Semimicroscopic Model Research Articles

Nuclear parton distributions and the Drell-Yan process

We study the nuclear parton distribution functions on the basis of our recently developed semi-microscopic model, which takes into account a number of nuclear effects including nuclear shadowing, Fermi motion and nuclear binding, nuclear meson-exchange currents, and off-shell corrections to bound nucleon distributions. We discuss in detail the dependencies of nuclear effects on the type of parton distribution (nuclear sea vs valence), as well as on the parton flavor (isospin). We apply the resulting nuclear parton distributions to calculate ratios of cross sections for proton-induced Drell-Yan production off different nuclear targets. We obtain a good agreement on the magnitude, target and projectile $x$, and the dimuon mass dependence of proton-nucleus Drell-Yan process data from the E772 and E866 experiments at Fermilab. We also provide nuclear corrections for the Drell-Yan data from the E605 experiment.

Ab initio calculation of double mass differences for near-magic nuclei

Double mass differences between nuclei with a magic number of protons (neutrons) and their neighbors differing from them by one or two protons (neutrons) are calculated within the semimicroscopic model proposed recently for the nuclear pairing problem. The main term in the effective nucleon interaction is calculated on the basis of the realistic Argonne nucleon-nucleon potential v18. This term is supplemented with a small phenomenological term involving one universal parameter common to protons and neutrons. The double mass differences are calculated for the proton neighbors of the Z = 82, 50, 28, and 20 lead, tin, nickel, and calcium isotopic chains and for the neutron neighbors of the N = 126, 82, 50, and 20 isotonic chains. The corrections to the model that are induced by the contribution of low-lying surface vibrations (phonons) are discussed.

Semi-microscopic folding model for the description of two-body halo nuclei

One-neutron halo nuclei, composed by a weakly-bound particle coupled to a core nucleus, are studied within a particle-plus-core model. A semi-microscopic method to generate the two-body Hamiltonian of such a system, including core excitation, is proposed. The method consists in generating the spin-independent part of the valence-core interaction using a single-folding procedure, convoluting a realistic nucleon-nucleon (NN) interaction with the core transition densities. The latter are calculated with the Antisymetrized Molecular Dynamics (AMD) method. The prescription is applied to the well known halo nucleus, $^{11}$Be, as a test case. The results show an important predictive power that opens a door to the understanding of other lesser known halo nuclei. In order to show the potential usefulness of the method, it is applied to analyze the structure of $^{19}$C.

Semi-microscopic description of the proton-and neutron-induced backbending phenomena in some deformed even-even rare earth nuclei

A semi-microscopic model to study the double backbending phenomenon in some deformed even-even nuclei from the rare earth region is proposed. The backbending phenomena are described by mixing four rotational bands, defined by a set of angular momentum projected states with a specific single-particle factor, and a model Hamiltonian describing a set of paired particles moving in a deformed mean field and interacting with a phenomenological deformed core. Due to the specific construction, the wave function acquires a complex structure which allows a quantitative description of the yrast states in the region of the two backbendings.

Semimicroscopic algebraic description ofαclustering in22Ne

The alpha-cluster states of $^{22}$Ne are studied within the framework of the semimicroscopic algebraic cluster model (SACM). The band structure, energy spectrum as well as E2 and E1 transitions are calculated and are compared with the experimental data. The results are also compared with those obtained from two microscopic models: the deformed-basis antisymmetrized molecular dynamics (DAMD) approach and the generator-coordinate method (GCM). It is found that the prominent bands obtained in the latter frameworks all have equivalents in the SACM and the agreement between the calculated spectroscopic properties is rather good, especially for positive-parity states.

Damping of high-energy particle-hole-type nuclear excitations: A semimicroscopic model

A semimicroscopic model (particle-hole dispersive optical model) is formulated to describe the main relaxation modes of high-energy particle-hole-type excitations in medium-heavy mass nuclei. Within this model, Landau damping and the single-particle continuum are considered microscopically, while the spreading effect is treated phenomenologically, employing a statistical assumption. Description of direct nucleon decay of the above-mentioned excitations (including giant resonances) is a unique feature of the proposed model, which in applying to closed-shell nuclei is arranged for practical implementations. The methodical similarity of formulations of the single-quasiparticle and particle-hole optical models is emphasized.

The geometric interpretation of the semimicroscopic algebraic cluster model and the role of the Pauli principle

We study the properties of the Semimicroscopic Algebraic Cluster Model (SACM) under phase transitions. We show that the SACM can undergo first and second order phase transitions and a critical line appears. When the Pauli principle is not observed, the critical line appears, but other non-physical properties arise. At the end the meaning of the SO(4) dynamical limit is discussed.

