AFDMC Method for Nuclear Physics and Nuclear Astrophysics

Size: px
Start display at page:

Download "AFDMC Method for Nuclear Physics and Nuclear Astrophysics"

Transcription

1 AFDMC Method for Nuclear Physics and Nuclear Astrophysics Thanks to INFN and to F. Pederiva (Trento)

2 Outline Motivations: NN scattering data few body theory. Few-body many body experiments/observations? The AFDMC method Test case: nuclei and neutron drops Neutron rich isotopes Equation of state (EOS) of nuclear and neutron matter Superfluid low-density neutron matter Conclusions

3 Motivations From scattering data and very light nuclei it is possible to fit very accurate realistic Hamiltonians, whose ground state is very hard (or impossible) to be solved. Properties of nuclei are well described by realistic NN and TNI interactions but limited to A=12 with GFMC technique (or less with other accurate few-body methods). EOS of nuclear and neutron matter relevant for nuclear astrophysics (evolution of neutron stars). Theoretical uncertainties on the calculation of symmetric EOS derive both from the approximations introduced in the many-body methods and/or from using model interactions. We address to the first problem.

4 Hamiltonian We consider A non-relativistic nucleons with an effective NN and TNI forces that model the pion-exchange between nucleons: H = 2 2m NN is usually written as v ij = A i=1 2 i + i<j v ij + i<j<k V ijk (1) M v p (r ij )O (p) (i, j) (2) p=1 where O (p) are operators including spin, isospin, tensor and others. The TNI models 2- and 3-π exchange between nucleons with also some excited state. The general form is V ijk = A PW 2π O 2π,PW ijk + A SW 2π O 2π,SW ijk + A R 3π O 3π, R ijk + A R Oijk R. (3)

5 NN and TNI interactions The main contribution to NN interaction is given by OPE, but also other processes are included. The most important operators are O p=1,8 ij = (1, σ i σ j, S ij, L ij S ij ) (1, τ i τ j ), (4) where L ij is the relative angular momentum, S ij is the total spin, and The TNI models following processes: S ij = 3( σ i ˆr ij )( σ j ˆr ij ) σ i σ j. (5) For example the Fujita-Miyazawa diagram gives: O 2π,PW ijk = cyc [ {X ij, X jk } {τ i τ j, τ j τ k } + 1 ] 4 [X ij, X jk ] [τ i τ j, τ j τ k ], (6)

6 DMC for central potentials The formal solution of a Schrodinger equation in imaginary time t is given by: ψ(r, t) = e (H E T )t ψ(r, 0) = = e (E 0 E T )t c 0 ψ 0 (R, 0) + n 0 e (En E T )t c n φ n (R, 0) In the limit of t it converges to the lowest energy eigenstate not orthogonal to ψ(r, 0).

7 DMC for central potentials The propagation is performed by means of the integral equation ψ(r, t) = R ψ(t) = dr G(R, R, t)ψ(r, 0) (7) The propagator is written explicitly only for short times: G(R, R, t) = R e H t R = = ( m ) 3A 2 2π 2 t h 2 2 t e V (R)+V (R ) 2 E T i t e m(r R ) 2 Then we need to iterate many times the above integral equation in the small time-step limit.

8 DMC and nuclear Hamiltonians The DMC technique is easy to apply when the interaction is purely central (spin isospin independent). For realistic NN potentials, the presence of quadratic spin and isospin operators in the propagator imposes the summation over all the possible good spin-isospin single-particle states because ( σ 1 σ 2 ) = (8) This is the approach of the GFMC of Pieper et al., including a huge number of states in the wave function: # A! Z!(A Z)! 2A (9)

9 Auxiliary Field DMC The basic idea of AFDMC is to sample spin-isospin states instead of the explicit summation. The application to pure neutron systems is due to Schmidt and Fantoni 1. Unfortunately the extension to proton-neutron systems interacting with some tensorial force was unexpectedly difficult (due to the bad constraint used to control the Fermion sign problem). 1 K.E. Schmidt and S. Fantoni, Phys. Lett. 445, 99 (1999)

10 Auxiliary Field DMC The method consists in using the Hubbard-Stratonovich transformation in order to reduce the spin-isospin operators in the Green s function from quadratic to linear: e 1 2 to2 = 1 2π dxe x2 2 +x to (10) We need to sample the x auxiliary fields.

11 Auxiliary Field DMC The trial wave function used for the projection has the following form: ψ T (R, S) = Φ J (R) A[φ i ( r j, s j )] (11) where R = ( r 1... r A ), S = (s 1...s A ) and {φ i } is a single-particle base. Φ J (R) is a Jastrow (scalar) factor: Φ J (R) = i<j f (r ij ) (12) Spin-isospin states are written as complex four-spinor components: a i s i b i c i = a i p + b i p + c i n + d i n, d i

12 Nuclei and neutron drops Nuclei and neutron drops: ideal tests to compare the ground state energy and the Spin-Orbit splitting (SOS) with other accurate methods. The Jastrow factor Φ J is a product of two-body factors related to the scalar component of the NN interaction The single-particle base is obtained from a radial part coupled to spherical harmonics; the wave function is an eigenstate of total angular momentum J For neutron drops the Hamiltonian includes an external well to confine neutrons: A H = T i + v ij + V ijk + i=1 i<j i<j<k i V ext (r i ) (13) The estimate of SOS is obtained as the difference between two excited states.

