Basis Of Shell Model Research Articles

Size dependence of the magnetic properties of antiferromagneticCr2O3nanoparticles

Magnetic properties of antiferromagnetic (AFM) ${\text{Cr}}_{2}{\text{O}}_{3}$ nanoparticles have been studied as a function of the nanoparticle size. The synthesized nanoparticles present an ellipsoidal shape with the major axis of approximately 170 nm and the minor axis that increases with the synthesis temperature from 30 to 70 nm. By magnetization and electron paramagnetic resonance experiments, we have obtained the parameters that characterize the AFM nanoparticles system. We have found that the N\'eel temperature, ${T}_{N}$, and the spin-flop field, ${H}_{\text{SF}}$, increase with the particle size from ${T}_{N}=288\text{ }\text{K}$ and ${H}_{\text{SF}}(5\text{ }\text{K})=10\text{ }\text{kOe}$ for the smaller nanoparticles and approach the bulk values [${T}_{N}=308\text{ }\text{K}$ and ${H}_{\text{SF}}(5\text{ }\text{K})=60\text{ }\text{kOe}$] for the larger particles. From the experimental results and the molecular-field theory applied to AFM coupled sublattices, we estimated the magnetic anisotropy, $K$, and the molecular-field constant, $\ensuremath{\lambda}$, as a function of the ${\text{Cr}}_{2}{\text{O}}_{3}$ nanoparticle size. When the size is reduced, $\ensuremath{\lambda}$ only diminishes $\ensuremath{\sim}8%$ with respect to its bulk value $(4.9\ifmmode\times\else\texttimes\fi{}{10}^{4}\text{ }{\text{Oe}}^{2}\text{ }\text{g}/\text{erg})$; instead, $K$ decreases more than an order of magnitude from $K=3.8\ifmmode\times\else\texttimes\fi{}{10}^{4}$ to $8.7\ifmmode\times\else\texttimes\fi{}{10}^{2}\text{ }\text{erg}/\text{g}$. We analyzed the results on the basis of a core shell model where the nanoparticle internal order consists of an antiferromagnetically ordered core and a disordered surface shell, which presents a frustrated magnetic state.

Triaxial projected shell model study of γ-vibrational bands in even-even Er isotopes

We expand the triaxial projected shell model basis to include triaxially deformed multi-quasiparticle states. This allows us to study the yrast and \ensuremath{\gamma}-vibrational bands up to high spins for both \ensuremath{\gamma}-soft and well-deformed nuclei. As a first application, a systematic study of the high-spin states in Er isotopes is performed. The calculated yrast and \ensuremath{\gamma} bands are compared with the known experimental data, and it is shown that the agreement between theory and experiment is quite satisfactory. The calculation leads to predictions for bands based on one- and two-\ensuremath{\gamma} phonons where current data are still sparse. It is observed that \ensuremath{\gamma} bands for neutron-deficient isotopes of $^{156}\mathrm{Er}$ and $^{158}\mathrm{Er}$ are close to the yrast band, and further these bands are predicted to be nearly degenerate for high-spin states.

Roles of tensor and pairing correlations on halo formation inLi11

We studied the roles of the tensor and pairing correlations on the halo formation in $^{11}\mathrm{Li}$ with an extended $^{9}\mathrm{Li}+n+n$ model. We first solved the ground state of $^{9}\mathrm{Li}$ in the shell-model basis by taking 2p-2h states using the Gaussian functions with variational size parameters to take into account the tensor correlation fully. In $^{11}\mathrm{Li}$, the tensor and pairing correlations in $^{9}\mathrm{Li}$ are Pauli blocked by additional two neutrons, which work coherently to make the configurations containing the $0{p}_{1/2}$-state pushed up and close to those containing the $1{s}_{1/2}$-state. Hence, the pairing interaction works efficiently to mix the two configurations by equal amount and develop the halo structure in $^{11}\mathrm{Li}$. For $^{10}\mathrm{Li}$, the inversion phenomenon of $s$- and $p$-states is reproduced in the same framework. Our model furthermore explains the recently observed Coulomb breakup strength and charge radius for $^{11}\mathrm{Li}$.

