Nuclear Theory·nucl-th

Tuesday·December 28, 2021

26 papers—13 primary·13 cross-listed

01
[Submitted on 23 Dec 2021]
Performing Bayesian analyses with AZURE2 using BRICK: an application to the $^{7}$ Be system
Daniel Odell · Carl R. Brune · Daniel R. Phillips · Richard James deBoer · Som Nath Paneru
Phenomenological $R$ -matrix has been a standard framework for the evaluation of resolved resonance cross section data in nuclear physics for many years. It is a powerful method for comparing different types of experimental nuclear data and combining the results of many different experimental measurements in order to gain a better estimation of the true underlying cross sections. Yet a practical challenge has always been the estimation of the uncertainty on both the cross sections at the energies of interest and the fit parameters, which can take the form of standard level parameters. Frequentist ( $χ^{2}$ -based) estimation has been the norm. In this work, a Markov Chain Monte Carlo sampler, \texttt{emcee}, has been implemented for the $R$ -matrix code \texttt{AZURE2}, creating the Bayesian $R$ -matrix Inference Code Kit (\texttt{BRICK}). Bayesian uncertainty estimation has then been carried out for a simultaneous $R$ -matrix fit of the $^{3}$ He $(α, γ)^{7}$ Be and $^{3}$ He $(α, α)^{3}$ He reactions in order to gain further insight into the fitting of capture and scattering data. Both data sets constrain the values of the bound state $α$ -particle asymptotic normalization coefficients in $^{7}$ Be. The analysis highlights the need for low-energy scattering data with well-documented uncertainty information and shows how misleading results can be obtained in its absence.
Subjects:
Nuclear Theory (nucl-th)
arXiv:
2112.12838 [pdf]
Front.in Phys.(2022)·40 citations
02
[Submitted on 24 Dec 2021]
Possible halo structure of $^{62, 72}$ Ca by forbidden-state-free locally peaked Gaussians
W. Horiuchi · Y. Suzuki · M. A. Shalchi · Lauro Tomio
In order to efficiently describe nucleon orbits around a heavy core nucleus, we propose locally peaked Gaussians orthogonalized to the occupied bound states in the core. We show the advantage of those functions in both numerical stability and fast convergence by taking examples of touchstone calcium isotopes $^{62, 72}$ Ca in $^{60, 70} Ca + n + n$ three-body models. Both weakly bound configurations and continuum coupling effect are taken into account. We evaluate the neutron radii and the occupation probabilities of two-neutron configurations not only for the ground state but also for some particle-bound excited states by varying the strength of the core-neutron interaction. The emergence of the halo structure in the ground state depends on the energy difference between $2 s_{1/2}$ and $0 g_{9/2}$ orbits. Two-neutron [consisting of $(s_{1/2})^{2}$ configuration] and one-neutron [consisting of $(g_{9/2} s_{1/2})$ configuration] halo structure of $^{62}$ Ca can coexist in narrow energy spacing provided that both of $2 s_{1/2}$ and $0 g_{9/2}$ orbits are almost degenerate and barely bound. The ground-state structure of $^{72}$ Ca is likely to be a two-neutron halo, although its emergence depends on the position of the $2 s_{1/2}$ level.
Comments:
10 pages, 5 figures, 2 tables, typos corrected, to appear in Phys. Rev. C
Subjects:
Nuclear Theory (nucl-th)
arXiv:
2112.12923 [pdf]
PRC(2022)·10 citations
03
[Submitted on 24 Dec 2021]
Quark-quark interaction and quark matter in neutron stars
Y. Yamamoto🇯🇵 · N. Yasutake🇯🇵 · Th.A. Rijken🇯🇵
Hyperon ( $Y$ ) mixing in neutron-star matter brings about a remarkable softening of the equation of state (EoS) and the maximum mass is reduced to a value far less than $2 M_{⊙}$ . One idea to avoid this "hyperon puzzle in neutron stars" is to assume that the many-body repulsions work universally for every kind of baryons. The other is to take into account the quark deconfinement phase transitions from a hadronic EoS to a sufficiently stiff quark-matter EoS. In the present approach, both effects are handled in a common framework. As well as the hadronic matter, the quark matter with the two-body quark-quark interactions are treated within the Brueckner-Bethe-Goldstone theory beyond the mean field frameworks, where interaction parameters are based on the terrestrial data. The derived mass-radius relations of neutron stars show that maximum masses reach over $2 M_{⊙}$ even in the cases of including hadron-quark phase transitions, being consistent with the recent observations for maximum masses and radii of neutron stars by the NICER measurements and the other multimessenger data.
