Nuclear Theory·nucl-th

Tuesday·May 18, 2021

15 papers—10 primary·5 cross-listed

01
Matrix-product state approach to the generalized nuclear pairing Hamiltonian
Roman Rausch🇩🇪 · Cassian Plorin🇩🇪 · Matthias Peschke🇳🇱 · Christoph Karrasch🇩🇪
We show that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a 1D tensor network (matrix-product state) despite the presence of long-range interactions. The ground state can be obtained using the density-matrix renormalization group (DMRG) algorithm, which is accurate up to machine precision even for large nuclei, is numerically as cheap as the widely used BCS (Bardeen-Cooper-Schrieffer) approach, and does not suffer from any mean-field artifacts. We apply this framework to compute the even-odd mass differences of all known lead isotopes from $^{178}$ Pb to $^{220}$ Pb in a very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. We also treat pairing with non-zero angular momentum and determine the lowest excited states in the full configuration space of one major shell, which we demonstrate for the $N = 126$ , $Z \geq 82$ isotones. To demonstrate the capabilities of the method beyond low-lying excitations, we calculate the first 100 excited states of $^{208}$ Pb with singlet pairing and the two-neutron removal spectral function of $^{210}$ Pb, which relates to a two-neutron pickup experiment.
nucl-thcond-mat.str-elAnnalen Phys.(2024)·2 citations
02
Derivation of the Grodzins relation in collective nuclear model
R.V. Jolos · E.A. Kolganova
Basing on the Bohr collective quadrupole Hamiltonian the $A$ -dependence of the Grodzins product is derived and the proportionality coefficient for the Grodzins relation is evaluated. The result obtained is in a correspondence with the experimental data.
nucl-thPLB(2021)·6 citations
03
Neutron--proton spin--spin correlations in the ground states of N=Z nuclei
P. Van Isacker🇫🇷 · A. O. Macchiavelli🇺🇸
We present expressions for the matrix elements of the spin--spin operator $S_{n} \cdot S_{p}$ in a variety of coupling schemes. These results are then applied to calculate the expectation value $⟨ S_{n} \cdot S_{p} ⟩$ in eigenstates of a schematic Hamiltonian describing neutrons and protons interacting in a single- $l$ shell through a Surface Delta Interaction. The model allows us to trace $⟨ S_{n} \cdot S_{p} ⟩$ as a function of the competition between the isovector and isoscalar interaction strengths and the spin--orbit splitting of the $j = l \pm \frac{1}{2}$ shells. We find negative $⟨ S_{n} \cdot S_{p} ⟩$ values in the ground state of all even--even $N = Z$ nuclei, contrary to what has been observed in hadronic inelastic scattering at medium energies. We discuss the possible origin of this discrepancy and indicate directions for future theoretical and experimental studies related to neutron--proton spin--spin correlations.
nucl-thEPJA(2021)·7 citations
04
Continuum random-phase approximation for gamma transition between excited states in neutron-rich nuclei
Teruyuki Saito🇯🇵 · Masayuki Matsuo🇯🇵
A characteristic feature of collective and particle-hole excitations in neutron-rich nuclei is that many of them couple to unbound neutron in continuum single-particle orbits. The continuum random phase approximation (cRPA) is a powerful many-body method that describes such excitations, and it provides a scheme to evaluate transition strengths from the ground state. In an attempt to apply cRPA to the radiative neutron capture reaction, we formulate in the present study an extended scheme of cRPA that describes gamma-transitions from the excited states under consideration, which decay to low-lying excited states as well as the ground state. This is achieved by introducing a non-local one-body operator which causes transitions to a low-lying excited state, and describing a density-matrix response against this operator. As a demonstration of this new scheme, we perform numerical calculation for dipole, quadrupole, and octupole excitations in $^{140}$ Sn, and discuss E1 and E2 transitions decaying to low-lying $2_{1, 2}^{+}$ and $3_{1}^{-}$ states. The results point to cases where the branching ratio to the low-lying states is larger than or comparable with that to the ground state. We discuss key roles of collectivity and continuum orbits in both initial and final states.
