CEA DSM Irfu 14 Oct. 2008- Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop1 Pairing vibrations study in the Time-Dependent Hartree-Fock Bogoliubov.

Slides:

Advertisements

Similar presentations

Giant resonances, exotic modes & astrophysics

Advertisements

Spectroscopy at the Particle Threshold H. Lenske 1.

Valence shell excitations in even-even spherical nuclei within microscopic model Ch. Stoyanov Institute for Nuclear Research and Nuclear Energy Sofia,

電気的に励起された岩田順敬 ( 東大理 ) Cedric Simenel (CEA/Saclay) 原子核の時間発展 Thanks to: 大塚孝治 ( 東大理、東大 CNS 、理研 ) Michael Bender (CEA/Saclay)

CEA DSM Irfu Shell evolution towards 100 Sn Anna Corsi CEA Saclay/IRFU/SPhN.

RIKEN, March 2006: Mean field theories and beyond Peter Ring RIKEN, March 20, 2006 Technical University Munich RIKEN-06 Beyond Relativistic.

Nicolas Michel Importance of continuum for nuclei close to drip-line May 20th, 2009 Description of drip-line nuclei with GSM and Gamow/HFB frameworks Nicolas.

1 Di-Neutron Correlation in Soft Octupole Excitations of Medium-Mass Nuclei near Drip-Line Y. Serizawa and M. Matsuo Niigata Univ.

Collective modes of excitation in deformed neutron-rich nuclei Kenichi May, 2009.

12 June, 2006Istanbul, part I1 Mean Field Methods for Nuclear Structure Part 1: Ground State Properties: Hartree-Fock and Hartree-Fock- Bogoliubov Approaches.

Mean-field calculation based on proton-neutron mixed energy density functionals Koichi Sato (RIKEN Nishina Center) Collaborators: Jacek Dobaczewski (Univ.

On the formulation of a functional theory for pairing with particle number restoration Guillaume Hupin GANIL, Caen FRANCE Collaborators : M. Bender (CENBG)

Continuum QRPA calculation with the Skyrme effective force Niigata University Kazuhito Mizuyama Masayuki Matsuo & Yasuyoshi Serizawa.

John Daoutidis October 5 th 2009 Technical University Munich Title Continuum Relativistic Random Phase Approximation in Spherical Nuclei.

Forces for extensions of mean-field PhD Thesis Marlène Assié Denis Lacroix (LPC Caen), Jean-Antoine Scarpaci (IPN Orsay)  Extensions of mean-field ? 

Double beta decay nuclear matrix elements in deformed nuclei O. Moreno, R. Álvarez-Rodríguez, P. Sarriguren, E. Moya de Guerra F. Šimkovic, A. Faessler.

15 June, 2006Istanbul, part 21 Mean Field Methods for Nuclear Structure Part 1: Ground State Properties: Hartree-Fock and Hartree-Fock- Bogoliubov Approaches.

The physics of nuclear collective states: old questions and new trends G. Colò Congresso del Dipartimento di Fisica Highlights in Physics 2005 October.

Systematics of the First 2 + Excitation in Spherical Nuclei with Skyrme-QRPA J. Terasaki Univ. North Carolina at Chapel Hill 1.Introduction 2.Procedure.

XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, ISTANBUL-06 Kazimierz Dolny, Sept. 25, 2008 Technical.

M. Girod, F.Chappert, CEA Bruyères-le-Châtel Neutron Matter and Binding Energies with a New Gogny Force.

Etat de lieux de la QRPA = state of the art of the QRPA calculations G. Colò / E. Khan Espace de Structure Nucléaire Théorique SPhN, Saclay, January 11-12,

DPG Tagung, Breathing mode in an improved transport model T. Gaitanos, A.B. Larionov, H. Lenske, U. Mosel Introduction Improved relativistic transport.

Tomohiro Oishi 1,2, Markus Kortelainen 2,1, Nobuo Hinohara 3,4 1 Helsinki Institute of Phys., Univ. of Helsinki 2 Dept. of Phys., Univ. of Jyvaskyla 3.