13 Light nuclei With the Argonne AV6 interaction our results for alpha particle and 8 He are in agreement of about 1% with those given by GFMC 2 and EIHH: method 4 He [MeV] 8 He [MeV] AFDMC -27.2(1) 23.6(5) GFMC (1) -23.6(1) EIHH (2) We also computed the ground state energy of 16 O with Argonne AV14 cut to v6 and our results are lower of about 8% with respect other variational estimates: method 16 O [MeV] AFDMC -90.8(1) VMC FHNC/SOC R.B. Wiringa and Steven C. Pieper, Phys. Rev. Lett. 89, 18 (2002)

14 Light nuclei We extended the calculation to the 40 Ca and nuclear matter using the Argonne AV6 3 : nucleus E AFDMC /A E exp /A 4 He He O Ca (1) -16 This simple NN interaction cannot give the experimental ground-state, but the resulting surface coefficient in the Weizsacker formula BE(A, Z) A 1 = a v a s A a Z(Z 1) (A 2Z) 2 1/3 c a A 4/3 sym A 2 + δ A, (14) is 20.5 MeV, not too far from the experimental value of MeV. 3 SG et al., Phys. Rev. Lett. 99, (2007)

15 SOS in Neutron drops In the neutron drop case the NN interaction is the Argonne AV8 and different form of TNI were considered. The AFDMC results for SOS are very close to that of GFMC 4 : TNI AFDMC-SOS GFMC-SOS UIX 1.55(5) 1.5(1) IL1 2.70(5) 2.8(3) IL2 2.93(5) 2.8(3) IL3 3.39(6) 3.6(4) IL4 2.47(6) 2.4(4) The previously constrained-path calculation using AV8 +UIX Hamiltonian estimated SOS=0.8 MeV 5. 4 S.C. Pieper et al., Phys. Rev. C 64, (2001) 5 F. Pederiva et al., Nucl. Phys. A742, 255 (2004)

16 Neutron rich isotopes Neutron rich isotopes 18 O 22 O and 42 Ca 48 Ca modeled by considering only valence neutrons in an external well, and interacting with realistic NN and TNI forces. Very good agreement with measured energies 6. 6 SG et al., Phys. Rev. C 73, (2006), SG et al., Eur. Phys. J. A 35, 207 (2008)

17 Nuclear Matter Nuclear and neutron matter For nuclear and neutron matter the Jastrow factor is essentially the same of that used for nuclei. Calculations were performed with nucleons in a periodic box for several densities. Single-particle orbitals are plane waves fitting the box.

18 Nuclear Matter We computed the energy of 28 nucleons interacting with Argonne AV8 cut to v6 for several densities 7, and we compare our results with those given by FHNC/SOC and BHF calculations 8 : Wrong prediction of equilibrium density ρ 0 =0.16 fm 3 (expected for the absence of TNI). 7 SG et al., Phys. Rev. Lett. 98, (2007) 8 I. Bombaci et al., Phys. Lett. B 609, 232 (2005)

19 Neutron matter The same calculation performed with GFMC 9 was repeated. Using the Argonne AV8 in the Hamiltonian, the energy of 14 neutrons in a periodic box is: ρ [fm 3 ] FP-AFDMC CP-GFMC UC-GFMC CP-AFDMC (2) 6.43(01) 6.32(03) (8) 10.02(02) 9.591(06) (6) 18.54(04) 17.00(27) 20.32(6) (9) 30.04(04) 28.35(50) The fixed-phase approximation improves the agreement between AFDMC and GFMC. 9 J. Carlson et al., Phys. Rev. C 68, (2003)

20 Neutron matter We use the realistic nuclear Hamiltonian AV8 +UIX and 66 neutrons in a periodic box. The AFDMC EOS is compared with the VCS one of Akmal, Pandharipande and Ravenhall 10. The VCS seems to overestimate the TNI contribution. 10 A. Akmal et al., Phys. Rev. C 58, 1804 (1998)

21 Neutron star structure We solved the TOV equation to compare the structure of the star predicted by AFDMC-EOS and the APR one. The less hardness predicted by APR essentially does not change the structure of the star.

22 Superfluid Neutron Matter Superfluid neutron matter The value of the superfluid gap is crucial to study the cooling process of neutron stars. It can be computed from even-odd staggering of estimated energies E(N) of neutron matter. The antisymmetric part of the trial wave function has a BCS structure with a projected number N of neutrons: Φ BCS = A[φ( r 1, s 1, r 2, s 2 )...φ( r i, s i, r j, s j )ψ k ( r l )] (15) The pairing orbitals have the form φ( r ij, s i, s j ) = α c α e i K α r ij ξ S (s i, s j ) (16) and the c α parameters are determined with a CBF calculation 11. The unpaired orbitals, needed for odd number of neutrons, are plane waves. 11 A. Fabrocini et al., Phys. Rev. Lett. 95, (2005)

23 Superfluid Neutron Matter We computed the superfluid gap considering N = and N = neutrons 12. The most recent results predict a larger value of than the previous estimates. The AFDMC calculation is the only one using the full Hamiltonian rather than an effective one. 12 SG et al., Phys. Rev. Lett. in press

24 Conclusions AFDMC useful to study properties of neutron matter with a realistic Hamiltonian, and nuclear matter with a semi-realistic Hamiltonian. The ground state energy of nuclei and neutron drops is in a very good agreement with other accurate methods. The energy of neutron rich isotopes in a well agreement with experimental data. We revisited the EOS of neutron matter and the structure of a neutron star. The 1 S 0 superfluid gap has been accurately computed including the full Hamiltonian rather then some effective interaction.

The EOS of neutron matter, and the effect of Λ hyperons to neutron star structure

The EOS of neutron matter, and the effect of Λ hyperons to neutron star structure The EOS of neutron matter, and the effect of Λ hyperons to neutron star structure Stefano Gandolfi Los Alamos National Laboratory (LANL) Nuclear Structure and Reactions: Weak, Strange and Exotic International

More information

Quantum Monte Carlo calculations of neutron and nuclear matter

Quantum Monte Carlo calculations of neutron and nuclear matter Quantum Monte Carlo calculations of neutron and nuclear matter Stefano Gandolfi Los Alamos National Laboratory (LANL) Advances and perspectives in computational nuclear physics, Hilton Waikoloa Village,

More information

Quantum Monte Carlo calculations of medium mass nuclei

Quantum Monte Carlo calculations of medium mass nuclei Quantum Monte Carlo calculations of medium mass nuclei Diego Lonardoni FRIB Theory Fellow In collaboration with: J. Carlson, LANL S. Gandolfi, LANL X. Wang, Huzhou University, China A. Lovato, ANL & UniTN

More information

The EOS of neutron matter, and the effect of Λ hyperons to neutron star structure