nucl-thPRC(2021)·4 citations
05
Structure of $^{46, 47}$ Ca from the $β^{-}$ decay of $^{46, 47}$ K in the framework of nuclear shell model
Priyanka Choudhary🇮🇳 · Anil Kumar🇮🇳 · Praveen C. Srivastava🇮🇳 · Toshio Suzuki🇯🇵
In the present work, we report a comprehensive theoretical study of the $lo g f t$ values for the allowed and forbidden $β^{-}$ decay transitions of $^{46}$ K and $^{47}$ K corresponding to recently available experimental data from the GRIFFIN spectrometer at TRIUMF-ISAC [Phys. Rev. C {\bf 100}, 054327 (2019); Phys. Rev. C {\bf 102}, 054314 (2020)]. We perform the nuclear shell-model calculation in $s d p f$ -valence space, with the SDPF-MU interaction, to calculate low-lying energy spectra of $^{46, 47}$ K and $^{46, 47}$ Ca. For further investigation, we also calculate spectroscopic properties of $^{46, 47}$ K, $^{46, 47}$ Ca and compare the results with the experimental data. We suggest spin-parity of several levels, which were previously tentative, in both the calcium isotopes. Based on the energy and $lo g f t$ values, we conclude that the state at 3.984 MeV in $^{46}$ Ca could be either $3^{-}$ or $2^{+}$ and a state at 4.432 MeV might be $3^{-}$ . The spin-parity of the states at 2.875, 3.951 and 4.453 MeV are predicted to be $1/ 2^{-}$ , $3/ 2^{-}$ and $1/ 2^{-}$ or $1/ 2^{+}$ , respectively, in $^{47}$ Ca. We also give the confirmation to spin-parity of 2.850, 3.889 and 4.606 MeV states for $^{47}$ Ca. Our results of level schemes of $^{46, 47}$ K are in a reasonable agreement with the experimental data, while the agreement of calculated $lo g f t$ values for the $β^{-}$ decay with the experimental data is limited.
nucl-thPRC(2021)·11 citations
06
Nuclear energy density functionals from machine learning
X. H. Wu🇨🇳 · Z. X. Ren🇨🇳 · P. W. Zhao🇨🇳
Machine learning is employed to build an energy density functional for self-bound nuclear systems for the first time. By learning the kinetic energy as a functional of the nucleon density alone, a robust and accurate orbital-free density functional for nuclei is established. Self-consistent calculations that bypass the Kohn-Sham equations provide the ground-state densities, total energies, and root-mean-square radii with a high accuracy in comparison with the Kohn-Sham solutions. No existing orbital-free density functional theory comes close to this performance for nuclei. Therefore, it provides a new promising way for future developments of nuclear energy density functionals for the whole nuclear chart.
nucl-thquant-phPRC(2022)·46 citations
07
Incompressibility and Symmetry Energy of Neutron Star
Ankit Kumar🇮🇳 · H. C. Das🇮🇳 · S. K. Patra🇮🇳
We trace a systematic and consistent method to precisely numerate the magnitude range for various structural and isospin compositional properties of the neutron star. Incompressibility, symmetry energy, slope parameter and curvature of a neutron star are investigated using the relativistic energy density functional within the framework of coherent density fluctuation model. The analytical expression for the energy density functional of the neutron star matter is motivated from the Br $u ¨$ ckner functional and acquired by the polynomial fitting of the saturation curves for three different relativistic mean-field parameter sets (NL3, G3 and IU-FSU). The modified functional is folded with the neutron star's density-dependent weight function to calculate the numerical values for incompressibility and symmetry energy using the coherent density fluctuation model. NL3 parameter set, being the stiffest equation of state, endue us with a higher magnitude of all the properties compared to the other two parameter sets.
