Semimicroscopic Model Research Articles

Subconductance states in a semimicroscopic model for a tetrameric pore.

A physical model for a structured tetrameric pore is studied. The pore is modeled as a device composed of four subunits, each one exhibiting two possible states (open and closed). The pore is located within a membrane that separates two reservoirs with ionic solutions. All variables of the model follow physical dynamical equationsaccounting for the internal structure of the pore, derived from a single energy functional and supplemented with thermal noises. An extensive study of the resulting ionic intensity is performed for different values of the control parameters, mainly membrane potential and reservoir ion concentrations. Two possible physical devices are studied: voltage-gated (including a voltage sensor in each subunit) and non-voltage-gated pores. The ionic flux through the pore exhibits several distinct dynamical configurations, in particular subconductance states, which indicate very different dynamical internal states of the subunits. Such subconductance states become much easier to observe in sensorless pores. These results are compared with available experimental data on tetrameric K channels and analytical predictions.

Semi-microscopic optical-model with channel coupling analysis to describe neutron-nucleus scattering of light and heavy nuclei

Many studies utilizing various potential models have been conducted on the scattering of nucleons from nuclei. In our study, we added channel coupling to a semi-microscopic optical model. With incident energies between 10 and 30 MeV, we sought to compare the predicted reaction observables for the neutron scattering of the following nuclei: 12C, 16O, 54Fe, 58Ni, 120Sn, and 208Pb. We did this twice, once using the density-dependent M3Y-Reid nucleon-nucleon effective bare interaction and once using the density-independent M3Y-Reid effective bare interaction. The remaining terms of the optical potential model take the form of Woods-Saxon and its derivatives, and the real volume term is obtained by folding the NN effective bare potential over the density of the nuclear target using the density-dependent M3Y-Reid NN effective bare interaction and density-independent M3Y-Reid NN effective bare interaction. To investigate how the potential characteristics depend on energy, the ground state is connected to a select few low-lying collective excited states. The density-dependent M3Y-Reid NN effective bare interaction-based semi-microscopic model reproduces the reaction features and forecasts the experimental total cross sections. The parameters of potential depth exhibit a linear energy dependence. We contrast the outcomes of the M3Y-Reid density-dependent model with those attained using the M3Y-Reid nucleon-nucleon effective bare interaction, which is density-independent. The M3Y Reid density-dependent model performs well when the two models are compared.

Quasielastic (p, n) reactions described by a microscopic optical model based on the Gogny force

In this work, we want to study quasielastic (p, n) exchange reactions using a semi-microscopic optical model derived from a previous work, Lopez Moraña and Viñas (2021 J. Phys. G48 035104) based on a nuclear matter approach where the real and imaginary parts are given by the first and second order terms, respectively, of the mass operator obtained by a Brueckner–Hartree–Fock calculation using a G-matrix built up with an effective Gogny interaction. The study of these quasielastic reactions is performed within a Distorted Wave Born Approximation to evaluate the wave functions in the entrance and exit channels, which in turn are used to compute the transition matrix elements. This model, which is free of adjustable parameters, provides a reasonably good agreement with the considered experimental data, namely differential cross sections, analyzing powers and total cross sections, of different reactions spanned along the periodic table at several energies.

Analysis of nucleon-nucleus scattering data using a density-dependent semi-microscopic optical model with channel coupling

