Structure of 0+ states of 28Si and particle-hole conjugation

Full sd-shell calculations for the 0⁺ states of ²⁸Si have been performed in the SU(3) basis so that the intrinsic deformation of the shell model states can be deduced by inspection. The shell model Hamiltonian is decomposed in a symmetric part H_S and an antisymmetric part H_A with respect to particle-hole conjugation. It is shown that the splitting of prolate and oblate states is due to the spin-orbit part of H_A. The different prediction for ²⁸Si obtained with Kuo and with Preedom-Wildenthal matrix elements can be attributed to the difference in a single parameter: the strength of the spin-orbit part of H_A.     

Antipairing and antistretching in 22Ne

The ground state rotational band of ²²Ne has been investigated with the angular momentum and particle number projected Hartree-Bogoliubov theory. Variation before projections was performed in the framework of the constrained Hartree-Bogoliubov theory with the quadrupole moment and the degree of pairing as constraints. It is shown that there is a clear decrease of the pairing correlations (antipairing) and a decrease of the quadrupole deformation (antistretching) with increasing angular momentum. The antipairing effect appears to be essential to reproduce the experimentally known deviation of the spectrum from the J(J + 1) rule. The antistretching indicated by the B(E2) values is much stronger than that indicated by the calculated static quadrupole moments. This amounts to a breakdown of the rotational picture which is possibly connected with the low band cut-off values in the sd shell. The antipairing effect decreases the antistretching only slightly. The interaction between the pairing and quadrupole degrees of freedom is found to be too weak to change the earlier conclusions concerning antipairing and antistretching in the whole sd shell. No inert core was assumed in the calculations. The effective G-matrix elements of the Hamada-Johnston potential were used as an interaction.     

High spin properties of 124Ba

The ¹²⁴Ba nucleus is investigated on the basis of the method of statistical mechanics by assuming the nucleons to move in triaxially deformed Nilsson potential. The variation in the Fermi energies of protons and neutrons is studied as a function of spin and temperature. The Fermi energies determined as a function of angular momentum is used to study the dependence of shell correction on angular momentum using the Strutinsky smoothing procedure. The most important observation is that the shell correction is almost the same for all spins for ¹²⁴Ba. The spin cutoff parameter and the single particle level density parameter are studied as a function of spin and temperature. Constant entropy lines drawn by plotting the excitation energy against angular momentum are found to be roughly at constant energy above the yrast line and are almost equally spaced. It is observed that no yrast traps are present for ¹²⁴Ba.     

The generator coordinate method as an approximation to the shell model: A comparison on 24Ne

The applicability of the generator coordinate method as an approximation to the complete shell model diagonalization is tested in the sd shell on ²⁴Ne. We use the quadrupole moment and the pairing energy as generator coordinates and choose as generating function a constrained Hartree-Bogoliubov solution projected on the subspace of good angular momentum and good proton and neutron number. The spectra obtained by the generator coordinate method and the complete diagonalization show good overall agreement. Also we draw some conclusions about the nature of some low-lying states in ²⁴Ne, interpreted in terms of vibrations.     

Microscopic calculations of fission barriers and critical angular momenta for excited heavy nuclear systems

An extended version of Strutinsky's macro-microscopic method is used to calculate effective potential energies for rotating, excited heavy compound nuclei undergoing fission. Nuclear deformation is parameterized in terms of Lawrence's family of shapes. A two-center single-particle potential corresponding to these shapes is employed, with BCS pairing added. Statistical excitation is introduced by temperature-dependent occupation of (quasi-) particle energy levels. We calculate shell corrections to the energy, the free energy and the entropy as functions of deformation and temperature. The associated average quantities are derived from a temperature-dependent liquid drop model. The resulting static deformation energy is augmented by the rotational energy to yield the isothermal effective potential energy as a function of deformation, temperature and angular momentum. Moments of inertia are obtained from the adiabatic cranking model with temperature-dependent pairing included.We have also calculated the effective potential for constant entropy rather than constant temperature. Although this isentropic process physically is more appropriate than the isothermal process, it has not been treated before. For the same amount of excitation energy in the spherical state of the compound nucleus, the isentropic barriers turn out higher than the isothermal ones. For both processes we have extracted the critical angular momentum (defined as the one for which the barrier approximately vanishes) as a function of excitation. Our model is applied to the super-heavy nuclei ²⁷⁰110, ²⁷⁸110, ²⁹⁸114, ²⁹²118 and ³²²128, which have been tried to form in krypton and argon induced heavy ion reactions.     

Investigation on phase and shape transitions in the hot rotating nucleus <Superscript>154</Superscript>Dy

A statistical theory for hot rotating nuclei incorporating deformation, collective and non-collective rotational degrees of freedom, shell effects and pairing correlations is used to investigate the occurrence of phase and shape transitions in the hot rotating deformed nucleus ¹⁵⁴Dy . The interplay of various degrees of freedom and their influence on the behavior of nuclei formed as fused compounds in heavy-ion reactions are studied. A phase transition from the superfluid to normal state in the nucleus with increasing temperature and angular momentum is observed. The effect of pairing on the level density parameter and nucleon separation energy has been analyzed and is found to be substantial. The neutron and proton separation energies extracted as a function of the angular momentum and temperature is found to decrease sharply for particular angular momentum states of the nucleus due to shape transitions from prolate collective to oblate non-collective at higher temperatures.     

Calculations of the giant dipole resonance for sd-shell nuclei in the open-shell random phase approximation

The systematics of the giant dipole resonance have been calculated in the open-shell RPA for all the self-conjugate sd-shell nuclei, using (i) a phenomenological Rosenfeld interaction, (ii) Barret, Hewitt and McCarthy G-matrix elements and (iii) Kuo G-matrix elements. The excitations are based on shell model ground states for all nuclei except ²⁸Si for which a projected Hartree-Fock ground state was used.     