1 The Random Phase Approximation in Nuclear Physics  Lay out of the presentation: 1. Linear response theory: a brief reminder 2. Non-relativistic RPA.

AUJOURD’ HUI…..et…. DEMAIN Keep contact with experimentalists, work together Beyond mean-field, but via Particle- Vibration Coupling.

Effects of self-consistence violations in HF based RPA calculations for giant resonances Shalom Shlomo Texas A&M University.

Angular Momentum Projection in TDHF Dynamics : application to Coulomb excitation and fusion C. Simenel 1,2 In collaboration with M. Bender 2, T. Duguet.

Nuclear Structure and dynamics within the Energy Density Functional theory Denis Lacroix IPN Orsay Coll: G. Scamps, D. Gambacurta, G. Hupin M. Bender and.

Stochastic quantum dynamics beyond mean-field. Denis Lacroix Laboratoire de Physique Corpusculaire - Caen, FRANCE Introduction to stochastic TDHF Application.

The calculation of Fermi transitions allows a microscopic estimation (Fig. 3) of the isospin mixing amount in the parent ground state, defined as the probability.

A new statistical scission-point model fed with microscopic ingredients Sophie Heinrich CEA/DAM-Dif/DPTA/Service de Physique Nucléaire CEA/DAM-Dif/DPTA/Service.

ESNT Saclay February 2, Structure properties of even-even actinides at normal- and super-deformed shapes J.P. Delaroche, M. Girod, H. Goutte, J.

Constraints on Nuclear Functionals from Collective Vibrations Gianluca Colò The 2 nd LACM-EFES- JUSTIPEN Workshop Oak Ridge, 25/1/2008.

Nuclear Collective Excitation in a Femi-Liquid Model Bao-Xi SUN Beijing University of Technology KITPC, Beijing.

Fission Collective Dynamics in a Microscopic Framework Kazimierz Sept 2005 H. Goutte, J.F. Berger, D. Gogny CEA Bruyères-le-Châtel Fission dynamics with.

Anomalous two-neutron transfer in neutron-rich Ni and Sn isotopes studied with continuum QRPA H.Shimoyama, M.Matsuo Niigata University 1 Dynamics and Correlations.

NEUTRON SKIN AND GIANT RESONANCES Shalom Shlomo Cyclotron Institute Texas A&M University.

Variational multiparticle-multihole configuration mixing approach

PAIRING CORRELATIONS AND COLLECTIVE

July 29-30, 2010, Dresden 1 Forbidden Beta Transitions in Neutrinoless Double Beta Decay Kazuo Muto Department of Physics, Tokyo Institute of Technology.

N. Schunck(1,2,3) and J. L. Egido(3)

First Gogny conference, TGCC December 2015 DAM, DIF, S. Péru QRPA with the Gogny force applied to spherical and deformed nuclei M. Dupuis, S. Goriely,

Giant and Pygmy Resonance in Relativistic Approach The Sixth China-Japan Joint Nuclear Physics May 16-20, 2006 Shanghai Zhongyu Ma China Institute of Atomic.

F. C HAPPERT N. P ILLET, M. G IROD AND J.-F. B ERGER CEA, DAM, DIF THE D2 GOGNY INTERACTION F. C HAPPERT ET AL., P HYS. R EV. C 91, (2015)

Couplage de phonons = state of the art of “extended” RPA calculations G. Colò Espace de Structure Nucléaire Théorique SPhN, Saclay, January 11-12, 2005.

Nuclear density functional theory with a semi-contact 3-body interaction Denis Lacroix IPN Orsay Outline Infinite matter Results Energy density function.

Time dependent GCM+GOA method applied to the fission process ESNT janvier / 316 H. Goutte, J.-F. Berger, D. Gogny CEA/DAM Ile de France.