Subjects:
Nuclear Theory (nucl-th); High Energy Astrophysical Phenomena (astro-ph.HE)
arXiv:
2112.12931 [pdf]
PRC(2022)·15 citations
04
[Submitted on 24 Dec 2021]
Chirality dependence in charge and heat transport in thermal QCD
Pushpa🇮🇳 · Binoy Krishna Patra🇮🇳
In the presence of weak magnetic field ( $B$ ), novel phenomena, similar to Hall effect in condensed matter physics, emerge both in charge and heat transport in a thermal QCD medium. Here, we have employed the kinetic theory approach within a quasiparticle framework, wherein the effective masses for left (L) and right-handed (R) chiral modes of quarks are seen different, lifting the prevalent degeneracy. Another implication of weak $B$ is that the coefficients assume a tensorial structure: The diagonal elements represent the usual conductivities: $σ_{Ohmic}$ and $κ_{0}$ as the coefficients of charge and heat transport, respectively and the off-diagonal elements denote their Hall counterparts: $σ_{Hall}$ and $κ_{1}$ , respectively. Finally, we have derived some coefficients, namely, the Knudsen number and Lorenz number in Wiedemann-Franz law. Lorenz number and Hall-Lorenz number for L-mode increases and for R-mode decreases with a magnetic field. it does not remain constant with $T$ hence violating the Wiedemann-Franz law.
Comments:
34 pages, 32 figures
Subjects:
Nuclear Theory (nucl-th); High Energy Physics — Phenomenology (hep-ph)
arXiv:
2112.12950 [pdf]
PRD(2022)·12 citations
05
[Submitted on 24 Dec 2021]
Microscopic description of cluster decays based on the generator coordinate method
K. Uzawa · K. Hagino · K. Yoshida
\noindent\textbf{Background:} While many phenomenological models for nuclear fission have been developed, a microscopic understanding of fission has remained one of the most challenging problems in nuclear physics. \noindent\textbf{Purpose:} We investigate an applicability of the generator coordinate method (GCM) as a microscopic theory for cluster radioactivities of heavy nuclei, which can be regarded as a fission with large mass asymmetry, that is, a phenomenon in between fission and $α$ -decays. \noindent\textbf{Methods:} Based on the Gamow theory, we evaluate the preformation probability of a cluster with GCM while the penetrability of the Coulomb barrier is estimated with a potential model. To this end, we employ Skyrme interactions and solve the one-dimensional Hill-Wheeler equation with the mass octupole field. We also take into account the dynamical effects of the pairing correlation using BCS wavefunctions constructed with an increased strength of the pairing interaction. \noindent\textbf{Results:} We apply this scheme to the cluster decay of $^{222}$ Ra, i.e., $^{222}$ Ra $\to^{14}$ C+ $^{208}$ Pb, to show that the experimental decay rate can be reproduced within about two order of magnitude. We also briefly discuss the cluster radioactivities of the $^{228}$ Th and $^{232}$ U nuclei. For these actinide nuclei, we find that the present calculations reproduce the decay rates with the same order of magnitude and within two or three order of magnitude, respectively. \noindent\textbf{Conclusions:} The method presented in this paper provides a promising way to describe microscopically cluster decays of heavy nuclei.
