Stady on the Energy Spectra of fp Odd A Nuclei 47Ti,47V,49Cr With PDHF Method

The approximate angular momentum projected Hartree-Fock(PDHF)method is used to some odd-A nuclei in the fp shell:⁴⁷Ti,⁴⁷V,⁴⁷Cr,⁴⁹Cr.Their energy spectra are calculated and compared with the experimental data.The results are fairly satisfactory.In addition,the characteristics of those spectra are analyzed with the particle-rotor model.It is found that those spectra possess the properties of the no alignment limit Spectra.     

Angular Momentum Projected Deformed HF Spectra of 46Ti and 48Cr With MSDI

Taking the modified surface delta interaction (MSDI) and using a spherical shell model basis set, we carry out the deformed Hartree-Fock (HF) calculation for the even-even nuclei ⁴⁶Ti and ⁴⁸Cr in the fp shell, and construct the deformed HF intrinsic states which are the Slater determinants from the HF single-particle states.The angular momentum projection program is then carried out and the reasonable results are obtained.     

APPLICATIONS OF THE MODIFIED SURFACE DELTA INTERACTION IN THE ANGULAR MOMENTUM PROJECTION DEFORMED HAREE-FOCK METHOD

In this paper a modified surface delta interaction with an angular momentum correction term is proposed.By using this interaction the deformed Hartree-Fock and the approximate angular momentum projection calculations are performed for even-even nuclei in mass region A=56—74.The single particle energy spectra of the ground state configurations obtained are more reasonable than that calculated with KB matrix elements.The agreement of the calculated binding energies and projection energy spectra with experimental ones is fairly good.     

Microscopical Studies of the Energy Staggering in γ-Soft Nuclei

The energy staggering in γ-or quasi γ-band of γ-soft even-even nuclei is studied with the approximate angular moment um projection of the deformed Hartree-Fock (DHF) states. In the calculations of DHF states the modified surface &interaction matrix elements are used. It is found that in the K = 2 band produced by the angular momentum projection of DHF state the energy staggering appears only in certain conditions. Some points concerning with the angular momentum projection of K = 2 DHF states are discussed. The energy spectra of nuclei ⁷⁴Se and ⁷⁶Kr are calculated and compared with the experimental data, which show the staggering pattern of γ-soft rotor, the coincidence between them are fairly good.     

Application of the Modified BUU Model to Reaction Induced by 16O on 197An at 20MeV≤E/u≤180 MeV:Dependence of the Angalar and Linear Momentum Transfer on Impact Parameter and Energy

The angular and linar momentum transfered to target residue on 20 to 180MeV/u ¹⁶O+¹⁹⁷Au system are calculated with BUU(Boltzmann-Uehling-Uhlenbeck) model in which the angular momentum conservation is added.The dependence of angular and linar momentum on impact parameter and incident energy is discussed.The deviations between calculated values of(1mt) and those from viola system are compared.The results of the simulations suggest that the saturation of angular momentum transfer with incident energy increase mainly comes from the loss of capture ability of the target on projectile.     

Centrifugal stretching in 158Er

A variational calculation after an approximate angular momentum projection for ¹⁵⁸Er indicates that the anomalous behaviour of the energy spacings of high spin states may be due to centrifugal stretching — an increase in deformation accompanied by a decrease in pairing correlations.     

A SEMI-CLASSICAL ANALYSIS ON THE REACTION 12C+209Bi AT BOMBARDING ENERGIES SLIGHTLY ABOVE THE COULOMB BARRIER

For reactions induced by light heavy ion such as ¹²C, at bombarding energy slightly above the coulomb barrier, using semi-classical theory, neglecting macroscopic frictional force, the reaction mechnisms are sorted by the orbital angular momentum of the entrance channel from the classical deflection functions fitting elastic scattering. Moreover, inserting a transfer probability factor representing the Q-Window effect into the semi-classical angular distribution formula of Kalinkin and Grabowski, we obtain a formula for the differential cross-section per unit energy interval. The calculated results, including the elastic scattering angular distributions, energy spectrum and angular distributions of emitted α-particles in quasi-elastic process, complete fusion cross-section, fusion-fission cross-sections and the exitation functions of evaporated neutron, agree with the experimental data on the reaction ¹²C+²⁰⁹Bi reported by our Institute.     