Gogny-TDHFB calculation of nonlinear vibrations in 44,52 Ti Yukio Hashimoto Graduate school of pure and applied sciences, University of Tsukuba 1.Introduction.

Congresso del Dipartimento di Fisica Highlights in Physics –14 October 2005, Dipartimento di Fisica, Università di Milano Contribution to nuclear.

Continuum quasiparticle linear response theory using the Skyrme functional for exotic nuclei University of Jyväskylä Kazuhito Mizuyama, Niigata University,

Pairing Correlation in neutron-rich nuclei

Active lines of development in microscopic studies of

Nuclear structure far from stability

Bubble structures in exotic nuclei

Nuclear Structure Tools for Continuum Spectroscopy

The Isovector Giant Quadrupole Resonance & Nuclear Matter

Structure and dynamics from the time-dependent Hartree-Fock model

Low energy nuclear collective modes and excitations

Microscopic studies of the fission process

The continuum time-dependent Hartree-Fock method for Giant Resonances

Deformed relativistic Hartree Bogoliubov model in a Woods-Saxon basis

AUJOURD’ HUI…..et…. DEMAIN

Medium polarization effects and transfer reactions in halo nuclei

INFN - Laboratori Nazionali del Sud

UWC Beyond mean-field: present and future

A self-consistent Skyrme RPA approach

Kyorin University Mitsuru Tohyama

Constraining the Nuclear Equation of State via Nuclear Structure observables 曹李刚中科院近物所第十四届全国核结构大会，湖州，

Department of Physics, Sichuan University

Presentation transcript:

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop1 Pairing vibrations study in the Time-Dependent Hartree-Fock Bogoliubov approach Benoît AVEZ – CEA/Irfu/SPhN Philippe CHOMAZ – CEA/Irfu Cédric SIMENEL – CEA/Irfu/SPhN

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop2 Introduction : Pairing vibrations Pairing correlations → « pairing vibrations » L=0 + –Low energy modes –« Giant Pairing Vibrations (GPV) » (analogous to giant resonances) → No experimental confirmation –Probes : Pair transfer reactions Tool : TDHFB formalism Results –Oxygen isotopes (comparison with QRPA) Khan et al., PRC 69, (2004) –Calcium isotopes Bès and Broglia, Nucl Phys. 80, 289 (1966) n ħω Fermi (n-1)ħω (n+1)ħω n ħω

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop3 TDHFB formalism : general considerations Energy density functional formalism : Approximate solution of the Time-dependent Schroedinger equation Microscopic approach Can account for nuclear superfluidity Structure and dynamics treated on an equal footing Few parameters (Skyrme, Gogny), large pannel of applications (structure, collective excitations, heavy ions collisions…)

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop4 Evolution of the generalized density matrix R(t) TDHFB formalism  quasiparticule vacuum at each time t 

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop5 Evolution of the generalized density matrix R(t) Energy functional E[ R(t) ] Variational method on the action → TDHFB equations TDHFB formalism H Bogoliubov Hamiltonien

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop6 TDHFB formalism : Implementation Implementation of TDHFB assuming spherical symmetry Energy density functional E[ R ] –ph channel : Sly4 parameterization Chabanat et al., NPA 635, (1998) –pp (hh) channel : Local, density-dependent pairing bulk+surface Cut-off E qp at 80 MeV,  c =0.32 fm -3, V 0 = MeV

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop7 TDHFB formalism : Implementation Spherical symmetry + energy defined only from local densities Iterative solution :

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop8 TDHFB formalism : Particle number conservation HFB states are NOT eigenstate of N –Fixed in average through a Lagrange constraint « - N » TDHFB : (t) = constant of motion What about ? If stationnary evolution, dropping :

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop9 TDHFB formalism : stationnary evolution → Evolution of normal and anomalous densities E (MeV) Example : 18 O ( |2  =14.77 MeV )

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop10 TDHFB formalism : Nambu-Goldstone mode Nambu-Goldstone mode → Evolution the initial Lagrange constraint Pot. landscape

