scholarly journals Restoration of particle number as a good quantum number in BCS theory

2001 ◽  
Vol 691 (3-4) ◽  
pp. 691-709 ◽  
Author(s):  
D.J. Rowe
Keyword(s):  
Quantum Number ◽  
Particle Number ◽  
Bcs Theory ◽  
Good Quantum Number

EFFECTIVE THEORY OF BOSONIC SUPERFLUIDS

1994 ◽  
Vol 08 (15) ◽  
pp. 2021-2039 ◽  
Author(s):  
ADRIAAN M.J. SCHAKEL
Keyword(s):  
Critical Temperature ◽  
Weak Coupling ◽  
Particle Number ◽  
Landau Theory ◽  
Effective Theory ◽  
Bcs Theory ◽  
Goldstone Mode ◽  
Zero Temperature ◽  
Temperature Expansion ◽  
High Temperature Expansion

We discuss the effective theory of a bosonic superfluid whose microscopic behavior is described by a nonrelativistic, weak-coupling Φ4 theory in the phase with broken particle number symmetry, both at zero temperature and in the vicinity of the phase transition. In the zero-temperature regime, the theory is governed by the gapless Goldstone mode resulting from the broken .symmetry. Although this mode is gapless, the effective theory turns out to be Gallilei invariant. The regime just below the critical temperature is approached in a high-temperature expansion which is shown to be consistent with the weak-coupling assumption of the theory. We calculate the critical temperature, the co-efficients of the Landau theory, and the finite-temperature sound velocity. A comparison with BCS theory is given.

SUPERHEAVY NUCLEI IN DIFFERENT PAIRING MODELS

2006 ◽  
Vol 15 (02) ◽  
pp. 452-456 ◽  
Author(s):  
ANDRZEJ BARAN ◽  
ZDZISŁAW ŁOJEWSKI ◽  
KAMILA SIEJA
Keyword(s):  
Spontaneous Fission ◽  
Particle Number ◽  
Mean Field ◽  
Projection Methods ◽  
Bcs Theory ◽  
Microscopic Description ◽  
Fission Process ◽  
State Dependent ◽  
Fission Barriers ◽  
Inertia Parameters

Pairing plays an important role in both mean-field and macroscopic-microscopic description of the fission process. We discuss two kinds of pairing models: monopole (g = const ) and state dependent (δ-type force). As is known the BCS theory leads to the particle number symmetry braking. To restore the symmetry one uses a projection methods (projection before- or after variation) or one solves the Lipkin-Nogami equations. We apply all these methods in the case of monopole pairing. Fission barriers, inertia parameters and spontaneous fission half-lives are studied in the case of Z = 112 isotopes.

scholarly journals Goodness of Generalized Seniority in Even-even Sn Isotopes.

2019 ◽  
Vol 6 (2) ◽  
pp. 147-154
Author(s):  
Bhoomika Maheshwari
Keyword(s):  
Nuclear Structure ◽  
Quantum Number ◽  
Excited States ◽  
High Spin ◽  
Magic Numbers ◽  
Selection Rules ◽  
Good Quantum Number ◽  
Spin Isomers ◽  
Configuration Mixing

Seniority has proved to be a unique and simple probe to address some of the complex issues underlying nuclear structure of nuclei close to magic numbers. An extension from the concept of seniority in single-j shell to generalized seniority in multi-j shell has recently been provided by us. We have, consequently, established new selection rules for gamma decays and discovered the new seniority isomers decaying via odd electric multipole operators. We have successfully explained the B(EL; L=1,2,3) behavior of various high spin isomers and other excited states. More specifically, we have been able to explain the long-standing puzzle of double hump in the B(E2) values for the first excited 2+ states of even-even Z=50 (Sn) isotopes. In the present paper, we review these generalized seniority calculations with emphasis on even-even Sn isotopes. We first discuss the generalized seniority results for the E1 decaying 13- isomers and E2 decaying 10+, 15- isomers, and then present the cases of first-excited 2+ and 3- states. The generalized seniority proves out to be a reasonably good quantum number. The significance of configuration mixing is found to be true. The calculated results has been validated till high seniority v=4 states and expected to be valid for higher seniority v=6,… states also.  

QUANTUM NUMBER PROJECTIONS OF NUCLEAR DEFORMED STATES

2006 ◽  
Vol 15 (03) ◽  
pp. 643-657 ◽  
Author(s):  
M. R. OUDIH ◽  
M. FELLAH ◽  
N. H. ALLAL ◽  
N. BENHAMOUDA
Keyword(s):  
Angular Momentum ◽  
Quantum Number ◽  
General Expression ◽  
Projection Method ◽  
Axial Symmetry ◽  
Particle Number ◽  
The Other ◽  
Equilibrium Deformation ◽  
System Energy ◽  
The One

We combine the exact particle-number projection method with the method of Peierls-Yoccoz in order to build the simultaneous eigen-functions of the particle number and the angular momentum operators. In the axial symmetry case, the general expression of the system energy resulting from this double projection is derived. In order to overcome the complexity of the method, the calculations are performed within the Gaussian overlap approximation. It turns out that, on the one hand, the double projection introduces a non–negligible correction of the energy of the system, and on the other hand, this correction is sensitive to the deformation. Future calculations have to therefore include an evaluation of the equilibrium deformation.

