Phenomenological Potential Research Articles

Analysis of elastic and inelastic scattering of Ne20 on Ge76 at 306 MeV

Angular distributions of the differential cross section for $^{20}\mathrm{Ne}+^{76}\mathrm{Ge}$ elastic and inelastic scattering at energy 306 MeV are analyzed in the framework of the optical model. The analysis is performed using the coupled-channels mechanism by taking into account the effect of the low-lying states, ${0}^{+}$ and ${2}^{+}$ for the projectile $^{20}\mathrm{Ne}$ $({E}_{\mathrm{ex}.}=1.634 \mathrm{MeV})$, target $^{76}\mathrm{Ge}$ $({E}_{\mathrm{ex}.}=0.563 \mathrm{MeV})$ nuclei, and their mutual excitation $({2}^{+},{2}^{+})$. Results are obtained with the conventional phenomenological Woods-Saxon potential and three different semimicroscopic potentials using the double folding model. Two real cluster potential models are calculated based upon the cluster structure of $^{20}\mathrm{Ne}$ nucleus as 5\ensuremath{\alpha} and $\ensuremath{\alpha}+^{16}\mathrm{O}$. For the sake of comparison, the real of the density-energy-dependent CDM3Y6 potential is considered. The imaginary part for the three real potentials is treated in a standard Woods-Saxon form. The calculations show that the experimental data can be reproduced successfully with a scale factor close to 1. The coupled channels have a weak effect on the elastic scattering with significant differences in calculations of the volume integrals and the total reaction cross sections compared to the available previous study for this reaction. Other future studies are, therefore, required.

IIB String Theory and Sequestered Inflation

AbstractWe develop sequestered inflation models, where inflation occurs along flat directions in supergravity models derived from type IIB string theory. It is compactified on a orientifold with generalized fluxes and O3/O7‐planes. At Step I, we use flux potentials which 1) satisfy tadpole cancellation conditions and 2) have supersymmetric Minkowski vacua with flat direction(s). The 7 moduli are split into heavy and massless Goldstone multiplets. At Step II we add a nilpotent multiplet and uplift the flat direction(s) of the type IIB string theory to phenomenological inflationary plateau potentials: α‐attractors with 7 discrete values . Their cosmological predictions are determined by the hyperbolic geometry inherited from string theory. The masses of the heavy fields and the volume of the extra dimensions change during inflation, but this does not affect the inflationary dynamics.

S-star dynamics through a Yukawa–like gravitational potential

We use S-stars observations to constrain a phenomenological Yukawa-like gravitational potential whose deviations from General Relativity are parametrized by two couplings, the strength of the potential, δ, and its length scale, λ. In order to constrain their value using the data of S-stars orbit, we adopt a fully relativistic approach which consists of solving the geodesic equations instead of just putting the modified gravitational potential in the standard Newton’s law. As a result, we do not detect any significant departure from GR, even using more stars simultaneously.

Scale dependence of the nucleon–nucleon potential

The scale-dependence of the nucleon–nucleon (NN) potential, which in recent years has been extensively analyzed within the context of chiral effective field theory, is, in fact, inherent in any models constrained by a fit to scattering data. A comparison between a purely phenomenological potential and a set of local interactions derived from chiral effective field theory suggests that — owing to the ability to describe NN scattering at higher energies, as well as the deuteron momentum distribution obtained from the [Formula: see text]-scaling analysis of electro-disintegration data — purely phenomenological potentials are best suited to describe nuclear dynamics at the scale relevant to neutron star matter and correlation effects in nuclei. The breakdown of the paradigm based on the description of nuclear systems in terms of point-like protons and neutrons is briefly discussed.

Collective states of even–even nuclei in γ-rigid quadrupole Hamiltonian with minimal length under the sextic potential

In the present paper, we study the collective states of even–even nuclei in γ-rigid mode within the sextic potential and the minimal length (ML) formalism in Bohr–Mottelson model. The eigenvalues problem for the latter is solved by combined means of quasi-exact solvability and a quantum perturbation method. Numerical calculations are performed for 35 nuclei: 98−108Ru, 100−102Mo, 116−130Xe, 180−196Pt, 172Os, 146−150Nd, 132−134Ce, 154Gd, 156Dy and 150−152Sm. Through this study, it appears that our elaborated model leads to an improved agreement of the theoretical results with the corresponding experimental data by reducing the rms with a rate going up to 63% for some nuclei. This comes from the fact that we have combined the sextic potential, which is a very useful phenomenological potential, with the formalism of the ML, which is based on the generalized uncertainty principle and which is in turn a quantum concept widely used in quantum physics. In addition, we investigate the effect of ML on energy ratios, transition rates, moments of inertia and a shape phase transition for the most numerous isotopic chains, namely Ru, Xe, Nd and Pt.

