# Nuclear Theory

## New submissions

[ total of 14 entries: 1-14 ]
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### New submissions for Fri, 19 Jan 18

[1]
Title: Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function
Comments: 7 pages, 3 figures and 1 table
Subjects: Nuclear Theory (nucl-th)

Recently a new $\Delta$-method for the calculation of asymptotic normalization coefficients (ANC) from phase-shift data has been formulated, proved and used for bound states. This method differs from the conventional one by fitting only the nuclear part of the effective-range function which includes a partial phase shift. It should be applied to large-charge nuclei when the conventional effective-range expansion or the Pad\'e-approximations using the effective-range function $K_l(k^2)$ fitting do not work. A typical example is the nucleus vertex $\alpha+^{12}$C $\longleftrightarrow ^{16}$O. Here we extend the $\Delta$-method, which totally excludes the effective-range function, to resonance states. In fact, we return to the initial re-normalized scattering amplitude with a denominator which defines the well-known pole condition. Concrete calculations are made for the resonances observed in the $^3$He-$^4$He, $\alpha$-$\alpha$ and $\alpha$-$^{12}$C collisions. The corresponding results are in a good agreement with those for the $S$-matrix pole (SMP) method which uses the differing formalism. The simple formula for narrow resonances given in the literature is used to check the deduced results.

[2]
Title: Influence of the coupling constant of $Δ$ to $δ$ meson on isospin dependent in-medium $\mbox{NN}\to \mbox{N}Δ$ cross section
Subjects: Nuclear Theory (nucl-th)

The isospin dependent in-medium $NN\rightarrow N\Delta$ cross sections in isospin asymmetric nuclear matter are investigated within the framework of the one boson exchange model with the $\delta$ meson taken into account. The influence of the coupling constant of $\Delta$ to $\delta$ meson ($g_{\delta\Delta\Delta}$ or $\kappa=g_{\delta\Delta\Delta}/g_{\delta NN}$) on the in-medium $NN\rightarrow N\Delta$ cross sections is analyzed. Our results show that the strength of the coupling constant $g_{\delta\Delta\Delta}$ largely influences the in-medium cross section and the medium correction factor, R=$\sigma^*_{NN\rightarrow N\Delta}/\sigma^{free}_{NN\rightarrow N\Delta}$, near the threshold energy. In the case of $\kappa$=1, the $\sigma^*_{pp\rightarrow n\Delta^{++}}$ ($\sigma^*_{nn\rightarrow p\Delta^{-}}$) is enhanced (suppressed) relative to its cross section in free space due to the shift of the spectral function of $\Delta$ resonance in medium. For $\kappa$=3, the medium correction has opposite effects, where the $\sigma^*_{pp\rightarrow n\Delta^{++}}$ ($\sigma^*_{nn\rightarrow p\Delta^{-}}$) is suppressed (enhanced) relative to its cross section in free space. It could influence the prediction on the multiplicity of pion and the $\pi^-/\pi^+$ ratio in the transport model simulations, and this uncertainty should be well understood in the transport models simulations before obtaining the accurate conclusion on the symmetry energy at suprasaturation density through the comparison with the pion data.

[3]
Title: Investigation of the 9B nucleus and its cluster-nucleon correlations
Subjects: Nuclear Theory (nucl-th)

In order to study the correlation between clusters and nucleons in light nuclei, we formulate a new superposed THSR wave function which describes both spatial large spreading and cluster-correlated dynamics of valence nucleons. By using the new THSR wave function, the binding energy of 9B is essentially improved comparing with our previous studies. We calculate the excited states of 9B and obtain the energy spectrum of 9B which is consistent with the experimental results, including prediction of the 1/2+ excited state of 9B which is not fixed yet experimentally. We study the proton dynamics in 9B and find that the cluster-proton correlation plays an essential role for the proton dynamics in the ground state of 9B. Further more, we discuss the density distribution of the valence proton with special attention to its tail structure. Finally, the resonance nature of excited states of 9B is illustrated by comparing root-mean-square radii between the ground and excited states.