Comparing the group theoretical approaches to the description of dipole and quadrupole collectivity in nuclei

The comparison of the two types of collectivity in nuclear dynamics is based on the equal realizations of their basic symmetries, represented by the algebra-chain u(3) ⊃ su(3) ⊃ so(3). We illustrate this on the example of two phenomenological algebraic models: the semimicroscopic algebraic cluster model (SACM) with one of the clusters considered as a scalar and the interacting two vector boson model (IVBM). In both of them the root group structure that leads to the above chain is based on the coupling of two different U(3) representations, with different physical interpretations. These similarities allow for the use of the same mathematical tools in building the theory, but there are important differences that come from the different higher symmetries in which this equal substructures are embedded.

Semi-microscopic description of the double backbending in some deformed even–even rare earth nuclei

A semi-microscopic model to study the neutron- and proton-induced backbending phenomena in some deformed even–even nuclei from the rare earth region is proposed. The space of particle–core states is defined by the angular momentum projection of a quadrupole deformed product state. The backbending phenomena are described by mixing four rotational bands, defined by a set of angular momentum projected states, and a model Hamiltonian describing a set of paired particles moving in a deformed mean field and interacting with a phenomenological deformed core. The ground band corresponds to the configuration where all particles are paired, while the other rotational bands are built on one neutron or/and one proton broken pair. Four rare earth even–even nuclei which present the second anomaly in the observed moments of inertia are successfully treated within the proposed model.

Phase transitions for excited states in 16O+α → 20Ne within the SACM

We present the cranking of the Semimicroscopic Algebraic Cluster Model (SACM) for two spherical clusters. A geometrical mapping is applied and a discussion on phase transition as a function of the cranking parameter is given. This parameter can be related to the average angular momentum of the nucleus. The particular cluster system considered is 16O+α → 20Ne. We also investigate the phase transition property when the Pauli exclusion principle is not observed. We show that phase transitions may occur within the same dynamical symmetry limit.

Calculation of double mass differences for near-magic nuclei on the basis of a semimicroscopic model

Double mass differences between nuclei having a magic number of protons (neutrons) and their neighbors differing by one or two protons (neutrons) have been calculated on the basis of a semimicroscopic model that has been proposed recently for the problem of nuclear pairing. A dominant term of the effective nucleonnucleon interaction has been calculated on the basis of the realistic Argonne nucleon-nucleon potential v18. It has been supplemented with a moderately small phenomenological term that contains one universal parameter common to protons and neutrons. Double mass differences have been calculated for proton neighbors of the lead-isotope chain (Z = 82) and for neutron neighbors of N = 82 isotones. Corrections to the model that are caused by the contribution of low-lying surface vibrations (phonons) have been estimated.

Phenomenological and microscopic cluster models. I. The geometric mapping

The geometrical mapping of algebraic nuclear cluster models is investigated within the coherent state formalism. Two models are considered: the Semimicroscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model (PACM), which is a special limit of the SACM. The SACM strictly observes the Pauli exclusion principle while the PACM does not. The discussion of the SACM is adapted to the coherent state formalism by introducing the new SO(3) dynamical symmetry limit and third-order interaction terms in the Hamiltonian. The potential energy surface is constructed in both models and it is found that the effects of the Pauli principle can be simulated by higher-order interaction terms in the PACM. The present study is also meant to serve as a starting point for investigating phase transitions in the two algebraic cluster models.

Phenomenological and microscopic cluster models. II. Phase transitions

Based on the results of a previous paper (Paper I), by performing the geometrical mapping via coherent states, phase transitions are investigated and compared within two algebraic cluster models. The difference between the semimicroscopic algebraic cluster model (SACM) and the phenomenological algebraic cluster model (PACM) is that the former strictly observes the Pauli exclusion principle between the nucleons of the individual clusters, while the latter ignores it. From the technical point of view the SACM is more involved mathematically, while the formalism of the PACM is closer to that of other algebraic models with different physical content. First- and second-order phase transitions are identified in both models, while in the SACM a critical line also appears. Analytical results are complemented with numerical studies on $\ensuremath{\alpha}$-cluster states of the ${}^{20}$Ne and ${}^{24}$Mg nuclei.

Damping of high-energy particle-hole-type nuclear excitations: a semi-microscopic model

A semi-microscopic model (particle-hole dispersive optical model) is formulated to describe the main relaxation modes of high-energy particle-hole-type excitations in medium-heavy mass nuclei. Within this model Landau damping and the single-particle continuum are considered microscopically, while the spreading effect is treated phenomenologically with taking a statistical assumption into account. Description of direct-nucleon-decay properties of the above-mentioned excitations (including giant resonances) is a unique feature of the proposed model, which in applying to closed-shell nuclei is arranged for practical implementations.

