EFFECT OF THE PARTICLE-NUMBER SYMMETRY RESTORATION ON ROOT MEAN SQUARE RADII OF EVEN–EVEN NEUTRON-DEFICIENT NUCLEI IN THE ISOVECTOR PAIRING CASE

2012 ◽  
Vol 21 (04) ◽  
pp. 1250046 ◽  
Author(s):  
M. DOUICI ◽  
N. H. ALLAL ◽  
M. FELLAH ◽  
N. BENHAMOUDA ◽  
M. R. OUDIH
Keyword(s):  
Experimental Data ◽  
Root Mean Square ◽  
Single Particle ◽  
Particle Number ◽  
Mean Field ◽  
Second Step ◽  
Mean Square ◽  
The One ◽  
Proton Pairing

The effect of the particle-number symmetry restoration on the root mean square (rms) proton and neutron radii of neutron-deficient nuclei is studied in the isovector pairing case. As a first step, an expression of the nuclear radii which includes the neutron–proton pairing effects and which strictly conserves the particle-number has been established using the SBCS (Sharp BCS) method. It is shown that this expression generalizes the one obtained in the pairing between like-particles case. As a second step, the proton and neutron rms radii are numerically evaluated for even–even nuclei such as 16⩽Z⩽56 and 0⩽(N-Z)⩽4 using the single-particle energies of a Woods–Saxon mean-field. The results are compared with experimental data when available and with the results obtained when one considers only the pairing between like-particles.

Moment of inertia of even–even proton-rich nuclei using a particle-number conserving approach in the isovector neutron–proton pairing case

2016 ◽  
Vol 25 (06) ◽  
pp. 1650032 ◽  
Author(s):  
Faiza Hammache ◽  
N. H. Allal ◽  
M. Fellah ◽  
M. R. Oudih
Keyword(s):  
Particle Number ◽  
Mean Field ◽  
Moment Of Inertia ◽  
Second Step ◽  
Nuclear Moment ◽  
Pairing Effect ◽  
Picket Fence ◽  
Projection Effect ◽  
The One ◽  
Proton Pairing

An expression of the particle-number projected nuclear moment of inertia (MOI) has been established in the neutron–proton (np) isovector pairing case within the cranking model. It generalizes the one obtained in the like-particles pairing case. The formalism has been, as a first step, applied to the picket-fence model. As a second step, it has been applied to deformed even–even nuclei such as [Formula: see text] and of which the experimentally deduced values of the pairing gap parameters [Formula: see text], [Formula: see text], are known. The single-particle energies and eigenstates used are those of a deformed Woods–Saxon mean-field. It was shown, in both models, that the np pairing effect and the projection one are non-negligible. In realistic cases, it also appears that the np pairing effect strongly depends on [Formula: see text], whereas the projection effect is practically independent from the same quantity.

NEUTRON–PROTON PAIRING EFFECT ON ONE-PROTON AND TWO-PROTON SEPARATION ENERGIES IN RARE-EARTH PROTON-RICH NUCLEI

2012 ◽  
Vol 21 (12) ◽  
pp. 1250100 ◽  
Author(s):  
F. HAMMACHE ◽  
N. H. ALLAL ◽  
M. FELLAH
Keyword(s):  
Wave Function ◽  
Rare Earth ◽  
Particle Number ◽  
Good Description ◽  
Mean Field ◽  
Pairing Effect ◽  
Pairing Correlations ◽  
The One ◽  
Proton Pairing ◽  
Realistic Choice

The one-proton and two-proton separation energies are studied for "ordinary" and rare-earth proton-rich nuclei by including the isovector neutron–proton (np) pairing correlations using the BCS approximation. Even–even as well as odd nuclei are considered. In the latter case, the wave function is defined using the blocked-level technique. The single-particle energies used are those of a deformed Woods–Saxon mean field. It is shown that the np isovector pairing effects on the one-proton and two-proton separation energies are non-negligible. However, the only isovector BCS approximation seems to be inadequate for a good description of these quantities when including the np pairing effects: either a particle-number projection or the inclusion of the isoscalar pairing effect seems to be necessary. Another possible improvement would be a more realistic choice of the pairing strengths.

Charge, proton and neutron systems and matter radii of N ≈ Z odd-mass nuclei using a particle-number projection approach in the T = 1 pairing case

2016 ◽  
Vol 25 (12) ◽  
pp. 1650108 ◽  
Author(s):  
N. H. Allal ◽  
M. Fellah ◽  
M. Douici ◽  
M. R. Oudih
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Single Particle ◽  
Particle Number ◽  
Mean Field ◽  
Variation Method ◽  
Charge Radii ◽  
Projection Approach

The charge radii, the proton and neutron systems radii, as well as the matter radii of [Formula: see text] odd-mass nuclei are studied using a particle-number projection approach in the neutron–proton (np) isovector ([Formula: see text]) pairing case. Expressions of the proton and neutron systems quadratic radii are first established within a projection after variation method (i.e., of PBCS type) using a recently proposed wave function for odd-mass nuclei. It is checked that they reduce to the ones obtained in the like-particles pairing case. The new expressions are then used to study numerically the various radii of nuclei such as [Formula: see text] and [Formula: see text], using the single-particle energies of a Woods–Saxon mean-field. It is shown that the few available experimental data are satisfactorily described by means of the present work approach. Furthermore, it appears that the np pairing and projection effects on the various radii are small on average in the case of odd-mass nuclei. However, the relative discrepancies with the values when only the pairing between like-particles is taken into account or the values obtained before the projection may reach up to 3% or 4% for some nuclei.

