RMF+BCS approach for drip-line isotopes of Si

2014 ◽  
Vol 92 (3) ◽  
pp. 253-258 ◽  
Author(s):  
G. Saxena ◽  
D. Singh ◽  
M. Kaushik ◽  
S. Somorendro Singh
Keyword(s):  
Single Particle ◽  
Mean Field ◽  
Drip Line ◽  
Wave Functions ◽  
Positive Energy ◽  
Particle Spectrum ◽  
Pairing Energy ◽  
Weakly Bound ◽  
Relativistic Mean Field ◽  
Si Isotopes

We have employed the relativistic mean field (RMF)+BCS approach, to study ground state properties of drip line isotopes of Si. In this approach the single particle continuum corresponding to the RMF is replaced by a set of discrete positive energy states for the calculations of pairing energy. Detailed analysis of separation energy, single particle spectrum, pairing energies, and densities of the nuclei predict weakly bound structure in neutron-rich Si isotopes, which is seen to be due to the large spatial extension of the wave functions for the weakly bound single particle states with low orbital angular momentum having very small centrifugal barriers.

WEAKLY BOUND STRUCTURES, HALOS AND MAGICITY IN NEUTRON RICH NUCLEI

2008 ◽  
Vol 23 (27n30) ◽  
pp. 2589-2592 ◽  
Author(s):  
G. SAXENA ◽  
D. SINGH ◽  
H. L. YADAV ◽  
A. HAGA ◽  
H. TOKI
Keyword(s):  
Single Particle ◽  
Resonant State ◽  
Mean Field ◽  
Magic Number ◽  
Bound State ◽  
Positive Energy ◽  
Magic Numbers ◽  
Weakly Bound ◽  
Relativistic Mean Field ◽  
State Dependent

Inspired by recent measurements indicating proton magic number at Z =14 in the vicinity of 42 Si , we have employed our relativistic mean-field (RMF) plus state dependent BCS approach for the study of even-even nuclei to obtain magic numbers and to look for nuclei exhibiting weakly bound structures and even halo formation. In our RMF+BCS approach the single particle continuum corresponding to the RMF is replaced by a set of discrete positive energy states for the calculations of pairing energy. It is found that in several nuclei the filling in of low lying single particle resonant state with large angular momentum, even before it becomes a bound state, helps to accommodate more neutrons but with extremely small increase in the binding energy. This gives rise to the occurrence of weakly bound system of neutron rich nuclei.

scholarly journals DESCRIPTION OF DRIP-LINE NUCLEI WITHIN THE RELATIVISTIC MEAN FIELD PLUS BCS APPROACH

2004 ◽  
Vol 13 (03) ◽  
pp. 647-696 ◽  
Author(s):  
H. L. YADAV ◽  
M. KAUSHIK ◽  
H. TOKI
Keyword(s):  
Single Particle ◽  
Ground State ◽  
Mean Field ◽  
Drip Line ◽  
Positive Energy ◽  
Neutron Separation Energy ◽  
General Validity ◽  
Relativistic Mean Field ◽  
Ground State Properties ◽  
Pairing Correlations

Recently, 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 drip-line neutron rich nuclei. The applicability of the 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 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 mean-field Lagrangian with 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 parametrization 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. In particular, 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. This 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 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.

scholarly journals RELATIVISTIC HARTREE APPROACH INCLUDING BOTH POSITIVE- AND NEGATIVE-ENERGY BOUND STATES

1999 ◽  
Vol 08 (04) ◽  
pp. 389-416 ◽  
Author(s):  
G. MAO ◽  
H. STÖCKER ◽  
W. GREINER
Keyword(s):  
Single Particle ◽  
Bound States ◽  
Mean Field Theory ◽  
Mean Field ◽  
Negative Energy ◽  
Energy Spectra ◽  
Positive Energy ◽  
Relativistic Mean Field ◽  
Spherical Nuclei ◽  
The One

We develop a relativistic model to describe the bound states of positive energy and negative energy in finite nuclei at the same time. Instead of searching for the negative-energy solution of the nucleon's Dirac equation, we solve the Dirac equations for the nucleon and the anti-nucleon simultaneously. The single-particle energies of negative-energy nucleons are obtained through changing the sign of the single-particle energies of positive-energy anti-nucleons. The contributions of the Dirac sea to the source terms of the meson fields are evaluated by means of the derivative expansion up to the leading derivative order for the one-meson loop and one-nucleon loop. After refitting the parameters of the model to the properties of spherical nuclei, the results of positive-energy sector are similar to that calculated within the commonly used relativistic mean field theory under the no-sea approximation. However, the bound levels of negative-energy nucleons vary drastically when the vacuum contributions are taken into account. It implies that the negative-energy spectra deserve a sensitive probe to the effective interactions in addition to the positive-energy spectra.

ASYMPTOTIC NORMALIZATION COEFFICIENTS FOR 7Be(p, γ)8B FROM RMF CALCULATION

2009 ◽  
Vol 24 (18) ◽  
pp. 1453-1460 ◽  
Author(s):  
CHENGBIN WANG ◽  
TIEKUANG DONG ◽  
Z. Y. ZHU ◽  
ZHONGZHOU REN
Keyword(s):  
Cross Sections ◽  
Single Particle ◽  
Mean Field ◽  
Drip Line ◽  
Mean Square ◽  
Asymptotic Normalization ◽  
Halo Structure ◽  
Relativistic Mean Field ◽  
Asymptotic Normalization Coefficient ◽  
Structure Properties

The asymptotic normalization coefficient (ANC) method is used to determine the cross sections of peripheral reactions at astrophysical energies because of existence of the Coulomb barriers. In this paper, we address an estimation of the ANC of 8 B with its single particle wavefunction obtained within the framework of relativistic mean field (RMF) theory. We test the force parameters used in the RMF theory by comparing the calculated structure properties of A = 7–9 drip-line nuclei with experimental results. Utilizing the corrected bound wavefunction of 8 B , the ANC [Formula: see text] is obtained and that indicates the S17(0) is 18.07 eV b. Additionally, we find that the root-mean-square (rms) radius for the loosely bound proton in 8 B is 3.98 fm. This confirms that 8 B has a proton halo structure.