On the direct and semidirect neutron radiative capture by medium-heavy mass nuclei

The new semimicroscopic model (particle-hole dispersive optical model) recently developed for de- scribing high-energy particle-hole-type excitations in medium-heavy mass nuclei is applied for the description of the simplest photonuclear reactions accompanied by excitation of the isovector giant dipole and quadrupole resonances. The calculated reaction cross sections and their derivatives are compared with corresponding experi- mental data and also with the similar results obtained within the previously developed semimicroscopic approach to the description of the giant resonances.

Anab initiotheory of double odd-even mass differences in nuclei

Two aspects of the problem of evaluating double odd-even mass differences D2 in semi-magic nuclei are studied related to existence of two components with different properties, a superfluid nuclear subsystem and a non-superfluid one. For the superfluid subsystem, the difference D2 is approximately equal to 2Δ, the gap Δ being the solution of the gap equation. For the non-superfluid subsystem, D2 is found by solving the equation for two-particle Green function for normal systems. Both equations under consideration contain the same effective pairing interaction. For the latter, the semi-microscopic model is used in which the main term calculated from the first principles is supplemented with a small phenomenological addendum containing one phenomenological parameter supposed to be universal for all medium and heavy atomic nuclei.

On limits of ab initio calculations of pairing gap in nuclei

A brief review of recent microscopic calculations of nuclear pairing gap is given. A semi-microscopic model is suggested in which the ab initio effective pairing interaction is supplemented with a small phenomenological addendum. It involves a parameter which is universal for all medium and heavy nuclei. Calculations for several isotopic and isotonic chains of semi-magic nuclei confirm the relevance of the model.

Phenomenological and semimicroscopic cluster models and their phase transitions

Two algebraic cluster models of nuclear structure which use the same Hamiltonian are explored: a Phenomenological Algebraic Cluster Model (PACM), and a Semi-microscopic Algebraic Cluster Model (SACM). The PACM does not incorporate the Pauli exclusion principle, while the SACM does. The Hamiltonian considered is an admixture of three dynamical symmetries; the SU(3), SO(4), and SO(3), with weighting of each determined by parameters. The classical potential is constructed using coherent states, and the model Hilbert space of the SACM is constructed in such a way as to include all shell model states which correspond to the cluster structure of interest. Phase transitions and their orders are investigated for each model, and parameter phase diagrams are presented, wherein it is found that consideration of the Pauli principle has significant consequences. Also shown are fits of Hamiltonian parameters for a nucleus of 2 spherical clusters, when moving between the symmetry limits.

Invariant Mass Spectroscopy for the Neutron Rich Nuclei

The neutron-rich carbon isotopes (19,17)C and a boron isotope (14)B are investigated respectively via proton inelastic and charge-exchange reactions on a liquid hydrogen target at around 70 MeV/nucleon at RIKEN. The invariant mass method in inverse kinematics involving coincidence detection of a charged fragment and a neutron both emitted at forward angles is employed to map the energy spectrum above the neutron decay threshold. Several resonance structures are revealed in the invariant mass spectra, and the nature for some of them is discussed from comparisons of differential cross section data with predictions of microscopic DWBA calculations based on spsdp f shell model wave functions and a recent parametrization of semi-microscopic nucleon-nucleus optical model potential (JLMB). By extrapolating the (p, n) cross sections leading to the 1(+) state at 1.27 MeV in (14)B to zero momentum transfer the Gamow-Teller transition strength is deduced. The value is found to compare well with that reported in a beta-delayed neutron emission study.

Semi-microscopic model of pairing in nuclei

A semi-microscopic model for nucleon pairing in nuclei is presented starting from the ab intio BCS gap equation with Argonne v18 force and the self-consistent Energy Density Functional Method basis characterized with the bare nucleon mass. The BCS theory is formulated in terms of the model space S0 with the effective pairing interaction calculated from the first principles in the subsidiary space S0. This effective interaction is supplemented with a small phenomenological addendum containing one phenomenological parameter universal for all medium and heavy atomic nuclei. We consider the latter as a phenomenological way to take into account both the many-body corrections to the BCS theory and the effective mass effects. For protons, the Coulomb interaction is introduced directly. Calculations made for several isotopic and isotonic chains of semi-magic nuclei confirm the validity of the model. The role of the self-consistent basis is stressed.