<i>Nuclear Theory</i>

Lane, A. M.; Hayward, Evans

doi:10.1063/1.3051741

Cited by 51 publications

(41 citation statements)

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“…The pairing energy values obtained in our RMF+BCS calculations are found to be of similar magnitude as those obtained in other mean field calculations 20,4,32 . Further from fig 23 it is seen that the results obtained using the TMA and NL-SH forces are very close to each other. However, slight differences occur in some of the Sn and Pb isotopes with large neutron numbers.…”

Section: Pairing Energysupporting

confidence: 56%

“…22 we have displayed for some of the neutron rich representative isotopes of O, Zr, Sn and Pb nuclei the pairing gap energies of single particle states located close to the Fermi level. For our purpose we have chosen 20 23.…”

Section: Isotopes Of O Zr Sn and Pb Nucleimentioning

confidence: 99%

“…Based on the single-particle spectrum calculated by the RMF described above, we perform a state dependent BCS calculations 23,24 . As we already mentioned, the continuum is replaced by a set of positive energy states generated by enclosing the nucleus in a spherical box.…”

Section: Theoretical Formulation and Modelmentioning

confidence: 99%

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Description of Drip-Line Nuclei Within the Relativistic Mean Field Plus BCS Approach

Yadav

Kaushik

Toki

2004

Int. J. Mod. Phys. E

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RMF + BCS description of drip-line nucleiRecently it has been demonstrated, considering Ni and Ca isotopes as prototypes, that the relativistic mean-field plus BCS (RMF+BCS) approach wherein the single particle continuum corresponding to the RMF is replaced by a set of discrete positive energy states for the calculation of pairing energy provides a good approximation to the full relativistic Hartree-Bogoliubov (RHB) description of the ground state properties of the drip-line neutron rich nuclei. The applicability of RMF+BCS approach even for the drip-line nuclei is essentially due to the fact that the main contribution to the pairing correlations for the neutron rich nuclei is provided by the low-lying resonant states, in addition to the contributions coming from the states close to the Fermi surface. In order to show the general validity of this approach we present here the results of our detailed calculations for the ground state properties of the chains of isotopes of O, Ca, Ni, Zr, Sn and Pb nuclei. The TMA force parameter set has been used for the effective meanfield Lagrangian with the nonlinear terms for the sigma and omega mesons. Further, to check the validity of our treatment for different mean-field descriptions, calculations have also been carried out for the NL-SH force parameterization usually employed for the description of drip-line nuclei. Comprehensive results for the two neutron separation energy, rms radii, single particle pairing gaps and pairing energies etc. are presented. Especially, the Ca isotopes are found to exhibit distinct features near the neutron drip line whereby it is found that further addition of neutrons causes a rapid increase in the neutron rms radius with almost no increase in the binding energy, indicating the occurrence of halos. It is mainly caused by the pairing correlations and results in the existence of bound states of extremely neutron rich exotic nuclei. Similar characteristics though less pronounced, are also exhibited by the neutron rich Zr isotopes. A comparison of these results with the available experimental data and with the recent continuum relativistic Hartree-Bogoliubov (RCHB) calculations amply demonstrates the validity and usefulness of this fast RMF+BCS approach for the description of nuclei including those near the drip-lines.

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Section: Pairing Energysupporting

confidence: 56%

Section: Isotopes Of O Zr Sn and Pb Nucleimentioning

confidence: 99%

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Description of Drip-Line Nuclei Within the Relativistic Mean Field Plus BCS Approach

Yadav

Kaushik

Toki

2004

Int. J. Mod. Phys. E

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“…We will use in our derivations separable forces so that those equations convert into the usual dispersion relation [7,8], i. e.…”

Section: Introductionmentioning

confidence: 99%

Two-Particle Resonant States in a Many-Body Mean Field

et al. 2002

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A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two particle states are calculated by using a single particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow Gamow resonances. However, they can be significantly affected by the continuum part of the spectrum. PACS number(s): 25.70. Ef,23.50.+z,25.60+v,21.60.Cs Typeset using REVT E X 1 The prospect of reaching and measuring very unstable nuclei, as is materializing now, opens the possibility of studying spectroscopic processes occuring in the continuum part of nuclear spectra. Much work has already been done in this subject, particularly regarding halo nuclei [1]. Still, the role played by single-particle resonances and of the continuum itself upon particles moving in the continuum of a heavy nucleus is not fully understood. For instance, one may wonder whether two particles outside a core where the Fermi level is immersed in the continuum may produce a quasibound state and, in this case, whether that state is built upon narrow single-particle resonances or by an interplay between the two-particle interaction and the continuum, or by a combination of these mechanisms, as it happens in typical halo nuclei. To answer such questions is a difficult undertaking, particularly because the resonances on the real energy axis do not correspond to a definite state. A way of approaching this problem is by solving the Schrödinger equation with outgoing boundary conditions. One thus obtains the resonances as poles of the S-matrix in the complex energy plane. These poles (Gamow resonances) can be considered discrete states on the same footing as bound states (see Ref.[2] and references therein). However, in this case one finds that physical quantities, like energies and probabilities, become complex. One may attempt to give meaning to these complex quantities. Thus, it is usually assumed that the imaginary part of the energy of a decaying resonance is (except a minus sign) half the width. Other examples are the interpretation of complex cross sections done by Berggren [3] or the widely used radioactive decay width evaluated by Thomas as the residues of the S-matrix [4]. All these interpretations are valid only if the resonances are isolated and, therefore, narrow. In this case the residues of the S-matrix becomes real. One may thus apply this theory and evaluate all resonances, giving physical meaning to the narrow ones only. To achieve this goal a representation consisting of bound states, Gamow resonances and the proper continuum was proposed some years ago [2] (Berggren representation). One chooses the proper continuum as a given contour in th...

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“…Based on the single-particle spectrum calculated by the RMF described above, we perform a state dependent BCS calculations [7,8]. The continuum is replaced by a set of positive energy states generated by enclosing the nucleus in a spherical box.…”

Section: Theoretical Formulation and Modelmentioning

confidence: 99%

RMF+BCS Description of Some Traditional Neutron Magic Isotones

Saxena

Singh

Kaushik

2014

EPJ Web of Conferences

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Abstract. The traditional neutron magic nuclei with N = 8, 20, 28, 50, 82 and 126, and those with neutron sub-magic number N = 40 are investigated within the relativistic mean-field plus BCS (RMF+BCS) approach. The results indicate appearance of new proton magic numbers as well as the disappearance of conventional magic numbers for nuclei with extreme isospin values. The calculated energies and densities do not indicate any tendency for the proton halo formations in any of the proton rich isotones due to Coulomb interaction and different single particle spectra. However, the potential barrier provided by the Coulomb interaction and that due to the centrifugal force may cause a long delay in the actual decay of proton rich nucleus resulting the extended drip line.

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Nuclear Theory

Cited by 51 publications

References 0 publications

Description of Drip-Line Nuclei Within the Relativistic Mean Field Plus BCS Approach

Description of Drip-Line Nuclei Within the Relativistic Mean Field Plus BCS Approach

Two-Particle Resonant States in a Many-Body Mean Field

RMF+BCS Description of Some Traditional Neutron Magic Isotones

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