Hallmarks of tunneling dynamics with broken reflective symmetry

We study features of tunneling dynamics in an exactly-solvable model of N=4 supersymmetric quantum mechanics with a multi-well potential and with broken reflective symmetry. Quantum systems with a phenomenological potential of this type demonstrate the phenomenon of partial localization of under-barrier states, possibly resulting in the appearance of the so-called “resonant” tunneling, or the phenomenon of coherent tunneling destruction, referring to the complete localization. Taking the partial localization and the coherent tunneling destruction as basic examples, we indicate main advantages of using isospectral exactly-solvable Hamiltonians in studies quantum mechanical systems with two- and three-well potentials. They, in particular, are: having enough freedom of changing the potential shape in a wide range, that allows one to choose an exactly-solvable model close to characteristics of the phenomenological one; ability of changing the number of local minima and symmetry characteristics of the potential (symmetric or deformed) without changing the main part of the spectrum; engaging a smart basis of states, that dramatically decreases the dimensionality of matrices used in the diagonalization procedure of the corresponding spectral problem.

The neutrino gravitational memory from a core collapse supernova: phenomenology and physics potential

General Relativity predicts that the passage of matter or radiation from an asymmetrically-emitting source should cause a permanent change in the local space-time metric. This phenomenon, called the gravitational memory effect, has never been observed, however supernova neutrinos have long been considered a promising avenue for its detection in the future. With the advent of deci-Hertz gravitational wave interferometers, observing the supernova neutrino memory will be possible, with important implications for multimessenger astronomy and for tests of gravity. In this work, we develop a phenomenological (analytical) toy model for the supernova neutrino memory effect, which is overall consistent with the results of numerical simulations. This description is then generalized to several case studies of interest. We find that, for a galactic supernova, the dimensionless strain, h(t), is of order ∼ 10-22 - 10-21, and develops over a typical time scale that varies between ∼ 0.1 - 10 s, depending on the time-evolution of the anisotropy of the neutrino emission. The characteristic strain, h c(f), has a maximum at a frequency f max ∼ \U0001d4aa(10-1) - \U0001d4aa(1) Hz. The detailed features of the time- and frequency-structure of the memory strain will inform us of the matter dynamics near the collapsed core, and allow to distinguish between different stellar collapse scenarios. Next generation gravitational wave detectors like DECIGO and BBO will be sensitive to the neutrino memory effect for supernovae at typical galactic distances and beyond; with Ultimate DECIGO exceeding a detectability distance of 10 Mpc.

Test of the nonrelativistic $$c\bar{c}$$ potential

We analyze the charmonium states by testing a phenomenological nonrelativistic potential and propose a new set of parameters. This new set of parameters is fixed using only the lowest lying S-wave states of charmonia where the spin-orbit and the tensor interactions will not contribute. After fitting the parameters, we analyze the whole fine structure of charmonium states taking into account the spin-orbit and the tensor interactions. Calculations showed that the nonrelativistic potential model with a phenomenologically defined parameters was indeed a good approximation for describing the charmonium states.

Transport Coefficients of Hyperonic Neutron Star Cores

We consider transport properties of the hypernuclear matter in neutron star cores. In particular, we calculate the thermal conductivity, the shear viscosity, and the momentum transfer rates for npΣ−Λeμ composition of dense matter in β–equilibrium for baryon number densities in the range 0.1–1 fm−3. The calculations are based on baryon interactions treated within the framework of the non-relativistic Brueckner-Hartree-Fock theory. Bare nucleon-nucleon (NN) interactions are described by the Argonne v18 phenomenological potential supplemented with the Urbana IX three-nucleon force. Nucleon-hyperon (NY) and hyperon-hyperon (YY) interactions are based on the NSC97e and NSC97a models of the Nijmegen group. We find that the baryon contribution to transport coefficients is dominated by the neutron one as in the case of neutron star cores containing only nucleons. In particular, we find that neutrons dominate the total thermal conductivity over the whole range of densities explored and that, due to the onset of Σ− which leads to the deleptonization of the neutron star core, they dominate also the shear viscosity in the high density region, in contrast with the pure nucleonic case where the lepton contribution is always the dominant one.

