# Nuclear Theory

## New submissions

[ total of 10 entries: 1-10 ]
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### New submissions for Thu, 22 Aug 19

[1]
Title: Renormalization of pionless effective field theory in the A-body sector
Comments: 14 pages, 7 figures, 2 tables. Contribution to the EPJA topical issue: "The tower of effective (field) theories and the emergence of nuclear phenomena"
Subjects: Nuclear Theory (nucl-th)

Current models of inter-nucleon interactions are built within the frame of Effective Field Theories (EFTs). Contrary to traditional nuclear potentials, EFT interactions require a renormalization of their parameters in order to derive meaningful estimations of observable. In this paper, a renormalization procedure is designed in connection with many-body approximations applicable to large-A systems and formulated within the frame of many-body perturbation theory. The procedure is shown to generate counterterms that are independent of the targeted A-body sector. As an example, the procedure is applied to the random phase approximation. This work constitutes one step towards the design of a practical EFT for many-body systems.

[2]
Title: Variation approach for pair determination in nucleon pair approximation
Authors: Y. Lei, H. Jiang
Subjects: Nuclear Theory (nucl-th)

We proposed a pair-condensation variation approach to evaluate the importance of collective pairs, and determine their structure in low-lying states. Based on such a variation, the nucleon pair approximation (NPA) could avoid the collective-pair uncertainty, which the previous NPA calculations have suffered a lot. With the trial calculation for transitional $^{132}$Ba, we exemplify the ability of our variation approach. In detail, the variation provides similar quadrupole deformation parameters to the Hartree-Fock calculations, and highlights the role of the pairing correlation in the $\gamma$ softness of $^{132}$Ba, with non-axisymmetric deformation degree of freedom. It conclusively helps the NPA to decide which collective pair is essential for obtaining lower yrast level scheme and reproducing the $I=10$ backbending. With the optimized condensation of neutron negative-parity pairs, we explain why the neutron negative-parity pairs have a large impact on the backbending behavior, and they are still not recommended. The collective-pair weights from the optimized pair condensation with cranking roughly have a positive correlation to the pair numbers in the NPA eigenstates with few exceptions, which reasonably establishes the validity of our variation approach.

[3]
Title: Consistent large-scale shell-model analysis of the two-neutrino $ββ$ and single $β$ branchings in $^{48}\rm Ca$ and $^{96}\rm Zr$
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)

Two-neutrino double-beta-decay matrix elements $M_{2\nu}$ and single beta-decay branching ratios were calculated for $^{48}$Ca and $^{96}$Zr in the interacting nuclear shell model using large single-particle valence spaces with well-tested two-body Hamiltonians. For $^{48}$Ca the matrix element $M_{2\nu}=0.0511$ is obtained, which is 5.5\% smaller than the previously reported value of 0.0539. For $^{96}$Zr this work reports the first large-scale shell-model calculation of the nuclear matrix element, yielding a value $M_{2\nu}=0.0747$ with extreme single-state dominance. If the scenario where the first $1^+$ state in $^{96}$Nb turns out to be correct, the matrix element is increased to 0.0854. These matrix elements, combined with the available $\beta\beta$-decay half-life data, yield effective values of the weak axial coupling which in turn are used to produce in a consistent way the $\beta$-decay branching ratios of $(7.5\pm2.8)$ % for $^{48}$Ca and $(18.4\pm0.09)$ % for $^{96}$Zr. These are larger than obtained in previous studies, implying that the detection of the $\beta$-decay branches could be possible in dedicated experiments sometime in the (near) future.

[4]
Title: Critical endpoint and universality class of neutron $^3P_2$ superfluids in neutron stars
Subjects: Nuclear Theory (nucl-th); Statistical Mechanics (cond-mat.stat-mech)

We study the thermodynamics and critical behavior of neutron $^3P_2$ superfluids in the inner cores of neutron stars. $^3P_2$ superfluids offer a rich phase diagram including uniaxial/biaxial nematic phases, the ferromagnetic phase, and the cyclic phase. Using the Bogoliubov-de Gennes (BdG) equation as superfluid Fermi liquid theory, we show that a strong (weak) magnetic field drives the first (second) order transition from the dihedral-two biaxial nematic phase to dihedral-four biaxial nematic phase in low (high) temperatures, and their phase boundaries are divided by the critical endpoint (CEP). We demonstrate that the set of critical exponents at the CEP satisfies the Rushbrooke, Griffiths, and Widom equalities, indicating a new universality class. At the CEP, the $^3P_2$ superfluid exhibits critical behavior with nontrivial critical exponents, indicating a new universality class. Furthermore, we find that the Ginzburg-Landau (GL) equation up to the 8th-order expansion satisfies three equalities and properly captures the physics of the CEP. This implies that the GL theory can provide a tractable way for understanding critical phenomena which may be realized in the dense core of realistic magnetars.