Shell model method for Gamow-Teller transitions in heavy, deformed nuclei

A method for calculation of Gamow-Teller transition rates is developed by using the concept of the Projected Shell Model (PSM). The shell model basis is constructed by superimposing angular-momentum-projected multiquasiparticle configurations, and nuclear wave functions are obtained by diagonalizing the two-body interactions in these projected states. Calculation of transition matrix elements in the PSM framework is discussed in detail, and the effects caused by the Gamow-Teller residual forces and by configuration-mixing are studied. With this method, it may become possible to perform a state-by-state calculation for beta-decay and electron-capture rates in heavy, deformed nuclei at finite temperatures. Our first example indicates that, while experimentally known Gamow-Teller transition rates from the ground state of the parent nucleus are reproduced, stronger transitions from some low-lying excited states are predicted to occur, which may considerably enhance the total decay rates once these nuclei are exposed to hot stellar environments.

Covariant response theory beyond RPA and its application

The covariant particle-vibration coupling model within the time-blocking approximation is employed to supplement the relativistic random phase approximation (RRPA) with coupling to collective vibrations. The Bethe—Salpeter equation in the particle—hole channel with an energy-dependent residual particle—hole (ph) interaction is formulated and solved in the shell-model Dirac basis as well as in the momentum space. The same set of coupling constants generates the Dirac—Hartree single-particle spectrum, the static part of the residual ph interaction, and the particle-phonon coupling amplitudes. This approach is applied to a quantitative description of damping phenomenon in even—even spherical nuclei with closed shells 208Pb and 132Sn. Since phonon coupling enriches the RRPA spectrum with a multitude of ph ⊗ phonon states, a noticeable fragmentation of giant monopole and dipole resonances is obtained in the examined nuclei. The results are compared with experimental data and results of the nonrelativistic approach.

Gamow shell model and realistic nucleon-nucleon interactions

We present a new and efficient method to obtain a Gamow shell-model basis and matrix elements generated by realistic nucleon-nucleon interactions. We derive a self-consistent Hartree-Fock potential from the renormalized N3LO interaction model. The corresponding Gamow one-body eigenstates are generated in a plane wave basis in order to build a Gamow shell-model set of basis states for the closed shell nuclei 4He and 16O. We address also the problem of representing a realistic nucleon-nucleon interaction in a two-particle Berggren basis in the laboratory frame. To achieve this, an expansion of matrix elements of the residual nucleon-nucleon interaction in a finite set of harmonic oscillator wave functions is used. We show that all loosely bound and narrow resonant states converge surprisingly fast. Even broad resonances in these two-particle valence systems converge within a reasonable number of harmonic oscillator functions. Examples of 6He and 18O Gamow shell-model calculations using 4He and 16}O as closed shell cores are presented. This procedure allows Gamow shell-model calculations to be performed with all realistic nucleon-nucleon interactions and with either momentum or position space representations for the Gamow basis. The possibility to remove the center of mass spuriosity of Gamow shell-model nuclear states with this method is also discussed. Perspectives for nuclear structure calculations of dripline nuclei are outlined.

Chemical ordering and fragility minimum in Cu–As–Se glasses

Modulated Differential Scanning Calorimetric (MDSC) studies have been performed on CuxAs40Se60−x glasses with x ranging between 0 and 30 at.%. The thermal parameters, namely the glass transition temperature (Tg), the heat capacity (Cp) and the jump in heat capacity at the glass transition (ΔCp) are measured. The composition dependence of these thermal parameters has been found to exhibit interesting variations particularly at x=20. Thermal crystallization studies show that the structural network is mainly characterized by the ternary Cu3AsSe4 units with As2Se3 and Cu2As3 units depending on the concentration of Cu. These structural differences arising as a function of composition are reflected in the Tg, Cp and ΔCp. The observed transitions are also understood on the basis of Formal Valence Shell (FVS) model and the classification of strong and fragile liquids.

Numerical aspects of the Gamow shell model

Recently, the shell model in the complex k-plane (the so-called Gamow shell model) has been formulated using a complex Berggren ensemble representing bound single-particle states, single-particle resonances and non-resonant continuum states. The single-particle basis used is that of the Hartree–Fock potential generated self-consistently by a finite-range residual interaction. In this framework, we shall discuss the numerical aspects of the Gamow shell model related to the optimization of the shell-model basis.

Ab initioabsorption spectra ofAln (n=2–13)clusters

We investigate the optical absorption spectra of ${\mathrm{Al}}_{n}$ $(n=2--13)$ clusters using the time-dependent spin-polarized local-density approximation. The overall shapes of the calculated spectra strongly depend on cluster geometries. It is observed that a simple jellium model is not valid for these clusters. In the size range of $nl~5,$ the spectra show discrete, atomiclike transitions. For $n=6--12,$ the shape of the absorption spectra can be explained on the basis of an ellipsoidal shell model. A strong collective excitation peak is observed for ${\mathrm{Al}}_{13}$ cluster, which is due to its spherical symmetry.