Tz = ±1 → 0 ISOSPIN SYMMETRY GAMOW-TELLER TRANSITIONS IN pf-SHELL NUCLEI

2010 ◽  
Vol 25 (21n23) ◽  
pp. 2003-2005 ◽  
Author(s):  
Y. FUJITA ◽  
T. ADACHI ◽  
H. FUJITA ◽  
Y. SHIMBARA ◽  
RCNP High Resolution ³He, t collabo ◽  
...  
Keyword(s):  
Quantum Number ◽  
Charge Exchange ◽  
Nuclear Physics ◽  
Isospin Symmetry ◽  
Exchange Reactions ◽  
Good Quantum Number ◽  
Key Issues ◽  
Pf Shell ◽  
Gamow Teller

Studying the Gamow-Teller (GT) transitions of stable as well as unstable pf-shell nuclei is one of the key issues in nuclear and astro-nuclear physics. Under the assumption that isospin T is a good quantum number, symmetry is expected for mirror nuclei and the GT transitions starting from the mirror nuclei. We study the GT transitions starting from Tz = ±1 mirror nuclei, respectively, by means of hadronic (3 He , t) charge-exchange reactions and complementary β decays.

scholarly journals Dipole States in 86Sr, 88Sr and 90Zr

1974 ◽  
Vol 27 (1) ◽  
pp. 21 ◽  
Author(s):  
RP Robertson
Keyword(s):  
Shell Model ◽  
Quantum Number ◽  
Ground State ◽  
Residual Interaction ◽  
Ground State Wavefunction ◽  
Model Method ◽  
Good Quantum Number ◽  
Realistic Force

A shell model method for calculating dipole states in N > Z even nuclei is discussed. By assuming isospin to be a good quantum number, the spectrum resolves into two classes of states differing in isospin. Applications of this model to 88Sr and 90Zr essentially differ from previous calculations by the use of a new realistic force in the residual interaction. Dipole states in 86Sr are also investigated along with the effect of correlating the ground state wavefunction

Evaluation of the β+ decay log ft value with inclusion of the neutron–proton pairing and particle number conservation

2015 ◽  
Vol 24 (02) ◽  
pp. 1550014 ◽  
Author(s):  
S. Kerrouchi ◽  
N. H. Allal ◽  
M. Fellah ◽  
M. R. Oudih
Keyword(s):  
Particle Number ◽  
Transition Probabilities ◽  
Bcs Theory ◽  
Nuclear Deformation ◽  
Β Decay ◽  
Deformation Effect ◽  
Particle Number Conservation ◽  
Fluctuation Effects ◽  
Proton Pairing ◽  
Gamow Teller

The particle number fluctuation effects, which are inherent to the Bardeen–Cooper–Schrieffer (BCS) theory, on the beta decay log ft values are studied in the isovector case. Expressions of the transition probabilities, of Fermi as well as Gamow–Teller types, which strictly conserve the particle number are established using a projection method. The probabilities are calculated for some transitions of isobars such as N ≃ Z. The obtained results are compared to values obtained before the projection. The nuclear deformation effect on the log ft values is also studied.

scholarly journals Manifestations of isospin in nearest neighbor spacing distributions for the f-p model space

2017 ◽  
Vol 26 (10) ◽  
pp. 1750060
Author(s):  
Michael Quinonez ◽  
Arun Kingan ◽  
Larry Zamick
Keyword(s):  
Energy Level ◽  
Quantum Number ◽  
Nearest Neighbor ◽  
Model Space ◽  
Strong Interactions ◽  
Good Quantum Number ◽  
Text Model

The strong interactions are charge independent. If we limit ourselves to the strong interactions, we have the isospin [Formula: see text] as a good quantum number. Here, we consider the lack of level repulsion of states of different isospin and how this effect manifests in nearest neighbor spacing (NNS) histograms, which provide a visual and statistical context in which to study distributions of energy level spacings. In particular, we study nucleons in the [Formula: see text] model space for the nucleus [Formula: see text]. We also compare NNS distributions produced in the isospin formalism to distributions produced in the proton–neutron formalism.

Is isospin a good quantum number for Σ hypernuclei?

1984 ◽  
Vol 138 (5-6) ◽  
pp. 337-340 ◽  
Author(s):  
C.B. Dover ◽  
A. Gal ◽  
D.J. Millener
Keyword(s):  
Quantum Number ◽  
Good Quantum Number
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