Nuclear binding energies: Global collective structure and local shell-model correlations (original) (raw)
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Nuclear binding energies: global collective structures and local shell-model correlations
2003
Nuclear binding energies and two-neutron separation energies are analysed starting from the liquid-drop model and the nuclear shell model in order to describe the global trends of the above observables. We subsequently concentrate on the Interacting Boson Model (IBM) and discuss a new method in order to provide a consistent description of both, ground-state and excitedstate properties. We address the artefacts that appear when crossing midshell using the IBM formulation and perform detailed numerical calculations for nuclei situated in the 50−82 shell. We also concentrate on local deviations from the above global trends in binding energy and two-neutron separation energies that appear in the neutron-deficient Pb region. We address possible effects on the binding energy, caused by mixing of low-lying 0 + intruder states into the ground state, using configuration mixing in the IBM framework. We also study ground-state properties using a macroscopic-microscopic * Postdoctoral fellow of the Fund for Scientific Research-Flanders (Belgium). † Visiting postdoctoral fellow of the Fund for Scientific Research-Flanders (Belgium). 1 model. Detailed comparisons with recent experimental data in the Pb region are amply discussed.
Nuclear Physics A, 2001
In the framework of the interacting boson model the three transitional regions (rotational-vibrational, rotational-γ-unstable and, vibrational-γunstable transitions) are reanalyzed. A new kind of plot is presented for studying phase transitions in finite systems such as atomic nuclei. The importance of analyzing binding energies and not only energy spectra and electromagnetic transitions, describing transitional regions is emphasized. We finally discuss a number of realistic examples. PACS numbers: 21.60-n, 21.60Fw, 21.60Ev * Visiting postdoctoral fellow of the Fund
Two neutron separation energies and phase transitions in the Interacting Boson Model
2002
In the framework of the interacting boson model the three transitional regions (rotational-vibrational, rotational-γ-unstable and, vibrational-γ-unstable transitions) are reanalyzed. A new kind of plot is presented for studying phase transitions in finite systems such as atomic nuclei. The importance of analyzing binding energies and not only energy spectra and electromagnetic transitions, describing transitional regions is emphasized and we discuss a new method in order to provide a consistent description of both, ground-state and excited-state properties.
Shell-model Monte Carlo studies of neutron-rich nuclei in the 1s-0d-1p-0f shells
Physical Review C, 1999
We demonstrate the feasibility of realistic Shell-Model Monte Carlo (SMMC) calculations spanning multiple major shells, using a realistic interaction whose bad saturation and shell properties have been corrected by a newly developed general prescription. Particular attention is paid to the approximate restoration of translational invariance. The model space consists of the full sd-pf shells. We include in the study some well-known T =0 nuclei and several unstable neutron-rich ones around N = 20, 28. The results indicate that SMMC can reproduce binding energies, B(E2) transitions, and other observables with an interaction that is practically parameter free. Some interesting insight is gained on the nature of deep correlations. The validity of previous studies is confirmed.
The Role of Shell Model in Determining Pairing Interaction in Nuclei
The role of the shell model in pairing interaction in nuclei is investigated by calculating the pairing energies of O-O (odd-odd), O-E (odd-even), E-E (even-even) and E-O (even-odd) isotopes of four elements namely; 15P, 25Mn, 40Zr and 60Nd. The pairing energies were computed using the values of binding energy (B) obtained from AME2016 atomic mass evaluation. The graphs of the pairing energies against the mass numbers revealed an increase of the pairing energies with the occurrence of periodic humps adjacent to the neutron magic numbers. The rise in the pairing energies is attributed to the bound states of heavy nuclei arising from the neutron-neutron pairs in the shell structures beyond the Fermi-surface, while in the light and intermediate nuclei, the rise in the pairing energies is due to the increase in the number of nucleons occupying the surface region. These neutron-neutron pairs formed beyond the Fermi-surface of nuclei of heavy elements have greater pairing energies, which contribute to greater binding energies associated with the heavy elements found in the neutron stars. It is concluded that the shell model can predict the existence of isotopes of heavy elements in the neutron stars and the criterion to ascertain their existence lies on the pairing energies. Calculations show that the isotopes with highest peaks among the heavy elements can predict the most abundant isotopes of the heavy elements in the neutron stars, for instance, 90 Zr, 91 Zr, 142 Nd, 145 Nd, 146 Nd, 148 Nd and 150 Nd nuclei.