The low-lying rotational bands of the neutron-rich nucleus <Superscript>172</Superscript>Tm

The microscopic mechanism of four experimentally observed bands in 172Tm is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions.The experimental results,including the moments of inertia and angular momentum alignments of four bands in 172Tm are reproduced well by the particle-number conserving calculations.The ω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each c...     

Angular momentum and energy dependence of fission andn,p,4He emission from194Hg compound nucleus

Spin and temperature dependence of the fission and particle emission is studied for¹⁹⁴Hg. The compound nucleus is described using the Strutinsky shell correction approach extended for finite angular momenta and temperature. The shell corrections to the potential energy, free energy and the angular momentum are calculated using the Woods-Saxon average field. Results are compared with the experimental data and show a good qualitative agreement. It is found that the inclusion of the shell effects is necessary to understand the decay properties of¹⁹⁴Hg even for temperatures as high as 1.5–2.0 MeV.     

Dynamic approach to the analysis of angular distributions of fission and quasi-fission fragments

A dynamic approach to the calculation of angular distributions of fission and quasi-fission fragments is proposed. The approach is tested in the analysis of the experimental data for the ²⁸Si, ³²S + ²⁰⁸Pb reactions at E _lab = 160–280 MeV. Dependence of the relaxation time for the degree of freedom related to the projection of the angular momentum onto the symmetry axis of the decaying system on the deformation and the angular momentum is discussed.     

Self-consistency in the projected shell model

The projected shell model is a shell-model theory built up over a deformed BCS mean field. Ground state and excited bands in even-even nuclei are obtained through diagonalization of a pairing plus quadrupole Hamiltonian in an angular momentum projected 0-, 2-, and 4-quasiparticle basis. The residual quadrupole-quadrupole interaction strength is fixed self-consistently with the deformed mean field and the pairing constants are the same used in constructing the quasiparticle basis. Taking ¹⁶⁰Dy as an example, we calculate low-lying states and compare them with experimental data. We exhibit the effect of changing the residual interaction strengths on the spectra. It is clearly seen that there are many J^π = 0⁺, 1⁺, 4⁺ bandheads whose energies can only be reproduced using the self-consistent strengths. It is thus concluded that the projected shell model is a model with essentially no free parameters. The predicted energy of the 2⁺ bandhead lies however in nearly twice the experimental value.     

On the impact of large amplitude pairing fluctuations on nuclear spectra

The influence of large amplitude pairing fluctuations is investigated in the framework of beyond mean field symmetry conserving configuration mixing calculations. In the numerical application the finite range density dependent Gogny force is used. We investigate the nucleus ⁵⁴Cr with particle number and angular momentum projected wave functions considering the axial quadrupole deformation and the pairing gap degree of freedom as generator coordinates. We find that the effects of the pairing fluctuations increase with the excitation energy and the angular momentum. The self-consistency in the determination of the basis states plays an important role.     

Isomeric yield ratios of fission products in the system of 24 MeV proton-induced fission of238U

Isomeric yield ratios of 30 fission products in 24 MeV proton-induced fission of²³⁸U were measured by the use of the ion-guide isotope separator on-line. The obtained isomeric yield ratios were converted to the angular momenta of primary fission fragments based on the statistical model. The deduced angular momenta were examined from various aspects. It is found that in general the angular momentum continuously increases with the fragment mass number including the region of symmetric mass division. However, there are some exceptions. For Sn isotopes the deduced angular momenta are quite small due to the spherical shape of the nuclear shell configuration. It is also concluded from the consideration of the charge distribution that the angular momentum of fission product scatters considerably within the narrow range of mass division. The dependence of the angular momentum on the available energy of fragments at scission point indicates that the individual fragment possesses a characteristic deformation at scission and/or the deduced angular momentum is seriously affected by the particle excitation after scission.     

Exact solution of the particle-rotor model,angular momentum spread and transition rates

The particle-plus-rotor model with valence particles in an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ shell is solved exactly including single-particle splitting and pairing forces. Backbending and the spread of angular momentum of the valence shell is studied in detail for the two lowest bands and quadrupole transition rates are calculated.     

High-K quasiparticle structures in 159Er and 160Er

A series of new strongly coupled high-K, multi-quasiparticle structures have been observed in the light erbium transitional nuclei, ¹⁵⁹Er and ¹⁶⁰Er. The interpretation of these bands is discussed within the framework of the cranked shell model. These sequences, when taken together with the existing quasiparticle excitations, form a near complete set of low-lying, multi-quasiparticle structures on which a coherent series of aligned angular momentum, band crossing and blocking arguments can be based. The measured B(M1)/B(E2) ratios are compared with geometrical calculations to test the proposed configuration assignments. Received: 19 November 1997     

Probing the low angular momentum window in fusion reactions

The angular correlation between two alpha particles evaporated from the compound nucleus is sensitive to the initial spin population, and can thus be used to test the possible existence of angular momentum windows in the fusion cross section. A model calculation performed for the ²⁸Si + ²⁸Si fusion reaction at E_cm = 60 MeV is used as an illustration.     

α-clustering in Be isotopes

The Be chain of isotopes is investigated within the Sernimicroscopic Algebraic Cluster Model (SACM). For that the SACM is extended to odd-mass p-shell nuclei. We show that the main features of the Be isotopes can be well explained. Though for the neutron halo nucleus ¹¹Be some problems remain, the shell model still can describe the rough structures of these nuclei. In ¹¹Be a shell inversion takesplace reflecting the high deformation of the system. The quadrupole—quadrupole interaction plays a dominant role in p-shell nuclei.