[5]
Title: Modification of effective interaction in pf-shell using spin-tensor decomposition
Subjects: Nuclear Theory (nucl-th)

In the present work, spin-tensor decomposition method of two-nucleon interaction is employed to improve the discrepancy of T = 1 tensor force monopole matrix elements of the latest shell-model effective interaction of GX-family used for pf-shell nuclei. The single-particle energies of $0f_{7/2}$, $0f_{5/2}$, and $1p_{3/2}$ orbitals are also modified to reproduce the E($2^{+}_{1}$) of $^{48, 54}$Ca. The improved interaction is named as GX1R, and used to calculate the effective-single particle energies of $\nu-0f1p$ orbitals in Ca chain, and low-lying states of $^{42-54}$Ca isotopes, consists of both even and odd-\textit{A} isotopes. The excitation energies of $2^{+}_{1}$ state of even Ti and Cr isotopes are also calculated. It is found that this new interaction satisfactorily describes N = 32 and 34 semi-magic shell gap in Ca isotopes, and fairly reproduces the excitation energy data of Ca, Ti and Cr isotopes.

### Cross-lists for Thu, 22 Aug 19

[6]  arXiv:1908.07605 (cross-list from hep-ph) [pdf, other]
Title: Magnetic fields in heavy ion collisions: flow and charge transport
Subjects: High Energy Physics - Phenomenology (hep-ph); Nuclear Experiment (nucl-ex); Nuclear Theory (nucl-th)

At the earliest times after a heavy-ion collision, the magnetic field created by the spectator nucleons will generate an extremely strong, albeit rapidly decreasing in time, magnetic field. The impact of this magnetic field may have detectable consequences, and is believed to drive anomalous transport effects like the Chiral Magnetic Effect (CME). We detail an exploratory study on the effects of a dynamical magnetic field on the hydrodynamic medium created in the collisions of two ultrarelativistic heavy-ions, using the framework of numerical ideal MagnetoHydroDynamics (MHD) with the ECHO-QGP code. In this study, we consider a magnetic field captured in a conducting medium, where the conductivity can receive contributions from the electromagnetic conductivity $\sigma$ and the chiral magnetic conductivity $\sigma_{\chi}$. We first study the elliptic flow of pions, which we show is relatively unchanged by the introduction of a magnetic field. However, by increasing the magnitude of the magnetic field, we find evidence for an enhancement of the elliptic flow in peripheral collisions. Next, we explore the impact of the chiral magnetic conductivity on electric charges produced at the edges of the fireball. This initial $\sigma_\chi$ can be understood as a long-wavelength effective description of chiral fermion production. We then demonstrate that this chiral charge, when transported by the MHD medium, produces a charge dipole perpendicular to the reaction plane which extends a few units in rapidity. Assuming charge conservation at the freeze-out surface, we show that the produced charge imbalance can have measurable effects on some experimental observables, like $v_1$ or $\langle \sin \phi \rangle$. This demonstrates the ability of a MHD fluid to transport the signature of the initial chiral magnetic fields to late times.

[7]  arXiv:1908.07986 (cross-list from gr-qc) [pdf, other]
Title: Glitching pulsars: unraveling the interactions of general relativity with quantum fields in the strong field regimes
Comments: 19 pages, 11 figures, research article
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Astrophysical Phenomena (astro-ph.HE); Nuclear Theory (nucl-th)

We present a modification of our previous model for the mechanisms underlying the glitch phenomena in pulsars and young neutron stars. Accordingly, pulsars are born with embryonic cores comprising of purely incompressible superconducting gluon-quark superfluid (henceforth SuSu-cores). As the ambient medium cools and spins down due to emission of magnetic dipole radiation, the mass and size of SuSu-cores are set to grow discretely with time, in accordance with the Onsager-Feynmann analysis of superfluidity. Presently, we propose that the spacetime embedding glitching pulsars is dynamical and of bimetric nature: inside SuSu-cores the spacetime must be flat, whereas the surrounding region, where the matter is compressible and dissipative, the spacetime is Schwarzschild. It is further proposed that the topological change of spacetime is derived by the strong nuclear force, whose operating length scales is found to increase with time to reach O(1) cm at the end of the luminous lifetimes of pulsars. The model presented here model is in line with the recent radio and GW observations of pulsars and NSs.

### Replacements for Thu, 22 Aug 19

[8]  arXiv:1706.02995 (replaced) [pdf, other]
Title: Optical properties of an anisotropic hot QCD medium
Comments: 12 pages, 6 figures, two column
Subjects: Nuclear Theory (nucl-th)
[9]  arXiv:1811.06434 (replaced) [pdf, ps, other]
Title: The spin parity of $Z_c^-$(4100), $Z_1^+$(4050) and $Z_2^+$(4250)
Authors: Xu Cao, Jian-Ping Dai