Efektywne teorie pola w układach jądrowych — od skali QCD

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1 Efektywne teorie pola w układach jądrowych — od skali QCD
do jąder egzotycznych Jacek Dobaczewski Instytut Fizyki Teoretycznej Warszawa, 3 grudnia 2005

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3 Fundamental matter and interaction fields
Nuclear Physics studies composite objects that are built of light quarks uds and interact by exchanging gluons g. The complete theory is defined by the QCD Lagrangian: where Quarks interact electro-weakly with electrons e and neutrinos, ne and nm , by exchanging photons g and bosons W -, W +, Z0.

4 Main players in Nuclear Physics
_ u _ u _ d _ d _ d _ g g g g g g g g g g u g d gluons quarks u d _ u d _ d _ u u d + pions (p+) protons neutrons nuclei

5 Scales of energy in Nuclear Physics
d _ g g QCD scale 1000 MeV u d _ g g d _ pion p+ ~140 MeV u g d _ u g u d _ pion-mass scale 100 MeV deuteron ~2.2 MeV u d _ N-binding scale 10 MeV collective ~1 MeV

6 The QCD vacuum Derek B. Leinweber

7 Hydrogen atom perturbed near the center
Relative errors in the S-wave binding energies are plotted versus: (i) the binding energy for the Coulomb theory (ii) the Coulomb theory augmented with a delta function in first-order perturbation theory (iii) the non-perturbative effective theory through a2, and (iv) the effective theory through a4.

8 Effective Theories, Reductionism, and Emergence
An effective theory (ET) is a theory which “effectively” captures what is physically relevant in a given domain. The most appropriate description of particle interactions in the language of quantum field theory (QFT) depends on the energy at which the interactions are studied. Reductionism: Constitutive reductionism, just the analytic method of studying an object by reducing it into its most basic constituents. Theory reductionism, postulating that `theories and laws formulated in one field of science can be shown to be special cases of theories and laws formulated in some other branch of science. Explanatory reductionism, which is `the view that the mere knowledge of its ultimate components would be sufficient to explain a complex system Objective reductionism (Weinberg): the convergence of arrows of scientific explanation. Emergence (Anderson): at each new level of complexity entirely new properties appear and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other. Elena Castellani, physics/

9 Effective Lagrangians

10 np phase parameters below 300 MeV lab. energy
Nucleon-nucleon potential at fourth order of chiral perturbation theory D.R. Entem1 and R. Machleidt, Phys. Rev. C68, (2003) np phase parameters below 300 MeV lab. energy Solid line = N3LO, dashed line = NNLO, dotted line = NLO Solid dots = Nijmegen data, open circles = VPI analysis

11 Nucleon-nucleon interaction at low momentum – Vlow k
A. Schwenk: int_05_3/People/Schwenk_A/Schwenk_INT_05-3.pdf

12 Nuclear densities as composite fields
Modern Mean-Field Theory º Energy Density Functional j, r, t, J, T, s, F, Hohenberg-Kohn Kohn-Sham Negele-Vautherin Landau-Migdal Nilsson-Strutinsky mean field Þ one-body densities zero range Þ local densities finite range Þ non-local densities

13 Complete local energy density
E. Perlińska, et al., Phys. Rev. C69 (2004) Mean field Pairing

14 Nuclear Landscape protons neutrons stable nuclei known nuclei
82 50 28 20 8 2 stable nuclei known nuclei terra incognita neutron stars 126 r-process rp-process

15 B. Fornal, XXIX Mazurian Lakes Conference on Physics (2005)

16 M.Honma et al., Eur. Phys. J. 25,s01 (2005) 499
B. Fornal, XXIX Mazurian Lakes Conference on Physics (2005)

17 VT = (t1t2) ( [s1s2](2) Y(2)(W) ) Z(r)
Evolution of the single particle orbitals with Z going from 28 to 20 B. Fornal, XXIX Mazurian Lakes Conference on Physics (2005) Tensor Interaction VT = (t1t2) ( [s1s2](2) Y(2)(W) ) Z(r) VT couples j> and j< orbitals and favors charge exchange processes pf7/2  nf5/2 T. Otsuka et al. Phys. Rev. Lett 87, (2001)

18 Tensor-even, tensor-odd, and spin-orbit interactions
where The corresponding energy density reads:

19 N=28 N=20 HFB+SLy5

20 HFB+SLy5

21 te=-100 HFB+SLy5

22 te= 200 HFB+SLy5

23 Podsumowanie Teoria efektywna ujmuje swoim opisem zjawiska istotne fizycznie w danym układzie i w danej skali energetycznej. Efektywna teoria pola pozwala systematycznie uwzględniać efekty wysoko-energetyczne w zjawiskach nisko-energetycznych i posługuje się szeregiem zależnych od pędu oddziaływań kontaktowych. Zastosowanie efektywnej teorii pola do oddziaływań nukleon-nukleon pozwala opisać przesunięcia fazowe do 300 MeV oraz znaleźć uniwersalną klasę oddziaływań dwu i trójciałowych. Teoria jądrowego funkcjonału gęstości jest teorią efektywną opisującą globalnie zjawiska struktury jądra atomowego.

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25 Emission of long electromagnetic waves

26 Emission of long electromagnetic waves

27 Blue-sky problem - Compton scattering

28 Nuclear densities as composite fields

29 Local energy density: (no isospin, no pairing)