Petr VeselýNuclear Physics Institute, Czech Academy of Sciencesgemma.ujf.cas.cz/~p.vesely/
seminar at UTEF ČVUT,Prague, November 2017
Application of Equation of Motion Phonon Method to Nuclear and Exotic Nuclear
Systems
MotivationPhysics of atomic nucleus: about 2500 known isotopes, 263 stable isotopes
estimate 4000 unobserved yet
MotivationPhysics of (hyper)nuclei: we add 3rd dimension to our nuclear chart
MotivationPhysics of atomic nucleus – what do we study:
Atomic nucleus as a bound system of
nucleons...
nucleons as a bound system of
quarks
Nuclear physics – scales
< 0.0001 fm: quarks
0.1-1 fm : baryons, mesons
1 fm: nucleons
10 fm : collective modes
What we see depends on resolution:
NN interaction
Description depends on resolution:
- quarks, gluons (as degrees of freedom) … color confinement
- nucleons, mesons (as degrees of freedom) … NN interaction as exchange of one or more mesons
NN interaction
Short Intermediate Long range
Tensor force
Central force
+
+Building blocks
(138) (600)(782) (770)
scalar meson
Exchanges of different types of mesons
NN interactionExistence of more-body interactions between nucleonsAs consequence of inner structure of nucleons
Analogy between NN and Van der Waals interaction
NN force not so much
strong !
NN interactionPossible approach to derive NN interactions
Only mesons here are pions. But pion exchanges 2,3, … till any order. Multi-pion exchangesreplace presence of other types of mesons.
Diagrams of NN scatering can be divided to orders – perturbative theory (?)
Effective field theory – instead of QCD field theory with elem. degreesof freedom (quarks, gluons) we build field theory with nucleons and pions. Must obey the same symmetries as QCD –> Chiral Perturbation Theory (ChPT)
What we can tell about nuclei
Existence of “magic”numbers in atomic physic:
Consequence of movement of electrons in Coulomb field of atomic nucleus Atomic nuclei
Weizs. formula -> “average“ part of B(A,Z)
Shell corrections-> magic numbers
How shell structure occurs in nucleus?
Magic numbers 2,8,20,28,50,126
What is “mean-field“ in nucleus ?
How mean field occurs in nucleus? → changeour perspective
nucleons as non-interacting particlesin potential well
mutual interaction of nucleons creates “mean field“ → nucleons move in this field
Hartree-Fock method – mean-field is generated “by itself“ = self-consistence
mean field
= ++
Nuclear ground state propertiesNN interaction - chiral NNLO
opt
A. Ekström et al., PRL 110, 192502 (2013)
at mean-field level lot of binding missing!
strongly interacting particles cannot be described as non-interacting particles in mean field
nuclear radii too compressed with mean-field calculations based on realistic NN interactions
Nuclear ground state properties2 ways to improve description of nuclear ground states
- interaction, 3-body NNN term is missing (in HF formalism this term reflects dependence on nuclear medium)
- many-body correlations – plenty of different models to treat them
full implementation of 3-body NNN term is very demanding
corrective density dependent term added to realistic NN interaction (simulates NNN force)
D. Bianco, F. Knapp, N. Lo Iudice, P. Vesely, F. Andreozzi, G. De Gregorio, A. Porrino, J. Phys. G: Nucl. Part. Phys. 41, 025109 (2014)
DD term shrink gaps between major shells
radial density
208Pb C
= 0
C = 2000
C = 3000
Equation of Motion Phonon Method
Tamm-Dancoff phonons
1ph excitations
2ph excitations
and in general
“more“-ph excitations
Hilbert space – divided into separate n-phononsubspaces
Equation of Motion Phonon Method
Equation of Motion (EoM) – recursive eq. to solve eigen-energies on each i-phonon subspace while knowing the (i-1)-phonon solution
total Hamiltonian mixes configurations from different Hilbert subspaces
non-diagonal blocks of Hamiltonian calculated from amplitudes
Equation of Motion Phonon Method
eigen-value problem
we diagonalize the total Hamiltonian
E = diag
correlations – wave functions of each state are superpositions of many configurations from different Hilbert subspaces
e.g.
Nuclear ground state properties
Nmax
– maximal osc. shell
(defines how big basis is)h – parameter of basis
Final energy must be converged with respect to N
max and for N
max big
enough independent on h
NN interaction - chiral NNLOopt
A. Ekström et al., PRL 110, 192502 (2013)
2-phonon correlations in the g.s.
EHF
EHF
+Ecorr.
G. De Gregorio, J. Herko, F. Knapp, N. Lo Iudice, P. Veselý, PRC 95, 024306 (2017)
Nuclear ground state propertiesNN interaction - chiral NNLO
opt
A. Ekström et al., PRL 110, 192502 (2013)
2-phonon correlations in the g.s.
G. De Gregorio, J. Herko, F. Knapp, N. Lo Iudice, P. Veselý, PRC 95, 024306 (2017)
Nuclear spectra2-phonon calculation of 208Pb – see in Phys. Rev. C 92, 054315 (2015), F. Knapp, N. Lo Iudice, P. Veselý, G. De Gregorio
nuclear density distribution
C = 3000
C = 2000
C = 0
study of the dipole photoabsorption spectrum B(E1, 0+
g.s. → 1-
exc.)
most of 1- states have configurations beyond 1ph
2-phonon configurations very important to describe richness of spectrum → multifragmentation of dipole resonance...we describe width of res.
