Nuclear Theory·nucl-th

Monday·October 19, 2020

6 papers—4 primary·2 cross-listed

01
Bound states in the B-matrix formalism for the three-body scattering
Sebastian M. Dawid🇺🇸 · Adam P. Szczepaniak🇺🇸
We consider a model of relativistic three-body scattering with a bound state in the two-body sub-channel. We show that the naïve K-matrix type parametrization, here referred to as the B-matrix, has nonphysical singularities near the physical region. We show how to eliminate such singularities by using dispersion relations and also show how to reproduce unitarity relations by taking into account all relevant open channels.
nucl-thhep-phhep-thPRD(2021)·18 citations
02
Microscopic coupled-channel calculation of proton and alpha inelastic scattering to the $4_{1}^{+}$ and $4_{2}^{+}$ states of $^{24}$ Mg
Yoshiko Kanada-En'yo · Kazuyuki Ogata
Background: The triaxial and hexadecapole deformations of the K=0+ and K=2+ bands of 24Mg have been investigated by the inelastic scatterings of various probes, including electrons, protons, and alpha particles, for a prolonged time. However, it has been challenging to explain the unique properties of the scatterings observed for the $4_{1}^{+}$ state through reaction calculations. Purpose: To investigate the structure and transition properties of the K=0+ and K=2+ bands of 24Mg employing the microscopic structure and reaction calculations via inelastic proton and alpha-scattering. Particularly, the E4 transitions to the $4_{1}^{+}$ and $4_{2}^{+}$ states were reexamined. Method: The structure of 24Mg was calculated employing the variation after the parity and total-angular momentum projections in the framework of the antisymmetrized molecular dynamics(AMD). The inelastic proton and alpha reactions were calculated by the microscopic coupled-channel (MCC) approach by folding the Melbourne g-matrix NN interaction with the AMD densities of 24Mg. Results: Reasonable results were obtained on the properties of the structure, including the energy spectra and E2 and E4 transitions of the K=0+ and K=2+ bands owing to the enhanced collectivity of triaxial deformation. The MCC+AMD calculation successfully reproduced the angular distributions of the $4_{1}^{+}$ and $4_{2}^{+}$ cross sections of proton scattering at incident energies of $E_{p}$ =40--100MeV and alpha-scattering at $E_{α}$ =100--400MeV. Conclusions: This is the first microscopic calculation that described the unique properties of the $0_{1}^{+} \to 4_{1}^{+}$ transition. In the inelastic scattering to the $4_{1}^{+}$ state, the dominant two-step process of the $0_{1}^{+} \to 2_{1}^{+} \to 4_{1}^{+}$ transitions and the deconstructive interference is the weak one-step process were essential.
nucl-thPTEP(2021)·2 citations
03
A new and practical formulation for overlaps of Bogoliubov vacua
B. G. Carlsson · J. Rotureau
In this letter we present a new expression for the overlaps of wavefunctions in Hartree-Fock-Bogoliubov based theories. Starting from the Pfaffian formula by Bertsch et al (Phys. Rev. Lett. 108,042505 (2012)), an exact and computationally stable formula for overlaps is derived. We illustrate the convenience of this new formulation with a numerical application in the context of the particle-number projection method. This new formula allows for substantially increased precision and versatility in chemical, atomic, and nuclear physics applications, particularly for methods dealing with superfluidity, symmetry restoration and uses of non-orthogonal many-body basis states.
nucl-thmath-phmath.MPPRL(2021)·29 citations
04
Isoscalar monopole and dipole transitions in $^{24}$ Mg, $^{26}$ Mg and $^{28}$ Si
P. Adsley🇿🇦 · V. O. Nesterenko🇷🇺 · M. Kimura🇯🇵 · L. M. Donaldson🇿🇦 · R. Neveling🇿🇦 · J. W. Brümmer🇿🇦 · D. G. Jenkins🇬🇧 · N. Y. Kheswa🇿🇦 · J. Kvasil🇨🇿 · K. C. W. Li🇿🇦 · D. J. Marin-Lámbarri🇿🇦 · Z. Mabika🇿🇦 and 7 other authors
Nuclei in the $s d$ -shell demonstrate a remarkable interplay of cluster and mean-field phenomena. The $N = Z$ nuclei, such as $^{24}$ Mg and $^{28}$ Si, have been the focus of the theoretical study of both these phenomena in the past. The cluster and vortical mean-field phenomena can be probed by excitation of isoscalar monopole and dipole states in scattering of isoscalar particles such as deuterons or $α$ particles. Inelastically scattered $α$ particles were momentum-analysed in the K600 magnetic spectrometer at iThemba LABS, Cape Town, South Africa. The scattered particles were detected in two multi-wire drift chambers and two plastic scintillators placed at the focal plane of the K600. In the theoretical discussion, the QRPA and AMD+GCM were used. The QRPA calculations lead us to conclude that: i) the mean-field vorticity appears mainly in dipole states with $K = 1$ , ii) the dipole (monopole) states should have strong deformation-induced octupole (quadrupole) admixtures, and iii) that near the $α$ -particle threshold, there should exist a collective state (with $K = 0$ for prolate nuclei and $K = 1$ for oblate nuclei) with an impressive octupole strength. The results of the AMD+GCM calculations suggest that some observed states may have a mixed (mean-field + cluster) character or correspond to particular cluster configurations. A tentative correspondence between observed states and theoretical states from QRPA and AMD+GCM was established. The QRPA and AMD+GCM analysis shows that low-energy isoscalar dipole states combine cluster and mean-field properties. The QRPA calculations show that the low-energy vorticity is well localized in $^{24}$ Mg, fragmented in $^{26}$ Mg, and absent in $^{28}$ Si.
nucl-thnucl-exPRC(2021)·12 citations
05
Constraints on the two-pion contribution to hadronic vacuum polarization
Gilberto Colangelo🇨🇭 · Martin Hoferichter🇨🇭 · Peter Stoffer🇺🇸
At low energies hadronic vacuum polarization (HVP) is strongly dominated by two-pion intermediate states, which are responsible for about $70%$ of the HVP contribution to the anomalous magnetic moment of the muon, $a_{μ}^{HVP}$ . Lattice-QCD evaluations of the latter indicate that it might be larger than calculated dispersively on the basis of $e^{+} e^{-} \to hadrons$ data, at a level which would contest the long-standing discrepancy with the $a_{μ}$ measurement. In this Letter we study to which extent this $2 π$ contribution can be modified without, at the same time, producing a conflict elsewhere in low-energy hadron phenomenology. To this end we consider a dispersive representation of the $e^{+} e^{-} \to 2 π$ process and study the correlations which thereby emerge between $a_{μ}^{HVP}$ , the hadronic running of the fine-structure constant, the $P$ -wave $π π$ phase shift, and the charge radius of the pion. Inelastic effects play an important role, despite being constrained by the Eidelman-Lukaszuk bound. We identify scenarios in which $a_{μ}^{HVP}$ can be altered substantially, driven by changes in the phase shift and/or the inelastic contribution, and illustrate the ensuing changes in the $e^{+} e^{-} \to 2 π$ cross section. In the combined scenario, which minimizes the effect in the cross section, a uniform shift around $4%$ is required. At the same time both the analytic continuation into the space-like region and the pion charge radius are affected at a level that could be probed in future lattice-QCD calculations.
↳ hep-phhep-exhep-latnucl-thPLB(2021)·162 citations
06
Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus
Andrey Chugunov (Ioffe Institute)
I discuss elastic properties of neutron star crust in the framework of static Coulomb solid model when atomic nuclei are treated as non-vibrating point charges; electron screening is neglected. The results are also applicable for solidified white dwarf cores and other materials, which can be modeled as Coulomb solids (dusty plasma, trapped ions, etc.). I demonstrate that the Coulomb part of the stress-strain tensor has additional symmetry: contraction $B_{ij i l} = 0$ . It does not depend on the structure (crystalline or amorphous) and composition. I show as a result of this symmetry the effective (Voigt averaged) shear modulus of the polycrystalline or amorphous matter to be equal to $- 2/15$ of the Coulomb (Madelung) energy density at undeformed state. This result is general and exact within the model applied. Since the linear mixing rule and the ion sphere model are used, I can suggest a simple universal estimate for the effective shear modulus: $\sum_{Z} 0.12 n_{Z} Z^{5/3} e^{2} / a_{e}$ . Here summation is taken over ion species, $n_{Z}$ is number density of ions with charge $Z e$ . Finally $a_{e} = (4 π n_{e} /3)^{- 1/3}$ is electron sphere radius. Quasineutrality condition $n_{e} = \sum_{Z} Z n_{Z}$ is assumed.
↳ astro-ph.HEastro-ph.SRcond-mat.mtrl-scinucl-th+1MNRAS(2020)·15 citations

Affiliations

first authorsco-authorsvia INSPIRE

Bound states in the B-matrix formalism for the three-body scattering

Microscopic coupled-channel calculation of proton and alpha inelastic scattering to the 41+​ and 42+​ states of 24Mg

A new and practical formulation for overlaps of Bogoliubov vacua

Isoscalar monopole and dipole transitions in 24Mg, 26Mg and 28Si

Constraints on the two-pion contribution to hadronic vacuum polarization

Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus

Affiliations

Microscopic coupled-channel calculation of proton and alpha inelastic scattering to the $4_{1}^{+}$ and $4_{2}^{+}$ states of $^{24}$ Mg

Isoscalar monopole and dipole transitions in $^{24}$ Mg, $^{26}$ Mg and $^{28}$ Si