Comments:
8 pages, 8 figures
Subjects:
Nuclear Theory (nucl-th)
arXiv:
2112.13037 [pdf]
PRC(2022)·8 citations
06
[Submitted on 25 Dec 2021]
Effects of variation of the fine structure constant $α$ and quark mass $m_{q}$ in Mössbauer nuclear transitions
Pavel Fadeev🇩🇪 · Julian C. Berengut🇦🇺 · Victor V. Flambaum🇩🇪
High accuracy measurements in Mössbauer transitions open up the possibility to use them in the search for temporal and spatial variation of the fine-structure constant $α$ , quark mass $m_{q}$ , and dark matter field which may lead to the variation of $α$ and $m_{q}$ . We calculate the sensitivity of nuclear transitions to variation of $α$ and $m_{q}$ . Mössbauer transitions have high sensitivity to variation of quark mass $m_{q}$ and the strong interaction scale $Λ_{QC D}$ , to which atomic optical clocks are not sensitive. The enhancement factors $K$ , defined by $\frac{δ f}{f} = K_{α} \frac{δ α}{α}$ and $\frac{δ f}{f} = K_{q} \frac{δ m _{q}}{m _{q}}$ where $f$ is the transition energy, may be large in some transitions. The 8~eV nuclear clock transition in $^{229}$ Th ( $K_{q} \approx 1 0^{4}$ ) and 76~eV transition in $^{235}$ U ( $K_{α} \approx K_{q} \approx 1 0^{3}$ ) may be investigated using laser spectroscopy methods.
Comments:
8 pages
Subjects:
Nuclear Theory (nucl-th); High Energy Physics — Phenomenology (hep-ph); Nuclear Experiment (nucl-ex); Atomic Physics (physics.atom-ph)
arXiv:
2112.13195 [pdf]
PRC(2022)·11 citations
07
[Submitted on 26 Dec 2021]
Microscopic collective inertial masses for nuclear reaction in the presence of nucleonic effective mass
Kai Wen · Takashi Nakatsukasa
Collective inertial mass coefficients with respect to translational, relative, and rotational motions are microscopically calculated, along the collective reaction path self-consistently determined, based on the adiabatic self-consistent collective coordinate (ASCC) method. The impact of the time-odd component of the mean-field potential on the inertial masses are investigated. The results are compared with those calculated with the cranking formulae. The inertial masses based on the ASCC method reproduce the exact total nuclear mass for the translational motion as well as the exact reduced masses as the asymptotic values for the relative and rotational motions. In contrast, the cranking formulae fail to do so. This is due to the fact that the (local) Galilean invariance is properly restored in the ASCC method, but violated in the cranking formulae. A model Hamiltonian for low-energy nuclear reaction is constructed with the microscopically derived potentials and inertial masses. The astrophysical S-factors are calculated, which indicates the importance of microscopic calculation of proper inertial masses.
Comments:
12 pages, 9 figures
Subjects:
Nuclear Theory (nucl-th)
arXiv:
2112.13317 [pdf]
PRC(2022)·5 citations
08
[Submitted on 26 Dec 2021]
Two-point functions from chiral kinetic theory in magnetized plasma
Lixin Yang🇨🇳
We study the two-point functions from chiral kinetic theory which characterize the response to perturbative vector and axial gauge fields in magnetized chiral plasma. In the lowest Landau level approximation, the solution of chiral kinetic equations gives density waves of electric and axial charges, which contain chiral magnetic wave implied by the axial anomaly and magnetic field. We then obtain the constitutive relations for covariant currents and stress tensor that involving the density waves. By considering the difference between consistent and covariant anomalies explicitly, the correlators of consistent currents and stress tensor satisfy derivative symmetry, and therefore allow an effective action for the perturbative gauge fields as the generating functional of the correlators. We also verify the derivative symmetry of the correlators agrees with the Onsager relations.
