1. LIVING WITH TRANSFER AS AN EXPERIMENTAL SPECTROSCOPIST WILTON CATFORD TRENTO WORKSHOP 4-8 Nov 13 FROM NUCLEAR STRUCTURE TO PARTICLE-TRANSFER REACTIONS AND BACK

2. NIGEL WILTON FRIENDS, …. LET’S TALK FRANKLY …. here is (almost) everything that confuses me and which I think is challenging in the interpretation of transfer reaction data

3. 1p3/2 Stable Exotic 1p3/2 Stable Exotic Utsuno et al., PRC,60,054315(1999) Monte-Carlo Shell Model (SDPF-M) N=20 Exotic Stable Removing d5/2 protons (Si  O) gives relative rise in (d3/2) Note: This changes collectivity, also…

4. Example of population of single particle state: 21 O 0d 5/2 1s 1/2 0d 3/2 The mean field has orbitals, many of which are filled. We probe the energies of the orbitals by transferring a nucleon This nucleon enters a vacant orbital In principle, we know the orbital wavefunction and the reaction theory But not all nuclear excited states are single particle states… 0d 5/2 1s 1/2 energy of level measures this gap J  = 3/2 + 2+2+ x 1/2 + We measure how the two 3/2 + states share the SP strength when they mix A. SINGLE PARTICLE STATES – EXAMPLE

5. SINGLE PARTICLE STATES – SPLITTING Plot: John Schiffer If we want to measure the SPE, splitting due to level mixing means that all components must be found, to measure the true single particle energy

6. But, in the presence of all these interesting issues, remember… Things to consider in measurements of the single-particle strength for a state can use single-nucleon transfer and “standard” spectroscopic factor method can use alternative ANC method that avoids some ambiguities in parameters can combine the two, to avoid model dependence (TexasA&M, MSU, Surrey) use high energy removal reactions (e.g. J.A. Tostevin approach) for hole states Also need to consider quenching of pure shell model spectroscopic factors for strongly bound nucleons effect of using realistic wavefunctions for transferred nucleon, or “standard well” breakup of deuteron (treat with R.C. Johnson approach, “Johnson-Soper” ADWA) And what do we really compare with? Clearly, the Large Basis Shell Model, but how exactly? Using a standard parameter set and ADWA, compare (unquenched) SM values Using realistic wavefunctions and ADWA, compare quenched values (cf knockout)

7. Ultimately, with single particle transfer reactions, we can certainly: make the measurements to highlight strong SP states measure the spin/parity for strong states associate experimental and Shell Model states and see when the shell model works (energies and spectroscopic factors) when the shell model breaks down whether we can adjust the interaction and fix the calculation how any such modifications can be interpreted in terms of NN interaction And clearly: monopole shifts need to be measured and understood because the changes In energy gaps fundamentally affect nuclear structure (collectivity, etc.)

8. A PLAN for how to STUDY STRUCTURE Use transfer reactions to identify strong single-particle states, measuring their spins and strengths Use the energies of these states to compare with theory Refine the theory Improve the extrapolation to very exotic nuclei Hence learn the structure of very exotic nuclei N.B. The shell model is arguably the best theoretical approach for us to confront with our results, but it’s not the only one. The experiments are needed, no matter which theory we use. N.B. Transfer (as opposed to knockout) allows us to study orbitals that are empty, so we don’t need quite such exotic beams.

9. USING RADIOACTIVE BEAMS in INVERSE KINEMATICS Single nucleon transfer will preferentially populate the states in the real exotic nucleus that have a dominant single particle character. Angular distributions allow angular momenta and (with gammas) spins to be measured. Also, spectroscopic factors to compare with theory. Around 10A MeV/A is a useful energy as the shapes are very distinctive for angular momentum and the theory is tractable. Calculated differential cross sections show that 10 MeV/A is good (best?)

10. 2030 1680 = 2 = 0 5/2+ 3/2+ 1/2+ = 2 0.80 0.15 0.44 1/2+ 3/2+ 5/2+ 3/2+ 5/2+ 9/2+ 7/2+ 5/2+ 0.49 0.10 0.11 0.004 n+ 24 Ne gs USD 0.63 In 25 Ne we used gamma-gamma coincidences to distinguish spins and go beyond orbital AM FIRST QUADRUPLE COINCIDENCE (p-HI-  -  ) RIB TRANSFER DATA Inversion of 3/2+ and 5/2+ due to monopole migration Summary of 25Ne Measurements Negative parity states (cross shell) also identified 4030 3330  = – = 1 ( = 3) 7/2 – 3/2 – 0.73 0.75 W.N. Catford et al., PRL 104, 192501 (2010)

11. 25 Ne 27 Ne 27 Ne 17 d3/2 level is 2.030 25Ne 4.03 1.80 0.76 3.33 1.80 7/2  0.76 3/2  N=17 ISOTONES ISOTOPE CHAINS MgNe

12. 27 Ne results we have been able to reproduce the observed energies with a modified WBP interaction, full 1hw SM calculation the SFs agree well also most importantly, the new interaction works well for 29 Mg, 25 Ne also so we need to understand why an ad hoc lowering of the fp-shell by 0.7 MeV is required by the data!