Background: The neutron scattering data was previously analyzed using a semi-microscopic optical model with channel coupling to inelastic excited states [Phys. Rev. C 100, 014603 (2019)]. The real part of the potential was constructed by single folding the density-independent M3Y-Paris bare nucleon-nucleon ($NN$) interaction, with zero-range knock-on exchange term, over the density of the target nucleus. The model reproduced the overall features of the inelastic angular distributions and polarization data. The elastic angular distributions were well reproduced.Purpose: In this work we test the effectiveness of the semi-microscopic optical model with channel coupling, but we employ a density-dependent BDM3Y1-Paris bare ($NN$) interaction, with the finite-range form of the knock-on exchange term, in describing the scattering observables, particularly, the inelastic distributions and polarization data.Method: The real volume term of the semi-microscopic model is constructed by single folding the density-dependent BDM3Y1-Paris bare ($NN$) interaction, over the matter distribution of the target nucleus. The ground state is coupled to low-lying inelastic excitation levels. The potential parameters are determined by fitting the elastic, inelastic, and polarization data corresponding to nucleon scattering off a wide range of mass numbers in the range $7\ensuremath{\le}A\ensuremath{\le}208$ for various energies from 10--95 MeV.Results: The density-dependent model resulted in significant improvements in the description of the inelastic angular distributions and analyzing power. In addition, the potential depths showed systematic linear dependence on incident energy, and one set of geometrical parameters is obtained for each nuclear target. We used our best-fit potential parameters to calculate the total cross sections corresponding to nucleon scattering off the considered nuclei. The calculated cross sections are in good agreement with the measured data.Conclusions: In a semi-microscopic optical model, construction of the real volume term by single folding the density-dependent BDM3Y1-Paris bare ($NN$) interaction, with finite form of the knock-on exchange term, results in significant improvements in reproducing the inelastic angular distributions and polarization data as compared to the case of using the density-independent M3Y-Paris bare nucleon-nucleon ($NN$) interaction, with either zero-range or finite-range exchange term.

Application of the cranking method to the semimicroscopic algebraic cluster model and nuclear molecules

A particular quantum phase transition (QPT) is studied at excited energies of light nuclei within the Semimicroscopic Algebraic Cluster Model (SACM), using a combination of catastrophe theory and a direct minimization of the potential. A distinct change from a compact nucleus to a nuclear molecule is described as a second order QPT occurring at a certain value of angular momentum. This finding is in accordance with experimental observations when nuclear molecules appear. The method has implication in the fission of heavy nuclei.

A semi-microscopic approach to transfer reactions

We develop a semi-microscopic model to describe transfer reactions. For the sake of simplicity, we focus on nucleon-transfer reactions, but the theory can be generalized to other transfer processes. The model makes use of overlap integrals computed in the microscopic Resonating Group Method (RGM). This technique is based on an effective nucleon-nucleon interaction and on the cluster approximation. It avoids the choice of a nucleon-core potential for the residual nucleus, and does not require any fit of spectroscopic factors. The model is therefore free of parameter. For the entrance channel, we use the Continuum Discretized Coupled Channel (CDCC) method where the breakup of the projectile is simulated by approximations of the continuum. This technique is well known for elastic scattering and for breakup reactions. It is well adapted to weakly bound nuclei such as the deuteron. The model is applied to the \(^{14}\mathrm{C}(d,p)^{15}C\) and \(^{6}\mathrm{He}(d,n)^{7}Li\) reactions with RGM wave functions of \(^{15}\)C and of \(^7\)Li. The \(^{15}\)C nucleus is described by \(^{14}\mathrm{C}(0^+,2^+)+n\) configurations whereas \(^7\)Li contains the \(\alpha +t\), \(^{6}\mathrm{He}(0^+)+p\) and \(^{6}\mathrm{Li}(1^+,0^+)+n\) configurations. The spectroscopic factors are in fair agreement with the literature. We show that the model provides an excellent description of the transfer cross sections considering that no parameter is adjusted.

Semimicroscopic model of two-proton emission

We propose a semi-microscopic model for the simultaneous emission of two protons. This model has the advantage of avoiding certain technical aspects of a fully microscopic 3-body framework, while also allowing the investigation of the influence of proton pairing on the total lifetime of the decaying nucleus. Thus, we use the standard singlet two-proton wave function on the nuclear surface, provided by the Bardeen-Cooper-Schrieffer (BCS) approach, as a boundary condition for the propagator operator. Our model allows for the estimation of all quantities related to the $2p$ emission process, since it provides the 3-body wave function over most of the domain. We show that reasonable agreement with experimental values can be reached by varying the $pp$ pairing strength outside the nucleus in an interval close to the "bare" singlet value.

