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Register a new userConfiguration mixing in $^{188}$Pb : band structure and electromagnetic properties
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In the present paper, we carry out a detailed analysis of the presence and mixing of various families of collective bands in $^{188}$Pb. Making use of the interacting boson model, we construct a particular intermediate basis that can be associated with the unperturbed bands used in more phenomenological studies. We use the E2 decay to construct a set of collective bands and discuss in detail the B(E2)-values. We also perform an analysis of these theoretical results (Q, B(E2)) to deduce an intrinsic quadrupole moment and the associated quadrupole deformation parameter, using an axially deformed rotor model.
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In this article we report the results of detailed interacting boson model calculations with configuration mixing for the neutron-deficient Pb isotopes. Calculated energy levels and $B(E2)$ values for $^{188-196}$Pb are discussed and some care is suggested concerning the current classification on the basis of level systematics of the $4_1^+$ and $6_1^+$ states in $^{190-194}$Pb. Furthermore, quadrupole deformations are extracted for $^{186-196}$Pb and the mixing between the different families (0p-0h, 2p-2h, and 4p-4h) is discussed in detail. Finally, the experimental and the theoretical level systematics are compared.
Inclusion of time-odd components into the wave function is important for reliable description of rotational motion by the angular-momentum-projection method; the cranking procedure with infinitesimal rotational frequency is an efficient way to realize it. In the present work we investigate the effect of this infinitesimal cranking for triaxially deformed nucleus, where there are three independent cranking axes. It is found that the effects of cranking about three axes on the triaxial energy spectrum are quite different and inclusion of all of them considerably modify the resultant spectrum from the one obtained without cranking. Employing the Gogny D1S force as an effective interaction, we apply the method to the calculation of the multiple gamma vibrational bands in $^{164}$Er as a typical example, where the angular-momentum-projected configuration-mixing with respect to the triaxial shape degree of freedom is performed. With this method, both the $K=0$ and $K=4$ two-phonon gamma vibrational bands are obtained with considerable anharmonicity. Reasonably good agreement, though not perfect, is obtained for both the spectrum and transition probabilities with rather small average triaxial deformation $gammaapprox 9^circ$ for the ground state rotational band. The relation to the wobbling motion at high-spin states is also briefly discussed.
We report an investigation of the structure of $^{12}$C nucleus employing a newly developed configuration-mixing method. In the three-dimensional coordinate-space representation, we generate a number of Slater determinants with various correlated structures using the imaginary-time algorithm. We then diagonalize a many-body Hamiltonian with the Skyrme interaction in the space spanned by the Slater determinants with parity and angular momentum projections. Our calculation reasonably describes the ground and excited states of $^{12}$C nucleus, both for shell-model-like and cluster-like states. The excitation energies and transition strengths of the ground-state rotational band are well reproduced. Negative parity excited states, $1_1^-$, $2_1^-$, and $3_1^-$, are also reasonably described. The second and third $0^+$ states, $0_2^+$ and $0_3^+$, appear at around 8.8 MeV and 15 MeV, respectively. The $0_2^+$ state shows a structure consistent with former results of the alpha-cluster models, however, the calculated radius of the $0_2^+$ state is smaller than those calculations. The three-{alpha} linear-chain configuration dominates in the $0_3^+$ state.
Applying a variational multiparticle-multihole configuration mixing method whose purpose is to include correlations beyond the mean field in a unified way without particle number and Pauli principle violations, we investigate pairing-like correlations in the ground states of $ ^{116}$Sn,$ ^{106}$Sn and $ ^{100}$Sn. The same effective nucleon-nucleon interaction namely, the D1S parameterization of the Gogny force is used to derive both the mean field and correlation components of nuclear wave functions. Calculations are performed using an axially symetric representation. The structure of correlated wave functions, their convergence with respect to the number of particle-hole excitations and the influence of correlations on single-particle level spectra and occupation probabilities are analyzed and compared with results obtained with the same two-body effective interaction from BCS, Hartree-Fock-Bogoliubov and particle number projected after variation BCS approaches. Calculations of nuclear radii and the first theoretical excited $0^+$ states are compared with experimental data.
The variational multiparticle-multihole configuration mixing approach (MPMH) to nuclei has been proposed about a decade ago. While the first applications followed rapidly, the implementation of the full formalism of this method has only been recently completed and applied in [C. Robin, N. Pillet, D. Pe~na Arteaga and J.-F. Berger, Phys. Rev. C 93, 024302 (2016)] to $^{12}$C as a test-case. The main objective of the present paper is to carry on the study that was initiated in that reference, in order to put the MPMH method to more stringent tests. To that aim we perform a systematic study of even-even sd-shell nuclei. The wave function of these nuclei is taken as a configuration mixing built on orbitals of the sd-shell, and both the mixing coefficients of the nuclear state and the single-particle wave functions are determined consistently from the same variational principle. The calculations are done using the D1S Gogny force. Various ground-state properties are analyzed. In particular, the correlation content and composition of the wave function as well as the single-particle orbitals and energies are examined. Binding energies and charge radii are also calculated and compared to experiment. The description of the first excited state is also examined and the corresponding transition densities are used as input for the calculation of inelastic electron and proton scattering. Special attention is paid to the effect of the optimization of the single-particle states consistently with the correlations of the system. Globally, the results are satisfying and encouraging. In particular, charge radii and excitation energies are nicely reproduced. However, the chosen valence-space truncation scheme precludes achieving maximum collectivity in the studied nuclei. Further refinement of the method and a better-suited interaction are necessary to remedy this situation.
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