Coexisting structures in 115Sn and 116Sn

Excited states up to I ≈ 20 in ¹¹⁵Sn and ¹¹⁶Sn, populated via the (¹⁸O, αxn) reactions, have been studied using the DORIS Ge detector array in conjunction with charged particle detectors. In both nuclei, spherical as well as regular, deformed level structures were found. The spherical states are interpreted to arise from pure neutron configurations, while the deformed, intruder bands obviously involve proton 2p-2h excitations across the Z = 50 shell gap.     

Chaoticity and intruder states for 147Gd and 115In

The number variance is calculated for the energy spectra of ¹⁴⁷Gd and ¹¹In, which have been previously calculated in a particle-core coupling model, eventually including the intruder states (1 particle-1 hole excitations across the major closed shell at N=82 or Z=50, respectively). The inclusion of intruder states leads to an increase of the degree of chaoticity.     

Application of a microscopic interacting boson model to single-closed-shell nuclei

The microscopic treatment of an extended IBM including the pairing vibrational modes is applied to single-closed-shell nuclei with N = 50 or Z = 50. The low-lying spectra in the N = 50 isotones are well described in terms of the quadrupole phonon and the pairing vibration. The Sn isotopes roughly resemble the N = 50 isotones. The behavior of the 0₂⁺, 0₃⁺ and 2₁⁺ levels can be explained fairly well by the present model. Introduction of the pairing-vibrational modes into the IBM is essential for describing the single-closed-shell nuclei.     

Electric monopole transitions from low energy excitations in nuclei

Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ϱ²(E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also pay attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between ϱ²(E0) and isotopic shifts.     

Calculated properties of superheavy nuclei

Ground-state properties of the heaviest nuclei are analyzed within a macroscopic-microscopic approach. The main attention is paid to such properties as deformation, deformation energy, energy of the first rotational state 2⁺ of a nucleus, and the branching ratio of α decay to this 2⁺ state with respect to the decay to the ground state 0⁺. The analysis concerns the problem of experimental confirmation of theoretically predicted deformed shapes of superheavy nuclei situated in the region around the nucleus ²⁷⁰Hs. A large region of even-even nuclei with proton, Z=82–128, and neutron, N=126–190, numbers is considered.     

Shape coexistence close to N=50 in the neutron-rich isotope ~(80)Ge investigated by IBM-2

The properties of the low-lying states,especially the relevant shape coexistence in~(80)Ge,close to one of most neutron-rich doubly magic nuclei at N=50 and Z=28,have been investigated within the framework of the proton-neutron interacting model(IBM-2).Based on the fact that the relative energy of the d neutron boson is different from that of the proton boson,the calculated energy levels of low-lying states and E2 transition strengths can reproduce the experimental data very well.Particularly,the first excited state 0_2~+,which is intimately related to the shape coexistence phenomenon,is reproduced quite nicely.Theρ~2(E0,0_2~+→0_1~+)transition strength is also predicted.The experimental data and theoretical results indicate that both collective spherical andγ-soft vibration structures coexist in~(80)Ge.     

Nuclear structure of the heavyN=82 isotones:144Sm and146Gd

For single-closed shell nuclei with a large number of extra-protons, outside theZ=50,N=82 double-closed shell nucleus, a standard shell-model calculation yields dimensions of the Hamiltonian matrices beyond the scope of present computer technology. A quasi-particle (QP) calculation however, is able to describe the most important proton-excitations in a much restricted configuration space. Extended BCS+TDA calculations are performed on the single-closed shell¹⁴⁴Sm and¹⁴⁶Gd nuclei with a Gaussian force as effective two-body interaction. The influence of the nonconservation of the exact number of extra-protons in the BCS-approach is studied by performing a projection onto the states with an exact number of extra-protons (BCS+P). The first excited 2⁺, 4⁺ and 6⁺ states in¹⁴⁶Gd are described mainly by the (1g7/2) ₀ ⁸ (2d5/2) ₀ ⁴ \((1h11/2)_{J^\pi }^2 \) configuration.     