The EOS of neutron matter, and the effect of Λ hyperons to neutron star structure The EOS of neutron matter, and the effect of Λ hyperons to neutron star structure Stefano Gandolfi Los Alamos National Laboratory (LANL) 12th International Conference on Hypernuclear and Strange Particle

More information

Neutron Matter: EOS, Spin and Density Response

Neutron Matter: EOS, Spin and Density Response Neutron Matter: EOS, Spin and Density Response LANL : A. Gezerlis, M. Dupuis, S. Reddy, J. Carlson ANL: S. Pieper, R.B. Wiringa How can microscopic theories constrain mean-field theories and properties

More information

The EOS of neutron matter and the effect of Λ hyperons to neutron star structure

The EOS of neutron matter and the effect of Λ hyperons to neutron star structure The EOS of neutron matter and the effect of Λ hyperons to neutron star structure Stefano Gandolfi Los Alamos National Laboratory (LANL) 54th International Winter Meeting on Nuclear Physics Bormio, Italy,

More information

The Nuclear Equation of State

The Nuclear Equation of State The Nuclear Equation of State Abhishek Mukherjee University of Illinois at Urbana-Champaign Work done with : Vijay Pandharipande, Gordon Baym, Geoff Ravenhall, Jaime Morales and Bob Wiringa National Nuclear

More information

Three-nucleon potentials in nuclear matter. Alessandro Lovato

Three-nucleon potentials in nuclear matter. Alessandro Lovato Three-nucleon potentials in nuclear matter Alessandro Lovato PRC 83, 054003 (2011) arxiv:1109.5489 Outline Ab initio many body method Nuclear Hamiltonian: 2- and 3- body potentials Density dependent potential

More information

Nuclear and Nucleon Matter Constraints on Three-Nucleon Forces

Nuclear and Nucleon Matter Constraints on Three-Nucleon Forces Nuclear and Nucleon Matter Constraints on Three-Nucleon Forces Robert B. Wiringa, Physics Division, Argonne National Laboratory Joe Carlson, Los Alamos Stefano Gandolfi, Los Alamos Alessandro Lovato, Argonne

More information

PROGRESS IN UNDERSTANDING THE PROPERTIED OF MANY-BODY SYSTEMS BY QUANTUM MONTE CARLO SIMULATIONS

PROGRESS IN UNDERSTANDING THE PROPERTIED OF MANY-BODY SYSTEMS BY QUANTUM MONTE CARLO SIMULATIONS PROGRESS IN UNDERSTANDING THE PROPERTIED OF MANY-BODY SYSTEMS BY QUANTUM MONTE CARLO SIMULATIONS Francesco Pederiva! Physics Department - University of Trento INFN - TIFPA, Trento Institute for Fundamental

More information

A Monte Carlo approach to the study of medium-light hypernuclei properties

A Monte Carlo approach to the study of medium-light hypernuclei properties A Monte Carlo approach to the study of medium-light hypernuclei properties Diego Lonardoni University of Trento - Physics Department INFN - Gruppo Collegato di Trento December 16, 2011 Outline 1. The method

More information

The Auxiliary Field Diffusion Monte Carlo Method for Nuclear Physics and Nuclear Astrophysics

The Auxiliary Field Diffusion Monte Carlo Method for Nuclear Physics and Nuclear Astrophysics Università degli Studi di Trento Facoltà di Scienze Matematiche Fisiche e Naturali arxiv:0712.1364v1 [nucl-th] 9 Dec 2007 Tesi di Dottorato di Ricerca in Fisica Ph.D. Thesis in Physics The Auxiliary Field

More information

Quantum Monte Carlo calculations with chiral Effective Field Theory Interactions

Quantum Monte Carlo calculations with chiral Effective Field Theory Interactions Quantum Monte Carlo calculations with chiral Effective Field Theory Interactions Alexandros Gezerlis East Lansing, MI 3rd International Symposium on Nuclear Symmetry Energy July 25, 2013 Motivation for

More information

Spin Orbit Interactions in Nuclear Matter with Auxiliary Field. Diffusion Monte Carlo. Jie Zhang

Spin Orbit Interactions in Nuclear Matter with Auxiliary Field. Diffusion Monte Carlo. Jie Zhang Spin Orbit Interactions in Nuclear Matter with Auxiliary Field Diffusion Monte Carlo by Jie Zhang A Dissertation Presented in Partial Fulfillment of the Requirement for the Degree Doctor of Philosophy

More information

E. Fermi: Notes on Thermodynamics and Statistics (1953))

E. Fermi: Notes on Thermodynamics and Statistics (1953)) E. Fermi: Notes on Thermodynamics and Statistics (1953)) Neutron stars below the surface Surface is liquid. Expect primarily 56 Fe with some 4 He T» 10 7 K ' 1 KeV >> T melting ( 56 Fe) Ionization: r Thomas-Fermi

More information

Superfluid Gap in Neutron Matter from a Microscopic Effective Interaction

Superfluid Gap in Neutron Matter from a Microscopic Effective Interaction Superfluid Gap in Neutron Matter from a Microscopic Effective Interaction Omar Benhar INFN and Department of Physics, Sapienza University I-00185 Roma, Italy Based on work done in collaboration with Giulia

More information

Toward a unified description of equilibrium and dynamics of neutron star matter

Toward a unified description of equilibrium and dynamics of neutron star matter Toward a unified description of equilibrium and dynamics of neutron star matter Omar Benhar INFN and Department of Physics Sapienza Università di Roma I-00185 Roma, Italy Based on work done in collaboration

More information

Dense Matter and Neutrinos. J. Carlson - LANL

Dense Matter and Neutrinos. J. Carlson - LANL Dense Matter and Neutrinos J. Carlson - LANL Neutron Stars and QCD phase diagram Nuclear Interactions Quantum Monte Carlo Low-Density Equation of State High-Density Equation of State Neutron Star Matter

More information

Local chiral NN potentials and the structure of light nuclei

Local chiral NN potentials and the structure of light nuclei Local chiral NN potentials and the structure of light nuclei Maria Piarulli @ELBA XIV WORKSHOP June 7-July 1 16, Marciana Marina, Isola d Elba PHYSICAL REVIEW C 91, 43(15) Minimally nonlocal nucleon-nucleon