A comparison between the Monte Carlo shell model method and the Monte Carlo spectroscopic method

A comparison is made between a variant of the Monte Carlo shell model method and the recently introduced Monte Carlo spectroscopic method. While the first method optimally determines a many-body shell model basis in which the Hamiltonian is diagonalized, and therefore relies on the determination of the most relevant part of the nuclear wavefunction, the second method stochastically samples observables including the full Hilbert space. Agreement is found between the two methods.

Localization in 2p1f nuclear shell-model wavefunctions

For the study of complexity and chaos in many-particle nuclear wavefunctions in large shell-model basis spaces, the localization length related to the number of principal components is calculated for several Ca, Sc and Ti isotopes, and compared to the predictions of the embedded Gaussian orthogonal ensemble. The large dimensionalities involved, up to many thousands, ensure good statistics, and the agreement is very good in the chaotic region of the spectra. The localization length of shell-model wavefunctions in Ca isotopes is much smaller than in Sc, showing a strong isospin dependence of nuclear chaos, in good agreement with previous results based on energy level fluctuation properties.

Effects of resonant single-particle states on pairing correlations

Effects of resonant single-particle (s.p.) states on the pairing correlations are investigated by an exact treatment of the pairing Hamiltonian on the Gamow shell model basis. We introduce the s.p. states with complex energies into the Richardson equations. The solution shows the property that the resonant s.p. states with large widths are less occupied. The importance of many-body correlations between bound and resonant particle pairs is shown.

Quadrupole and octupole softness in theN=Znucleus64Ge

Quadrupole and octupole softness in the even-even N=Z nucleus 64Ge is studied on the spherical shell model basis. We carry out the shell model calculation using the pairing plus quadrupole (QQ) plus octupole (OO) interaction with monopole corrections. It is shown that 64Ge is an unstable nucleus with respect to both the quadrupole and octupole deformations, which is consistent with the previous discussions predicting the gamma softness and octupole instability. It is demonstrated that proton-neutron part QpQn of the QQ interaction is important for the gamma softness or triaxiality.

24.5 A MeV 6He+ p elastic and inelastic scattering

The structure of 6He is explored with proton elastic and inelastic scattering to the first 2 + excited state ( Q=−1.8 MeV) of 6He in the inverse kinematics using a 24.5 A MeV 6He beam. The distorted wave approximation (DWA) with an optical potential obtained by folding an effective nucleon–nucleon (NN) g-matrix with the 6He density matrix elements as given by a large basis shell model is used to analyse the data. The comparison of predictions with the data confirms the view that 6He has an extended (halo) neutron matter distribution.

Weak interaction rates involving12C,14N,and16O

Muon capture and neutrino scattering cross sections in ${}^{12}\mathrm{C},$ ${}^{14}\mathrm{N},$ and ${}^{16}\mathrm{O}$ are calculated within a large shell-model basis. The effects of quenching of the isovector strength on these quantities are studied.

The canonical nuclear many-body problem as an effective theory

Recently it was argued that it might be possible treat the conventional nuclear structure problem -- nonrelativistic point nucleons interacting through a static and rather singular potential -- as an effective theory in a shell-model basis. In the first half of this talk we describe how such a program can be carried out for the simplest nuclei, the deuteron and 3He, exploiting a new numerical technique for solving the self-consistent Bloch-Horowitz equation. Some of the properties of proper effective theories are thus illustrated and contrasted with the shell model. In the second half of the talk we use these examples to return to a problem that frustrated the field three decades ago, the possibility of reducing the effective interactions problem to perturbation theory. We show, by exploiting the Talmi integral expansion, that hard-core potentials can be systematically softened by the introduction of a series of contact operators familiar from effective field theory. The coefficients of these operators can be run analytically by a renormalization group method in a scheme-independent way, with the introduction of suitable counterterms. Once these coefficients are run to the shell model scale, we show that the renormalized coefficients contain all of the information needed to evaluate perturbative insertions of the remaining soft potential. The resulting perturbative expansion is shown to converge in lowest order for the simplest nucleus, the deuteron.

