The Nuclear Many-Body problem. Lecture 3

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1 The Nuclear Many-Body problem Lecture 3 Emergent phenomena at the drip lines. How do properties of nuclei change as we move towards the nuclear driplines? Many-body open quantum systems. Unification of Reaction and Structure

2 Nuclear landscape and consequences. ~ 300 stable nuclei N/Z~1 for light nuclei N/Z~1.5 for 208 Pb ~ unstable nuclei decay by α, β, 1p, 2p, 1n, cluster emission, fission

external quantum system, the environment.

4 Open Quantum Systems From Wikipedia, the free encyclopedia: In physics, an open quantum system is a quantum system which is found to be in interaction with an external quantum system, the environment. The open quantum system can be viewed as a distinguished part of a larger closed quantum system, the other part being the environment.

6 Physics of neutron rich nuclei Physics of neutron-rich nuclei requires: i. Accurate treatment of many-body correlations, ii. Proper inclusion of coupling with continuum degrees of freedom and open channels iii. Inclusion of both two- and three-nucleon forces. Physics of neutron rich nuclei Many-body correlations Open channels Interactions

7 Nuclear halos a manifestation of openness 11 Li matter radii unusually large compared to neighboring nuclei. 11 Li is the holy grail of nuclear halos I. Tanihata et al, Phys. Rev. Lett. 55, 2676 (1985) Borromean Rings

8 Carbon-22, which has a nucleus comprised of 16 neutrons and 6 protons, is the heaviest atom yet discovered to exhibit a "halo nucleus."

9 Modification and quenching of shell structure at the dripline. 25 O neutron separation energy: -820 kev the width was measured to be 90(30) kev giving a lifetime of t ~ 7x10-21 sec C. Hoffman PRL 100, (2008).

function: Large spectroscopic factor for the removal of a neutron in the s 1/2

10 Spectroscopic factors as a signature of shell closure? The spectroscopic factor is defined as the norm of the one-nucleon overlap function: Large spectroscopic factor for the removal of a neutron in the s 1/2 orbit points to shell closure in 24 O. Ø. Jensen et al arxiv: v1 R. Kanungo et al, Phys. Rev. Lett. 102, (2009).

Threshold effects and spectroscopic factors. Near the scattering threshold for one-neutron decay the spectroscopic factors are Significantly influenced by the presence of The continuum.

11 Threshold effects and spectroscopic factors. Near the scattering threshold for one-neutron decay the spectroscopic factors are Significantly influenced by the presence of The continuum. The standard shell model approximation to spectroscopic factors completely fails in this region. N. Michel et al Phys. Rev. C 75, (2007) N. Michel et al Nucl. Phys. A 794, 29 (2007) Top and middle: Bottom :

12 Modification of shell structure at the drip lines! Quenching of 82 shell gap when neutron drip line is approached. Also observed in lighter nuclei Caution: Shell structure seen in many observables. J. Dobaczewski et al, PRL 72 (1994) 981.

First ab-initio description of the parity inverted ground state in 11

13 Ab-initio no-core shell model and resonanting group method for scattering. First ab-initio description of the parity inverted ground state in 11 Be. Phase shifts for scattering of neutrons on 4 He using the NCSM/RGM approach. S. Quaglioni and P. Navratil, Phys.Rev.Lett.101:092501,2008

14 Continuum induced correlations and effects on binding energies Continuum shell model calculations of oxygen isotopes. The effect of continuum correlations for nuclei with low neutron emission thresholds can be significant. N. Michel et al, J. Phys. G (2010).

The effect of continuum correlations Is significant on the ½ + proton halo state and on the d3/2-

15 Coupled-cluster and continuum correlations in the singleparticle states of 17 F and 17 O. Single particle states in 17 F. The effect of continuum correlations Is significant on the ½ + proton halo state and on the d3/2- d5/2 spin-orbit splitting. G. Hagen et al, Phys. Rev. Lett. 104, (2010) Coupled-cluster calculations of bound And unbound single-particle states in 17 F and 17 O.

18 Theory does not support the existence of a tetra neutron.

Superheavy hydrogen isotopes. The most exotic system ever found! System with a N/Z =6 can exist! Gives important information on the existence of a tetra neutron (4N).

19 Superheavy hydrogen isotopes. The most exotic system ever found! System with a N/Z =6 can exist! Gives important information on the existence of a tetra neutron (4N). Fitting to a Breit-Wigner distribution the extracted resonance value is 0.57 MeV above the 3H+4N threshold and with a width 0.09 MeV. Need for theory!! ( 2007 ) M. Caamano PRL 99,

20 Clustering in nuclei a near threshold phenomena

21 Cluster states near threshold. 8 Be 12 C

23 Halo structures Thomas-Ehrmann effect C+n C+p 3/2 1/ /2 13 C 7 13 N 6 Spectra and matter distribution modified by the proximity of scattering continuum

24 8He charge radii: theory vs. experiment 8He charge radii measurements using the measured isotope shift with the help of precision atomic theory calculations. ( 2007 ) P. Mueller et al., PRL 99,

25 Unification of structure and reaction (i) Spectra and matter distribution modified by the proximity of scattering continuum (ii) Structure of nuclei impact on scattering and reaction properties Need for unification of 'structure' and 'reaction'

Major challenges for nuclear theory Mathematical formulation within the Hilbert space of nuclear states embedded in the continuum of decay channels goes back

- develop theories and algorithms that would allow to understand properties of those exotic physical systems - unify structure and reaction aspects of

(1977-1999 - 2005) H.W.Bartz et al, NP A275 (1977) 111 R.J. Philpott, NP A289 (1977) 109 K. Bennaceur et al, NP A651 (1999) 289 J.

26 Major challenges for nuclear theory Mathematical formulation within the Hilbert space of nuclear states embedded in the continuum of decay channels goes back to H. Feshbach ( ), U. Fano (1961), and C. Mahaux and H. Weidenmüller (1969). - develop theories and algorithms that would allow to understand properties of those exotic physical systems - unify structure and reaction aspects of weakly-bound or unbound nuclei based on the open quantum system (OQS) formalism Open quantum system many-body framework Continuum (real-energy) Shell Model ( ) H.W.Bartz et al, NP A275 (1977) 111 R.J. Philpott, NP A289 (1977) 109 K. Bennaceur et al, NP A651 (1999) 289 J. Rotureau et al, PRL 95 (2005) Gamow (complex-energy) Shell Model (2002 -) N. Michel et al, PRL 89 (2002) R. Id Betan et al, PRL 89 (2002) N. Michel et al, PRC 70 (2004) G. Hagen et al, PRC 71 (2005) J. Rotureau et al, PRL 97 (2006)

states embedded in the continuum. Need for unifying nuclear structure and reaction theory.

27 Summary of Open-Quantum Systems Physics of nuclei beyond the valley of beta stability is very challenging. Properties emerge towards the drip lines not seen in ordinary stable matter such as : Halo densities, extreme matter clusterization, and bound states embedded in the continuum. Need for unifying nuclear structure and reaction theory. Discussion: What are the characteristics of halo nuclei? What can we learn about the nuclear interaction from the physics of halo nuclei? What are the signatures for shell closure? How do we determine whether we have a new magic number?

Nuclear structure theory

Nuclear structure theory Thomas Papenbrock and Lecture 2: Traditional shell model National Nuclear Physics Summer School 2008 George Washington University Shell structure in nuclei Mass differences: Liquid