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.

Particle-number conservation in odd mass proton-rich nuclei in the isovector pairing case

2015 ◽  
Vol 24 (06) ◽  
pp. 1550042 ◽  
Author(s):  
M. Fellah ◽  
N. H. Allal ◽  
M. R. Oudih
Keyword(s):  
Ground State ◽  
State Energy ◽  
Particle Number ◽  
Mean Field ◽  
Expectation Values ◽  
Deformation Effect ◽  
Pairing Effect ◽  
Projection Effect ◽  
Particle Number Conservation ◽  
The One

An expression of a wave function which describes odd–even systems in the isovector pairing case is proposed within the BCS approach. It is shown that it correctly generalizes the one used in the pairing between like-particles case. It is then projected on the good proton and neutron numbers using the Sharp-BCS (SBCS) method. The expressions of the expectation values of the particle-number operator and its square, as well as the energy, are deduced in both approaches. The formalism is applied to study the isovector pairing effect and the number projection one on the ground state energy of odd mass N ≈ Z nuclei using the single-particle energies of a deformed Woods–Saxon mean-field. It is shown that both effects on energy do not exceed 2%, however, the absolute deviations may reach several MeV. Moreover, the np pairing effect rapidly diminishes as a function of (N - Z). The deformation effect is also studied. It is shown that the np pairing effect, either before or after the projection, as well as the projection effect, when including or not the isovector pairing, depends upon the deformation. However, it seems that the predicted ground state deformation will remain the same in the four approaches.

scholarly journals STRUCTURE EFFECT ON ONE-NEUTRON REMOVAL REACTION USING RELATIVISTIC MEAN FIELD DENSITIES IN GLAUBER MODEL

2011 ◽  
Vol 20 (12) ◽  
pp. 2505-2519 ◽  
Author(s):  
R. N. PANDA ◽  
S. K. PATRA
Keyword(s):  
Experimental Data ◽  
Cross Sections ◽  
Mean Field ◽  
Reaction Cross ◽  
Glauber Model ◽  
Halo Nuclei ◽  
Relativistic Mean Field ◽  
The Difference ◽  
The One ◽  
Good Agreement

We calculate the one-neutron removal reaction cross-section (σ-1n) for a few stable and neutron-rich Boron and Carbon halo nuclei with 12 C as target, using relativistic mean field (RMF) densities, in the frame work of Glauber model. The results are compared with the experimental data. Study of the stable nuclei with the deformed densities have shown a good agreement with the data. However, it differs significantly for the halo nuclei. We observe that while estimating the σ-1n value from the difference of reaction cross-sections of two neighboring nuclei with mass number A and that of A-1 in an isotopic chain, we get good agreement with the known experimental data for the halo cases.

scholarly journals A NEW PHENOMENOLOGICAL FORMULA FOR GROUND-STATE BINDING ENERGIES

2011 ◽  
Vol 20 (01) ◽  
pp. 179-190 ◽  
Author(s):  
G. GANGOPADHYAY
Keyword(s):  
Binding Energy ◽  
Single Particle ◽  
Ground State ◽  
Liquid Drop ◽  
Alpha Decay ◽  
Binding Energies ◽  
Present Calculation ◽  
Mean Square ◽  
Liquid Drop Model ◽  
The One

A phenomenological formula based on liquid drop model has been proposed for ground-state binding energies of nuclei. The effect due to bunching of single particle levels has been incorporated through a term resembling the one-body Hamiltonian. The effect of n–p interaction has been included through a function of valence nucleons. A total of 50 parameters has been used in the present calculation. The root mean square (r.m.s.) deviation for the binding energy values for 2140 nuclei comes out to be 0.376 MeV, and that for 1091 alpha decay energies is 0.284 MeV. The correspondence with the conventional liquid drop model is discussed.

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.

Proton-proton correlations in dp and 16Op interactions

Open Physics ◽  
2011 ◽  
Vol 9 (6) ◽  
Author(s):  
Viktor Glagolev ◽  
Gabriela Martinská ◽  
Jan Mušinský ◽  
Jozef Urbán ◽  
Khosim Olimov ◽  
...  
Keyword(s):  
Experimental Data ◽  
Correlation Function ◽  
Bubble Chamber ◽  
Proton Emission ◽  
Hydrogen Bubble ◽  
Mean Square ◽  
Hydrogen Bubble Chamber ◽  
Proton Proton ◽  
Proton Source ◽  
The One

AbstractCorrelations between two protons emitted in dp and 16Op collisions at momenta 3.3 GeV/c and 52.6 GeV/c, respectively, are presented. The experimental data have been obtained using the one metre hydrogen bubble chamber exposed to nuclear beams from the synchrophasotron, JINR, Dubna. Data show a clear interference effect as expected for identical fermions. A Gaussian parametrization is used to determine the size of the proton emission source. The root mean square radius of the proton source calculated from the correlation function has been found to be equal to (2.10−0.35+0.43) fm and (2.67−0.38+0.54) fm for d and 16O respectively. It agrees with the known radii of these nuclei.

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