Neutrino-12C reactions and the LSND and KARMEN experiments on neutrino oscillations

We present new theoretical results of the flux-averaged 12C(ν e , e−)12N and 12C(ν μ , μ−)12N cross sections with ν μ (ν e ) coming from the decay-in-flight (decay-at-rest) of π+(μ+). These cross sections are relevant for the interpretation of the recent experiments on neutrino oscillation performed by the LSND and KARMEN collaborations. The microscopic approaches used are charge-exchange random phase approximation (RPA), charge-exchange RPA among quasiparticles (QRPA), and the Shell Model. We show that the exclusive cross sections are in nice agreement with the experimental values for both reactions when a large-scale shell-model calculation is performed. Concerning the inclusive cross section for ν μ coming from the decay-in-flight of π+, the calculated value keeps overestimating the experimental one by 20–30%, while the inclusive cross section due to ν e coming from the decay-at-rest of μ+ is in agreement within experimental error bars with the measured values. The shell-model prediction for the decay-in-flight neutrino cross section is reduced compared to the RPA one because of the different kind of correlations in the calculation of the spin modes (in particular, the quenching of the 1+) and partially due to the shell-model configuration basis, which is not large enough, as we show using arguments based on sum rules.

Transition quadrupole moments in γ-soft nuclei and the triaxial projected shell model

Transition probabilities of the ground-state bands in γ-soft nuclei are studied for the first time using the triaxial projected shell model approach. It is observed that the angular-momentum dependence of the transition quadrupole moment Q t is related to the triaxial deformation of the nuclear mean-field potential. The introduction of the γ-degree of freedom in the shell model basis is shown to have a little influence on the constant behavior of the low-spin Q t in a well-deformed nucleus. However, the increasing collectivity with spin for the low-spin states in a γ-soft nucleus can only be explained by considering the triaxial mean-field deformation.

Properties of isovector 1+ states in A=28 nuclei and nuclear muon capture

A method is proposed for taking into account, in a calculation of partial rates of muon capture by nuclei, experimental information about strength functions for Gamow-Teller and isovector M1 transitions. The method, which amounts to choosing an orthogonal transformation that acts in the subspace of wave functions for excited states, requires neither modifying transition operators nor introducing effective charges. The matrix of the above transformation is constructed as a product of the matrices of reflection in a plane. All calculations are performed on the basis of the multiparticle shell model. Numerical results are obtained for isovector states in A=28 nuclei. Strength functions for Gamow-Teller and isovector M1 transitions in 28Si are considered, and the lifetimes of 1+ states in 28Al and the branching fractions for gamma decays of this state are calculated. Owing to taking into account experimental information about the properties of isovector states, the branching fractions for the γ decays of the 1+ state at 2.201 MeV in 28Al are successfully described for the first time. The above transformation of the wave functions changes substantially the distribution of partial rates of allowed muon capture by a 28Si nucleus among the 1+ states of the final nucleus 28Al in relation to the results of the calculations with the eigenfunctions of the Hamiltonian of the multiparticle shell model. The muon-capture rates calculated with the transformed functions agree well with experimental data.

Microscopic calculation of double-dipole excitations

In the last decade experimental and theoretical research has led to the discovery of double giant resonances—a giant resonance built on top of another giant resonance. The double-dipole resonance was first identified in a pion charge exchange reaction @1# and was predicted earlier @2#. Later the double dipole was detected in Coulomb excitation in heavyion reactions @3–5#. Properties of double dipole modes and other types of double resonances were studied and are reviewed in several review articles @2–4,6#. Theoretical studies have been mostly of the ‘‘macroscopic’’ type, introducing collective coordinates in the description of double giant resonances @2–4,6#. Some papers used semimicroscopic models in which the random phase approximation ~RPA! was employed to define the collective phonon states. Some extensions of the RPA have also been suggested @7,8#. Truly microscopic calculations are very difficult. A shell-model calculation requires very large spaces involving configurations made up of particles excited to several major shells. One must therefore truncate the space and limit the calculation to one-particle–one-hole (1p-1h) and two-particle– two-hole (2p-2h) configurations involving particles and holes in several major shells. Studies of this type were performed for some nuclei a few years ago @9#. In this work we present shell-model calculations of the double giant dipole state in O and Ca. By choosing light nuclei we are able to include a relatively large space of 1p-1h and 2p-2h configurations and therefore are able to study in detail the distribution of strength and the splitting of strength into the various allowed spin and isospin components. In the case of O we are able to account for the coupling of J50 and 2, 1p-1h states to the corresponding 2p-2h configurations. We also discuss energy weighted sum rules ~EWSR! and the relationship between these sum rules for the single and double giant resonances ~see also Ref. @10#!. The sum rules are evaluated in the shell model basis ~numerically! and in a boson model.