VIETNAM ATOMIC ENERGY INSTITUTE INSTITUTE FOR NUCLEAR SCIENCE AND TECHNOLOGY

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1 VIETNAM ATOMIC ENEGY INSTITUTE INSTITUTE FO NUCLEA SCIENCE AND TECHNOLOGY Address: Hoang Quoc Viet, Nghia Do, Cau Giay - Hanoi - Vietnam Tel: ; Fax.: Website: vkhkthn@vaec.gov.vn

2 INST * Institute for Nuclear Science and Technology was founded in * Staff: 104, including 12 PhD and 20 MSc. Main Functions: esearch on nuclear science and technology; Development of methodology and techniques on radiation protection and nuclear safety; Technical support and services on radiation protection and nuclear safety; Education and training scientific and technical personnel in the field of nuclear energy; International co-operation in the above fields.

3 CENTE FO FUNDAMENTAL ESEACH AND COMPUTATION esearch on nuclear and high energy physics esearch on cosmic rays physics & radioastronomy Developing and applying computing techniques in physics and simulation.

4 LIA, FAI & ANPhA Symposium in 2011

5 Why do we need to study the nuclear symmetry energy? Dao Tien Khoa Institute for Nuclear Science & Technology, Vinatom - Equation of state of the b - stable npem matter at zero temperature - TOV equations Properties of neutron star NM symmetry energy - Charge-exchange reactions a probe of NM symmetry energy

6 Neutron-proton asymmetry in finite nuclei d = N-Z/A d is large in unstable nuclei with N > Z or Z > N, with d max =0.5 for 8 He! Z N

7 Proton fraction x=r p /r =0.5*1-d r = 0.5 ~ 1r 0 d = 0.94 ~ 0.90 x = 0.03 ~ 0.05 r 0 ~ 0.17 nucleon/fm -3 r = 2 ~ 6r 0 d = 0.86 ~ 0.80 x = 0.07 ~ 0.10 Sly EOS by Douchin & Haensel Astronomy & Astrophysics Experimentally d <=> Symmetry Energy still unknown at large r!

8 EOS of asymmetric nuclear matter Determined by the isospin dependence of in-medium NN interaction! Exploratory HF study: D.T. Khoa, W. von Oertzen A.A. Ogloblin, Nucl. Phys. A Density dependent M3Y interaction

9 E/A= HF results given by some mean-field interaction CDM3Yn: D.T. Khoa, G.. Satchler, and W. von Oertzen, Phys. ev. C 56, ; D.T. Khoa, H.S. Than, and D.C. Cuong, Phys. ev. C 76, M3Y-Pn: H. Nakada, Phys. ev. C 78, D1S: J.F. Berger, M. Girod, and D. Gogny, Comp. Phys. Comm. 63, D1N: F. Chappert, M. Girod, and S. Hilaire, Phys. Lett. B 668, SLy4: E. Chabanat et al., Nucl. Phys. A 635, Ab-initio variational calculation using Argon V18 NN + NNN inter. AP: A. Akmal, V.. Pandharipande, and D.G. avenhall, Phys. ev. C 58,

10 M3Y-Pn, D1S, D1N fail to reproduce empirical pressure of neutron matter!

11 Two distinct scenarios for NM symmetry energy: Asy-soft & Asy-stiff H.S. Than, D.T. Khoa, N.V. Giai, Phys. ev. C 80, Neutron star cooling? Empirical estimates of S L. Trippa, G. Colo, E. Vigezzi, Phys. ev. C 77, J. Furnstahl, Nucl. Phys. A 706, M. B. Tsang et al., Phys. ev. Lett. 102, Microscopic results for S A. Akmal, V.. Pandharipande, D.G. avenhall, Phys. ev. C 58, = AP S. Gandolfi et al., Mon. Not.. Astron. Soc. 404, L = MMC

12 Equation of state of the b - stable npem matter Hartree-Fock energy density elativistic Fermi gases The lepton number densities determined from the charge neutrality and b-equilibrium conditions Fractions of the constituent particles uniquely at a given baryon number density can be determined NS Crust: Sly4 EOS by Douchin & Haensel, Astronomy & Astrophysics

13 below the muon threshold density charge neutrality condition gives Parabolic approximation Crucial role of the symmetry energy in the determination of the proton abundance in neutron star matter above the muon threshold density EOS of the b - stable npem matter

