The mass parameters for the average mean-field potential

Starting from a mean-field hamiltonian with pairing interaction, we use the generator coordinate method (GCM) and a generalized gaussian overlap approximation to derive a multidimensional collective hamiltonian for large-amplitude motion. Numerical calculations are performed for Nilsson and Woods-Saxon potentials with BCS pairing. The BCS wave function is taken as the generator function and the deformation parameters of the single-particle mean field are used as the generator coordinates. We find that the GCM mass parameters on the average are smaller than those of the cranking (+ BCS) model by a factor of $\text{～}\text{2}\text{3}$. In the present approach, the zero-point energy correction to the collective potential is shown to vanish identically.     

Application of Dyson mapping to odd-mass nuclei

The Dyson mapping is applied to the analysis of low-lying collective states in odd-mass nuclei. The original fermion (quasiparticle) space is truncated to a collective subspace which consists of products of collective phonons and a single fermion (quasiparticle). This subspace is mapped on an ideal boson-fermion space by the Dyson mapping and a simple but non-hermitian hamiltonian is obtained. The eigenvalue equations for the hamiltonian are numerically solved for the cases of the unique-parity states in the odd-mass Rh isotopes. The results show that the Dyson mapping is quite useful for analyses of phonon-particle coupling in odd-mass nuclei.     

Collective excitations and a backbending phenomenon in <Superscript>156</Superscript>Dy

We propose a self-consistent practical method to study collective excitations in rotating nuclei within the cranking + random phase approximation approach. It consists in solving the cranking Hartree-Bogolyubov equations for the modified Nilsson potential + monopole pairing forces. Further, the mean field results are used to construct collective vibrations treated in the random phase approximation (RPA). Special attention is paid to fulfill all conservation laws in the RPA to separate spurious and physical solutions. We demonstrate that the backbending in ¹⁵⁶Dy can be explained as a result of the disappearance of collective γ vibrations of the positive signature in the rotating frame.     

On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson

The generator coordinate method is used to relate the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; anharmonic coupling terms render the collective potential to be velocity-dependent.     

Collective potential and mass parameters derived from the generator coordinate method

The collective hamiltonian for the axial quadrupole vibrations was derived from theQQ+PP model. The generator coordinate method was applied and the results obtained through the symmetric moments expansion and the gaussian overlap approximation were compared. It was found that the collective potential and the average magnitude of the mass parameter obtained in both approximations are close to each other.     

A geometric classical model of collective motion in nuclei

A collective phase space of dimension 12 is introduced to study a classical model of nuclear collective motion. The model employs the 6 components of the coordinate quadrupole and 6 corresponding generalized momenta and can be related to properties of closed-shell nuclei. Vibrational and rotational coordinates are introduced, and purely rotational solutions are studied. The model demonstrates hamiltonian non-rigid motion with a fixed shape of the nucleus. The relation between the coordinate quadrupole tensor and the ellipsoids related to the angular momentum and angular velocity is analyzed for simple forms of the collective potential.     

Restoring of broken symmetries in the generator-coordinate method

Corrections to the potential and kinetic part of the collective hamiltonian due to particle-number projection have been derived within the generator-coordinate plus generalized gaussian-overlap (GCM + GOA) approach. The collective Schrödinger equation was constructed from the single-particle plus pairing hamiltonian using BCS generating functions. This approximation, connected with a rotation in gauge space, turns out to yield results very close to those of an exact particle-number projection. No corrections to the mass parameters were found. The GCM approach to the particle-number projection is simply generalized to restoring any broken symmetry, such as e.g. angular-momentum projection.     

Sum rule approach to radiative pion capture: A full hamiltonian calculation for 1p shell nuclei

A sum-rule approach to radiative pion capture is given for the self-conjugated nuclei in the 1p shell. The non-energy-weighted and the energy-weighted sum rules are evaluated for the full effective hamiltonian. Total branching ratios and mean photon energies are determined from these sum rules. A comparison with the Kroll-Rudermann approximation shows that the mean photon energies are practically unaffected, while the total branching ratios increases of the order of 10%.     

On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson. II

The generator coordinate method is used to relate the interacting boson model of Arima and lachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; unharmonic coupling terms render the collective potential to be velocity dependent. The mapping of operators of the interacting boson model onto those of the Bohr-Mottelson model turns out to be of Holstein-Primakoff type.     

