Download presentation

Presentation is loading. Please wait.

Published byKimberly McCormack Modified over 4 years ago

1
Neutron-Rich Nuclei within a realistic shell-model approach Angela Gargano Napoli A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli L. Coraggio (Napoli) A. Covello (Napoli) N. Itaco (Napoli) T.T.S. Kuo (Stony Brook )

2
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Plan of the talk Theoretical framework : Renormalization of the bare NN potential by means of the V low-k approach Derivation of the model space effective interaction by means of the plus folded diagram method Outline of calculations Results: neutron-rich nuclei northeast of 132 Sn and comparison with conterpart nuclei in the stable 208 Pb region neutron-rich Ca isotopes neutron-rich C isotopes Summary

3
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Shell-model calculations 3. Two-body matrix elements 1. Model space 2. Single-particle energies (taken from the experimental spectra of nuclei with one-valence nucleon or treated as free parameters) 4. Construction and diagonalization of the energy matrices Traditional approach: Two-body matrix elements treated as free parameters Two-body matrix elements treated as free parameters Empirical effective interactions containing adjustable parameters Empirical effective interactions containing adjustable parameters [e.g., s-d shell nuclei, B. A. Brown and B. H. Wildenthal, Ann. Rev. Nucl. Part. Sci.38, 28(1988)] defined within a reduced model space and acting only between valence nucleons

4
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Ab-initio calculations: Greens function Montecarlo method, no-core shell model, coupled cluster method, UCOM (three-nucleon interactions have been also taken into account ) nuclear properties, such as binding and excitation energies, are calculated directly from first principles of quantum mechanics, using an appropriate computational scheme Challenge for nuclear physics : understand the properties of nuclei starting from the forces among nucleons

5
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Realistic shell-model calculations: We start from where U is a one-body auxiliary potential introduced to define a convenient single-paticle basis and define the effective shell-model Hamiltonian through the model-space Schrödinger equation where the E and the corresponding are required to be a subset of the eigenvalues and eigenvectors of the original Hamiltonian The P operator projects into the chosen model space

6
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli all modern NN potentials fit equally well the deuteron properties and the NN scattering data up the inelastic threshold 2 /N data ~ 1 Choice of the nucleon-nucleon potential Derivation of V eff Note these potentials cannot be used directly in the derivation of V eff due to their strong short-range repulsion, but a due to their strong short-range repulsion, but a Renormalization procedure is needed Renormalization procedure is needed CD-Bonn, Argonne V 18, Chiral potentials,…

7
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Renormalization of the NN interaction Traditional approach: Brueckner G-matrix method V low-k approach: construction of a low-momentum NN potential V low-k confined within a momentum-space cutoff S. Bogner,T.T.S. Kuo,L. Coraggio,A. Covello,N. Itaco, Phys. Rev C 65, 051301(R) (2002) S. Bogner, T.T.S. Kuo, A. Schwenk, Phys. Rep. 386, 1 (2003). L. Coraggio et al, Prog. Part. Nucl. Phys. 62 (2009) 135

8
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli V low-k approach Derived from the original V NN by integrating out the high-momentum components of the original V NN potential down to the cutoff momentum V low-k decouples high- and low-energy degrees of freedom preserves the physics of the original NN interaction the deuteron binding energy scattering phase-shifts up to the cutoff momentum Λ How to contruct V low-k ? Effective interaction technique based on the the Lee-Suzuki similariry transformation (Prog. Theor Phys 64 (1980) 2091 ) low-momentum space Q complementary space X similarity transformation Decoupling equation solved by the iterative procedure proposed by Andreozzi (Phys Rev. C 54 (1996) 684)

9
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Features of V low-k real effective potential in the momentum space (indipendent from the starting energy or from the model space, as instead the case of the G matrix defined in the nuclear medium) eliminates sources of non-perturbative behavior can be used directly in nuclear structure calculations gives an approximately unique representation of the NN potential for 2 fm -1 E Lab 350 MeV - V low-k s extracted from various phase-shift equivalent potentials are very similar to each other Note V low-k is developed for the two-body system èfor A>2 the low-energy observables are not the same of the original NN potential of the original NN potential and depend (to a certain extent) on the value of and depend (to a certain extent) on the value of This may be removed complementing the two-body V low-k with three- and higher-body components

10
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli + folded diagram method collection of irreducible valence-linked diagrams with V low-k replacing V NN in the interaction vertices FiFi i-folded diagrams (expressed in terms ofderivatives) T.T.S. Kuo and E. Osnes, Lecture Notes in Physics, vol 364 (1990) L. Coraggio et al, Prog. Part. Nucl. Phys. 62 (2009) 135 V eff,constructed for two valence particles, is defined - in the nuclear medium - in a subspace of the Hilbert space accounts perturbatively for configurations excluded from the chosen model space excitations of the core nucleons developed within the framework of the time-dependent perturbative approach by Kuo and co-workers

11
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Calculation of : inclusion of diagrams up to a finite order in the interaction truncation of the intermediate-state summation Sum of the folded series by the Lee-Suzuki method [Prog. Theor. Phys. 64, 2091 (1980)] + + … Construction of V eff NoteNote Diagramatic expression of the single-particle energies TB component of the shell-model Hamiltoniam

12
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Results

13
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli neutrons protons nuclei beyond the N=82 shell n-rich nuclei n-rich Ca isotopes n-rich C isotopes magic nature of 132 Sn? N=34 shell closure? location of the neutron drip line?