Properties of Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei: A semimicroscopic description

The basic version of the semimicroscopic particle-hole dispersive optical model is adopted and implemented to describe main properties of the Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei. Calculation results obtained for $^{48}\mathrm{Ca}, ^{90}\mathrm{Zr}, ^{132}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ are compared with available experimental data.

Symplectic Symmetry and Clustering in Atomic Nuclei

A new symplectic-based shell-model approach to clustering in atomic nuclei is proposed by considering the simple system $^{20}$Ne. Its relation to the collective excitations of this system is mentioned as well. The construction of the Pauli allowed Hilbert space of the cluster states with maximal permutational symmetry is given for the $^{16}$O+$^{4}$He $\rightarrow$ $^{20}$Ne channel in the case of one-component many-particle nuclear system. The equivalence of the obtained cluster model space to that of the semi-microscopic algebraic cluster model is demonstrated.

Cross section measurements of proton capture reactions on Sr isotopes for astrophysics applications

Background: Abundance calculations of a certain class of proton-rich isotopes, known as $p$ nuclei, require knowledge of the cross sections of thousands of nuclear reactions entering a reaction network. As a result, the solution of the latter relies on the predictions of the Hauser-Feshbach (HF) theory and, hence, on the reliability of the models describing the nuclear parameters entering the HF calculations, notably the optical model potential (OMP), the nuclear level density (NLD) and the $\ensuremath{\gamma}$-ray strength function ($\ensuremath{\gamma}\mathrm{SF}$).Purpose: The present work reports on a systematic study of proton capture reactions on Sr isotopes at energies relevant to the $p$ process which is responsible for the production of the $p$ nuclei at explosive stellar sites. The purpose of the work reported here is to perform a validity test of the different OMP, NLD, and $\ensuremath{\gamma}\mathrm{SF}$ models through extensive and detailed comparisons between HF calculations and experimental cross section data. This test is necessary to understand the origin of discrepancies between the $p$-nuclei abundances observed in the solar system and those predicted by the different astrophysical models, known as $p$-process models, aiming at describing the nucleosynthesis of the $p$ isotopes.Method: Cross sections were determined from $\ensuremath{\gamma}$-angular distribution measurements and from angle-integrated $\ensuremath{\gamma}$ spectra taken with the $4\ensuremath{\pi}\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}$-summing technique. Cross-section data and the resulting astrophysical $S$ factors were compared with Hauser-Feshbach calculations obtained with the latest version 1.95 of the nuclear reaction code talys using combinations of global semi-microscopic and phenomenological models of optical potentials (OMPs), nuclear level densities (NLDs), and $\ensuremath{\gamma}$-ray strength functions ($\ensuremath{\gamma}\mathrm{SFs}$).Results: Total cross sections as well as cross sections to the ground and metastable states were determined for the reactions $^{86}\mathrm{Sr}(p,\ensuremath{\gamma})^{87}\mathrm{Y}$, $^{87}\mathrm{Sr}(p,\ensuremath{\gamma})^{88}\mathrm{Y}$, and $^{88}\mathrm{Sr}(p,\ensuremath{\gamma})^{89}\mathrm{Y}$ at incident proton-beam energies from 2.5 to 3.6, 2 to 5, and 1.5 to 5 MeV, respectively.Conclusions: The experimental data reported in the present work are in very good agreement with the talys 1.95 calculations obtained with the default combination of OMP, NLD, and $\ensuremath{\gamma}\mathrm{SF}$ models. This combination is based on purely phenomenological models. A semimicroscopic proton-nucleus optical model potential was optimized at low energies leading to an equally good agreement between experimental data and theoretical calculations based solely on combinations of fully semimicroscopic models of OMP, NLD, and $\ensuremath{\gamma}\mathrm{SF}$. Our results highlight the need for a continued effort on the systematic study of proton-capture reactions to reduce the range of uncertainties arising from global nuclear models for as wide a range of relevant nuclei as possible. In this regard, new ($p,\ensuremath{\gamma}$) data at the lowest possible energies below the opening of the neutron channel are of key importance to improve global proton-nucleus optical model potentials.