Expansion and evaporation of hot nuclei: Comparison between semi-classical and quantal mean-field approaches

We present a general discussion of the mean field dynamics of finite nuclei prepared under extreme conditions of temperature and pressure We compare the prediction of semi-classical approximation with complete quantum simulations. Many features of the dynamics are carefully studied such as the collective expansion, the evaporation process, the different time-scale, etc. This study points out many quantitative differences between quantum and semi-classical approaches. Part of the differences are related to numerical features inherent in semi-classical simulations but most of them are a direct consequence of the non-treatment of nuclei as quantal objects. In particular, we show that because of a too strong damping in semi-classical approaches the expansion of hot nuclei is quenched and the speed of the collective motion reduced.     

Multidimensional dynamical-statistical model for describing the fission of excited nuclei

A multidimensional stochastic model for describing the decay of excited nuclei is presented. The model takes into account the dynamics of thermal fluctuations of collective variables, the dissipation of the kinetic energy of collective motion, and the emission of light particles from excited nuclei. The potential energy of a deformed nucleus is calculated within the liquid-drop model with a sharp surface and within the finiterange-interaction model. The friction parameters are calculated on the basis of the one-body-dissipation model. The inertia parameters are found in the Werner-Wheeler approximation. The drift components of forces are determined in terms of the entropy of an excited nucleus. The latter in turn is computed within the Fermi gas approximation with allowance for the deformation dependence of the density-level parameter. The fission probability, the mean multiplicity of neutrons emitted prior to scission (prescission neutrons), and the variances of the mass distributions of fission fragments at the most probable kinetic-energy value are calculated on the basis of the model developed here and are compared with experimental data. The dependences of these quantities on the model parameters are considered in detail.     

Do we understand IBM parameters?

A microscopic calculation of interacting-boson model (IBM) parameters is performed for Xe isotopes within the framework of the broken-pair model. We employ a shell-model hamiltonian which reproduces the spectra of near-magic and semi-magic nuclei. As a first approximation we adopt the idea of Otsuka, Arima and Iachello, that IBM states represent fermion states built from collective S- and D-pairs — the SD space. We show that at least two effects are needed to explain the empirical values of IBM parameters. Firstly there is a reduction in collectivity of S- and D-pairs in states with several broken pairs, due to the Pauli-blocking effect of the latter. Secondly the shell-model hamiltonian mixes the SD space with other fermion states which are not explicitly represented in the IBM. Among the latter, states with a collective G-pair (J = 4) are the most important, but they contribute less than half of the total renormalization of the parameters. The calculated IBM parameters χ of the E2 transition operators exhibit similar trends to those which occur in the IBM hamiltonian.We explain the IBM Majorana force as a renormalization effect on states with even J; not as a repulsion in states with odd J. The latter emerge as rather pure states which mix little with the non-collective fermion space. This indicates that they may be experimentally observable.With our calculated parameters the IBM spectra and E2 transitions are of comparable quality to those obtained in IBM fits of the data.     

The interacting boson approximation in nuclei with a few valence nucleons

In order to investigate microscopically nuclear collective models, the generator coordinate method as a means for deriving the effective hamiltonian for nuclear collective states is discussed. A simple case is treated as an illustration. Perfect agreement of the result with the exact solution testifies to the adequacy of the method. This method is applied to nuclei with a few valence nucleons and gives us the results of the interacting model in the SU(5) limit. The possibility of application to nuclei with many valence nucleons is also briefly discussed.     

Collective motion of fermions and boson expansion (I)

A new method is proposed to derive a collective boson Hamilton operator in an equation of motion approach starting from a microscopic shell-model hamiltonian with effective residual interactions. The method is used to describe pairing vibrations in spherical open shell nuclei in terms of interacting bosons. The results are in fair agreement with experimental data.     

The time dependent mean field method and the interacting Boson Model

The time dependent mean field approximation is applied to calculate excitation energies in the U(5)-O(6) transitional region of the Interacting Boson Model. A classical hamiltonian is constructed using coherent states parametrized in terms of five coordinates and their conjugate momenta. Energies are obtained using a Bohr-Sommerfeld type requantization condition.     

Fission fragment mass yields of Th to Rf even-even nuclei

Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part, and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass yields of the nuclei considered are evaluated within a 3D collective model using the Born-Oppenheimer approximation.