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Efektywne teorie pola w układach
jądrowych — od skali QCD
do jąder egzotycznych
Jacek Dobaczewski
Instytut Fizyki Teoretycznej
Warszawa, 3 grudnia 2005
Jacek Dobaczewski
Jacek Dobaczewski
http://www.cpepweb.org/
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.
http://www.cpepweb.org/
Jacek Dobaczewski
Main players in Nuclear Physics
g g g g
g
g g
g
g
g
g
_
ud
gluons
+
_
ud
+
_ _ _
u u u
u u u
quarks
_
ud
uu
d
pions (p+)
protons
nuclei
Jacek Dobaczewski
_ _ _
d d d
d d d
ud
d
neutrons
Scales of energy in Nuclear Physics
u
g g
g g
g
g
g g
g
g
g
g
_
d
_
_
u d u_ d
d
u
uu
u
_ d_
d ud ud d
QCD scale
1000 MeV
pion-mass scale
100 MeV
_
ud
_
u d_
ud
pion p+
~140 MeV
deuteron
~2.2 MeV
N-binding scale
10 MeV
collective ~1 MeV
Jacek Dobaczewski
Derek B. Leinweber
The QCD vacuum
http://hermes.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/QCDvacuum/welcome.html
Jacek Dobaczewski
Hydrogen atom perturbed near the center
Relative errors in the Swave 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.
Jacek Dobaczewski
1.
2.
3.
4.
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.
Jacek Dobaczewski
Elena Castellani, physics/0101039
Effective Theories, Reductionism, and Emergence
Effective Lagrangians
Jacek Dobaczewski
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
Jacek Dobaczewski
D.R. Entem1 and R. Machleidt, Phys. Rev. C68, 041001 (2003)
Nucleon-nucleon potential at fourth order of chiral perturbation theory
A. Schwenk: http://www.int.washington.edu/talks/WorkShops/
int_05_3/People/Schwenk_A/Schwenk_INT_05-3.pdf
Nucleon-nucleon interaction at low momentum – Vlow k
Jacek Dobaczewski
-3
Particle density (fm )
Nuclear densities as composite fields
0.10
100
Sn
(n)
100
Zn
(n)
(p)
(p)
0.05
0.00
0
2
4
6
8
2
4
6
8
10
R (fm)
Modern Mean-Field Theory  Energy Density Functional
r, t,
Hohenberg-Kohn
Kohn-Sham
Negele-Vautherin
Landau-Migdal
Nilsson-Strutinsky
Jacek Dobaczewski

J,

j,

T,

s,

F,
mean field one-body densities
zero range local densities
finite range non-local densities
Mean field
Jacek Dobaczewski
Pairing
E. Perlińska, et al.,
Phys. Rev. C69
(2004) 014316
Complete local energy density
Nuclear Landscape
126
stable nuclei
82
known nuclei
protons
terra incognita
50
82
28
20
50
8
28
2
20
2 8
Jacek Dobaczewski
neutrons
neutron stars
Jacek Dobaczewski
B. Fornal, XXIX Mazurian Lakes Conference on Physics (2005)
B. Fornal, XXIX Mazurian Lakes Conference on Physics (2005)
Jacek Dobaczewski
M.Honma et al., Eur. Phys. J. 25,s01 (2005) 499
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, 082502 (2001)
Jacek Dobaczewski
B. Fornal, XXIX Mazurian Lakes Conference on Physics (2005)
Evolution of the single particle orbitals
with Z going from 28 to 20
Tensor-even, tensor-odd, and spin-orbit
interactions
where
The corresponding energy density reads:
Jacek Dobaczewski
2s_1/2
0
1d_3/2
N
 (MeV)
1d_5/2
-10
2p_1/2
2p_3/2
-20
1f_5/2
HFB+SLy5
-30
30
20
Proton Number Z
Jacek Dobaczewski
1f_7/2
10
2s
(MeV)
(MeV)

0
-10
1d

cent
SO
2
1d
2p
1f
6
2p
-20
HFB+SLy5
1f
-30
30
20
Proton Number Z
Jacek Dobaczewski
10
(MeV)
SO

0
2s
-10
te=100
1d

cent
(MeV)
2
1d
2p
1f
6
2p
-20
HFB+SLy5
1f
-30
30
20
Proton Number Z
Jacek Dobaczewski
10
(MeV)
SO

0
2s
te= 200
1d
-10

cent
(MeV)
2
1d
2p
1f
6
2p
-20
HFB+SLy5
1f
-30
30
20
Proton Number Z
Jacek Dobaczewski
10
Podsumowanie
1. Teoria efektywna ujmuje swoim opisem zjawiska
istotne fizycznie w danym układzie i w danej skali
energetycznej.
2. Efektywna teoria pola pozwala systematycznie
uwzględniać efekty wysoko-energetyczne w
zjawiskach nisko-energetycznych i posługuje się
szeregiem zależnych od pędu oddziaływań
kontaktowych.
3. Zastosowanie efektywnej teorii pola do oddziaływań
nukleon-nukleon pozwala opisać przesunięcia
fazowe do 300 MeV oraz znaleźć uniwersalną klasę
oddziaływań dwu i trójciałowych.
4. Teoria jądrowego funkcjonału gęstości jest teorią
efektywną opisującą globalnie zjawiska struktury
jądra atomowego.
Jacek Dobaczewski
Jacek Dobaczewski
http://www.cpepweb.org/
Emission of long electromagnetic waves
Jacek Dobaczewski
Emission of long electromagnetic waves
Jacek Dobaczewski
Blue-sky problem - Compton scattering
Jacek Dobaczewski
Nuclear densities as composite fields
Jacek Dobaczewski
Local energy
density:
(no isospin,
no pairing)
Jacek Dobaczewski