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop11 TDHFB formalism : Linear response Perturbation at t=0 Fourier transform of « Strength » function Excitations in the next A±2 nuclei (with ground-state energies ≈ E A ±2 ) Linear response : TDHFB ↔ QRPA

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop12 Example : the 18 O case Small amplitude excitation t=0 Higher order effects (> QRPA) Width of the 1st oscillation

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop13 « Strength » function 18 O±2n TDHFB Example : the 18 O case Small amplitude excitation Fourier

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop14 s 1/2 f 7/2 Continuum Level scheme, neutrons d 3/2 d 5/2 s 1/2 εFεF p 3/2 p 1/2 « Strength » function 18 O±2n TDHFB Example : the 18 O case Small amplitude excitation Fourier s 1/2 d 3/2, (p 1/2 ) f 7/2, (p 3/2 ) s 1/2 d 3/2, (p 1/2 ) f 7/2, (p 3/2 )

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop15 18 O+2n E. Khan et al., PRC69, (2004) (dotted : box-QRPA – solid : c-QRPA) QRPA s 1/2 d 3/2 f 7/2 s 1/2 d 3/2, (p 1/2 ) f 7/2, (p 3/2 ) s 1/2 f 7/2 Continuum Level scheme, neutrons d 3/2 d 5/2 s 1/2 εFεF p 3/2 p 1/2 « Strength » function 18 O±2n TDHFB Example : the 18 O case Good agreement with QRPA -Possible differences : ≠ Pairing functionnal ≠ implementation s 1/2 d 3/2, (p 1/2 ) f 7/2, (p 3/2 )

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop16 Results : Oxygen isotopes TDHFB response HFB response (unperturbed spectrum) 18 O±2n 20 O±2n 22 O±2n Unperturbed spectrum : 2qp excitations (from the static ground state solution)

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop17 Results : Oxygen isotopes « residual interaction » effect –S F (ħω) increases dynamical pairing → collectivity –Shift towards low energy (attractive character of the pairing) 18 O±2n 20 O±2n 22 O±2n TDHFB response HFB response (unperturbed spectrum)

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop18 Results : Oxygen isotopes GPV 18 O±2n 20 O±2n 22 O±2n « residual interaction » effect –S F (ħω) increases dynamical pairing → collectivity –Shift towards low energy (attractive character of the pairing) GPV +2n mainly f 7/2 TDHFB response HFB response (unperturbed spectrum)

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop19 Results : Oxygen and Calcium isotopes GPV 18 O±2n 20 O±2n 22 O±2n 42 Ca±2n 46 Ca±2n 44 Ca±2n

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop20 Conclusions Effect of the dynamical pairing correlations on pairing vibrations Applications on Oxygen and Calcium isotopes Good comparison with QRPA (Oxygen isotopes) Presence of the GPV confirmed in Oxygen isotopes Not seen in Calcium isotopes Outlook Heavier nuclei (Sn, Pb) Treatment of the continuum Application of TDHFB to nuclear reactions

CEA DSM Irfu 14 Oct Benoît Avez - [Pairing vibrations with TDHFB] - ESNT Workshop21 Acknowledgements and references Michael BENDER, CENBG, Bordeaux Karim BENNACEUR, IPN, Lyon Thomas DUGUET,CEA/Irfu/SPhN, Saclay Hubert FLOCARD, CSNSM, Orsay Elias KHAN, IPN, Orsay Denis LACROIX, GANIL, Caen Initial conditions for the TDHFB code : K. Bennaceur, J. Dobaczewski, Comp. Phys. Com. 168, 96 (2005) Pairing vibrations B. Avez, C. Simenel and Ph. Chomaz, arXiv:nucl-th/ (2008) (accepted for publication in Phys. Rev. C) D.R. Bès and R.A. Broglia, Nucl. Phys. 80, 289 (1966) E. Khan, N. Sandulescu, N. Van Giai, and M. Grasso, PRC 69, (2004)