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INST * Institute for Nuclear Science and Technology was founded in 1991. * 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.
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.
LIA, FAI & ANPhA Symposium in 2011
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
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
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 380 2001 151 Experimentally d <=> Symmetry Energy still unknown at large r!
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. A602 1996 98 Density dependent M3Y interaction
E/A= HF results given by some mean-field interaction CDM3Yn: D.T. Khoa, G.. Satchler, and W. von Oertzen, Phys. ev. C 56, 954 1997; D.T. Khoa, H.S. Than, and D.C. Cuong, Phys. ev. C 76, 014603 2007. M3Y-Pn: H. Nakada, Phys. ev. C 78, 054301 2008. D1S: J.F. Berger, M. Girod, and D. Gogny, Comp. Phys. Comm. 63, 365 1991. D1N: F. Chappert, M. Girod, and S. Hilaire, Phys. Lett. B 668, 420 2008. SLy4: E. Chabanat et al., Nucl. Phys. A 635, 231 1998 Ab-initio variational calculation using Argon V18 NN + NNN inter. AP: A. Akmal, V.. Pandharipande, and D.G. avenhall, Phys. ev. C 58, 1804 1998
M3Y-Pn, D1S, D1N fail to reproduce empirical pressure of neutron matter!
Two distinct scenarios for NM symmetry energy: Asy-soft & Asy-stiff H.S. Than, D.T. Khoa, N.V. Giai, Phys. ev. C 80, 064312 2009. Neutron star cooling? Empirical estimates of S L. Trippa, G. Colo, E. Vigezzi, Phys. ev. C 77, 061304 2008.. J. Furnstahl, Nucl. Phys. A 706, 85 2002. M. B. Tsang et al., Phys. ev. Lett. 102, 122701 2009 Microscopic results for S A. Akmal, V.. Pandharipande, D.G. avenhall, Phys. ev. C 58, 1804 1998 = AP S. Gandolfi et al., Mon. Not.. Astron. Soc. 404, L35 2010 = MMC
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 380 2001 151
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
b-unstable Soft-type interactions
D.T. Loan, N.H. Tan, D.T. Khoa, J.Margueron, Phys. ev. C 83, 0658009 2011. b-equilibrium Stiff-type interactions
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!
D.T. Loan, N.H. Tan, D.T. Khoa, J.Margueron, Phys. ev. C 83, 0658009 2011. 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
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.
G Mass- radius data observed for binaries: 4U1608-248, EXO1745-248, 4U1820-30 Ozel, Baym, and Guver, Phys. ev. D82, 101301 2010. 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, 0658009 2011.
Further test of the nuclear symmetry energy with CDM3Yn inter. M3Y-Paris DTK, Satchler, von Oertzen, Phys. ev. C 56, 954 1997; adjusted to the BHF results Jeukenne, Lejeune, Mahaux, Phys. ev. C 16, 80 1977; DTK, Than, Cuong, Phys. ev. C 76, 014603 2007. DTK, von Oertzen, Ogloblin, Nucl. Phys. A602, 98 1996.
b-equilibrium b-unstable
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, 0658009 2011. NS data: F. Ozel et al., Phys. ev. D 82, 101301 2010.
NS data: A.W. Steiner, J.M. Lattimer, and E. F. Brown, Astrophys. J. 722, 33 2010.
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 = = =
~ ~ n A IAS pa A IAS n pa = 2 2 1 2 2 2 2 1 ~ 1 0 ~ 1 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 = = 1 2 2 1 0 1 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, B637 1964
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, 014603 2007. MSU data:.. Doering et al. Phys. ev. C 12, 378 1975.
Crust - core interface 1 st -order phase transition from the NS crust to its uniform liquid core Douchin & Haensel, Astron. & Astrophysics 380, 151 2001. Sym. Energy can be probed by p,n IAS data ONLY at low NM densities!
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, 89 1990. Further studies are in progress!
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