A semimicroscopic algebraic cluster model for heavy nuclei

An extension of the Semimicroscopic Algebraic Cluster Model (SACM) is proposed, based on the pseudo-SU(3) model. The Hamiltonian and the spectroscopic factor operator of the model are presented and a procedure of constructing the model space. Because a huge number of SU(3) irreducible representations (irrep) appear, one has to be careful in designing a practical, consistent path to reduce the Hilbert space. The concept of forbiddenness, taking into account excitations of the clusters, is introduced and applied. The applications are to two systems with a low forbiddenness, namely to 236U -> 210Pb + 26Ne and 224Ra -> 210Pb + 14C, and to 236U -> 146Xe + 90Sr, which appears in the fission of 236U, which requires a large forbiddenness. Energies, electromagnetic transitions and spectroscopic factors are calculated.

Detailed analysis for 6Li+40Ca elastic scattering using different potentials

The available experimental differential cross-section data for the 6Li+40C nuclear system in the energy range of 20–240 MeV have been reanalyzed using the framework of the phenomenological optical model (OM), the semi-microscopic cluster folding optical model (CFOM), and the microscopic cluster folding model (CFM) motivated by the well-known cluster structure of 6Li. Reasonable fits to the experimental data have been obtained using OM, CFOM, and CFM over the entire energy range considered in this study. For the real cluster folding potential, the extracted average renormalization factors from CFM and CFOM calculations are 0.46 ± 0.14 and 0.56 ± 0.05, respectively. Due to the well-developed cluster structure of 6Li and the effect of its breakup on other reaction channels, the strength of the real cluster folding potentials was required to be reduced by ∼44%–54% in order to describe the experimental data.

Properties of isoscalar giant multipole resonances in medium-heavy closed-shell nuclei: A semimicroscopic description

The semimicroscopic particle-hole dispersive optical model (PHDOM) is implemented to describe main properties of Isoscalar Giant Multipole Resonances (up to L=3) in medium-heavy closed-shell nuclei. The main properties are characterized by the strength distribution, transition density, partial and total probabilities of direct one-nucleon decay. Calculation results obtained for the 208Pb nucleus are compared with available experimental data.

Phase transition thermal dependence of ferroelectric and dielectric properties in H-bonded $$\hbox {PbHPO}_{4}$$ (LHP) crystal

In this paper, the ferroelectric phase transition and dielectric properties in order-disorder type $$\hbox {PbHPO}_{4}$$ crystal are theoretically investigated. We consider the two sublattice pseudospin lattice coupled mode (PLCM) model Hamiltonian modified by adding third and fourth-order phonon anharmonic interactions, indirect coupling interactions, direct spin–spin coupling interaction, and an applied electric field term within mean-field approximation (MFA). The model is developed as a generalization of the semi-microscopic Mitsui mode model. By using the Green’s function theory, two sublattice PLCM model Hamiltonian and Dyson’s equation, the expressions of soft mode frequency, dielectric constant and loss tangent have been derived for $$\hbox {PbHPO}_{4}$$ crystal. The numerical analysis has been performed by fitting the various model parameters in the obtained expressions and the thermal variations of the soft mode frequency, dielectric constant and loss tangent have been obtained. Our theoretical results are compare good with the experimental data of Negran et al. for lead monohydrogen phosphate (LHP) crystal.

Results on quantum phase transitions within the semimicroscopic algebraic cluster model and extension to deformed clusters

The properties of quantum phase transitions in the semimicroscopic algebraic cluster model are investigated. The order of the quantum phase transition is shown to depend on the path taken in the parameter space and a novel procedure to obtain the Maxwell set separatrix is discussed. The first steps toward a description of systems of deformed cluster and heavy nuclei are presented.