Shell Model Calculations for Nuclei with A=20
2012
Binding energy of the ground state, energy levels and the reduced probability for E2 transitions for O, F, Ne, Na and Mg nuclei with mass number A=20 and nucleon numbers between 8 and 12 have been calculated through shell model calculations using the shell model code OXBASH for Windows by employing the usdapn interaction for neutron and proton particles orbits in sd-shell. The binding energies calculations are in good agreement with experimental data. The predicted low-lying levels (energies, spins and parities) and the reduced probability for E2 transitions results are reasonably consistent with the available experimental data.
1999
The spin-orbit splittings in the spectra of nuclei with mass numbers 5, 15 and 17 are studied within the framework of shell-model configuration mixing calculations including 2$\hbar \omega$ excitations. The contributions of the two-body spin-orbit and tensor components of the nucleon-nucleon interaction are studied in various model spaces. It is found that the effects of the two-body spin-orbit interaction are dominant and quite sensitive to the size of the model-space considered. The effects of the tensor interaction are weaker. The correlations effects which are included in the larger (0+2) hbaromega\hbar \omegahbaromega shell-model space reduce the spin-orbit splitting in the case of A=5 by 20%, and enhance it for A=15 by about the same 20%. However, it is found that the correlations have a very small effect on the d3/2−d5/2d_{3/2} - d_{5/2}d3/2−d5/2 splitting in A=17.
Shell model calculations of some nuclei near 208Pb region
Journal of Physical Studies, 2017
Untruncated large scale shell model calculations have been performed to study energy levels, reduced electric transition probabilities B(E2; 0 + 1 → 2 + 1), and the binding energy for even-even of 210−212 Pb, 210−212 Po in the neutron deficit region π(hf pi)ν(igdsj) valance space above the 208 Pb core using four effective interactions khpba, khpbu, khp and khpe. The calculated energy spectra, reduced electric transition probabilities B(E2; 0 + 1 → 2 + 1), and the binding energy are compared with the recently available experimental data. A very good agreement was obtained for all nuclei.
Frontiers and challenges of the nuclear shell model
The European Physical Journal A, 2002
Two recent developments of the nuclear shell model are presented. One is a breakthrough in computational feasibility owing to the Monte Carlo Shell Model (MCSM). By the MCSM, the structure of low-lying states can be studied with realistic interactions for a wide, nearly unlimited basically, variety of nuclei. The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed.
Off-Shell Effects in Nuclear Matter
Physical Review C, 1971
We examine the binding energy of nuclear matter for exactly phase-shift-equivalent potentials. We generate these potentials by applying a short-range unitary transformation to the Reid soft-core potential. All potentials have a one-pion-exchange tail. We find that, for the potentials studied, variations of up to 9.5 MeV in the binding energy and 0.33 F in the saturation density occur. The variations in binding energy Are linearly correlated with the wound integral K for those potentials that give nearly the same deuteron electric form factor. An increase in K leads to less binding in nuclear matter. The sensitivity of the binding energy is somewhat greater to the S&+ D& contribution to K than to the So contribution to K. We give a theoretical explanation, based on the modified Moszkowski-Scott separation approximation, to account for the sensitivity of the binding energy to the So and S&+ D& contributions to K. We also discuss the relation of K and the binding energy of nuclear matter to the off-shell elements of the T matrix. We discover that far-off-shell elements (q 6 F ) play a significant role in nuclear matter.