Collective bands in even mass Sn isotopes

Positive parity bands in ^{112, 114, 116, 118}Sn have been excited up to levels with spin and parity J^π = 12⁺ using Cd(α, 2nγ)Sn reactions. The experiments consisted of γ-ray excitation function, γ-γ coincidence, lifetime, γ-ray angular distribution, γ-ray linear polarization and conversion electron measurements. The observed bands show strong resemblances with ground-state bands of transitional nuclei in this mass region. It is pointed out that the J^π = 0⁺ band-heads originate from 2p-2h excitations in the Z = 50 proton shell. The excitation energies of the band-heads are calculated by means of the macroscopic-microscopic renormalization method. Pair correlations between the 2h and 2p configurations are included separately in a phenomenological way by taking into account the pairing energies of the Cd and Te ground states with respect to the Sn ground state.     

The (p,t) reactions on nuclei in the rare earth region

The (p, t) reactions on isotopic targets of ^{178, 180}Hf and all the stable isotopes of Yb and on natural targets of Gd, Dy, Er, Hf, Ta, W, Os and Au were studied at a beam energy of 19 MeV with an average resolution of 12 keV. A split-pole magnetic spectrometer was used to measure (p, t) Q-values and absolute differential cross sections. On the basis of angular distribution shapes definite 0⁺ and tentative 2⁺ assignments were made. Rotational bands were identified assuming an I(I+1) spacing. The (p, t) reaction populates excited 0⁺ states strongly in ¹⁷⁴Yb, ¹⁷⁶Hf, ¹⁶⁶Yb and several Gd, Dy and Er isotopes. The ¹⁷⁴Yb and ¹⁷⁶Hf 0⁺ states are discussed in terms of the pairing phase transition and in terms of Nilsson orbitals with unequal (p, t) reaction amplitudes. Members of gamma and octupole vibrational bands were observed in the even-N nuclei. The lowest L = 0 transfers to states in ^{169, 171}Yb were found to have less than 55% of the strength to ground states in adjacent even-N nuclei. A strong L = 0 transfer to a state at 1513 keV in ¹⁷¹Yb indicates the presence of a possible K = 0 core vibration coupled to the unpaired $\text{5}\text{2}$[512] neutron. The natural targets have furnished information on trends in cross sections for members of ground bands, gamma bandheads, 3^? octupole states, and strongly excited 0⁺ states.     

Low-spin states of 106Pd studied by the ARC technique

An average resonance capture (ARC) study of ¹⁰⁶Pd has been performed, resulting in the identification of a complete set of low-spin states (J^π = 0⁺–5⁺ and 1⁻–4⁻) up to an energy of 2.5 MeV. Several quasi-rotational bands have been tentatively identified. None of the bands can be positively identified as a rotational-like intruder configuration.     

A PSDPF interaction to describe the 1 ?ω intruder states in sd shell nuclei

In the level schemes of sd shell nuclei, there is generally at relatively low excitation energies, coexistence of normal 0 ?ω positive parity states and of intruder 1 ?ω negative parity states. The aim of the present work is to describe these intruder states in the full p-sd-pf model space with a ⁴He core allowing one nucleon jump between the major shells. To construct our PSDPF interaction, we first modified the p-sd and sd-pf cross-monopole terms and then applied a fitting procedure to adjust all PSDPF parameters by comparing an extended set of experimental and calculated excitation energies. Results obtained with the new interaction have been finally compared with experimental data for nuclei throughout the sd shell.     

A study of the (3He,n) reaction on isotopes of tin

The (³He, n) reaction has been studied on^{112,116,118,120,124}Sn at 25.4 MeV. Angular distributions were measured over the range 0°–25° and the results compared with predictions of zero-range DWBA calculations. In addition to the around-state transitions, L = 0 transitions were also observed to low-lying states in every case. Simple two component wave functions, as well as those obtained from a more sophisticated pairing model, are compared with the data in order to explain the appearance of the anomalously low-lying excited 0⁺ states observed. L = 2 transitions were observed to low-lying 2⁺ states, but the strength of these transitions was much less than expected from the systematics of (t, p) results for N = 50 nuclei.     