Sub-barrier fusion of 34,36S+204,206,208Pb: Signature of isotopic dependence of repulsive core potential in heavy-ion fusion reactions

The measurements of the excitation function for the heavy-ion fusion-fission cross sections in negative Q-value systems 34S+204,206,208Pb and 36S+204,206,208Pb have been analyzed by coupled-channels (CC) calculations based on the M3Y double-folding (DF) potential that is supplemented with a short-ranged repulsive potential. The standard Aage Winther potential is also employed to explore the occurrence of the unexpected steep fall-off phenomenon of the measured cross sections in fusion between sulfur and lead nuclei. Our analysis based on the deep phenomenological potentials clearly demonstrates that the fusion data are strongly hindered at incident energies well below the Coulomb barrier for the four heavy-ion systems 34S+206Pb, 34S+208Pb, 36S+206Pb and 36S+208Pb. In addition, a first indication of a maximum in the trend of the experimental data of the S-factor representation has been observed for each of the fusions of 34,36S with 206,208Pb targets. It is shown that the M3Y+Repulsion potential accompanied by the CC calculations provides a satisfactory description of the experimental fusion cross sections and S factors in the whole energy range under study for all the six cases of interest. A discussion is also presented concerning the isotopic dependence of the parameters existing in simulation of the repulsive core potential. Our detailed study reveals that the strength of the repulsive interaction and incompressibility of the nuclear matter (NM) increases and decrease linearly with addition of neutrons in the isotopic systems, respectively. Further, we show that the repulsive part of the density distribution becomes more diffuse with increasing neutrons from 34S+204Pb to 36S+208Pb.

Fermi polaron in low-density spin-polarized neutron matter

We study the properties of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons. In particular, we analyze its energy ($E_\downarrow$), effective mass ($m^*_\downarrow$) and quasiparticle residue ($Z_\downarrow$). Results are compared with those of state-of-the-art quantum Monte Carlo calculations of the attractive Fermi polaron realized in ultracold atomic gases experiments, and with those of previous studies of the neutron polaron. Calculations are performed within the Brueckner--Hartree--Fock approach using the chiral two-body nucleon-nucleon interaction of Entem and Machleidt at N$^3$LO with a 500 MeV cut-off and the Argonne V18 phenomenological potential. Only contributions from the $^1S_0$ partial wave, which is the dominant one in the low-density region considered, are included. Contributions from three-nucleon forces are expected to be irrelevant at these densities and, therefore, are neglected in the calculation. Our results show that for Fermi momenta between $\sim 0.25$ and $\sim 0.45$ fm$^{-1}$ the energy, effective mass and quasiparticle residue of the impurity vary only slightly, respectively, in the ranges $-0.604\,E_F < E_\downarrow < -0.635\,E_F $, $1.300\,m < m^*_\downarrow < 1.085\, m$ and $0.741 <Z_\downarrow< 0.836$ in the case of the chiral interaction, and $-0.621\,E_F < E_\downarrow < -0.643\,E_F $, $1.310\,m < m^*_\downarrow < 1.089\, m$ and $0.739 <Z_\downarrow< 0.832$ when using the Argonne V18 potential. These results are compatible with those derived from ultracold atoms and show that a spin-down neutron impurity in a free Fermi gas of spin-up neutrons with a Fermi momentum in the range $0.25\lesssim k_F \lesssim 0.45$ fm$^{-1}$ exhibits properties very similar to those of an attractive Fermi polaron in the unitary limit.

Low-Density Neutron Matter and the Unitary Limit

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

Study of the threshold anomaly effect in the reaction ^{7}Li+^{208}Pb at energies around the Coulomb barrier

The elastic scattering in the reaction ^{7}Li+^{208}Pb was investigated in the bombarding energy range from 25 to 39 MeV. The real and imaginary parts of the optical potential were analyzed by using a phenomenological potential. A dispersion relation analysis is presented in order to investigate the threshold anomaly effect. It is concluded that ^{7}Li has an intermediate behavior between the tightly bound nuclei such as ^{16}O and the loosely bound nuclei such as ^{6}Li where the lack of the threshold anomaly is unambiguously observed. Reaction cross sections are also extracted from the elastic scattering data and its comparison with the ones of other systems has been performed to draw hints on the effect of the breakup channel.

Woods-Saxon type of mean-field potentials with effective mass derived from the D1S Gogny force

Analytic average mean-field potentials of the Fermi-function (Woods-Saxon) type for the whole nuclear chart with space-dependent effective mass are deduced from the D1S Gogny force. Those ready-for-use potentials are advertised as an alternative to other existing phenomenological mean-field potentials.

Electron-exciton interactions in the exciton-polaron problem

Recently, it has been demonstrated that the absorption of moderately doped two-dimensional semiconductors can be described in terms of exciton polarons. In this scenario, attractive and repulsive polaron branches are formed due to interactions between a photoexcited exciton and a Fermi sea of excess charge carriers. These interactions have previously been treated in a phenomenological manner. Here, we present a microscopic derivation of the electron-exciton interactions which utilizes a mixture of variational and perturbative approaches. We find that the interactions feature classical charge-dipole behavior in the long-range limit, and that they are only weakly modified for moderate doping. We apply our theory to the absorption properties and show that the dependence on doping is well captured by a model with a phenomenological contact potential.

