142 research outputs found
Converging Many-Body Perturbation Theory for Ab Initio Nuclear Structure: II. Brillouin-Wigner Perturbation Series for Open-Shell Nuclei
No full textInternational audienceBrillouin-Wigner (BW) perturbation theory is developed for both ground and excited states of open-shell nuclei. We show that with optimal partitioning of the many-body Hamiltonian proposed earlier by the authors [Z. Li and N. Smirnova, arXiv:2306.13629], one can redefine the BW perturbation series for a given state of the effective Hamiltonian in a small P-space to be converging under the condition that the energy of this state is below the lowest eigenvalue of the Hamiltonian matrix block belonging to the complement of the P-space, characterized by the same good quantum numbers as the state under consideration. Specifically, the BW perturbative calculations for the lowest states are always converging due to the variational principle. This property does hold for both soft and hard internucleon interactions in the harmonic oscillator basis. To illustrate this method and check the convergence behavior, we present numerical studies of low-energy spectra of Li using the Daejeon16 and bare N3LO potentials
Converging Many-Body Perturbation Theory for Ab Initio Nuclear Structure: II. Brillouin-Wigner Perturbation Series for Open-Shell Nuclei
No full textBrillouin-Wigner (BW) perturbation theory is developed for both ground and
excited states of open-shell nuclei. We show that with optimal partitioning of
the many-body Hamiltonian proposed earlier by the authors [Z. Li and N.
Smirnova, arXiv:2306.13629], one can redefine the BW perturbation series for a
given state of the effective Hamiltonian in a small P-space to be converging
under the condition that the energy of this state is below the lowest
eigenvalue of the Hamiltonian matrix block belonging to the complement of the
P-space, characterized by the same good quantum numbers as the state under
consideration. Specifically, the BW perturbative calculations for the lowest
states are always converging due to the variational principle. This
property does hold for both soft and hard internucleon interactions in the
harmonic oscillator basis. To illustrate this method and check the convergence
behavior, we present numerical studies of low-energy spectra of Li
using the Daejeon16 and bare N3LO potentials.Comment: 15 pages, 13 figure
Advances in many-body perturbation theory for closed- and open-shell nuclei
No full textDans ce travail, nous nous concentrons sur les développements et les applications de la théorie des perturbations à N corps (MBPT) dans les formalismes de Brillouin-Wigner (BW) et de Rayleigh-Schrödinger (RS) pour les noyaux à couches fermées et ouvertes. Premièrement, dans le formalisme BW, la convergence ordre par ordre de MBPT en termes d'interaction nucléon-nucléon est étudiée. Une partition générale de l’hamiltonien et un critère de convergence pour une série de perturbations BW sont proposés. La dérivation analytique montre qu'avec une partition de l’hamiltonien appropriée, le critère de convergence pour les états fondamentaux des noyaux à couches fermées et ouvertes peut toujours être satisfait. Cette propriété est attribuée au principe variationnel et elle est indépendante du choix de l'interaction inter-nucléon et du choix de la base. Pour les états excités, uniquement pour ceux dont les énergies sont inférieures à la plus basse valeur propre de l'hamiltonien dans l'espace Q exclu, on peut obtenir une série de perturbations BW convergente avec une partition optimisée de l’hamiltonien. Pour construire efficacement ces développements perturbatifs d'ordre élevé numériquement, une nouvelle fonction de sommet appelée K-box est conçue. Les calculs des énergies des états fondamentaux de 4He et 16O, ainsi que des états excités de basse énergie de certains noyaux de la couche p, en utilisant les potentiels Daejeon16 et le N3LO dans la base de l'oscillateur harmonique et dans la base Hartree-Fock sont présentés. Deuxièmement, nous étudions également RS MBPT avec sa représentation diagrammatique de Goldstone, qui est largement appliquée aux calculs des énergies des états fondamentaux et à la construction d'hamiltoniens effectifs pour le modèle en couches avec interaction (ISM). Cependant, les applications existantes de cette méthode diagrammatique s'arrêtent généralement au 3ème ou au plus au 4ème ordre du développement perturbatif, en raison du grand nombre de diagrammes impliqués au-delà du 3ème ordre. Dans ce travail, nous développons un programme pour générer et évaluer