Nuclear Theory·nucl-th

Friday·January 19, 2018

11 papers—7 primary·4 cross-listed

01
Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function
B. F. Irgaziev · Yu. V. Orlov
Recently, a new $Δ$ 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 Padé-approximations using the effective-range function $K_{l} (k^{2})$ fitting do not work. A typical example is the nucleus vertex $α +^{12}$ C $⟷^{16}$ O. Here we apply the $Δ$ method, which totally excludes the effective-range function, to isolated resonance states. In fact, we return to the initial renormalized 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, $α$ - $α$ , and $α$ - $^{12}$ C collisions. We use the experimental phase-shift and resonant energy data including their uncertainties and find the ANC variations for the states considered. The corresponding results are in a good agreement with those for the $S$ -matrix pole method which uses the differing formalism. The simple formula for narrow resonances given in the literature is used to check the deduced results. The related ANC function clearly depends on the resonance energy ( $E_{0}$ ) and width ( $Γ$ ), which is used to find the ANC uncertainty ( $Δ$ ANC) through the energy ( $Δ E_{0}$ ) and the width ( $ΔΓ$ ) uncertainties.We also discuss the $Δ$ method differences between bound and resonance states pole conditions.
nucl-thPRC(2018)·9 citations
02
In-medium $\mbox N N \to \mbox N Δ$ cross section and its dependence on effective Lagrange parameters in isospin-asymmetric nuclear matter
Ying Cui🇨🇳 · Yingxun Zhang🇨🇳 · Zhuxia Li🇨🇳
The in-medium $N N \to N Δ$ cross section and its differential cross section in isospin asymmetric nuclear medium are investigated in the framework of the one-boson exchange model by including the isovector mesons, i.e., $δ$ and $ρ$ mesons. Our results show that the in-medium $N N \to N Δ$ cross sections are suppressed with density increasing, and the differential cross sections become isotropic with the density increasing at the beam energy around the $Δ$ threshold energy. The isospin splitting on the medium correction factor, $R = σ_{N N \to N Δ}^{*} / σ_{N N \to N Δ}^{free}$ is observed for different channels of $N N \to N Δ$ , especially around the threshold energy for all the effective Lagrangian parameters. By analyzing the selected effective Lagrangian parameters, our results show that the larger effective mass is, the weaker medium correction $R$ is.
nucl-thCPC(2019)·8 citations
03
Investigation of the 9B nucleus and its cluster-nucleon correlations
Qing Zhao🇨🇳 · Zhongzhou Ren🇨🇳 · Mengjiao Lyu🇨🇳 · Hisashi Horiuchi🇯🇵 · Yasuro Funaki🇯🇵 · Gerd Röpke🇩🇪 · Peter Schuck🇫🇷 · Akihiro Tohsaki🇯🇵 · Chang Xu🇨🇳 · Taiichi Yamada🇯🇵 · Bo Zhou🇯🇵
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.
nucl-thPRC(2018)·21 citations
04
On the stability of super-heavy nuclei
K. Pomorski🇵🇱 · B. Nerlo-Pomorska🇵🇱 · J. Bartel🇫🇷 · C. Schmitt🇫🇷
The potential-energy surfaces of an extended set of heavy and super-heavy even-even nuclei with $92 \leq Z \leq 126$ and isospins $40 \leq N - Z \leq 74$ 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.
nucl-thPRC(2018)·30 citations
05
Constraining Transfer Cross Sections Using Bayes' Theorem
A. E. Lovell · F. M. Nunes
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.
nucl-thPRC(2018)·44 citations
06
Neutron moderation spectrum considering inelastic scattering
V.D. Rusov · V.A. Tarasov · S.A. Chernezhenko · A.A. Kakaev · V.V. Urbanevich · V.M. Vashchenko
For the first time an analytic expression was obtained for the inelastic neutron scattering law with an isotropic neutron source within the gas model, considering moderating medium temperature as a parameter. The inelastic scattering law is obtained, based on the solution of the kinematic problem of neutron inelastic scattering on 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 expressions are found for the neutron flux density and moderation spectrum in reactor fissile medium, both in case of the elastic scattering law, obtained earlier by the authors, and in case of the inelastic scattering law obtained in this paper. Both elastic and inelastic scattering laws are considered to be dependent on the medium temperature. The obtained expressions for neutron moderation spectra enable reinterpretation of physical nature of the processes that determine the shape of neutron spectrum in a wide energy range.
nucl-th0 citations
07
Nuclear deformation in the configuration-interaction shell model
Y. Alhassid · G.F. Bertsch · C.N. Gilbreth · M.T. Mustonen
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 $β, γ$ 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.
nucl-thcond-mat.mes-hallcond-mat.stat-mechJ.Phys.Conf.Ser.(2018)·1 citation

Affiliations

first authorsco-authorsvia INSPIRE

Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function

In-medium \mboxNN→\mboxNΔ cross section and its dependence on effective Lagrange parameters in isospin-asymmetric nuclear matter

Investigation of the 9B nucleus and its cluster-nucleon correlations

On the stability of super-heavy nuclei

Constraining Transfer Cross Sections Using Bayes' Theorem

Neutron moderation spectrum considering inelastic scattering

Nuclear deformation in the configuration-interaction shell model

Affiliations

In-medium $\mbox N N \to \mbox N Δ$ cross section and its dependence on effective Lagrange parameters in isospin-asymmetric nuclear matter