“Quasiparticles“ in nuclei
nuclei with semi-closed shell
nucleons “jumping“ between energetically very close levels
“smearing“ of Fermi energy
occupations of levels 0 < V
i
2 < 1
becomes probabilistic
quasiparticle states - partially occupied orbits
Nuclear spectra – open-shell nucleiquasiparticle formulation of multiphonon model – useful for description of nuclei which are not doubly magic – see in Phys. Rev. C 93, 044314 (2016)P. Veselý, F. Knapp, N. Lo Iudice, G. De Gregorio
20O
much richer low lying spectrum (with 2-phonon configs.)
density of states in agreement with experiment
composition of states
Nuclear spectra – open-shell nuclei
first two 1- levels clearly have dominantly 2-phonon origin
11
- … 91% 2-phonon1
2- … 78% 2-phonon
G. De Gregorio, F. Knapp, N. Lo Iudice, P. Veselý, Phys. Rev. C 93, 044314 (2016)
recent experimental measurement on 20O N. Nakatsuka et al., Physics Letters B 768, 387–392 (2017)
Ex (MeV) ISD EWSR(%)
5.660 0.59
6.617 2.19
[exp.] E. Tryggestad et al., Phys. Rev. C 67, 064309 (2003)
Nuclear spectra – odd nuclei
explicit coupling of nucleon to general excitations of the nuclear core
then diagonalization of complete Hamiltonian
Hilbert space – divided into separate n-phononsubspaces
Tamm-Dancoff phonons
Nuclear spectra – odd nuclei
application of EMPM on the odd nuclear systems:G. De Gregorio, F. Knapp, N. Lo Iudice, P. Vesely, Phys. Rev. C94, 061301(R) (2016)
NNN forceNN+NNN interaction - NNLO
sat (Ekström et al. Phys. Rev. C 91 (2015) 051301R )
HO basis N = (2n + l)
h = 20 MeV Nmax
up to 4
charged radii HF energy
test calculations in minimal configuration spacebut most of qualitative effect from NNN already there!
NNN interaction shrinks gaps between major shells
radial density
NNN forceNN+NNN interaction - NNLO
sat (Ekström et al. Phys. Rev. C 91 (2015) 051301R )
HO basis N = (2n + l)
h = 20 MeV Nmax
up to 4
charged radii HF energy
test calculations in minimal configuration spacebut most of qualitative effect from NNN already there!
TDA calculation of photoabsorption cross section – shrinked s.p. spectra shifts giant resonance down in energy
NNN interaction shrinks gaps between major shells → important for correct description of giant resonance
Description of hypernucleiapplication of approach HF(B)+(Q)TDA+EMPM on exotic nuclear systems → single hypernuclei
NN+NNN interaction - NNLOsat
(Ekström et al. Phys. Rev. C 91 (2015) 051301R )
ΛN interaction - LO (H. Polinder, J. Haidenbauer, U. Meissner, Nucl. Phys. A 779 (2006) 244)cut-off = 550 MeV
extension of HF+TDA formalism on hypernuclei → proton-neutron- HF + N TDA
(replacement of the nucleon by )
formalism derived also for 3-body NN forces – but these forces not present yet (only leading order N interaction used) … alternatively NN may appear indirectly as SRG induced from N
main effect of 3-body NNN force on single particle energies of:
interacts with nuclear core via N interaction
NNN force modifies nuclear core (distribution of density, s.p. energies of nucleons)
modification of nuclear core modifies single particle energies of
so far implemented:
NNN force – effect on hypernuclei
NN+NNN interaction - NNLOsat
(Ekström et al. Phys. Rev. C 91 (2015) 051301R )
ΛN interaction - LO (H. Polinder, J. Haidenbauer, U. Meissner, Nucl. Phys. A 779 (2006) 244)cut-off = 550 MeV
HO basis
N = (2n + l)
Nmax
up to 4
h = 20 MeV
only qualitative study → we need to enlarge configuration space
sd-shell in hypercarbon not realistic due to small space
main effect:
NNN force shrinks gaps between major shells also for !
relative energies between s- & p- shells realistic but absolute scale wrong
Problems:
- wrong order spin-orbit partners 0p
3/2 & 0p
1/2 in
hyperoxygen
- strong dependence on cut-off of N force
s.p. energies:
NNN force – effect on hypernuclei
NN+NNN interaction - NNLOsat
(Ekström et al. Phys. Rev. C 91 (2015) 051301R )
ΛN interaction - LO (H. Polinder, J. Haidenbauer, U. Meissner, Nucl. Phys. A 779 (2006) 244)cut-off = 550 MeV
NN+NNN interaction - NNLOsat
ΛN interaction - LO
NN interaction - NNLOopt
ΛN interaction - LO
NNN force – effect on hypernuclei
NN+NNN interaction - NNLOsat
(Ekström et al. Phys. Rev. C 91 (2015) 051301R )
ΛN interaction - LO (H. Polinder, J. Haidenbauer, U. Meissner, Nucl. Phys. A 779 (2006) 244)cut-off = 550 MeV
to solve problems – highly desirable to improve ΛN interaction: NLO N includes the tensor term which may solve problem of 0p
3/2 & 0p
1/2
documented by toy model calculation with purely phenomenological tensor term
also necessity to implement mixing
NLO N interaction
where
17
0p3/2
0p1/2
0s1/2
Outlook - further study on effect of NNN interaction (revision of results of EMPM) - further improvements of multiphonon calcs. (3-phonon in Ca isotopes) - study on odd-odd nuclei - application of EMPM on other effects – beta or double-beta decays - calculations of deformed nuclei - in hypernuclei: - Effect of - coupling and improvment of N interaction - Coupling of single particle with phonon and multi-phonon configurations - Any other ideas for further improvements are welcome
List of Collaborators
Thank you!!
Nuclear Physics Institute, Czech Academy of Sciences
Petr VeselýJan PokornýGiovanni De GregorioPetr Bydžovský
Institute of Nuclear and Particle Physics, Charles University
František Knapp
Universita degli Studi Federico II, Napoli
Nicola Lo Iudice