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.

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.

scholarly journals Charge radii of potassium isotopes in the RMF(BCS)* approach

2022 ◽  
Author(s):  
Rong An ◽  
Shisheng Zhang ◽  
Li-Sheng Geng ◽  
Feng-Shou 张丰收 Zhang
Keyword(s):  
Experimental Data ◽  
Density Functional Theory ◽  
Density Functional ◽  
Mean Field ◽  
Field Studies ◽  
Nuclear Density ◽  
Isotopic Chain ◽  
Functional Theory ◽  
Charge Radii ◽  
Nuclear Density Functional Theory

Abstract We apply the recently proposed RMF(BCS)* ansatz to study the charge radii of the potassium isotopic chain up to $^{52}$K. It is shown that the experimental data can be reproduced rather well, qualitatively similar to the Fayans nuclear density functional theory, but with a slightly better description of the odd-even staggerings (OES). Nonetheless, both methods fail for $^{50}$K and to a lesser extent for $^{48,52}$K. It is shown that if these nuclei are deformed with a $\beta_{20}\approx-0.2$, then one can obtain results consistent with experiments for both charge radii and spin-parities. We argue that beyond mean field studies are needed to properly describe the charge radii of these three nuclei, particularly for $^{50}$K.

Determination of the pairing-strength constants in the isovector plus isoscalar pairing case

2016 ◽  
Vol 25 (06) ◽  
pp. 1650035 ◽  
Author(s):  
D. Mokhtari ◽  
M. Fellah ◽  
N. H. Allal
Keyword(s):  
Single Particle ◽  
Mean Field ◽  
Bcs Theory ◽  
Charge Radii ◽  
Pairing Strength

A method for the determination of the pairing-strength constants, in the neutron–proton (n–p) isovector plus isoscalar pairing case, is proposed in the framework of the BCS theory. It is based on the fitting of these constants to reproduce the experimentally known pairing gap parameters as well as the root-mean-squared (r.m.s) charge radii values. The method is applied to some proton-rich even–even nuclei. The single-particle energies used are those of a deformed Woods–Saxon mean field. It is shown that the obtained value of the ratio [Formula: see text] is of the same order as the ones, arbitrary chosen, of some previous works. The effect of the inclusion of the isoscalar n–p pairing in the r.m.s matter radii is then numerically studied for the same nuclei.

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.

THE RELATIVISTIC MEAN FIELD THEORY AND LOW ENERGY QUADRUPOLE COLLECTIVE EXCITATIONS

2004 ◽  
Vol 13 (01) ◽  
pp. 217-224 ◽  
Author(s):  
L. PRÓCHNIAK ◽  
P. RING
Keyword(s):  
Field Theory ◽  
Experimental Data ◽  
Single Particle ◽  
Mean Field Theory ◽  
Mean Field ◽  
Low Energy ◽  
Collective Excitations ◽  
Relativistic Mean Field ◽  
Calculated Mass ◽  
Theoretical Results

We present an attempt to describe low lying quadrupole collective excitations within the frame of the RMF theory. Single particle wavefunctions obtained from the RMF are used to calculate mass parameters in the cranking approximation of the ATDHFB. The general Bohr hamiltonian with the calculated mass parameters yields collective energies and wavefunctions. Theoretical results are compared with the experimental data in the case of the γ soft 110 Ru and 126 Ba nuclei.

Multiple Impurity Scattering

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Wave Function ◽  
Single Particle ◽  
Mean Field ◽  
Impurity Scattering ◽  
Dyson Equation ◽  
High Angle ◽  
Many Body ◽  
Potential Approximation ◽  
T Matrix ◽  
Basic Ideas

Furnished with basic ideas about the scattering on a single impurity, the motion of a particle scattered by many randomly distributed impurities is approached. In spite of having a single particle only, this system already belongs to many-body physics as it combines randomising effects of high-angle collisions with mean-field effects due to low-angle collisions. The averaged wave function leads to the Dyson equation. Various approximations are systematically introduced and discussed ranging from Born, averaged T-matrix to coherent potential approximation. The effective medium and the effective mass as wave function renormalisations are discussed and the various approximations are accurately compared.

scholarly journals Mobility Enhancement in Square Quantum Wells: Symmetric Modulation of the Envelop Wave Function

2010 ◽  
Vol 20 (3) ◽  
pp. 193
Author(s):  
Doan Nhat Quang ◽  
Nguyen Huyen Tung ◽  
Nguyen Trung Hong ◽  
Tran Thi Hai
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Low Temperature ◽  
Quantum Wells ◽  
Quantum Transport ◽  
Variational Approach ◽  
Theoretical Study ◽  
Recent Experimental Data ◽  
Carrier Distribution ◽  
Analytic Expressions

We present a theoretical study of the effects from symmetric modulation of the envelop wave function on quantum transport in square quantum wells (QWs). Within the variational approach we obtain analytic expressions for the carrier distribution and their scattering in symmetric two-side doped square QWs. Roughness-induced scattering are found significantly weaker than those in the asymmetric one-side doped counterpart. Thus, we propose symmetric modulation of the wave function as an efficient method for enhancement of the roughness-limited QW mobility. Our theory is able to well reproduce the recent experimental data about low-temperature transport of electrons and holes in two-side doped square QWs, e.g., the mobility dependence on the channel width, which have not been explained so far.

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