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Register a new userRotational Bands and Electromagnetic Transitions of some even-even Neodymium Nuclei in J-Projected Hartree-Fock Model
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Rotational structures of even-even $^{148-160}$Nd nuclei are studied with the self-consistent deformed Hartree-Fock (HF) and angular momentum (J) projection model. Spectra of ground band, recently observed $K=4^{-}$, $K=5^{-}$ and a few more excited, positive and negative parity bands have been studied upto high spin values. Apart from these detailed electromagnetic properties (like E2, M1 matrix elements) of all the bands have been obtained. There is substantial agreement between our model calculations and available experimental data. Predictions are made about the band structures and electromagnetic properties of these nuclei. Some 4-qasiparticle K-isomeric bands and their electromagnetic properties are predicted.
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We expand the triaxial projected shell model basis to include triaxially-deformed multi-quasiparticle states. This allows us to study the yrast and gamma-vibrational bands up to high spins for both gamma-soft and well-deformed nuclei. As the first application, a systematic study of the high-spin states in Er-isotopes is performed. The calculated yrast and gamma-bands are compared with the known experimental data, and it is shown that the agreement between theory and experiment is quite satisfactory. The calculation leads to predictions for bands based on one- and two-gamma phonon where current data are still sparse. It is observed that gamma-bands for neutron-deficient isotopes of 156Er and 158Er are close to the yrast band, and further these bands are predicted to be nearly degenerate for high-spin states.
The reanimation of the investigations dedicated to 0^{+} states energies and E0 transitions between them is provoked by new and more precise experimental techniques that not only made revision of the previous data but also gave a possibility to obtain a great amount of new 0^{+} states energies and conversion electrons data. We suggest one phenomenological model for estimation of the E0 transition nuclear matrix elements. Recently theoretical calculations [1] predicted existence of a 0^{+} state with energy 0.68 MeV in ^{160}Dy nucleus. Powerful enough arguments in favor of existence of 681.3 keV state in ^{160}Dy nucleus are presented.
We calculate the ground-state properties of well deformed, even-even N=Z nuclei in the region between Ni-56 and Sn-100 within two different approaches, focusing on the binding energy and deformation and pairing properties. First, we employ the Hartree-Fock-BCS (HFBCS) approximation with the Skyrme effective nucleon-nucleon interaction and discuss how the results depend on the parameterization of the interaction and on the pairing force parameters adjusted in various schemes to reproduce the experimental odd-even mass differences. Then, within the Higher Tamm-Dancoff Approximation (HTDA), which explicitly conserves the particle number, we calculate the same properties starting from the HFBCS solutions. The HTDA treatment of the ground-state correlations is converged within a n-particle-n-hole expansion using up to n=4 particle-hole excitations of the pair type (in the sense of Cooper pairs). We compare the ground-state properties calculated in these two descriptions of pairing correlations and deduce the importance of the particle-number conservation in weak pairing regimes. Finally, we extend the HTDA calculations so as to include the proton-neutron residual interaction and investigate the role of proton-neutron pairing on the above ground-state properties.
A unitary description for wobbling motion in even-even and even-odd nuclei is presented. In both cases compact formulas for wobbling frequencies are derived. The accuracy of the harmonic approximation is studied for the yrast as well as for the excited bands in the even-even case. Important results for the structure of the wave function and its behavior inside the two wells of the potential energy function corresponding to the Bargmann representation are pointed out. Applications to $^{158}$Er and $^{163}$Lu reveal a very good agreement with available data. Indeed, the yrast energy levels in the even-even case and the first four triaxial super-deformed bands, TSD1,TSD2,TSD3 and TSD4, are realistically described. Also, the results agree with the data for the E2 and M1 intra- as well as inter-band transitions. Perspectives for the formalism development and an extensive application to several nuclei from various regions of the nuclides chart are presented.
We benchmark angular-momentum projected Hartree-Fock calculations as an approximation to full configuration-interaction results in a shell model basis. For such a simple approximation we find reasonably good agreement between excitation spectra, including for many odd-$A$ and odd-odd nuclides. We frequently find shape coexistence, in the form of multiple Hartree-Fock minima, which demonstrably improves the spectrum in the $sd$- and $pf$-shells. The complex spectra of germanium isotopes present a challenge: for even $A$ the spectra are only moderately good and those of odd $A$ bear little resemblance to the configuration-interaction results. Despite this failure we are able to broadly reproduce the odd-even staggering of ground state binding energies, save for germanium isotopes with $N > 40$. To illustrate potential applications, we compute the spectrum of the recently measured dripline nuclide $^{40}$Mg. All in all, projected Hartree-Fock often provides a better description of low-lying nuclear spectra than one might expect. Key to this is the use of gradient descent and unrestricted shapes.
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