14 b-unstable Soft-type interactions

15 D.T. Loan, N.H. Tan, D.T. Khoa, J.Margueron, Phys. ev. C 83, b-equilibrium Stiff-type interactions

16 Neutron star cooling The interior of a proto neutron star loses energy at a rapid rate by neutrino emission. Urca processes are dominant neutrino cooling reactions in which thermally excited particles alternately undergo beta and inverse-beta decays. The most efficient is the direct Urca DU process involving nucleons Momentum conservation and charge neutrality in b-equilibrium Proton fraction must exceed a threshold x DU x p > x DU if x p < x DU => the NS cooling must proceed via modified Urca process which has reaction rates million times smaller than the direct Urca process! Modified Urca reaction involves additional nucleon N in order to conserve momentum!

17 D.T. Loan, N.H. Tan, D.T. Khoa, J.Margueron, Phys. ev. C 83, x p at the maximum central density Direct Urca DU process is possible with the EOS given by CDM3Yn inter. All soft-type interactions have x p << 11.1% => modified Urca process

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19 Tolman-Oppenheimer-Volkov equations for gravitationally bound NS Different EOS s r,p sets TOV equations are integrated from the NS center, with the boundary conditions at r = 0 : P0 = P c ; m0 = 0; r0 = r c to the stellar surface at r = determined from the boundary condition P = 0, with the total gravitational mass determined as M = m. Solutions of the TOV equations give different NS models in terms of one-parameter families that can be labeled by the central pressure P c or equivalently by the central density r c of the neutron star.

20 G Mass- radius data observed for binaries: 4U , EXO , 4U Ozel, Baym, and Guver, Phys. ev. D82, G CDM3Yn give a better agreement with the empirical mass & radius M ~ 1.5 M o and ~ 10 km Inclusion of hyperons at n b > 3 n 0 Inadequacy of D1N interaction? D.T. Loan, N.H. Tan, D.T. Khoa, J.Margueron, Phys. ev. C 83,

21 Further test of the nuclear symmetry energy with CDM3Yn inter. M3Y-Paris DTK, Satchler, von Oertzen, Phys. ev. C 56, ; adjusted to the BHF results Jeukenne, Lejeune, Mahaux, Phys. ev. C 16, ; DTK, Than, Cuong, Phys. ev. C 76, DTK, von Oertzen, Ogloblin, Nucl. Phys. A602,

22 b-equilibrium b-unstable

23 Symmetry energy changing from stiff to soft => reduction of gravitational M away from empirical values D.T. Loan, N.H. Tan, D.T. K, J.Margueron, Phys. ev. C 83, NS data: F. Ozel et al., Phys. ev. D 82,

24 NS data: A.W. Steiner, J.M. Lattimer, and E. F. Brown, Astrophys. J. 722,

25 Probing the symmetry energy isospin dependence of the proton and 3 He optical potentials with the charge exchange reactions => IAS A T A Z N E U E U E U A 2,,,, 1 0 = = =

26 ~ ~ n A IAS pa A IAS n pa = ~ 1 0 ~ pa A n A n A n n A A pa p c A p U A T E U A T U K U A T E V U A T U K IAS IAS = = U A T U U U A T U U A n A o p = = => the coupled channels equations for quasi-elastic p,n or 3 He,t scattering K pn and E pn are the kinetic-energy operators and center-of-mass energies of the entrance-channel and the exit-channel The explicit isospin coupling based on the total wave function Central OP in the entrance channel Central OP in the exit channel Density- and isospin dependent NN interaction Folding model F pn Isospin coupling formalism by G.. Satchler et al., Phys. ev. 136, B

27 Strength of the isospin dependence of the CDM3Yn interaction has been adjusted to p,n data for IAS excitation! D.T. Khoa, H.S. Than, and D.C. Cuong, Phys. ev. C 76, MSU data:.. Doering et al. Phys. ev. C 12,

28 Crust - core interface 1 st -order phase transition from the NS crust to its uniform liquid core Douchin & Haensel, Astron. & Astrophysics 380, Sym. Energy can be probed by p,n IAS data ONLY at low NM densities!

29 Density dependence of NM symmetry energy can be probed by 3 He,t IAS reaction but there are very few complete data sets available! data: A.S. Demyanova et al. Physica Scripta T32, Further studies are in progress!

30 Thank you! Cám ơn!