More information

Nuclear structure III: Nuclear and neutron matter. National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016

Nuclear structure III: Nuclear and neutron matter. National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016 Nuclear structure III: Nuclear and neutron matter Stefano Gandolfi Los Alamos National Laboratory (LANL) National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016

More information

Sum rules of electromagnetic response functions in 12 C

Sum rules of electromagnetic response functions in 12 C Sum rules of electromagnetic response functions in 12 C Alessandro Lovato In collaboration with: Stefano Gandolfi, Ralph Butler, Joseph Carlson, Ewing Lusk, Steven C. Pieper, and Rocco Schiavilla. Introduction

More information

Charge Form Factor and Sum Rules of electromagnetic and neutral-current response functions in 12 C

Charge Form Factor and Sum Rules of electromagnetic and neutral-current response functions in 12 C Charge Form Factor and Sum Rules of electromagnetic and neutral-current response functions in 12 C Alessandro Lovato In collaboration with: Stefano Gandolfi, Ralph Butler, Joseph Carlson, Ewing Lusk, Steven

More information

Many-Body Theory of the Electroweak Nuclear Response

Many-Body Theory of the Electroweak Nuclear Response Many-Body Theory of the Electroweak Nuclear Response Omar Benhar INFN and Department of Physics Università La Sapienza, I-00185 Roma Collaborators N. Farina, D. Meloni, H. Nakamura, M. Sakuda, R. Seki

More information

arxiv:nucl-th/ v1 16 Jul 2002

arxiv:nucl-th/ v1 16 Jul 2002 Evolution of Nuclear Spectra with Nuclear Forces R. B. Wiringa[*] and Steven C. Pieper[ ] Physics Division, Argonne National Laboratory, Argonne, IL 60439 (Dated: February 8, 2008) We first define a series

More information

Few Body Methods in Nuclear Physics - Lecture I

Few Body Methods in Nuclear Physics - Lecture I Few Body Methods in Nuclear Physics - Lecture I Nir Barnea The Hebrew University, Jerusalem, Israel Sept. 2010 Course Outline 1 Introduction - Few-Body Nuclear Physics 2 Gaussian Expansion - The Stochastic

More information

Nuclear structure from chiral-perturbation-theory two- plus three-nucleon interactions

Nuclear structure from chiral-perturbation-theory two- plus three-nucleon interactions Nuclear structure from chiral-perturbation-theory two- plus three-nucleon interactions Petr Navratil Lawrence Livermore National Laboratory* Collaborators: W. E. Ormand (LLNL), J. P. Vary (ISU), E. Caurier

More information

arxiv: v2 [nucl-th] 29 Apr 2015

arxiv: v2 [nucl-th] 29 Apr 2015 Quantum Monte Carlo methods for nuclear physics J. Carlson Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 S. Gandolfi Theoretical Division, Los Alamos National Laboratory, Los

More information

Few- Systems. Selected Topics in Correlated Hyperspherical Harmonics. Body. A. Kievsky

Few- Systems. Selected Topics in Correlated Hyperspherical Harmonics. Body. A. Kievsky Few-Body Systems 0, 11 16 (2003) Few- Body Systems c by Springer-Verlag 2003 Printed in Austria Selected Topics in Correlated Hyperspherical Harmonics A. Kievsky INFN and Physics Department, Universita

More information

arxiv: v2 [nucl-th] 19 Jan 2010

arxiv: v2 [nucl-th] 19 Jan 2010 Mon. Not. R. Astron. Soc. 000, 000 000 (0000) Printed 19 January 2010 (MN LATEX style file v2.2) Microscopic calculation of the equation of state of nuclear matter and neutron star structure arxiv:0909.3487v2

More information

1 Introduction. 2 The hadronic many body problem

1 Introduction. 2 The hadronic many body problem Models Lecture 18 1 Introduction In the next series of lectures we discuss various models, in particluar models that are used to describe strong interaction problems. We introduce this by discussing the

More information

Nuclear equation of state with realistic nuclear forces

Nuclear equation of state with realistic nuclear forces Nuclear equation of state with realistic nuclear forces Hajime Togashi (RIKEN) Collaborators: M. Takano, K. Nakazato, Y. Takehara, S. Yamamuro, K. Sumiyoshi, H. Suzuki, E. Hiyama 1:Introduction Outline

More information

Quantum Theory of Many-Particle Systems, Phys. 540

Quantum Theory of Many-Particle Systems, Phys. 540 Quantum Theory of Many-Particle Systems, Phys. 540 IPM? Atoms? Nuclei: more now Other questions about last class? Assignment for next week Wednesday ---> Comments? Nuclear shell structure Ground-state

More information

c E If photon Mass particle 8-1

c E If photon Mass particle 8-1 Nuclear Force, Structure and Models Readings: Nuclear and Radiochemistry: Chapter 10 (Nuclear Models) Modern Nuclear Chemistry: Chapter 5 (Nuclear Forces) and Chapter 6 (Nuclear Structure) Characterization

More information

TRIUMF. Three-body forces in nucleonic matter. Weakly-Bound Systems in Atomic and Nuclear Physics. Kai Hebeler (TRIUMF) INT, Seattle, March 11, 2010

TRIUMF. Three-body forces in nucleonic matter. Weakly-Bound Systems in Atomic and Nuclear Physics. Kai Hebeler (TRIUMF) INT, Seattle, March 11, 2010 Three-body forces in nucleonic matter Kai Hebeler (TRIUMF) INT, Seattle, March 11, 21 TRIUMF A. Schwenk, T. Duguet, T. Lesinski, S. Bogner, R. Furnstahl Weakly-Bound Systems in Atomic and Nuclear Physics

More information

Pairing in Nuclear and Neutron Matter Screening effects

Pairing in Nuclear and Neutron Matter Screening effects Pairing Degrees of Freedom in Nuclei and Nuclear Medium Seattle, Nov. 14-17, 2005 Outline: Pairing in Nuclear and Neutron Matter Screening effects U. Lombardo pairing due to the nuclear (realistic) interaction

More information

Alex Gezerlis. New Ideas in Constraining Nuclear Forces ECT*, Trento, Italy June 5, 2018

Alex Gezerlis. New Ideas in Constraining Nuclear Forces ECT*, Trento, Italy June 5, 2018 Quantum Monte Carlo interactions with From microscopic to effective Chiral Effective Field Theory Interactions using Quantum Monte Carlo Alex Gezerlis New Ideas in Constraining Nuclear Forces ECT*, Trento,

More information

The Nuclear Many-Body Problem. Lecture 2

The Nuclear Many-Body Problem. Lecture 2 The Nuclear Many-Body Problem Lecture 2 How do we describe nuclei? Shell structure in nuclei and the phenomenological shell model approach to nuclear structure. Ab-initio approach to nuclear structure.