automatiquement des diagrammes de Goldstone pour les ordres supérieurs. Ces diagrammes sont en outre utilisés pour calculer l'énergie des états fondamentaux des noyaux à couches fermées (jusqu'au 6ème ordre avec la mise en œuvre actuelle) et pour construire des hamiltoniens effectifs pour dans la couche p pour l'ISM (jusqu'au 5ème ordre) en utilisant le potentiel Daejeon16.In this work, we focus on developments and applications of many-body perturbation theory (MBPT) in both Brillouin-Wigner (BW) and Rayleigh-Schrödinger (RS) formulations for closed- and open-shell nuclei. First, within the BW formalism, order-by-order convergence of MBPT in terms of nucleon-nucleon interaction is investigated. A general Hamiltonian partitioning and a convergence criterion for a BW perturbation series are proposed. Analytic derivation shows that with an appropriate Hamiltonian partitioning, the convergence criterion for the ground states of closed- and open-shell nuclei can always be satisfied. This property attributes to the variational principle and is independent of the choice of the inter-nucleon interaction and the choice of the basis. For excited states, only for those with energies lower than the lowest eigenvalue of the Hamiltonian in the excluded Q-space, one can get converging BW perturbation series with an optimized Hamiltonian partitioning. To efficiently construct these high-order perturbative expansions numerically, a novel vertex function called K-box is devised. Calculations of the ground-state energies of 4He and 16O, as well as of the low-lying energy states of selected p-shell nuclei, using Daejeon16 and the bare N3LO potential in the harmonic oscillator and Hartree-Fock bases, are presented. Second, we study also RS MBPT with its Goldstone diagrammatic representation, widely applied to ground-state energy calculations and construction of effective Hamiltonians for the interacting shell model (ISM). However, existed applications of this diagrammatic method usually stop at 3rd or at most at 4th order of perturbative expansion, because of the large number of diagrams involved beyond the 3rd order. In this work, we develop a program to automatically generate and evaluate Goldstone diagrams at higher orders. These diagrams are further used to calculate the ground-state energy for closed-shell nuclei (up to the 6th order with the current implementation) and to construct effective p-shell Hamiltonian for the ISM (up to the 5th order) using the Daejeon16 potential
Radial overlap correction to superallowed nuclear decays using the shell model with Hartree-Fock radial wave functions
No full textThe radial overlap correction δRO is reexamined for 30 superallowed 0+→0+ nuclear β decays using the shell model with Hartree-Fock (HF) radial wave functions. Our mean-field calculation is based on the effective Skyrme interaction including Coulomb, charge-symmetry-breaking (CSB), and charge-independence-breaking (CIB) terms. In addition, the electromagnetic corrections such as those due to the gradient of charge density, vacuum polarization, Coulomb spin orbit, and finite size of nucleons are also considered. In order to avoid the spurious isospin mixing, the local equivalent potential is constructed from the solution of a HF calculation for the Z=N nucleus with charge-dependent forces neglected. Then the obtained mean field is solved noniteratively for the parent and daughter nuclei. It turns out that the CIB term has no significant impact on δRO throughout the mass range between 10 and 74. On the other hand, the CSB term makes δRO increase systematically between 10% and 30%. Similarly, the gradient density leads to a further increase of δRO between 2% and 14%, while other estimated electromagnetic corrections are negligible. The effect of the suppression of isospin spuriosity is somewhat complicated. In general, it produces a significantly larger value of δRO; however, there are a few cases for which δRO is mostly unaffected or even reduced, especially the even-even emitters in the light mass region. All these improvements partly explain the long-standing discrepancy between the correction values obtained with Woods-Saxon (WS) and HF radial wave functions. Nevertheless, the remaining discrepancy is still significant, except for the emitters with A≤26. In addition, the local odd-even staggering present in the results obtained with the phenomenological potential [J. C. Hardy and I. S. Towner, Phys. Rev. C 102, 045501 (2020); L. Xayavong and N. A. Smirnova, Phys. Rev. C 97, 024324 (2018)] is not well reproduced by our calculations. This subsequently leads to a large difference in the predicted mirror ft ratios. These problems might relate to the errors of the calculated charge radii as well as the deformation and other correlation effects on the data of separation energies used for constraining the asymptotic radial wave functions