[4]
Title: On the stability of super-heavy nuclei
Subjects: Nuclear Theory (nucl-th)

The potential-energy surfaces of an extended set of heavy and super-heavy even-even nuclei with $92 \le Z \le 126$ and isospins $40 \le N-Z \le 74$ are evaluated within the recently developed Fourier shape parametrization. Ground-state and decay properties are studied for 324 different even-even isotopes in a four-dimensional deformation space, defined by non-axiality, quadrupole, octupole, and hexadecapole degrees of freedom. Nuclear deformation energies are evaluated in the framework of the macroscopic-microscopic approach, with the Lublin-Strasbourg-Drop model and a Yukawa-folded mean-field potential. The evolution of the ground-state equilibrium shape (and possible isomeric, metastable states) is studied as a function of $Z$ and $N$. Alpha-decay $Q$-values and half-lives, as well as fission-barrier heights, are deduced. In order to understand the transition from asymmetric to symmetric fission along the Fm isotopic chain, the properties of all identified fission paths are investigated. Good agreement is found with experimental data wherever available. New interesting features about the population of different fission modes for nuclei beyond Fm are predicted.

[5]
Title: Constraining Transfer Cross Sections Using Bayes' Theorem
Comments: 17 pages, 12 figures, submitted to PRC
Subjects: Nuclear Theory (nucl-th)

Being able to rigorously quantify the uncertainties in reaction models is crucial to moving this field forward. Even though Bayesian methods are becoming increasingly popular in nuclear theory, they are yet to be implemented and applied in reaction theory problems. The purpose of this work is to investigate, using Bayesian methods, the uncertainties in the optical potentials generated from fits to elastic scattering data and the subsequent uncertainties in the transfer predictions. We also study the differences in two reaction models where the parameters are constrained in a similar manner, as well as the impact of reducing the experimental error bars on the data used to constrain the parameters. We use Bayes' Theorem combined with a Markov Chain Monte Carlo to determine posterior distributions for the parameters of the optical model, constrained by neutron-, proton-, and/or deuteron-target elastic scattering. These potentials are then used to predict transfer cross sections within the adiabatic wave approximation or the distorted-wave Born approximation. We study a number of reactions involving deuteron projectiles with energies in the range of $10-25$ MeV/u on targets with mass $A=48-208$. The case of $^{48}$Ca(d,p)$^{49}$Ca transfer to the ground state is described in detail. A comparative study of the effect of the size of experimental errors is also performed. Five transfer reactions are studied, and their results compiled in order to systematically identify trends. Uncertainties in transfer cross sections can vary significantly (25-100\%) depending on the reaction. While these uncertainties are reduced when smaller experimental error bars are used to constrain the potentials, this reduction is not trivially related to the error reduction. We also find smaller uncertainties when using the adiabatic formulation than when using distorted-wave Born approximation.

[6]
Title: Neutron moderation spectrum considering inelastic scattering
Subjects: Nuclear Theory (nucl-th)

For the first time an analytic expression for inelastic neutron scattering law for isotropic neutron source considering moderating medium temperature as a parameter was obtained in the present paper within gas model. The obtained scattering law is based on solution of kinematic problem of inelastic scattering of a neutron at a nucleus in laboratory coordinate system ($L$-system) in general case. I.e. in case not only a neutron but also a nucleus have arbitrary velocity vector in $L$-system. Analytic expression for neutron flux density and neutron moderation spectrum in reactor fission medium are found for elastic scattering law obtained by the authors before and for new law of inelastic scattering. They consider elastic and inelastic scattering and depend on medium temperature. The obtained expressions for neutron moderation spectra enable reinerpretation of physical nature of processes that determine the shape of neutron spectrum in thermal neutron energy range.

[7]
Title: Nuclear deformation in the configuration-interaction shell model
Comments: 6 pages, 4 figures, Proceedings of the Twelfth International Spring Seminar on Nuclear Physics
Subjects: Nuclear Theory (nucl-th); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Statistical Mechanics (cond-mat.stat-mech)

We review a method that we recently introduced to calculate the finite-temperature distribution of the axial quadrupole operator in the laboratory frame using the auxiliary-field Monte Carlo technique in the framework of the configuration-interaction shell model. We also discuss recent work to determine the probability distribution of the quadrupole shape tensor as a function of intrinsic deformation $\beta,\gamma$ by expanding its logarithm in quadrupole invariants. We demonstrate our method for an isotope chain of samarium nuclei whose ground states describe a crossover from spherical to deformed shapes.