The angular momentum dependence of correlations in the ground state rotational spectra of20Ne and22Ne

Multi-Configuration-Hartree-Fock (MCHF) calculations with angular momentum projection before the variation of the internal degrees of freedom have been performed for the nuclei²⁰Ne and²²Ne. This procedure yields different correlated intrinsic states for the different members of a rotational band. Thus the angular momentum dependence of correlations has been studied. Experimentally, the ground state spectra of²⁰Ne and²²Ne show properties similar to the phase transitions observed in some rare earth nuclei which have been well reproduced through the present calculations. The calculated spectra andBE2-values show a significant improvement compared to the ones obtained by variation before the angular momentum projection is effected.     

Structure calculations in18O nucleus

A multishell Hartree-Fock calculation for¹⁸O nucleus has been done with the Tabakin and Hamada-Johnston interactions followed by pairing correlations and angular momentum projection. TheB(E2) transition rates have been reproduced with an effective charge of 1.5e for protons and 0.5e for neutrons, but the fit to energy levels is poor. An approximate alternative formalism has then been developed which casts the eighteen-particle problem into a two-valence nucleon problem. The two valence nucleons interact through the RPA-type oscillation modes of the core. Calculations with the two interactions mentioned above have reproduced roughly the uncorrelated projected Hartree-Fock spectrum. Lastly, the excited band spectra of¹⁸O have been examined in the TDA approach followed by band mixing.     

THE ENERGY SPECTRA OF 1f7/2 SHELL NUCLEI WITH NONIDENTICAL NUCLEONS CONFIGURATION AND THE TWO BODY SPIN-ORBIT COUPLING FORCES

The central and two body spin-orbit coupling forces as the residual interaction and the pure configuration are used to calculate the energy spectra of 1f_7/2 shell nuclei (⁴³Sc,⁴⁴Ti,⁵²Fe,⁵³Fe,⁵³Co) with nonidentical configuration. The consistency bettween the calculated energy spectra of the nuclei and the experimental data are rather satisfactory.     

The Study of α Emission Induced by 46.7MeV/u 12C on 58Ni、115In and 197Au

The energy spectra and angular distribution of α particles emitted from ¹²C induced reactions with ⁵⁸Ni,¹¹⁵In and ¹⁹⁷Au have been measured.Three moving sources of emitting α particle are clearly seen from invariant cross section distribution in velocity coordinates.The experimental data were analyzed by using three moving sources.Extracted parameters of the source with half-beam velocity are in agreement with the systematic values from Fermi Gas Model.The energy spectra and the extracted parameters for various targets are discussed.The low energy peak in energy spectra is possibly from the emitted α particle from equilibrium system after pre-equilibrium emission of target-like products.The energetic α particles are mainly from projectile fragmentation and projectile-like fragmentation.     

Temperatures and Excitation Energies of Hot Nuclei in Reactions of 40Ar+natAg,209Bi at MeV/u

Coincidence measurements of fission fragment and light charged particle have been perfotrmed for the reactions of ⁴⁰Ar+^natAg,²⁰⁹Bi at E/A=25MeV using 4 PPAC and 11 sets of ΔE-E telescopes.Angular correlations of fission fragment were ploted as a function of the folding angle between the two detected fission fragments.The linear momentum transfer distributions were derived by measuring angular correlations.The backward spectra of light particles detected in coincidence with fission fragments having different average〈LMT〉are analyzed with Maxwell distribution.After some corrections the initial temperatures of the hot nuclei are determined from the energy spectra.The excitation energies corresponding to the different average〈LMT〉are obtained considering the reaction Q values and pre-equilibrum emission.In the central collision of the ⁴⁰Ar+^natAg,²⁰⁹Bi reactions,excitation energies are measured to be about 4.2MeV/u,2.4MeV/u and temperatures about 6.1MeV,5.5MeV,respecdvely.In semi-central collision,excitaionen energies are measured to be about 3.5MeV/u,1.9MeV/u and temperatures about 5.8MeV,4.8MeV respectively.     

A description of decoupled bands using the angular momentum projection method applied to the coherent phonon state

The decoupled bands of the odd-A La-isotopes are described by the angular momentum projection method. The coherent phonon state is assumed for the intrinsic wave function of the core. The present model covers the particle-vibrator and the particle-rotor coupling model. The results are in good agreement with the experimental energy spectra.     