More information

arxiv: v1 [nucl-th] 1 Nov 2018

arxiv: v1 [nucl-th] 1 Nov 2018 Contact representation of short range correlation in light nuclei studied by the High-Momentum Antisymmetrized Molecular Dynamics arxiv:1811.00271v1 [nucl-th] 1 Nov 2018 Qing Zhao, 1, Mengjiao Lyu, 2,

More information

Hybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction

Hybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction Prog. Theor. Exp. Phys. 2015, 00000 (10 pages) DOI: 10.1093/ptep/0000000000 Hybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction

More information

Correlations and realistic interactions in doubly closed shell nuclei

Correlations and realistic interactions in doubly closed shell nuclei Correlations and realistic interactions in doubly closed shell nuclei A. Fabrocini 1), F.Arias de Saavedra 2) and G.Co 3) 1 ) Dipartimento di Fisica, Università dipisa, and Istituto Nazionale di Fisica

More information

Nuclear Structure for the Crust of Neutron Stars

Nuclear Structure for the Crust of Neutron Stars Nuclear Structure for the Crust of Neutron Stars Peter Gögelein with Prof. H. Müther Institut for Theoretical Physics University of Tübingen, Germany September 11th, 2007 Outline Neutron Stars Pasta in

More information

Symmetry Energy within the Brueckner-Hartree-Fock approximation

Symmetry Energy within the Brueckner-Hartree-Fock approximation Symmetry Energy within the Brueckner-Hartree-Fock approximation Isaac Vidaña CFC, University of Coimbra International Symposium on Nuclear Symmetry Energy Smith College, Northampton ( Massachusetts) June

More information

Allowed beta decay May 18, 2017

Allowed beta decay May 18, 2017 Allowed beta decay May 18, 2017 The study of nuclear beta decay provides information both about the nature of the weak interaction and about the structure of nuclear wave functions. Outline Basic concepts

More information

NUCLEAR STRUCTURE AB INITIO

NUCLEAR STRUCTURE AB INITIO December, 6:8 WSPC/Trim Size: 9in x 6in for Proceedings master NUCLEAR STRUCTURE AB INITIO H. FELDMEIER AND T. NEFF Gesellschaft für Schwerionenforschung mbh Planckstr., D-69 Darmstadt, Germany E-mail:

More information

Quantum Monte Carlo with

Quantum Monte Carlo with Quantum Monte Carlo with QuantumField Monte Carlo Interactions with Chiral Effective Theory Chiral Effective Field Theory Interactions From matter to nuclei Alexandros Gezerlis ECT*-EMMI Workshop Neutron-Rich

More information

Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction

Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction Lecture 5 Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction WS0/3: Introduction to Nuclear and Particle Physics,, Part I I. Angular Momentum Operator Rotation R(θ): in polar coordinates the

More information

The Nuclear Many Body Problem Lecture 3

The Nuclear Many Body Problem Lecture 3 The Nuclear Many Body Problem Lecture 3 Shell structure in nuclei and the phenomenological shell model approach to nuclear structure Ab initio approach to nuclear structure. Green's function Monte Carlo

More information

NN-Correlations in the spin symmetry energy of neutron matter

NN-Correlations in the spin symmetry energy of neutron matter NN-Correlations in the spin symmetry energy of neutron matter Symmetry energy of nuclear matter Spin symmetry energy of neutron matter. Kinetic and potential energy contributions. A. Rios, I. Vidaña, A.

More information

arxiv: v1 [nucl-th] 22 Jan 2015

arxiv: v1 [nucl-th] 22 Jan 2015 Neutron Matter from Low to High Density 1 Neutron Matter from Low to High Density Stefano Gandolfi, 1 Alexandros Gezerlis, 2 J. Carlson 1 arxiv:1501.05675v1 [nucl-th] 22 Jan 2015 1 Theoretical Division,

More information

RFSS: Lecture 8 Nuclear Force, Structure and Models Part 1 Readings: Nuclear Force Nuclear and Radiochemistry:

RFSS: Lecture 8 Nuclear Force, Structure and Models Part 1 Readings: Nuclear Force Nuclear and Radiochemistry: RFSS: Lecture 8 Nuclear Force, Structure and Models Part 1 Readings: Nuclear and Radiochemistry: Chapter 10 (Nuclear Models) Modern Nuclear Chemistry: Chapter 5 (Nuclear Forces) and Chapter 6 (Nuclear

More information

Central density. Consider nuclear charge density. Frois & Papanicolas, Ann. Rev. Nucl. Part. Sci. 37, 133 (1987) QMPT 540

Central density. Consider nuclear charge density. Frois & Papanicolas, Ann. Rev. Nucl. Part. Sci. 37, 133 (1987) QMPT 540 Central density Consider nuclear charge density Frois & Papanicolas, Ann. Rev. Nucl. Part. Sci. 37, 133 (1987) Central density (A/Z* charge density) about the same for nuclei heavier than 16 O, corresponding

More information

Small bits of cold, dense matter

Small bits of cold, dense matter Small bits of cold, dense matter Alessandro Roggero (LANL) with: S.Gandolfi & J.Carlson (LANL), J.Lynn (TUD) and S.Reddy (INT) ArXiv:1712.10236 Nuclear ab initio Theories and Neutrino Physics INT - Seattle

