Isovector pairing in odd-A proton-rich nuclei

Engel, J.; Langanke, K.; Vogel, P.

doi:10.1016/s0370-2693(98)00477-8

Cited by 22 publications

(35 citation statements)

References 9 publications

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“…Fig. 2 of [17]). The value of the splitting for the considered nuclei corresponds to y = G/G c somewhat larger than one.…”

Section: Spherical Potentialmentioning

confidence: 97%

“…Engel et al [16,17], Langanke et al [18][19][20][21], Dean et al [22], Poves and Martinez-Pinedo [23], and Martinez-Pinedo et al [24] investigated the strength of np pair correlations by analyzing the results of large-scale Shell Model calculations, for which there is a certain ambiguity in quantifying the correlation strength, as none of the authors calculated the pair transfer amplitude, which is the most direct measure. Refs.…”

Section: Spherical Potentialmentioning

confidence: 99%

“…Refs. [16,17] used the pair counting operators (13), which are not a direct measure of the correlations. They count the total number of pairs, which is different from zero in the uncorrelated system.…”

Section: Spherical Potentialmentioning

confidence: 99%

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Overview of neutron–proton pairing

Frauendorf

Macchiavelli

2014

Progress in Particle and Nuclear Physics

187

179

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The role of neutron-proton pairing correlations on the structure of nuclei along the N = Z line is reviewed. Particular emphasis is placed on the competition between isovector (T = 1) and isoscalar (T = 0) pair fields. The expected properties of these systems, in terms of pairing collective motion, are assessed by different theoretical frameworks including schematic models, realistic Shell Model and mean field approaches. The results are contrasted with experimental data with the goal of establishing clear signals for the existence of neutron-proton (np) condensates. We will show that there is clear evidence for an isovector np condensate as expected from isospin invariance. However, and contrary to early expectations, a condensate of deuteron-like pairs appears quite elusive and pairing collectivity in the T = 0 channel may only show in the form of a phonon. Arguments are presented for the use of direct reactions, adding or removing an np pair, as the most promising tool to provide a definite answer to this intriguing question.

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“…Fig. 2 of [17]). The value of the splitting for the considered nuclei corresponds to y = G/G c somewhat larger than one.…”

Section: Spherical Potentialmentioning

confidence: 97%

Section: Spherical Potentialmentioning

confidence: 99%

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Overview of neutron–proton pairing

Frauendorf

Macchiavelli

2014

Progress in Particle and Nuclear Physics

187

179

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“…We consider isovector, T = 1, L = 0, and isoscalar, T = 0, L = 1, pairs (7). For both limiting cases of pure isovector and isoscalar pairing, N T can be calculated using group algebra, see for example [28]. In the states of degenerate isovector pairing model…”

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confidence: 99%

Invariant correlational entropy as a signature of quantum phase transitions in nuclei

Volya

Zelevinsky

2003

Physics Letters B

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We study phase transformations in finite nuclei as a function of interaction parameters. The signature of a transition is given by invariant correlational entropy that reflects the sensitivity of an individual many-body state to changes of external parameters; peaks in this quantity indicate the critical regions. This approach is able to reveal the pairing phase transition, identify the isovector and isoscalar pairing regions and determine the role of other interactions. We show the examples of the phase diagram in the parameter space.Recently, an appreciable effort has been applied to understand and classify quantum phase transitions [1][2][3]. Although the concept of a phase transition is strictly applicable in the thermodynamic limit only, there are numerous examples of structural changes in mesoscopic systems, ranging from molecular clusters and semiconductors to atomic nuclei or quark systems, under variation of control parameters. Proper understanding of such transitions is crucial for areas from cosmology and formation of the universe to quantum computing and decoherence. The typical feature of phase transitions in small systems is the absence of discontinuities in the observables, and, therefore, difficulty for identification and classifications of E-mail address: volya@anl.gov (A. Volya). such transitions. The counterparts of phase changes in small systems involve restructuring, critical sensitivity to parameters, and chaotic large-scale fluctuations. In this work we study mesoscopic phase transitions in atomic nuclei using shell model interactions, which are known to reproduce the low-lying states in selected nuclei with a remarkable quality. The instrument we suggest for such studies can be similarly applied to other finite quantum systems.We identify the presence of a phase transformation as an enhancement in the invariant correlational entropy (ICE) which was introduced in [4]. ICE provides a measure of sensitivity of a given state in the many-body system to variations of external parameters. From earlier studies of bosonic models the increase of ICE is known to be associated with critical points [5]. We do not consider here thermal phase tran-0370-2693/$ -see front matter 

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“…51 Let us note that most of the previously cited works deal with either even-even systems or odd-odd ones: only few works were devoted to odd mass nuclei (see e.g., Refs. 37,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

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

Fellah

Allal

Oudih

2015

Int. J. Mod. Phys. E

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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.

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Isovector pairing in odd-A proton-rich nuclei

Cited by 22 publications

References 9 publications

Overview of neutron–proton pairing

Overview of neutron–proton pairing

Invariant correlational entropy as a signature of quantum phase transitions in nuclei

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

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