Comments:
27 pages, 0 figures
Subjects:
Nuclear Theory (nucl-th); High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Theory (hep-th)
arXiv:
2112.13351 [pdf]
PRD(2022)·3 citations
09
[Submitted on 27 Dec 2021]
Effects of the momentum dependence of nuclear symmetry potential on pion observables in Sn + Sn collisions at 270 MeV/nucleon
Gao-Feng Wei · Xin Huang · Qi-Jun Zhi · Ai-Jun Dong · Chang-Gen Peng · Zheng-Wen Long
Within a transport model, we study effects of the momentum dependence of nuclear symmetry potential on pion observables in central Sn + Sn collisions at 270 MeV/nucleon. To this end, a quantity $U_{sy m}^{\infty} (ρ_{0})$ , i.e., the value of nuclear symmetry potential at the saturation density $ρ_{0}$ and infinitely large nucleon momentum, is used to characterise the momentum dependence of nuclear symmetry potential. It is shown that with a certain $L$ (i.e., slope of nuclear symmetry energy at $ρ_{0}$ ) the characteristic parameter $U_{sy m}^{\infty} (ρ_{0})$ of symmetry potential affects significantly the production of $π^{-}$ and $π^{+}$ as well as their pion ratios. Moreover, through comparing the charged pion yields, pion ratios as well the spectral pion ratios of theoretical simulations for the reactions $^{108}$ Sn + $^{112}$ Sn and $^{132}$ Sn + $^{124}$ Sn with the corresponding data in S $π$ RIT experiments, we find that our results favor a constraint on $U_{sy m}^{\infty} (ρ_{0})$ , i.e., $- 16 0_{- 9}^{+ 18}$ ~MeV, and the $L$ is also suggested within a range, i.e., $62.7 < L < 93.1$ ~MeV. In addition, it is shown that the pion observable of $^{197}$ Au + $^{197}$ Au collisions at 400~MeV/nucleon also supports the extracted value for $U_{sy m}^{\infty} (ρ_{0})$ .
Comments:
11 pages, 14 figures, add several references and several figures to interpret the results; original conclusion is not changed qualitatively, more stringent constraints on $U_{sy m}^{\infty} (ρ_{0})$ are concluded quantitatively. Accepted for publication in Nuclear Science and Techniques
Subjects:
Nuclear Theory (nucl-th); Nuclear Experiment (nucl-ex)
arXiv:
2112.13518 [pdf]
Nucl.Sci.Tech.(2022)·11 citations
10
[Submitted on 27 Dec 2021]
Quantum statistics effects near the critical point in systems with different inter-particle interactions
S.N. Fedotkin🇺🇦 · A.G. Magner🇺🇦 · U.V. Grygoriev🇺🇦
Equation of state with quantum statistics corrections is derived for systems of the Fermi and Bose particles by using their van der Waals (vdW) and effective density-dependent Skyrme mean-field interactions. First few orders of these corrections over the small quantum statistics parameter, $ε \approx ℏ^{3} n (m T)^{- 3/2} g^{- 1}$ , where $n$ and $T$ are the particle number density and temperature, $m$ and $g$ the mass and degeneracy factor of particles, are analytically obtained. For interacting system of nucleon and $α$ - particles, a small impurity of $α$ - particles to a nucleon system at leading first order in both $α$ -particle and nucleon small parameters $ε$ does not change much the basic results for the symmetric nuclear matter in the quantum vdW consideration. Our approximate analytical results for the quantum vdW and Skyrme mean-field approaches are in a good agreement with accurate numerical calculations.
Comments:
10 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:2012.09695
Subjects:
Nuclear Theory (nucl-th); High Energy Physics — Theory (hep-th)
arXiv:
2112.13704 [pdf]
PRC(2022)·3 citations
11
[Submitted on 27 Dec 2021]
Inferring nuclear structure from heavy isobar collisions using Trajectum
Govert Nijs🇺🇸 · Wilke van der Schee🇨🇭
Nuclei with equal number of baryons but varying proton number (isobars) have many commonalities, but differ in both electric charge and nuclear structure. Relativistic collisions of such isobars provide unique opportunities to study the variation of the magnetic field, provided the nuclear structure is well understood. In this Letter we simulate collisions using several state-of-the-art parametrizations of the $_{40}^{96}$ Zr and $_{44}^{96}$ Ru isobars and show that a comparison with the exciting STAR measurement arXiv:2109.00131 of ultrarelativistic collisions can uniquely identify the structure of both isobars. This not only provides an urgently needed understanding of the structure of the Zirconium and Ruthenium isobars, but also paves the way for more detailed studies of nuclear structure using relativistic heavy ion collisions.