14
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli 132 Sn region CD-Bonn + V low-k : second-order calculation Single-particle energies from the experimental spectra of 133 Sb and 133 Sn 132 Sn core Valence neutron levels: 1f7/2, 2p3/2, 0h9/2, 2p1/2, 1f5/2, 0i13/2 Valence proton levels: 0g7/2, 1d5/2, 1d3/2, 0h11/2, 2s1/2 n-rich Ca isotopes CD-Bonn + V low-k : third-order calculation Single-neutron energies from a fit to exp energies of 47 Ca and 49 Ca 40 Ca core Valence neutron levels: 0f7/2, 0f5/2, 1p3/2, 1p1/2 n-rich C isotopes N 3 LOW [ chiral potential with a sharp momentum cutoff at 2.1 fm -1 ] : third-order calculation Theoretical single-neutron energies 14 C core Valence neutron levels: 0d5/2, 0d3/2, 1s1/2 Input of our calculations

15
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Theory B(E2;0 + 2 + ) = 0.033 e 2 b 2 134 Sn Coulex (Oak Ridge) B(E2;0 + 2 + ) = 0.029(4) e 2 b 2 Theory 0.726 134 S n Expt. from the f 7/2 p 1/2 configuration their location below the 8 + due to the new position of the p 1/2 level measured @ ORNL p1/2 =1.36 MeV (old value: 1.66 MeV) [Nature 465 (2010)]

16
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli 134 Sn 132 Sn + 2 ( f 7/2 ) 2 multiplet 210 Pb 208 Pb + 2 ( g 9/2 ) 2 multiplet J J

17
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli J 136 Sn 132 Sn + 4 212 Pb 208 Pb + 4

18
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli A 134 Sn 135 Sn 136 Sn 137 Sn BE Calc relative to 132 Sn 5.918.3011.8614.18 BE Expt relative to 132 Sn 5.92* BE/A Calc8.278.238.208.15 N/Z 1.70 1.72 1.74 1.68 124 Sn(stable) with N/Z=1.48 BE/A=8.46 * M. Dworschak et al. Phys. Rev. Lett. 100, (2008) 072501 Old value (Fogelberg et al., 1999): 6.365 MeV neutron shell gap at N= 82 restored

19
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli B(E2;4 2 ) = 1.64 W.u. B(E2;6 4) = 0.81 W.u. B(E2;2 2 2) = 0.34 W.u. B(E2;2 2 4) = 0.22 W.u. Q(2) = -1.3 efm 2 µ(2) = -0.56 nm 134 Sn (Theoretical predictions)

20
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli 136 Sb is at present the most exotic open-shell nucleus beyond 132 Sn for which information exists on excited states 136 Sb Expt Theory

21
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli L. Coraggio et al. Phys. Rev. C 80, (2009) 044311 J.J. Valiente Dobón et al. PRL 102, 242502 (2009) ExptTheory ExptTheory 50 Ca 52 Ca

22
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Ca isotopes - Ground-state energy per valence neutron A

23
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli A * M. Honma et al. EPJ A 25, 499 (2005 ) * no shell gap at N=34 Ca isotopes Excitation energies of the J =2 1 + states

24
Effective single particle energies of the f 5/2 and p 1/2 levels (relative to the p 3/2 level ) A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli

25
-427 keV * A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli C isotopes from 16 C to 24 C – ground-state energy ( relative to 14 C ) *to reproduce the exp g.s. energy of 15 C relative to 14 C E gs (calc)=-0.79 ; E gs (exp)= -1.22 MeV 22 C is the last bound isotope K. Tanaka et al PRL 104, 062701 (2010) S 2n (evaluation)=420 keV S 2n (calc)=601 keV L. Coraggio et al. PR C 81, 064303 (2010)

26
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli C isotopes Excitation energies of the J =2 1 + states ESPE (MeV) N no subshell closure at N=14 g.s. in 20 C: 14% of ( d 5/2 ) 6 configuration

27
A. Gargano JAPEN-ITALY EFES Workshop Torino- 2010 Napoli Reliability of realistic shell-model calculations for light heavy nuclei This outcome gives confidence in its predictive power, and may stimulate and be helpful to future experiments. Three-body forces seem to contribute mainly to the absolute energy of the single-particle. Role of three-body forces needs futher investigations It is of key importance to gain more experimental information Summary

Similar presentations

OK

M. Girod, F.Chappert, CEA Bruyères-le-Châtel Neutron Matter and Binding Energies with a New Gogny Force.

M. Girod, F.Chappert, CEA Bruyères-le-Châtel Neutron Matter and Binding Energies with a New Gogny Force.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google