DEPENDENCE OF THE MECHANISM AND CROSS SECTION OF THE α PARTICLES EMITTED FROM 12C+64Ni REACTION ON INCIDENT ENERGY

Energy spectra and angular distributions of the particles emitted from ¹²C+⁶⁴Ni reaction at eight energies in the region of 36.5MeV—69.4MeV are measured. The angular distributions of α particles change from forward peaked one to that peaked near by the grazing angle with decreasing incident energy. This result show that the emission mechanism of non-evaporation α particle is different in different energy regions.     

Evaluation of angular momentum projected energy at small deformations

An expression for angular momentum projected energy at small deformations is given which can, of course, be used for large deformations as well. Numerical calculations are carried out for the nucleus ¹²⁰Sn. It is shown that the Hartree-Fock-Bogolyubov theory with angular momentum projection always produces non-spherical equilibrium shapes.     

Angular-momentum-projected cranked hfb approach to the study of nuclear rotations

Employing a pairing-plus-quadrupole interaction hamiltonian and projecting out good angular momentum states from the cranked Hartree-Fock-Bogoliubov (CHFB) intrinsic wave functions the yrast spectra of ¹⁵⁸Dy and ¹⁶⁸Yb are calculated up to moderately high spins (I_max = 16) as to include the backbending region. Then the variation of pairing correlation, g-factor and rotational alignment of neutron spin as a function of total angular momentum is studied. The effect of particle number projection on the spin-projected CHFB wave functions is also investigated and is found to be unimportant for the calculation of g-factors. On the other hand, corrections of the excitation energies for number fluctuations in the CHFB wave functions are essential. Furthermore, looking at the distribution of the total projection quantum number K in various cranking wave functions we are able to throw some light on the K ≠ 0 nature of the aligned s-band.A variation-after-spin projection calculation strictly for the axial shape, without cranking, is also carried out for both the nuclei considered here. In the low-spin region this numerically “cheaper” scheme produces energy spectra similar to that of the CHFB method, and may thus be used to readjust the interaction parameters.     

MEASUREMENTS OF ANGULAR MOMENTUM EFFECT OF FISSION BARRIER

The fission cross sections and the evaporation residue cross sections for ¹²C+²⁰⁹Bi and ¹⁴N+Pb reactions were measured with the gold surface barrier silicon detectors and the mica nuclear track detectors.The critical angular momentum l_er was deduced from the measured evaporation residue cross section σ_er on the basis of the sharp-off model.The fission barrier with the particular angular momentum i derived from the condition Γ_f/Γ_n=1 at l=l_e The angular momentum effect of the fission barrier was studied experimentally.     

Electromagnetic properties of high spin states in158Dy and164Dy

We present calculations of electromagnetic properties of¹⁵⁸Dy and¹⁶⁴Dy based on the solution of the self-consistent cranking model and approximate angular momentum projection technique developed earlier. The calculated values compare fairly well with the existing experimental data.     

Low-lying nuclear deformed states and angular momentum projection

A fast computational method for approximate angular momentum projection is proposed for low-lying deformed nuclear states. The accuracy of the method is demonstrated by calculating the low-lying states of the ground-state band and the two 0⁺ excited bands in ¹⁶⁸Er with good experimental comparison.     

THE MEASUREMENT OF LIGHT PARTICLE EMISSION FROM 12C+159Tb,Ag AND 89Y REACTIONS

The energy spectra and angular distributions of α-particle emitted from ¹²C-induced reactions with ¹⁵⁹Tb, Ag and ⁸⁹Y targets have been measured. Meanwhile the emitted deutron's angular distributions with ¹⁵⁹Tb and ⁸⁹Y targets and proton's with ⁸⁹Y target have been also obtained.
The α-energy spectra associated with mentioned reactions have bell-like shape with probable energy near coulomb barrier. However, the main characteristic of the α-angular distribution for ¹⁵⁹Tb and Ag targets is peaked at or near the grazing angles. For the case of ⁸⁹Y target, α-differential cross-sections monotonically decrease with angles beyond 40º. The angular distributions of potons and deutrons nearly decrease exponentially.
The measured α-angular distributions could be divided into two components, one coming from α-evaporation is isotropic, another is anisotropic. The anisotropic component may be explained incomplete-fusion process in which the cross-section can be reproduced by a "Sum-Rule Model" due to J.Wliczynski.
In order to explain the anisotropic component of emitted α-particle, we propose in complete fusion model with a strong-damped sticking rotation, in which the rotation angles and interaction time of the composite system are also estimated.