More information

Joint ICTP-IAEA Workshop on Nuclear Structure Decay Data: Theory and Evaluation August Introduction to Nuclear Physics - 1

Joint ICTP-IAEA Workshop on Nuclear Structure Decay Data: Theory and Evaluation August Introduction to Nuclear Physics - 1 2358-19 Joint ICTP-IAEA Workshop on Nuclear Structure Decay Data: Theory and Evaluation 6-17 August 2012 Introduction to Nuclear Physics - 1 P. Van Isacker GANIL, Grand Accelerateur National d'ions Lourds

More information

Variational calculations with explicit energy functionals for fermion systems at zero temperature

Variational calculations with explicit energy functionals for fermion systems at zero temperature Journal of Physics: Conference Series PAPER OPEN ACCESS Variational calculations with explicit energy functionals for fermion systems at zero temperature To cite this article: M Takano et al 216 J. Phys.:

More information

arxiv: v1 [nucl-th] 26 Jul 2012

arxiv: v1 [nucl-th] 26 Jul 2012 Comparative study of neutron and nuclear matter with simplified Argonne nucleon-nucleon potentials arxiv:127.6314v1 [nucl-th] 26 Jul 212 M. Baldo, 1 A. Polls, 2 A. Rios, 3 H.-J. Schulze, 1 and I. Vidaña

More information

Quantum Theory of Many-Particle Systems, Phys. 540

Quantum Theory of Many-Particle Systems, Phys. 540 Quantum Theory of Many-Particle Systems, Phys. 540 Questions about organization Second quantization Questions about last class? Comments? Similar strategy N-particles Consider Two-body operators in Fock

More information

Short-Ranged Central and Tensor Correlations. Nuclear Many-Body Systems. Reaction Theory for Nuclei far from INT Seattle

Short-Ranged Central and Tensor Correlations. Nuclear Many-Body Systems. Reaction Theory for Nuclei far from INT Seattle Short-Ranged Central and Tensor Correlations in Nuclear Many-Body Systems Reaction Theory for Nuclei far from Stability @ INT Seattle September 6-, Hans Feldmeier, Thomas Neff, Robert Roth Contents Motivation

More information

Low- and High-Energy Excitations in the Unitary Fermi Gas

Low- and High-Energy Excitations in the Unitary Fermi Gas Low- and High-Energy Excitations in the Unitary Fermi Gas Introduction / Motivation Homogeneous Gas Momentum Distribution Quasi-Particle Spectrum Low Energy Excitations and Static Structure Function Inhomogeneous

More information

Neutrino Mean Free Path in Neutron Stars

Neutrino Mean Free Path in Neutron Stars 1 Neutrino Mean Free Path in Neutron Stars U. Lombardo a, Caiwan Shen a,n.vangiai b,w.zuo c a INFN-LNS,via S.Sofia 44 95129 Catania, Italy b Institut de Physique Nucléaire,F-91406, Orsay France c Institute

More information

Correlations derived from modern nucleon-nucleon potentials

Correlations derived from modern nucleon-nucleon potentials Correlations derived from modern nucleon-nucleon potentials H. Müther Institut für Theoretische Physik, Universität Tübingen, D-72076 Tübingen, Germany A. Polls Departament d Estructura i Costituents de

More information

GFMC Calculations of Carbon

GFMC Calculations of Carbon GFMC Calculations of Carbon Steven C. Pieper, Physics Division, Argonne National Laboratory Partners in crime Ralph Butler (Middle Tennessee State) Joseph Carlson (Los Alamos) Stefano Gandolfi (Los Alamos)

More information

Pairing wave functions for quantum Monte Carlo methods

Pairing wave functions for quantum Monte Carlo methods Pairing wave functions for quantum Monte Carlo methods KE Schmidt Department of Physics Arizona State University Tempe, AZ 85287 USA Auxiliary field formalism Represent importance sampled wave function

More information

Nuclear physics: a laboratory for many-particle quantum mechanics or From model to theory in nuclear structure physics

Nuclear physics: a laboratory for many-particle quantum mechanics or From model to theory in nuclear structure physics Nuclear physics: a laboratory for many-particle quantum mechanics or From model to theory in nuclear structure physics G.F. Bertsch University of Washington Stockholm University and the Royal Institute

More information

Realistic nucleon force and X-ray observations of neutron stars

Realistic nucleon force and X-ray observations of neutron stars Realistic nucleon force and X-ray observations of neutron stars Pawe l Haensel haensel@camk.edu.pl New perspectives on neutron star interiors ECT*, Trento, Italy, October Pawe l Haensel (CAMK) Nucleon

More information

Mean-field concept. (Ref: Isotope Science Facility at Michigan State University, MSUCL-1345, p. 41, Nov. 2006) 1/5/16 Volker Oberacker, Vanderbilt 1

Mean-field concept. (Ref: Isotope Science Facility at Michigan State University, MSUCL-1345, p. 41, Nov. 2006) 1/5/16 Volker Oberacker, Vanderbilt 1 Mean-field concept (Ref: Isotope Science Facility at Michigan State University, MSUCL-1345, p. 41, Nov. 2006) 1/5/16 Volker Oberacker, Vanderbilt 1 Static Hartree-Fock (HF) theory Fundamental puzzle: The

More information

arxiv:nucl-th/ v1 8 Feb 2000

arxiv:nucl-th/ v1 8 Feb 2000 Quantum Monte Carlo calculations of A = 8 nuclei R. B. Wiringa and Steven C. Pieper Physics Division, Argonne National Laboratory, Argonne, IL 60439 J. Carlson Theoretical Division, Los Alamos National

More information

Quantum Monte Carlo calculations of two neutrons in finite volume

Quantum Monte Carlo calculations of two neutrons in finite volume Quantum Monte Carlo calculations of two neutrons in finite volume Philipp Klos with J. E. Lynn, I. Tews, S. Gandolfi, A. Gezerlis, H.-W. Hammer, M. Hoferichter, and A. Schwenk Nuclear Physics from Lattice

More information

Chapter 6. Isospin dependence of the Microscopic Optical potential for Neutron rich isotopes of Ni, Sn and Zr.