Nucleon-nucleus optical potential computed with the Gogny interaction

The ability of the Gogny forces of the D1 family to describe the nucleon-nucleus scattering is studied. To this end, we use an optical model (OM) potential built up using a semi-microscopic nuclear matter (NM) approach. The real and imaginary parts of the OM are provided by the first and second-order terms, respectively, of the Taylor expansion of the mass operator calculated within the Brueckner–Hartree–Fock (BHF) method using the reaction G-matrix built up with the effective Gogny force instead of a microscopic interaction. The optical potential in finite nuclei is obtained through the local density approximation (LDA) using the neutron and proton densities provided by a quasi-local Hartree–Fock (HF) calculation with the same Gogny force for the sake of consistency. A reasonable good agreement is found between the theoretical differential cross-sections and the analyzing powers (AP) of the elastic neutron and proton scattering along the periodic table from Ca to Pb calculated with the Gogny forces and the corresponding values predicted by the global phenomenological potential of Koning and Delaroche. To investigate the limits of the approximations used in this work, comparisons with the results of nucleon-nucleus elastic scattering in 40Ca and 48Ca obtained using the nuclear structure model (NSM) are also performed.

The São Paulo Potential and the 3He Breakup Reaction at 130 MeV on 93Nb and 197Au

Nuclear reactions induced by weakly bound nuclei often result in the emission of light particles as products of the projectile breakup. The incident particle is expected to fragment before reaching the interior of the target nuclei, a characteristic that tends to favor forward angular emission. Although the first models developed for such reactions were proposed many decades ago by Udagawa and Tamura, Ichimura, Austern, Vincent, and Kasano, and Hussein and McVoy, to this date most of the attention has been dedicated to the breakup of the deuteron and other very weakly bound systems, while more strongly bound projectiles have not been fully explored. Here, we describe the production of protons and deuterons from the breakup of 3He. The breakup of 3He on two heavy targets, 93Nb and 197Au, is analyzed in this study. However, the incoming energy involved is much larger than that of the standard phenomenological optical potentials available in the literature for the 3He entrance channel. We have overcome this difficulty by using the São Paulo potential and adjusting the nuclear diffusivity. The deuteron inclusive spectra were calculated at several angles and compared well with the experimental data. Theoretical proton emission predictions are also given for future reference, since no inclusive measurements were performed for the targets under study. One of our goals is to verify the description of deuteron emission from fast projectiles, for which many partial waves contribute to the scattering process.

ПРОБЛЕМА РЕЛИГИОЗНОГО ЯЗЫКА И РЕАЛИСТИЧЕСКАЯ ФЕНОМЕНОЛОГИЯ: НА МАТЕРИАЛЕ ГЕТТИНГЕНСКИХ ЛЕКЦИЙ А. РАЙНАХА

The article aims to discover potential of realistic phenomenology for analysis of prayer as the most significant form of religious language. To that end, the prayer thematization in the framework of religious discourse (as exemplified in works of metropolitan Anthony of Sourozh and R. Schaeffler) is compared to theoretical statements of Reinach’s lecture course “Einleitung in die Philosophie”. The study of texts by metropolitan Anthony and Schaeffler on prayer identifies a basic opposition – between a canonic liturgical text and subjective experience of the one who prays, that opposition manifests itself in reasoning of ordinary discussions on the topic and is overpassed in different ways by the religious thinkers. At another point Reinach’s reflections on some regularities of inner experience, concentrating on the example of artistic forms, offer a new approach to the opposition between formalised ritual and personal experience. While analysing a phenomenon of empathy, Reinach concludes that traditional terms of “the one’s own and the stranger’s” applying to experience must be substituted with an opposition between the immediate and the mediated. From such point of view hymnography is comprehended as a form of symbolic mediation of the ideal contents of religious experience, which allows to speak about the “deprivatization” of religious experience as an original contribution of realistic phenomenology to the philosophy of religion.

Momentum Distributions and Short-Range Correlations in Few-Nucleon Systems Using Realistic Interactions

We present predictions for the single-nucleon and spin-isospin projected two-nucleon momentum distributions in 3H and 3He, obtained using phenomenological potentials, as well as the most recent high-quality chiral nucleon-nucleon potentials, with and without three-nucleon force. Three-nucleon interaction contributions as well as chiral order-by-order convergence are briefly discussed. An outlook for further studies is also presented.

Eikonal method for charge-exchange reactions at intermediate energies

A novel description of charge-exchange reactions at intermediate energies is developed, based on both phenomenological or microscopic eikonal phase-shift functions. The results obtained within this eikonal approach are in good agreement with the distorted-wave Born approximation calculations within the energy region where both approximations should be valid. They also compare well with the experimental data, even at relatively low energy domain. At higher energies, relativistic kinematics have also been added and shown to be relevant. Owing to the microscopic feature of the formulation, our theory also has the advantage that it can be applied to high energies where the phenomenological optical potentials are rarely available.