Shell-like quarteting in heavy nuclei: Algebraic approaches based on the pseudo- and proxy-SU(3) schemes

Background: The semimicroscopic algebraic quartet model (SAQM) generates the excitation spectra of shell-like quartets, formed by two protons and two neutrons in a well-defined shell configuration. It is based on the SU(3) symmetry, which is valid only in light nuclei. Algebraic quartet models have been proposed for heavy nuclei, too, but their shell model background is not known.

Alpha-Resonances in Medium and Heavy Nuclei I. Review of Microscopic Models

We review microscopic approaches describing α-like resonances in nuclei with Z ≥ 50. We give a microscopic explanation of α-like rotational bands in the 40Ca+α system in terms of single particle Gamow resonances. On the other hand, we show that for α-decaying nuclei the decay width can be described only in terms of a preformed α-cluster, existing on the nuclear surface in addition to the standard mean field cluster. Thus, we use a semi-microscopic hybrid model combining the mean field formation with a preformed α-cluster in order to explain the order of magnitude of the experimental decay width. Finally, we analyze proton-neutron versus α-like correlations.

Excitation functions of the Zn(p,xn)Ga reactions

The excitation functions for 64,66,67,68,70Zn(p,n)64,66,67,68,70Ga and 64,66,67,68,70Zn(p,2n)63,65,66,67,69Ga have been calculated for incident proton energies from threshold values to 30 MeV using the statistical model code TALYS-1.6. The (p,n) and (p,2n) cross sections have been calculated using both phenomenological Koning and Delaroche (KD) and semimicroscopic Jeukenne-Lejeune-Mahaux-Bruyeres (JLMB) optical model potentials. The phenomenological back-shifted Fermi gas model (BFM) and microscopic Hartree-Fock (HF) approaches for calculation of level densities have been compared in the present work. The pre-equilibrium process has been treated using exciton model. The sensitivity of cross section data to different models of optical model potential and level density have been investigated. It is found that the (p,n) and (p,2n) cross section calculations with semimicroscopic JLMB optical model potential and microscopic HF level density show agreement with the data. The (p,n) and (p,2n) cross section calculations have been compared with corresponding cross sections from nuclear data library, TENDL-2019. The (p,xn) cross sections obtained will be useful in several applications, particularly, for optimization of production routes for Ga isotopes.

Challenging microscopic structure and reaction models for nucleon scattering off nuclei in the A=208 mass region

We present a microscopic description of neutron and proton elastic and inelastic scattering off $^{206,207,208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ together with new medium-energy (7.5--15.5 MeV) neutron elastic and inelastic scattering measurements for various low-energy levels. The Jeukenne, Lejeune, Mahaux (JLM) semimicroscopic folding model provides the relevant optical and transition potentials used to calculate the elastic and inelastic cross sections. Rearrangement corrections that account for proton and neutron density variations during the transition are considered. The nuclear diagonal and transition densities are calculated from a (quasiparticle) random phase approximation [(Q)RPA] structure model implemented with the Gogny D1S interaction. Calculated differential elastic and inelastic cross sections are mostly in very good agreement with available data. Predicted nuclear structure properties as well as scattering calculations and measurements for the yrast quadrupole excitation in $^{206}\mathrm{Pb}$ are carefully discussed. The rearrangement corrections to inelastic scattering form factors are shown to reduce medium energy nucleon inelastic cross section by up to 55%. The magnitude of these corrections changes depending on the probe, incident energy, multipolarity, and nature of the transitions considered. The combined analysis of nuclear structure properties and those for nucleon scattering cross sections measured previously over a range of incident energies provides stringent tests of present microscopic models and helps distinguish those scattering data which most likely call for revision.

Quantum Phase Transitions within the Semimicroscopic Algebraic Cluster Model

Quantum Phase Transition (QPT) properties are investigated within the Semimicroscopic Algebraic Cluster Model (SACM), as an example of a model with involved structure. The catastrophe theory is applied to obtain a physical insight and analytic formulas for the process of QPTs. QPTs are obtained up to the third order. We propose a novel procedure which can be used in several models in various sectors of physics.