Chapter 6. Isospin dependence of the Microscopic Optical potential for Neutron rich isotopes of Ni, Sn and Zr. Chapter 6 Isospin dependence of the Microscopic Optical potential for Neutron rich isotopes of Ni, Sn and Zr. (6.1) Introduction: Experiments with radioactive nuclear beams provide an opportunity to study

More information

Nuclear structure I: Introduction and nuclear interactions

Nuclear structure I: Introduction and nuclear interactions Nuclear structure I: Introduction and nuclear interactions Stefano Gandolfi Los Alamos National Laboratory (LANL) National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July

More information

New Frontiers in Nuclear Structure Theory

New Frontiers in Nuclear Structure Theory New Frontiers in Nuclear Structure Theory From Realistic Interactions to the Nuclear Chart Robert Roth Institut für Kernphysik Technical University Darmstadt Overview Motivation Nucleon-Nucleon Interactions

More information

arxiv:nucl-th/ v2 6 Mar 2001

arxiv:nucl-th/ v2 6 Mar 2001 1 Quantum Monte Carlo Calculations of Light Nuclei arxiv:nucl-th/0103005v2 6 Mar 2001 Steven C. Pieper and R. B. Wiringa Physics Division, Argonne National Laboratory, Argonne, IL 60439; email: spieper@anl.gov,

More information

From hypernuclei to the Inner Core of Neutron Stars: A Quantum Monte Carlo Study

From hypernuclei to the Inner Core of Neutron Stars: A Quantum Monte Carlo Study Journal of Physics: Conference Series OPE ACCESS From hypernuclei to the Inner Core of eutron Stars: A Quantum Monte Carlo Study To cite this article: D Lonardoni et al 2014 J. Phys.: Conf. Ser. 529 012012

More information

Structures and Transitions in Light Unstable Nuclei

Structures and Transitions in Light Unstable Nuclei 1 Structures and Transitions in Light Unstable Nuclei Y. Kanada-En yo a,h.horiuchi b and A, Doté b a Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization, Oho 1-1, Tsukuba-shi

More information

PHYS3031 -Advanced Optics and Nuclear Physics, Paper 2. Session 2, 2014

PHYS3031 -Advanced Optics and Nuclear Physics, Paper 2. Session 2, 2014 THE UNIVERSITY OF NE\V SOUTH \ivales SCHOOL OF PHYSICS FINAL EXAMINATION PHYS3031 -Advanced Optics and Nuclear Physics, Paper 2 Session 2, 2014 1. Time allowed - 2 hours 2. Total number of questions -

More information

arxiv: v1 [nucl-th] 20 Jun 2016

arxiv: v1 [nucl-th] 20 Jun 2016 Local chiral potentials and the structure of light nuclei M. Piarulli a, L. Girlanda b,c, R. Schiavilla d,e, A. Kievsky f, A. Lovato a, L.E. Marcucci g,f, Steven C. Pieper a, M. Viviani f, and R.B. Wiringa

More information

Chiral forces and quantum Monte Carlo: from nuclei to neutron star matter

Chiral forces and quantum Monte Carlo: from nuclei to neutron star matter Chiral forces and quantum Monte Carlo: from nuclei to neutron star matter Diego Lonardoni FRIB Theory Fellow In collaboration with: J. Carlson, LANL S. Gandolfi, LANL X. Wang, Huzhou University, China

More information

Introduction to nuclear structure

Introduction to nuclear structure Introduction to nuclear structure A. Pastore 1 Department of Physics, University of York, Heslington, York, YO10 5DD, UK August 8, 2017 Introduction [C. Diget, A.P, et al Physics Education 52 (2), 024001

More information

Renormalized Fermi hypernetted chain approach in medium-heavy nuclei

Renormalized Fermi hypernetted chain approach in medium-heavy nuclei Renormalized Fermi hypernetted chain approach in medium-heavy nuclei F. Arias de Saavedra a, C. Bisconti b, G. Co b A. Fabrocini c a Departamento de Física Atómica, Molecular y Nuclear, Universidad de

More information

Lisheng Geng. Ground state properties of finite nuclei in the relativistic mean field model

Lisheng Geng. Ground state properties of finite nuclei in the relativistic mean field model Ground state properties of finite nuclei in the relativistic mean field model Lisheng Geng Research Center for Nuclear Physics, Osaka University School of Physics, Beijing University Long-time collaborators

More information

Dynamics of nuclear four- and five-body systems with correlated Gaussian method

Dynamics of nuclear four- and five-body systems with correlated Gaussian method Journal of Physics: Conference Series OPEN ACCESS Dynamics of nuclear four- and five-body systems with correlated Gaussian method To cite this article: W Horiuchi and Y Suzuki 214 J. Phys.: Conf. Ser.

More information

Spin-Orbit Interactions in Nuclei and Hypernuclei

Spin-Orbit Interactions in Nuclei and Hypernuclei Ab-Initio Nuclear Structure Bad Honnef July 29, 2008 Spin-Orbit Interactions in Nuclei and Hypernuclei Wolfram Weise Phenomenology Aspects of Chiral Dynamics and Spin-Orbit Forces Nuclei vs. -Hypernuclei:

More information

Nucleon-nucleon interaction

Nucleon-nucleon interaction Nucleon-nucleon interaction Shell structure in nuclei and lots more to be explained on the basis of how nucleons interact with each other in free space QCD Lattice calculations Effective field theory Exchange

More information

Abstract. Keywords: Light nuclei, translation invariant shell model, binding energy, root meansquare. SCIREA Journal of Physics.