The emergence of literary ethnography in the Russian Empire: from the far east to the pale of settlement, 1845-1917
No full textThis dissertation examines the intersection of ethnography and literature in the works of two Russian and two Russian Jewish writers and ethnographers. Fyodor Dostoevsky, Vladimir Korolenko, Vladimir Bogoraz, and Semyon An-sky wrote fiction in the genre of literary ethnography. This genre encompasses discursive practices and narrative strategies in the analysis of the different peoples of the Russian Empire. To some extent, and in some cases, these authors' ethnographic works promoted the growth of Russian and Jewish national awareness between 1845 and 1914. This dissertation proposes a new interpretive model, literary ethnography, for the study of the textualization of ethnic realities and values in the Russian Empire in the late nineteenth-century. While the writers in question were aware of the ethnographic imperial discourses then in existence, I argue that their works were at times in tune with and reflected the colonial ambitions of the empire, and at other times, contested them. I demonstrate that the employment of an ethnographic discourse made possible the incorporation of different voices and diverse cultural experiences. My multicultural approach to the study of the Russian people, the indigenous peoples of the Russian Far East, and the Jews of Tsarist Russia documents and conceptualizes the diversity and multi-voicedness of the Russian Empire during the late nineteenth and early twentieth centuries. In addition, my dissertation contributes to the field of Russian and Jewish studies by primarily examining works that are either unpublished, less well-known, or have been ignored by scholars.Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2018-08-01The student, Nadezda Berkovich, accepted the attached license on 2016-07-06 at 12:41.The student, Nadezda Berkovich, submitted this Dissertation for approval on 2016-07-06 at 12:42.This Dissertation was approved for publication on 2016-07-08 at 08:42.DSpace SAF Submission Ingestion Package generated from Vireo submission #9781 on 2016-11-10 at 12:20:21Made available in DSpace on 2016-11-10T18:27:42Z (GMT). No. of bitstreams: 2
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Brisure de la symétrie d'isospin dans les noyaux de la couche sd
No full textDans cette thèse, nous avons développé une approche microscopique de la description des effets de la brisure de symétrie d’isospin dans les noyaux de la couche sd. Le travail est effectué dans le cadre du modèle en couches.Nous avons ajouté à un Hamiltonien nucléaire traditionnel, qui conserve l’isospin, l’interaction de Coulomb et le potentiel de type Yukawa d'échange de mésons pour modéliser les forces nucléaires dépendantes de la charge. La base de données sur les coefficients expérimentaux de l'équation des multiplets de masse isobariques (IMME) a été mise au point dans le cadre de cette thèse et a été utilisée pour ajuster les paramètres de l’hamiltonien. L'hamiltonien ainsi construit fournit une description théorique très précise du mélange d’isospin dans les états nucléaires. Nous montrons la pertinence de cette approche dans deux applications importantes : (i) le calcul des amplitudes d'émission de proton interdites par isospin, essentiels dans le cadre d’astrophysique nucléaire et (ii) le calcul de corrections (dues au mélange d'isospin) aux transitions bêta superpermises du type Fermi, cruciales pour les tests des symétries fondamentales du Modèle Standard de l’interaction électrofaible.In the thesis, we develop a microscopic approach to describe theisospin-symmetry breaking effects in sd-shell nuclei.The work is performed within the nuclear shell model.A realistic isospin-conserving Hamiltonian is supplementedby a charge-dependent part consisting of the Coulomb interaction andYukawa-type meson exchange potentials to model charge-dependent forces ofnuclear origin. The extended database of the experimental isobaric mass multiplet equation coefficients is compiled during the thesis work and is used in a fit of the Hamiltonian parameters.The constructed Hamiltonian provides an accurate theoretical description ofthe isospin mixing nuclear states. A specific behaviour of the IMME coefficients have been revealed.We present two important applications (i) calculations of isospin-forbiddenproton emission amplitudes, which is often of interest for nuclearastrophysics, and (ii) calculation on corrections to nuclear Fermi beta decay, which is crucial for the tests of fundamental symmetries of the weak interaction