### Cross-lists for Fri, 19 Jan 18

[8]  arXiv:1705.05177 (cross-list from nucl-ex) [pdf, ps, other]
Title: Observation of Narrow $N^+(1685)$ and $N^0(1685)$ Resonances in $γ N \to ηπN$ Reactions
Journal-ref: JETP Letters, 106, 693 (2017)
Subjects: Nuclear Experiment (nucl-ex); High Energy Physics - Experiment (hep-ex); High Energy Physics - Phenomenology (hep-ph); Nuclear Theory (nucl-th)

Observation of a narrow structure at $W\sim 1.68$ GeV in the excitation functions of some photon- and pion-induced reactions may signal a new narrow isospin-1/2 $N(1685)$ resonance. New data on the $\gamma N \to \pi \eta N$ reactions from GRAAL seems to reveal the signals of both $N^+(1685)$ and $N^0(1685)$ resonances.

[9]  arXiv:1801.06067 (cross-list from hep-ph) [pdf, other]
Title: The radiative corrections to double-Dalitz decays revisited
Subjects: High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Experiment (hep-ex); Nuclear Theory (nucl-th)

In this study, we revisit and complete the full next-to-leading order corrections to pseudoscalar double-Dalitz decays within the soft-photon approximation. Comparing to the previous study, we find small differences, which are nevertheless relevant for extracting information about the pseudoscalar transition form factors. Concerning the latter, these processes could offer the opportunity to test them-for the first time-in their double-virtual regime

[10]  arXiv:1801.06163 (cross-list from cond-mat.quant-gas) [pdf, other]
Title: Nature of pairing correlations in the homogeneous Fermi gas at unitarity
Comments: 5 pages, 2 figures, and 3 pages, 5 figures of supplemental material
Subjects: Quantum Gases (cond-mat.quant-gas); Superconductivity (cond-mat.supr-con); High Energy Physics - Lattice (hep-lat); Nuclear Theory (nucl-th)

In the two-component Fermi gas with contact interactions a pseudogap regime, in which pairing correlations are present without superfluidity, can exist at temperatures between the superfluid critical temperature $T_c$ and a temperature $T^* > T_c$. However, the existence of a pseudogap in the unitary limit of infinite scattering length is debated. To help address this issue, we have used finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the spin-balanced homogeneous unitary Fermi gas on a lattice. We present results for the thermal energy, heat capacity, condensate fraction, a model-independent pairing gap, and spin susceptibility, and compare them to experimental data when available. Our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. We find that the energy-staggering pairing gap vanishes above $T_c$ and that $T^*$ at unitarity, as determined from the spin susceptibility, is lower than previously reported in AFMC simulations.

[11]  arXiv:1801.06173 (cross-list from quant-ph) [pdf, ps, other]
Title: On the vacuum-polarization Uehling potential for a Fermi charge distribution
Comments: submitted to European Physical Journal D
Subjects: Quantum Physics (quant-ph); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Nuclear Theory (nucl-th); Atomic Physics (physics.atom-ph)

We present analytical formulas for the vacuum-polarization Uehling potential in the case where the finite size of the nucleus is modeled by a Fermi charge distribution. Using a Sommerfeld-type development, the potential is expressed in terms of multiple derivatives of a particular integral. The latter and its derivatives can be evaluated exactly in terms of Bickley-Naylor functions, which connection to the Uehling potential was already pointed out in the pure Coulomb case, and of usual Bessel functions of the second kind. The cusp and asymptotic expressions for the Uehling potential with a Fermi charge distribution are also provided. Analytical results for the higher-order-contribution K\"all\`en-Sabry potential are given.

### Replacements for Fri, 19 Jan 18

[12]  arXiv:1704.08699 (replaced) [pdf, other]
Title: Fluid Dynamics far from Local Equilibrium
Authors: Paul Romatschke
Comments: 7 pages, 2 figures; v2: minor changes; v3: matches published version
Journal-ref: Phys. Rev. Lett. 120, 012301 (2018)
Subjects: High Energy Physics - Theory (hep-th); Nuclear Theory (nucl-th); Fluid Dynamics (physics.flu-dyn)
[13]  arXiv:1705.06522 (replaced) [pdf, other]
Title: Low energy peripheral scaling in Nucleon-Nucleon Scattering and uncertainty quantification
Comments: 16 pages, 12 figures. Extended discussion with SAID-400 analysis and figures and references added
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
[14]  arXiv:1710.03234 (replaced) [pdf, other]
Title: Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
Authors: Paul Romatschke
Comments: 13 pages, 2 figures; v2: minor changes (typos, etc.); v3: matches published version
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Nuclear Theory (nucl-th)
[ total of 14 entries: 1-14 ]
[ showing up to 2000 entries per page: fewer | more ]

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