Abstract. Keywords: Light nuclei, translation invariant shell model, binding energy, root meansquare. SCIREA Journal of Physics. SCIREA Journal of Physics http://www.scirea.org/journal/physics November 1, 2016 Volume 1, Issue 1, October 2016 Applications of the Translation Invariant Shell Model and the Variational Monte Carlo Method

More information

Sloppy Nuclear Energy Density Functionals: effective model optimisation. T. Nikšić and D. Vretenar

Sloppy Nuclear Energy Density Functionals: effective model optimisation. T. Nikšić and D. Vretenar Sloppy Nuclear Energy Density Functionals: effective model optimisation T. Nikšić and D. Vretenar Energy Density Functionals the nuclear many-body problem is effectively mapped onto a one-body problem

More information

Nuclear Structure V: Application to Time-Reversal Violation (and Atomic Electric Dipole Moments)

Nuclear Structure V: Application to Time-Reversal Violation (and Atomic Electric Dipole Moments) T Symmetry EDM s Octupole Deformation Other Nuclei Nuclear Structure V: Application to Time-Reversal Violation (and Atomic Electric Dipole Moments) J. Engel University of North Carolina June 16, 2005 T

More information

Hyperon equation of state for core-collapse simulations based on the variational many-body theory Hajime Togashi Outline

Hyperon equation of state for core-collapse simulations based on the variational many-body theory Hajime Togashi Outline Hyperon equation of state for core-collapse simulations based on the variational many-body theory Hajime Togashi RIKEN Nishina Center, RIKEN Collaborators: E. Hiyama (RIKEN), M. Takano (Waseda University)

More information

Shell Eects in Atomic Nuclei

Shell Eects in Atomic Nuclei L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 1/37 Shell Eects in Atomic Nuclei Laurent Gaudefroy 1 Alexandre Obertelli 2 1 CEA, DAM, DIF - France 2 CEA, Irfu - France Shell Eects in Finite Quantum

More information

EFFECTIVE FIELD THEORY FOR LATTICE NUCLEI

EFFECTIVE FIELD THEORY FOR LATTICE NUCLEI EFFECTIVE FIELD THEORY FOR LATTICE NUCLEI Francesco Pederiva Physics Deparment Unversity of Trento INFN-TIFPA, Trento Institue for Fundamental Physics and Applications LISC, Interdisciplinary Laboratory

More information

Simple Atom, Extreme Nucleus: Laser Trapping and Probing of He-8. Zheng-Tian Lu Argonne National Laboratory University of Chicago

Simple Atom, Extreme Nucleus: Laser Trapping and Probing of He-8. Zheng-Tian Lu Argonne National Laboratory University of Chicago Simple Atom, Extreme Nucleus: Laser Trapping and Probing of He-8 Zheng-Tian Lu Argonne National Laboratory University of Chicago Funding: DOE, Office of Nuclear Physics Helium Atom fm Å e - Ionization

More information

Introduction to NUSHELLX and transitions

Introduction to NUSHELLX and transitions Introduction to NUSHELLX and transitions Angelo Signoracci CEA/Saclay Lecture 4, 14 May 213 Outline 1 Introduction 2 β decay 3 Electromagnetic transitions 4 Spectroscopic factors 5 Two-nucleon transfer/

More information

Translationally Invariant Treatment of Light Nuclei

Translationally Invariant Treatment of Light Nuclei Translationally Invariant Treatment of Light Nuclei Theodoros Leontiou Department of Physics, UMIST, Manchester, UK A thesis submitted to the University of Manchester Institute of Science and Technology

More information

Effects of state dependent correlations on. nucleon density and momentum. distributions

Effects of state dependent correlations on. nucleon density and momentum. distributions Effects of state dependent correlations on arxiv:nucl-th/9610036v1 24 Oct 1996 nucleon density and momentum distributions F. Arias de Saavedra Departamento de Fisica Moderna, Universidad de Granada, E-18071

More information

Shell model Monte Carlo level density calculations in the rare-earth region

Shell model Monte Carlo level density calculations in the rare-earth region Shell model Monte Carlo level density calculations in the rare-earth region Kadir Has University Istanbul, Turkey Workshop on Gamma Strength and Level Density in Nuclear Physics and Nuclear Technology

More information

Structure of Atomic Nuclei. Anthony W. Thomas

Structure of Atomic Nuclei. Anthony W. Thomas Structure of Atomic Nuclei Anthony W. Thomas JLab Users Meeting Jefferson Lab : June 2 nd 2015 The Issues What lies at the heart of nuclear structure? Start from a QCD-inspired model of hadron structure

More information

Nuclear interactions with modern three-body forces lead to the instability of neutron matter and neutron stars

Nuclear interactions with modern three-body forces lead to the instability of neutron matter and neutron stars Eur. Phys. J. A (214) 5: 118 DOI 1.114/epja/i214-14118-6 Regular Article Theoretical Physics THE EUROPEAN PHYSICAL JOURNAL A Nuclear interactions with modern three-body forces lead to the instability of

More information

Nucleon Pairing in Atomic Nuclei

Nucleon Pairing in Atomic Nuclei ISSN 7-39, Moscow University Physics Bulletin,, Vol. 69, No., pp.. Allerton Press, Inc.,. Original Russian Text B.S. Ishkhanov, M.E. Stepanov, T.Yu. Tretyakova,, published in Vestnik Moskovskogo Universiteta.

More information

Quantum Monte Carlo calculations of the equation of state of neutron matter with chiral EFT interactions

Quantum Monte Carlo calculations of the equation of state of neutron matter with chiral EFT interactions Quantum Monte Carlo calculations of the equation of state of neutron matter with chiral EFT interactions Ingo Tews (Institute for Nuclear Theory Seattle) In collaboration with A.Gezerlis, J. Carlson, S.

More information

Cluster Models for Light Nuclei

Cluster Models for Light Nuclei Cluster Models for Light Nuclei N. Itagaki, T. Otsuka, University of Tokyo S. Aoyama, Niigata University K. Ikeda, RIKEN S. Okabe, Hokkaido University Purpose of the present study Cluster model explore

More information

The Nuclear Many-Body Problem

The Nuclear Many-Body Problem The Nuclear Many-Body Problem relativistic heavy ions vacuum electron scattering quarks gluons radioactive beams heavy few nuclei body quark-gluon soup QCD nucleon QCD few body systems many body systems

More information

Structure of the deuteron

Structure of the deuteron Seminar II Structure of the deuteron Author : Nejc Košnik Advisor : dr. Simon Širca Department of Physics, University of Ljubljana November 17, 004 Abstract Basic properties of the deuteron are given.

More information