Application of Equation of Motion Phonon Method to Nuclear and Exotic Nuclear Systems

Application of Equation of Motion Phonon Method to Nuclear and Exotic Nuclear Systems Petr Veselý Nuclear Physics Institute, Czech Academy of Sciences gemma.ujf.cas.cz/~p.vesely/ seminar at UTEF ČVUT, Prague, November 2017

Motivation Physics of atomic nucleus: about 2500 known isotopes, 263 stable isotopes estimate 4000 unobserved yet

Motivation Physics of (hyper)nuclei: we add 3rd dimension to our nuclear chart

Motivation Physics 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 What we see depends on resolution: < 0.0001 fm: quarks 0.1-1 fm : baryons, mesons 1 fm: nucleons 10 fm : collective modes

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 Central force Long range Intermediate scalar meson + Tensor force + Exchanges of different types of mesons Building blocks (138) (600) (782) (770)

NN interaction Existence of more-body interactions between nucleons As consequence of inner structure of nucleons Analogy between NN and Van der Waals interaction NN force not so much strong!

NN interaction Possible approach to derive NN interactions Effective field theory instead of QCD field theory with elem. degrees of freedom (quarks, gluons) we build field theory with nucleons and pions. Must obey the same symmetries as QCD > Chiral Perturbation Theory (ChPT) Only mesons here are pions. But pion exchanges 2, 3, till any order. Multi-pion exchanges replace presence of other types of mesons. Diagrams of NN scatering can be divided to orders perturbative theory (?)

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 Magic numbers 2,8,20,28,50,126 How shell structure occurs in nucleus?

What is mean-field in nucleus? How mean field occurs in nucleus? change our perspective nucleons as non-interacting particles in 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 properties NN interaction - chiral NNLOopt 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 properties 2 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) Pb 208 C = 0 C = 2000 C = 3000 DD term shrink gaps between major shells radial density

Equation of Motion Phonon Method 1ph excitations Tamm-Dancoff phonons 2ph excitations and in general more -ph excitations Hilbert space divided into separate n-phonon subspaces

Equation of Motion Phonon Method total Hamiltonian mixes configurations from different Hilbert subspaces Equation of Motion (EoM) recursive eq. to solve eigen-energies on each i-phonon subspace while knowing the (i-1)-phonon solution 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 NN interaction - chiral NNLOopt 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) Nmax maximal osc. shell (defines how big basis is) h parameter of basis EHF EHF+Ecorr. Final energy must be converged with respect to Nmax and for Nmax big enough independent on h

Nuclear ground state properties NN interaction - chiral NNLOopt 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 spectra 2-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 = 0 C = 2000 C = 3000 study of the dipole photoabsorption spectrum B(E1, 0+g.s. 1-exc.) 2-phonon configurations very important to describe richness of spectrum multifragmentation of dipole resonance... we describe width of res. most of 1- states have configurations beyond 1ph

Quasiparticles in nuclei nuclei with semi-closed shell nucleons jumping between energetically very close levels smearing of Fermi energy occupations of levels 0 < Vi2 < 1 becomes probabilistic quasiparticle states - partially occupied orbits

Nuclear spectra open-shell nuclei quasiparticle 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 20 O much richer low lying spectrum (with 2-phonon configs.) density of states in agreement with experiment composition of states

Nuclear spectra open-shell nuclei G. De Gregorio, F. Knapp, N. Lo Iudice, P. Veselý, Phys. Rev. C 93, 044314 (2016) first two 1- levels clearly have dominantly 2-phonon origin 11-91% 2-phonon 12-78% 2-phonon Ex (MeV) ISD EWSR(%) 5.660 0.59 6.617 2.19 [exp.] E. Tryggestad et al., Phys. Rev. C 67, 064309 (2003) recent experimental measurement on 20O N. Nakatsuka et al., Physics Letters B 768, 387 392 (2017)

Nuclear spectra odd nuclei Tamm-Dancoff phonons Hilbert space divided into separate n-phonon subspaces explicit coupling of nucleon to general excitations of the nuclear core then diagonalization of complete Hamiltonian

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 force NN+NNN interaction - NNLOsat (Ekström et al. Phys. Rev. C 91 (2015) 051301R ) test calculations in minimal configuration space but most of qualitative effect from NNN already there! HO basis h = 20 MeV N = (2n + l) Nmax up to 4 radial density NNN interaction shrinks gaps between major shells charged radii HF energy

NNN force NN+NNN interaction - NNLOsat (Ekström et al. Phys. Rev. C 91 (2015) 051301R ) test calculations in minimal configuration space but most of qualitative effect from NNN already there! NNN interaction shrinks gaps between major shells important for correct description of giant resonance HO basis h = 20 MeV N = (2n + l) Nmax up to 4 TDA calculation of photoabsorption cross section shrinked s.p. spectra shifts giant resonance down in energy charged radii HF energy

Description of hypernuclei application 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 so far implemented: 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

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 s.p. energies: main effect: HO basis NNN force shrinks gaps between major N = (2n + l) shells also for! Nmax up to 4 relative energies between s- & p- shells h = 20 MeV realistic but absolute scale wrong only qualitative study we need to enlarge configuration space sd-shell in hypercarbon not realistic due to small space Problems: - wrong order spin-orbit partners 0p3/2 & 0p1/2 in hyperoxygen - strong dependence on cut-off of N force

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 interaction - NNLOopt ΛN interaction - LO NN+NNN interaction - NNLOsat 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 interaction NLO N includes the tensor term which may solve problem of 0p3/2 & 0p1/2 documented by toy model calculation with purely phenomenological tensor term where 17 0p3/2 0p1/2 0s1/2 also necessity to implement mixing

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 Nuclear Physics Institute, Czech Academy of Sciences Petr Veselý Jan Pokorný Giovanni De Gregorio Petr Bydžovský Institute of Nuclear and Particle Physics, Charles University František Knapp Universita degli Studi Federico II, Napoli Nicola Lo Iudice Thank you!!