Comments:
10 pages, 6 figures. Trajectum can be downloaded at https://sites.google.com/view/govertnijs/trajectum, output files and plotting routines at http://wilkevanderschee.nl
Subjects:
Nuclear Theory (nucl-th); High Energy Physics — Phenomenology (hep-ph); Nuclear Experiment (nucl-ex)
arXiv:
2112.13771 [pdf]
SciPost Phys.(2023)·58 citations
12
[Submitted on 27 Dec 2021]
Low-energy enhancement in the magnetic dipole $γ$ -ray strength functions of heavy nuclei
P. Fanto · Y. Alhassid
A low-energy enhancement (LEE), observed experimentally in the $γ$ -ray strength function ( $γ$ SF) describing the decay of compound nuclei, would have profound effects on $r$ -process nucleosynthesis if it persists in heavy neutron-rich nuclei. The LEE was shown to be a feature of the magnetic dipole ( $M 1)$ strength function in configuration-interaction shell-model calculations in medium-mass nuclei. However, its existence in heavy nuclei and its evolution with neutron number remain open questions. Here, using a combination of many-body methods, we find the LEE in the $M 1$ $γ$ SFs of heavy samarium nuclei. In particular, we use the static-path plus random-phase approximation (SPA+RPA), which includes static and small-amplitude quantal fluctuations beyond the mean field. Using the SPA+RPA strength as a prior, we apply the maximum-entropy method (MEM) to obtain finite-temperature $M 1$ $γ$ SFs from exact imaginary-time response functions calculated with the shell model Monte Carlo (SMMC) method. We find that the slope of the LEE in samarium isotopes is roughly independent of the average initial energy over a wide range below the neutron separation energy. As the neutron number increases, strength transfers to a low-energy excitation, which we interpret as the scissors mode built on top of excited states.
Comments:
7 pages, 4 figures
Subjects:
Nuclear Theory (nucl-th); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
arXiv:
2112.13772 [pdf]
PRC(2024)·9 citations
13
[Submitted on 27 Dec 2021]
Mass-Energy Equivalence in Bound Three-Nucleon Systems
I. Filikhin · V.M. Suslov · B. Vlahovic
The mass defect formula reflects the equivalence of mass and energy for bound nuclear systems. We study three-nucleon systems $^{3}$ H and $^{3}$ He, considering the neutron and proton as indistinguishable particles ( $AAA$ model) or taking into account the real masses of neutrons and protons ( $AA B$ model). We have focused on conceptual problems of the $AAA$ model, which is widely used for $3 N$ calculations. In particular, the $AAA$ model is incompatible with the mass defect formula, which naturally corresponds to the $AA B$ model. In addition, the $AAA$ model has a cyclic permutation symmetry, which is breaking in the natural $AA B$ model. The latter problem cannot be eliminated within the perturbative $AAA$ approach, in which the mass difference effect is simulated by correcting the kinetic energy operator. Earlier it was reported that the accuracy of such $AAA$ calculations is 1~keV. An example of the $AA B$ calculation, we numerically estimate the effect of the difference between the neutron and proton masses on the energy calculated without any approximation with the accuracy of 0.1~keV. Another manifestation of the equivalence of mass $m$ and energy $E$ can be expressed by the formula $d E / d m = C o n s t$ . To show this dependence of the three-body energy on the nucleon mass, we performed realistic calculations within the $AAA$ approximation, varying the averaged nucleon mass. The mass-energy compensation effect for the three-body Hamiltonian is shown. According to this, we have determined the effective nucleon mass required to compensate for the perturbative effect of a three-body potential.
Comments:
14 pages, 5 figures
Subjects:
Nuclear Theory (nucl-th)
arXiv:
2112.13827 [pdf]
Phys.Atom.Nucl.(2023)·3 citations

Affiliations

first authorsco-authorsvia INSPIRE