Coulomb displacement energies of the T = 1, J = 0 states of A = 42 nuclei

Coulomb displacement energies of the T = 1, J = 0⁺ and 6₁⁺ states of A = 42 nuclei are analyzed with previously known charge dependent forces and effects, and with the available HartreeFock single-particle wave functions. From the study of the Coulomb displacement energies of the 6₁⁺ states, it is found that the present knowledge on the charge dependence, including a phenomenological charge symmetry breaking force previously introduced so as to help explain the Nolen-Schiffer anomaly, gives a sufficient and consistent explanation for both single-particle and twoparticle systems. From the study of the 0⁺ states, we found that the Coulomb displacement energies of the second 0₂⁺ states can be explained with a compensation between the smaller Coulomb energies of the second lowest two-particle state and larger ones of the deformed 4p-2h state.     

First excited 0+ states in the germanium isotopes via the Se(d, 6Li) reaction

A systematic study of the even-A germanium isotopes with mass 70 ≦ A ≦ 78 via the Se(d, ⁶Li) reaction has been performed at E_d = 45 MeV. The reaction products were momentum analysed and mass identified with a QMG/2 magnetic spectrograph and the accompanying focal-plane detector system. The main emphasis of this investigation was on the nature of the first excited 0⁺ states. The striking variation in strength from one isotope to the other already observed in the (p, t) reactions to the same final nuclei is also seen for the α-pickup reaction. Previously derived wave functions that assume the excited 0⁺₂ states to be pure proton configuration states can also account for the present results.     

Techniques to Treat the Continuum Applied to Electromagnetic Transitions in 8Be

Bremsstrahlung emission in collisions between charged nuclei is equivalent to nuclear gamma decay between continuum states. The way the continuum spectrum can be treated is not unique, and efficiency and accuracy of cross section calculations depend on the chosen method. In this work we describe, relate, and compare three different methods in practical calculations of inelastic cross sections, that is, by (i) treating the initial and final states as pure continuum states on the real energy axis, (ii) discretizing the continuum states on the real energy axis with a box boundary condition, and (iii) complex rotation of the hamiltonian (complex scaling method). The electric quadrupole transitions, 2⁺ → 0⁺ and 4⁺ → 2⁺, in α + α scattering are taken as an illustration.     

A systematic study of the fission and evaporation residue excitation functions in complete fusion reactions with weakly bound stable nuclei

We carry out a systematic study on the fusion-fission and evaporation residue excitation functions for the reactions of ^6,7Li, ⁹Be, ^10,11B + ²⁰⁹Bi and ^6,9Li, ⁹Be + ²⁰⁸Pb, in which the projectiles are loosely bound and have low threshold energies against breakup. The fusion cross sections are calculated by the coupled-channel model. The compound nuclei decay are analyzed with the standard statistical model. The fission and evaporation residue excitation functions are well reproduced by our calculations, proving the validity of the standard statistical model in describing the compound nuclei decay in these characteristic reactions. For the compound nuclei with A=215-220 and Z=86-88, the liquid drop fission barriers need to be scaled by 0.80-1.02 to reproduce the experimental data. And a decreasing trend of the scaling factor with increasing fissionability parameter Z²/(50A) is found.     

Collective bands in doubly even Sn nuclei

Starting from a simplified picture treating proton two-particle two-hole excitations coupled with spherical quadrupole vibrations, in interaction with the low-lying quadrupole vibrational states in the doubly even Sn nuclei, we are able to account for a regular ΔJ = 2 band structure on top of excited J^π = 0⁺ states. We compare in some detail results for ¹¹⁶Sn concering energy spectra and E2 transition rates.