Isobaric-multiplet mass equation in a macroscopic-microscopic approach
No full textInternational audienceWe study the a, b, and c coefficients of the isobaric-multiplet mass equation (IMME) using a macroscopic-microscopic approach developed by P. Möller and collaborators [At. Data Nucl. Data Tables 59, 185 (1995)ADNDAT0092-640X10.1006/adnd.1995.1002; At. Data Nucl. Data Tables 109-110, 1 (2016)ADNDAT0092-640X10.1016/j.adt.2015.10.002]. We show that already the macroscopic part of the finite-range liquid-drop model (FRLDM) describes the general trend of the a and b coefficients relatively well, while the staggering behavior of b coefficients for doublets and quartets can be understood in terms of the difference of average proton and neutron pairing energies. The sets of isobaric masses, predicted by the full macroscopic-microscopic approaches, are used to explore the general trends of IMME coefficients up to A=100. We conclude that while the agreement for a coefficients is quite satisfactory, the full approaches have less sensitivity to predict the IMME b and c coefficients in detail. The best set of theoretical b coefficients, as given by the modified macroscopic part of the FRLDM, is used to predict masses of proton-rich nuclei based on the known experimental masses of neutron-rich mirror partners, and subsequently to investigate their one- and two-proton separation energies in proton-rich nuclei up to the A=100 region. The estimated position of the proton drip line is in fair agreement with known experimental data. These masses are important for simulations of the astrophysical rp process
Isospin-Symmetry Breaking within the Nuclear Shell Model: Present Status and Developments
No full textThe paper reviews the recent progress in the description of isospin-symmetry breaking within the nuclear shell model and applications to actual problems related to the structure and decay of exotic neutron-deficient nuclei and nuclei along the N=Z line, where N is the neutron number and Z the atomic number. The review recalls the fundamentals of the isospin formalism for two-nucleon and many-nucleon systems, including quantum numbers, the spectrum’s structure and selection rules for weak and electromagnetic transitions; and at the end, summarizes experimental signatures of isospin-symmetry breaking effects, which motivated efforts towards the creation of a relevant theoretical framework to describe those phenomena. The main approaches to construct accurate isospin-nonconserving Hamiltonians within the shell model are briefly described and recent advances in the description of the structure and (isospin-forbidden) decay modes of neutron-deficient nuclei are highlighted. The paper reviews major implications of the developed theoretical tools to (i) the fundamental interaction studies on nuclear decays and (ii) the estimation of the rates of nuclear reactions that are important for nuclear astrophysics. The shell model is shown to be one of the most suitable approaches to describing isospin-symmetry breaking in nuclear states at low energies. Further efforts in extending and refining the description to larger model spaces, and in developing first-principle theories to deal with isospin-symmetry breaking in many-nucleon systems, seem to be indispensable steps towards our better understanding of nuclear properties in the precision era
Isospin Non-Conservation in Shell Model Approach and Applications*
No full textUp to now, empirical shell-model Hamiltonians for valence space calculations provide the most accurate description of the low-energy spectra and individual transitions of sd- and pf-shell nuclei. These features made them of particular importance for the description of the isospin-symmetry-breaking phenomena, such as energy splitting of the isobaric multiplets or isospin-forbidden transition rates. In this contribution, we demonstrate the applications of a recently constructed isospin non-conserving (INC) Hamiltonian in sd shell [Lam et al. Phys. Rev. C 87, 054304 (2013)]. First, we explore the partial decay scheme of 24Si and discuss the states affected by the Thomas-Ehrman shift. Second, we show the accuracy of the INC Hamiltonian for the description of the mirror energy differences
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