nucl-thastro-ph.HEPRC(2021)·11 citations
08
The drip lines of kaonic nuclei
J. Guo🇨🇳 · D. H. Chen🇨🇳 · Xian-Rong Zhou🇨🇳 · Q. B. Chen🇨🇳 · H.-J. Schulze🇮🇹
The effects of an additional $K^{-}$ meson on the neutron and proton drip lines are investigated within Skyrme-Hartree-Fock approach combined with a Skyrme-type kaon-nucleon interaction. While an extension of the proton drip line is observed due to the strongly attractive $K^{-} p$ interaction, contrasting effects (extension and reduction) on the neutron drip line of Be, O, and Ne isotopes are found. The origin of these differences is attributed to the behavior of the highest-occupied neutron single-particle levels near the neutron drip line.
nucl-thnucl-ex0 citations
09
Shell-model description for the first-forbidden $β^{-}$ decay of $^{207}$ Hg into the one-proton-hole nucleus $^{207}$ Tl
Anil Kumar🇮🇳 · Praveen C. Srivastava🇮🇳
In this work, we have performed large-scale shell-model calculations for the first-forbidden $β^{-}$ decay of $^{207}$ Hg into the one-proton-hole nucleus $^{207}$ Tl corresponding to the recently available experimental data from ISOLDE-CERN [T. A. Berry et al., Phys. Rev. C 101, 054311 (2020)]. We have used the one-particle one-hole ( $1 p$ - $1 h$ ) truncation for both protons and neutrons simultaneously across the doubly-shell closure at $^{208}$ Pb in the final states of $^{207}$ Tl. In our calculations, we have also considered the effect of mesonic enhancement $ϵ_{mec} = 2.01 \pm 0.05$ in the rank-0 for the axial-charge matrix element $γ_{5}$ . Here, we have calculated the $lo g f t$ values from the ground-state of $^{207}$ Hg to the several excited states of $^{207}$ Tl and obtained a good agreement between the calculated and the experimental data. In the experimental data spin and parity for some states are not yet confirmed, thus based on the shell-model results for the $lo g f t$ values we have given the prediction for these states. This is the first theoretical calculation for the $lo g f t$ values for these transitions.
nucl-thNPA(2021)·14 citations
10
Azimuthal dependence of two-particle transverse momentum current correlations
Niseem Magdy🇺🇸 · Sumit Basu🇸🇪 · Victor Gonzalez🇺🇸 · Ana Marin🇩🇪 · Olga Evdokimov🇺🇸 · Roy A. Lacey🇺🇸 · Claude Pruneau🇺🇸
Two-particle transverse momentum correlation functions are a powerful technique for understanding the dynamics of relativistic heavy-ion collisions. Among these, the transverse momentum correlator $G_{2} (Δ η, Δ φ)$ is of particular interest for its potential sensitivity to the shear viscosity per unit of entropy density $η / s$ of the quark-gluon plasma formed in heavy-ion collisions. We use the UrQMD, AMPT, and EPOS models for Au--Au at $s_{NN}$ = 200~GeV and Pb--Pb at $s_{NN}$ = 2760~GeV to investigate the long range azimuthal dependence of $G_{2} (Δ η, Δ φ)$ , and explore its utility to constrain $η / s$ based on charged particle correlations. We find that the three models yield quantitatively distinct transverse momentum Fourier harmonics coefficients $a_{n}^{p_{T}}$ . We also observe these coefficients exhibit a significant dependence on $η / s$ in the context of the AMPT model. These observations suggest that exhaustive measurements of the dependence of $G_{2} (Δ φ)$ with collision energy, system size, collision centrality, in particular, offer the potential to distinguish between different theoretical models and their underlying assumptions. Exhaustive analyses of $G_{2} (Δ φ)$ obtained in large and small systems should also be instrumental in establishing new constraints for precise extraction of $η / s$ .
nucl-thhep-phnucl-exEPJC(2021)·3 citations

Affiliations

first authorsco-authorsvia INSPIRE