RELATIVISTIC MEAN FIELD PLUS BCS APPROACH TO DRIP-LINE NUCLEI

2002 ◽  
Vol 17 (38) ◽  
pp. 2523-2533 ◽  
Author(s):  
H. L. YADAV ◽  
S. SUGIMOTO ◽  
H. TOKI
Keyword(s):  
Fermi Surface ◽  
Strong Evidence ◽  
Mean Field ◽  
Detailed Comparison ◽  
Drip Line ◽  
Positive Energy ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Resonant States ◽  
Pairing Correlations

Based on a relativistic mean field (RMF) framework, we analyze the BCS approximation to the relativistic Hartree–Bogoliubov (RHB) approach for the case of nuclei close to the drip line. In the BCS calculations the single particle continuum corresponding to RMF is replaced by a set of discrete positive energy states generated by enclosing the nucleus in a box. It is found that the main contribution to the pairing correlations for the neutron-rich nuclei is given by the low-lying resonant states, in addition to the contributions coming from the states close to the Fermi surface. Towards this end we present the results of our calculations for the entire chain of even–even 48–98Ni isotopes. Results for the neutron-rich nucleus 84Ni is discussed in detail as a prototype. A detailed comparison of our results for the nucleus 84Ni with those obtained in similar studies using RHB, nonrelativistic Hartree–Fock–Bogoliubov (HFB), and a recently proposed resonant continuum HF+BCS method provides strong evidence for the applicability of the RMF+BCS approach for the treatment of neutron-rich nuclei as well. Additional results of extensive calculations for the isotopes of O, Ca, Zr, Sn and Pb nuclei further reinforce our conclusions. From amongst these calculations, the results of the even–even 32–76Ca isotopes with two different RMF force parametrizations, and their agreement with the recent continuum relativistic Hartree–Bogoliubov (CRHB) results are discussed briefly for illustration purposes.

Implications of occupancy of 2s1/2 state in sd-shell within RMF+BCS approach

2017 ◽  
Vol 26 (11) ◽  
pp. 1750072 ◽  
Author(s):  
G. Saxena ◽  
M. Kumawat ◽  
M. Kaushik ◽  
U. K. Singh ◽  
S. K. Jain ◽  
...  
Keyword(s):  
Mean Field ◽  
The Other ◽  
Magic Numbers ◽  
Neutron Density ◽  
Shell Closure ◽  
Weakly Bound ◽  
Density Profiles ◽  
Relativistic Mean Field ◽  
Structure Formula ◽  
Bubble Structure

We employ the relativistic mean-field plus BCS (RMF+BCS) approach to study the behavior of [Formula: see text]-shell by investigating in detail the single particle energies, and proton and neutron density profiles along with the deformations and radii of even–even nuclei. Emergence of new shell closure, weakly bound structure and most recent phenomenon of bubble structure are reported in the [Formula: see text]-shell. [Formula: see text]C, [Formula: see text]O and [Formula: see text]S are found to have a weakly bound structure due to particle occupancy in 2[Formula: see text] state. On the other hand [Formula: see text]O, [Formula: see text]Ca and [Formula: see text]Si are found with depleted central density due to the unoccupied 2[Formula: see text] state and hence they are the potential candidates of bubble structure. [Formula: see text]C and [Formula: see text]O emerge as doubly magic with [Formula: see text] in accord with the recent experiments and [Formula: see text]S emerges as a new proton magic nucleus with [Formula: see text]. [Formula: see text] and [Formula: see text] are predicted as magic numbers in doubly magic [Formula: see text]O, [Formula: see text]Ca and [Formula: see text]Si, respectively. These results are found in agreement with the recent experiments and have consistent with the other parameters of RMF and other theories.

scholarly journals TEMPERATURE DEPENDENCE OF THE NUCLEAR ENERGY IN RELATIVISTIC MEAN-FIELD THEORY

2005 ◽  
Vol 14 (03) ◽  
pp. 505-511 ◽  
Author(s):  
B. NERLO-POMORSKA ◽  
K. POMORSKI ◽  
J. SYKUT ◽  
J. BARTEL
Keyword(s):  
Single Particle ◽  
Level Density ◽  
Mean Field Theory ◽  
Mean Field ◽  
Correction Method ◽  
Shell Correction ◽  
Shell Effects ◽  
Relativistic Mean Field ◽  
Single Particle Level ◽  
Particle Level

Self-consistent relativistic mean-field (RMF) calculations with the NL3 parameter set were performed for 171 spherical even-even nuclei with 16≤A≤224 at temperatures in the range 0≤T≤4 MeV . For this sample of nuclei single-particle level densities are determined by analyzing the data obtained for various temperatures. A new shell-correction method is used to evaluate shell effects at all temperatures. The single-particle level density is expressed as function of mass number A and relative isospin I and compared with previous estimates.

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