the base line a method becomes available enabling the separation of the residual interaction from properties of the average potential defined in the framework of the shell model. The following examples in different mass regions are discussed: the change of the pairing energy due to the blocking effect atA ≈ 70; the breakdown of the pairing correlation atA ≈ 105 is interpreted as neutron-proton interaction; similar effects in the mass region 150<A<170 are discussed with neutron-proton interaction and the backbending phenomen. Finally it will be shown that there is no enhancement of states due to collective properties of nuclei at high excitation energy.     

Empirical pairing gaps and neutron-proton correlations

Analysis of various mass formulas related to neutron-proton correlations in atomic nuclei is carried out.Using the example of the N =Z chain it is shown that for self-adjoint nuclei various formulas proposed in literature for estimating the np pairing energy lead to similar results. Significant differences between the calculation methods arise when nuclei with N = Z are considered, which allows to reveal the complexity of neutron-proton correlations in different types of atomic nuclei and to make assumptions on the correspondence of the mass relation to the real effect of np pairing. The Shell Model parametrization of the binding energy makes it possible to draw additional conclusions on the structure of mass formulas and their relationship.     

Deuteron structure and diffractive deuteron-nucleus interaction

A nonrelativistic deuteron wave function involving the D-wave state and having a correct asymptotic behavior is constructed on the basis of the experimentally measured deuteron charge form factor G _C(q) and deuteron structure function A(q). The differential cross section for elastic deuteron-nucleus scattering is calculated by using this wave function and is found to agree with experimental data at an energy of 110 MeV. Integrated cross sections for various processes involving deuteron-nucleus interactions are also calculated. The distribution in the emission angle of the center of mass of the neutron-proton system produced in the diffractive dissociation of 110-MeV deuterons in the field of ²⁰⁸Pb nuclei is obtained.     

Reactions with fast radioactive beams of neutron-rich nuclei

The neutron dripline has presently been reached only for the lightest nuclei up to the element oxygen. In this region of light neutron-rich nuclei, scattering experiments are feasible even for dripline nuclei by utilizing high-energy secondary beams produced by fragmentation. In the present article, reactions of high-energy radioactive beams will be exemplified using recent experimental results mainly derived from measurements of breakup reactions performed at the LAND and FRS facilities at GSI and at the S800 spectrometer at the NSCL. Nuclear and electromagnetically induced reactions allow probing different aspects of nuclear structure at the limits of stability related to the neutron-proton asymmetry and the weak binding close to the dripline. Properties of the valence-neutron wave functions are studied in the one-neutron knockout reaction, revealing the changes of shell structure when going from the beta-stability line to more asymmetric loosely bound neutron-rich systems. The vanishing of the N = 8 shell gap for neutron-rich systems like ¹¹Li and ¹²Be, or the new closed N = 14, 16 shells for the oxygen isotopes are examples. The continuum of weakly bound nuclei and halo states can be studied by inelastic scattering. The dipole response, for instance, is found to change dramatically when going away from the valley of stability. A redistribution of the dipole strength towards lower excitation energies is observed for neutron-rich nuclei, which partly might be due to a new collective excitation mode related to the neutron-proton asymmetry. Halo nuclei, in particular, show strong dipole transitions to the continuum at the threshold, being directly related to the ground-state properties of the projectile. Finally, an outlook on future experimental prospects is given.     

Excited collective states of heavy even-even nuclei

Quadrupole-type collective excitations of even-even nuclei are analyzed. In this analysis, transverse γ vibrations of the nuclear surface are taken into account effectively, while longitudinal beta vibrations remain free. A potential energy of the exponential form is used for free surface longitudinal beta vibrations. The behavior of the energy levels of excited states in the ground-state, β, and γ bands of heavy nuclei is studied, and the predictive potential of the model used is demonstrated for transfermium nuclei.     

Decay of 129Ce to low-lying positive-parity states in 129La

Low-lying levels of the ¹²⁹La isotope have been investigated through the β⁺/EC decay of ¹²⁹Ce. The radioactive nuclei were produced in the ⁹⁴Mo+⁴⁰Ca reaction at a bombarding energy of 255 MeV and transported with a He-jet system. On-line mass separation was used to select the ¹²⁹Ce beta-decay γ-γ-t, X- γ- t, e^?-γ -t coincidence measurements as well as time multi-analysis were performed. Internal conversion electrons were recorded with a magnetic selector and multipolarities deduced. The level scheme of ¹²⁹La is discussed and compared with the calculations made in the frame of the neutron-proton Interacting Boson-Fermion Model (IBFM-2).     

Isospin Effect on the Emission Mechanism of Hot Nuclei in 35MeV/u 40Ar +112Sn/124Sn Reactions

As an extension of radioactive ion beam physics, the research on isospin dependent properties of hot nuclei has increasingly attracted considerable interest. The isospin effect on the decay of hot nuclei in reactions 35MeV/u ⁴⁰Ar+¹¹²Sn/¹²⁴Sn has been investigared. It is concluded that due to Coulomb repulsion and instability, proton-rich hot nuclei probably emit prides such as a with high energy to increase their neutron-proton ratio. Moreover, the decay chain for those particles is seemingly long and the emission Probability is high. Thus, the conventional observations, for instance, the ‘slope temperature’ extracted from energy spectrum, may very appreciably with the measured particles.     

Mass and charge distributions with correlated exchange

The dependence of the inclusive variancesσ _A ² ,σ _Z/2 andσ _N ² in nuclear collisions is investigated as a function of the correlation coefficient ρ for isospin correlated nuclon exchange on the dinuclear potential energy surface (PES). Variances for neutron-proton cluster exchange (single step process with zero net momentum between the constituents) are also evaluated. This analysis is helpful to understand the nature of the exchange mechanism. There exist a few experimental data which are at variance with either uncorrelated neutron-proton exchange or with isospin correlated exchange. An explanation of this data may possibly lie in coexisting neutron-proton cluster exchange.     

The effect of neutron-proton pairing correlations on the transfer of a neutron-proton pair

A theory of neutron-proton pairing interaction is developed considering bothJ=0T=1 andJ≠0T=0 correlations. The model of a singlej-shell is investigated explicitly forN=Z nuclei. Instead of solving the full HFB (Hartree Fock Bogoliubov) problem a variational method is used for determining the ground state energy and wavefunction. Our model shows that the best solutions contain either onlyT=0 or onlyT=1 correlations. A solution mixingT=0 andT=1 is energetically worse. It is estimated in PWBA (Plane Wave Born Approximation) that for ground state transitions at light nuclei in the transfer of a neutron-proton pair the cross section is enhanced up to a factor 3 by pairing correlations compared with shell model calculations.     

Proton-neutron interactions in nuclei withA∼90

An extension of the cluster-(quadrupole-octupole) phonon model is proposed for nuclei withA～90 to describe simultaneously positive- and negative-parity states, in which quadrupole as well as octupole vibrations of the⁸⁸Sr core are allowed. The cluster states include particle and particle-hole core excitations. The residual interaction is a delta-function force with spin-spin exchange plus a quadrupole-quadrupole force. The model is applied to⁸⁷Sr,⁸⁹Sr,⁸⁸Y, and⁹⁰Y nuclei. For each case, energy levels, spectroscopic factors, and electromagnetic properties are calculated and compared with experiment.