Neutron-Proton Mass Difference in Nuclear Matter and in Finite Nuclei and the Nolen-Schiffer Anomaly

Meißner, Ulf‐G.; Rakhimov, Abdulla; Wirzba, A.; Yakhshiev, Ulugbek

doi:10.1051/epjconf/20100306008

Cited by 5 publications

(11 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The electromagnetic and isospin breaking contributions to the mass have been thoroughly studied for A = 1, mostly in the context of the computation of the proton-neutron mass difference [23][24][25], but are usually neglected, to a first approximation, for higher A since they are not expected to overcome the large binding energies predicted by the model. There are also practical reasons why they are seldom taken into account.…”

Section: Coulomb Energy and Isospin Breakingmentioning

confidence: 99%

“…Of course, one can invoke the fact that isospin is not an exact symmetry to improve the predictions. Several attempts have been proposed to parametrize the isospin symmetry breaking term within the Skyrme Model [24,25]. Here we shall assume for simplicity that this results in a contribution proportional to the third component of isospin…”

Section: Coulomb Energy and Isospin Breakingmentioning

confidence: 99%

See 1 more Smart Citation

Near-BPS Skyrmions: Constant baryon density

Beaudoin

Marleau

2014

Nuclear Physics B

View full text Add to dashboard Cite

Although it provides a relatively good picture of the nucleons, the Skyrme Model is unable to reproduce the small binding energy in nuclei. This suggests that Skyrme-like models that nearly saturate the Bogomol'nyi bound may be more appropriate since their mass is roughly proportional to the baryon number A. For that purpose, we propose a near-BPS Skyrme Model. It consists of terms up to order six in derivatives of the pion fields, including the nonlinear and Skyrme terms which are assumed to be relatively small. For our special choice of mass term, we obtain well-behaved analytical BPS-type solutions with constant baryon density configurations, as opposed to the more complex shell-like configurations found in most extensions of the Skyrme Model. Fitting the four model parameters, we find a remarkable agreement for the binding energy per nucleon B/A with respect to experimental data. These results support the idea that nuclei could be near-BPS Skyrmions.Comment: Matches version to bepublished in Nucl.Phys. B. arXiv admin note: substantial text overlap with arXiv:1205.141

show abstract

Section: Coulomb Energy and Isospin Breakingmentioning

confidence: 99%

Section: Coulomb Energy and Isospin Breakingmentioning

confidence: 99%

Near-BPS Skyrmions: Constant baryon density

Beaudoin

Marleau

2014

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…Such an effect is of course also present in the Skyrmions description of nuclei since the static configuration has non-vanishing charge density. The electromagnetic and isospin breaking contributions to the mass have been thoroughly studied for A = 1, mostly in the context of the computation of the proton-neutron mass difference [14][15][16][17][18][19][20], but are usually neglected, to a first approximation, for higher A since they are not expected to overcome the large binding energies predicted by the model. There are also practical reasons why they are seldom taken into account.…”

Section: Coulomb Energy and Isospin Breakingmentioning

confidence: 99%

“…On the other hand, isospin is not an exact symmetry, a fact that may be traced back to the up and down quark mass difference. Several attempts have been made to modelize the isospin symmetry breaking term within the Skyrme model [19,20]. Here we shall assume for simplicity that this results in a contribution proportional to the third component of isospin…”

Section: Coulomb Energy and Isospin Breakingmentioning

confidence: 99%

“…The second issue concerns the inclusion of the Coulomb energy and the isospin symmetry breaking term in the calculation of nuclear masses. In the context of the Skyrme model, these contributions have been thoroughly studied for A = 1 [14][15][16][17][18][19][20] but are usually neglected, to a first approximation, for higher A since they are not expected to overcome the binding energies which are usually large and also because finding the configurations is already numerically challenging so that only small A solutions are known (e.g. approximate toroidal, tetrahedral, cubic configurations for A = 1, 2, 3 standard Skyrmions, respectively).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Near-BPS Skyrmions: Nonshell configurations and Coulomb effects

2012

View full text Add to dashboard Cite

The relatively small binding energy in nuclei suggests that they may be well represented by near-BPS Skyrmions since their mass is roughly proportional to the baryon number A. For that purpose, we propose a generalization of the Skyrme model with terms up to order six in derivatives of the pion fields and treat the nonlinear σ and Skyrme terms as small perturbations. For our special choice of mass term (or potential) V , we obtain well-behaved analytical BPS-type solutions with nonshell configurations for the baryon density, as opposed to the more complex shell-like configurations found in most extensions of the Skyrme model . Along with static and (iso)rotational energies, we add to the mass of the nuclei the often neglected Coulomb energy and isospin breaking term. Fitting the four model parameters, we find a remarkable agreement for the binding energy per nucleon B/A with respect to experimental data. These results support the idea that nuclei could be near-BPS Skyrmions.

show abstract

Nuclear binding energies from a Bogomol'nyi-Prasad-Sommerfield Skyrme model

et al. 2013

View full text Add to dashboard Cite

Recently, within the space of generalized Skyrme models, a BPS submodel was identified which reproduces some bulk properties of nuclear matter already on a classical level and, as such, constitutes a promising field theory candidate for the detailed and reliable description of nuclei and hadrons. Here we extend and further develop these investigations by applying the model to the calculation of nuclear binding energies. Concretely, we calculate these binding energies by including the classical soliton energies, the excitation energies from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies and a small explicit isospin symmetry breaking, which accounts for the mass difference between proton and neutron. The integrability properties of the BPS Skyrme model allow, in fact, for an analytical calculation of all contributions, which may then be compared with the semi-empirical mass formula. We find that for heavier nuclei, where the model is expected to be more accurate on theoretical grounds, the resulting binding energies are already in excellent agreement with their physical values. This result provides further strong evidence for the viability of the BPS Skyrme model as a distinguished starting point and lowest order approximation for the detailed quantitative investigation of nuclear and hadron physics.

show abstract

Neutron-Proton Mass Difference in Nuclear Matter and in Finite Nuclei and the Nolen-Schiffer Anomaly

Cited by 5 publications

References 51 publications

Near-BPS Skyrmions: Constant baryon density

Near-BPS Skyrmions: Constant baryon density

Near-BPS Skyrmions: Nonshell configurations and Coulomb effects

Nuclear binding energies from a Bogomol'nyi-Prasad-Sommerfield Skyrme model

Contact Info

Product

Resources

About