Masses and Structure in Exotic Nuclei R. F. Casten WNSL, Yale Eurorib’10, June, 2010

1. Masses and Structure in Exotic NucleiR. F. CastenWNSL, Yale Eurorib’10, June, 2010

2. Structural Evolution: Simple Observables - Even-Even Nuclei 2+ 1300 1000 4+ 400 2+ Masses 0 0+ Jπ E (keV)

3. Rotor E(I)  (ħ2/2I )I(I+1) R4/2= 3.33 Doubly magic plus 2 nucleons R4/2< 2.0 Vibrator (H.O.) E(I) = n (0 ) R4/2= 2.0 8+. . . 6+. . . n = 2 2+ n = 1 0+ n = 0

4. Broad perspective on structural evolution The remarkable regularity of these patterns is one of the beauties of nuclear structural evolution and one of the challenges to nuclear theory. Whether they persist far off stability is one of the fascinating questions for the future R. B. Cakirli

5. Structural evolution – rapid structural change Spherical-deformed trans. Near N ~ 90 Cakirli

6. Rotor R4/2 across this region Vibrator ! Often, esp. in exotic nuclei, R4/2 is not available. E(21+) is easier to measure, works as well !!! Better to use in the form 1/ E(21+)

7. Physics from different perspectives Mid-sh. magic Onset of deformation as a phase transition mediated by a change in shell structure Onset of deformation “Crossing” and “Bubble” plots as indicators of phase transitional regions mediated by sub-shell changes Cakirli and Casten, PRC 78, 041301(R) (2008)

8. The importance of the p-n interaction Sn – Magic: no valence p-n interactions Both valence protons and neutrons

9. Potentials involved In Phase transitions Microscopic origins of phase transitional behavior Valence pn interactions

10. Can we Measure p-n Interaction Strengths? dVpn Average p-n interaction between last protons and last neutrons Double Difference of Binding Energies Vpn (Z,N)  =  ¼ [ {B(Z,N) - B(Z, N-2)}  -  {B(Z-2, N) - B(Z-2, N-2)} ] Ref: J.-y. Zhang and J. D. Garrett

11. Valence p-n interaction: Can we measure it? Vpn (Z,N)  =  ¼[ {B(Z,N) - B(Z, N-2)} -  {B(Z-2, N) - B(Z-2, N-2)} ] - - - p n p n p n p n - Int. of last two n with Z protons, N-2 neutrons and with each other Int. of last two n with Z-2 protons, N-2 neutrons and with each other Empirical average interaction of last two neutrons with last two protons Cakirli based on Zhang and Garrett

12. Empirical interactions of the last proton with the last neutron Vpn (Z, N) = ¼{[B(Z, N ) – B(Z, N - 2)] - [B(Z - 2, N) – B(Z - 2, N -2)]}

13. dVpn has singularities for N = Z in light nuclei • Wigner energy, related to SU(4), supermultiplet theory, spin-isospinsymmetry. • Physics is high overlaps of the last proton and neutron wave functions when they fill identical orbits. • Expected to vanish in heavy nuclei due to: Coulomb force for protons; spin-orbit force which brings UPOs into different positions in each shell; protons and neutrons occupy different major shells. This effect should not persist in heavy nuclei. Does it? In a way, yes!

14. Rare-earth region 62Sm: dVpn(max) at N=94: 12 valence protons, 12 valence neutrons Gd 14-14 (?) , Dy  16-16 (?), Er  18-18, Yb  20-20, Hf, W  22,24, and 24,24 dVpnhas peaks for Nval ~ Zval !!!! considering only the number of valence particles, a possible mini-valence Wigner energy !! R. B. Cakirli, R. F. Casten and K. Blaum, to be published

15. Agreement is remarkable. Especially so since these DFT calculations reproduce known masses only to ~ 1 MeV – yet the double difference embodied in dVpn allows one to focus on sensitive aspects of the wave functions that reflect specific correlations M. Stoitsov, R. B. Cakirli, R. F. Casten, W. Nazarewicz, and W. Satula PRL 98, 132502 (2007)

16. Masses, Separation energies Models Exp. A “de-linearization” approach

17. BindingEnergies Two-neutron separation energies Normal behavior: ~ drops after closed shells with linear segments in between Discontinuities at first order phase transitions Note that the range of values in S2nis ~ 18 MeV

18. Many Methods to estimate • Mass models – semi-empirical • Microscopic calculations – many approaches including RMFT, DFT, etc • Collective models – e.g., IBA, for the collective contribution to binding • A new approach – pattern recognition techniques, • aided by a linear subtraction method

19. Collective contributions to masses can vary significantly for small parameter changes in collective models, especially for well-deformed nuclei where collective binding can be quite large. S2n(Coll.) for alternate fits to Er with N = 100 Gd – Garcia Ramos et al, 2001 Masses: a new opportunity – complementary observable to spectroscopic data in pinning down structure. Strategies for best doing that are still being worked out. Particularly important far off stability where data will be sparse. Cakirli, Casten, Winkler, Blaum, and Kowalska, PRL 102, 082501(2009)

20. Pattern Recognition “Physics-free” (therefore not biased) – can it tell us any physics??? Analyse the 2-D “surface” of an observable by Fourier transforms Extrapolate to predict observables in unknown regions How good is it? To date and longer term prospects Try on separation energies. Test case: mask portion of data

21. Pattern recognition for separation energies – Not so good. Rapidly accumulate errors of a few MeV . Can we do better?

22. Remove the linear dependence S2n-TOTAL = S2n-Linear + S2n-coll. isolate and amplify collective effects More sensitive tests of nuclear models

23. Subtract linear function, A + BN, from S2n plot S2n-coll. (Z=50-82, N=82-126) Cakirli, Casten and Blaum, in progress The range of S2nis now~ 2-3 MeV

24. S2n-total S2n-collective Greatly enhanced sensitivity of S2n-coll.

25. Now use pattern recognition to fit the S2n-coll values. Then add back the linear function Very good agreement. Extrapolating ~ 12 mass units Pb Nd Frank, Morales, Cakirli, Casten and Blaum, in progress Work is in progress. Where will it lead? We don‘t have a clue. We will see. Work just beginning.

26. Principal Collaborators R. BurcuCakirli Klaus Blaum MagdaKowalska Alejandro Frank Irving Morales

27. Backups

28. Correlations of Collective Observables 4+ 2+ 0+