13. More on N=15 Odd d 5/2 proton  25 Ne states Probe p-n interaction across N=20 25 Na (d,p) 26 Na

14. CX FUSION-EVAP 26 Na had been studied a little, beforehand (N=15, quite neutron rich) ALL of the states seen in (d,p) are NEW (except the lowest quadruplet) We can FIND the states with simple structure, Measure their excitation energies, and feed this back into the shell model negative parity positive parity

15. Johnson-Soper Model: an alternative to DWBA that gives a simple prescription for taking into account coherent entangled effects of deuteron break-up on (d,p) reactions [1,2] does not use deuteron optical potential – uses nucleon-nucleus optical potentials only formulated in terms of adiabatic approximation, which is sufficient but not necessary [3] uses parameters (overlap functions, spectroscopic factors, ANC’s) just as in DWBA [1] Johnson and Soper, PRC 1 (1970) 976 [2] Harvey and Johnson, PRC 3 (1971) 636; Wales and Johnson, NPA 274 (1976) 168 [3] Johnson and Tandy NPA 235 (1974) 56; Laid, Tostevin and Johnson, PRC 48 (1993) 1307 Spectroscopic Factor Shell Model: overlap of  (N+1)  with  (N)  core  n ( j) Reaction: the observed yield is not just proportional to this, because the overlap integral has a radial-dependent weighting or sampling REACTION MODEL FOR (d,p) TRANSFER – the ADWA WILTON CATFORD JUNE 2008

16. Spectroscopic Factor Shell Model: overlap of  (N+1)  with  (N)  core  n ( j) Reaction: the observed yield is not just proportional to this, because the overlap integral has a radial-dependent weighting or sampling Hence the observed yield depends on the radial wave function and thus it depends on the geometry of the assumed potential well or other structure model REACTION MODEL FOR (d,p) TRANSFER – the ADWA WILTON CATFORD JUNE 2008 overlap integral spectroscopic factor Actual wave function: orbital n ( j) in  (N+1)  may not be the same as the shell model n ( j) as implicitly assumed in SM spectroscopic factor

17. u(r) V(r) REMARKS ABOUT INTERPRETING (d,p) TRANSFER Geometry Correlations Desire Relatives Peripheral: forward angles, lower energies E b defines the wavefunction asymptotics Independence of the ANC on geometry Geometry Dependence of high energy (d,p) on geometry Is the effective well geometry even the same for all orbitals? (coupled channels treatments address this) surface region

18. REMARKS ABOUT INTERPRETING (d,p) TRANSFER Geometry Correlations Desire Relatives J J States built in SM space J states are mixed by residual interactions … and are not pure SP states mixing via SHORT RANGE correlations MY ANSWER: WEIGHTED E x S.P. energies If the quenched SF’s are used Don’t use “traditional” method of calculating weighted SPE Do use the “traditional” SF that can be compared to SM Use SM SF to associate experimental and SM states Use this to refine SM residual interaction Gain improved understanding of important structural effects WEIGHTED E x S.P. energies (traditional approach) Must use SM SF’s (not quenched)

19. WHAT DO WE WANT TO MEASURE? REMARKS ABOUT INTERPRETING (d,p) TRANSFER Geometry Correlations Desire Relatives MY ANSWER: Both “quenched” and “SM comparable” are interesting They tell us about different things We need to be clear, always, which we think we are discussing There is still this problem that (SM orbital)  (actual orbital) e.g. halo state THE SPECTROSCOPIC FACTOR HAS TWO (at least!) PROBLEMS: Occupancy of SM geometry orbital (cf e.g. Oxbash output) Occupancy of actual nuclear orbital Is it the occupancy of some defined orbital that may not equal the actual orbital in the real nucleus? Do we want to measure the “quenched” (= “real”) or the “shell model” (= “comparable”) SF ?

20. REMARKS ABOUT INTERPRETING (d,p) TRANSFER Geometry Correlations Desire Relatives ARE RELATIVE SF’s MORE ACCURATE THAN ABSOLUTE? … ALWAYS? If so, is this good enough? Possible to live with? If not, um… really? Can we really believe the quenching measured with transfer SF’s ? As much as for knockout? If not, what about astrophysics ?

21. Formalism used in present work

22. Ground state Excited states USDA/USDB Excited states GXPF1A M.B. Tsang and J. Lee et al., PRL 95, 222501 (2005) No short term NN correlations and other correlations included in SM. Why the agreement? Predictions of cross-sections Test of SM interactions Extraction of structure information SF EXP =SF SM

23. BOUND STATES: d( 20 O,t) 19 O (pick-up)‏ A. Ramus PhD. Thesis Universite Paris XI C 2 S=4.76(94) C 2 S=0.50(11) 0d 5/2 = 6.80(100) 1s 1/2 = 2.04(39) J π = 1/2+ J π = 5/2+ Sum Rules: M. Baranger et al., NPA 149, 225 (1970) v1s1/2 partially occupied in 20 O : correlations Full strength for 0d 5/2 and 1s 1/2 measured !

24. Updates on the different trends from transfer and knockout Slide credit: Jenny Lee

25. 26 Ne(d,t) 25 Ne 26 Ne(p,d) 25 Ne g.s. 1/2+ 1.703 5/2+ 3.300 5/2+ First 5/2+ Second excited 5/2+ GAMMA ENERGY 26 Ne(d,t  ) 25 Ne 1701 keV 1600 keV Preliminary results for 26 Ne(d,t) 25 Ne and also (p,d) INDIVIDUAL DECAY SPECTRA OF EXCITED 5/2+ STATES JEFFRY THOMAS, SURREY

26. A PLAN for how to STUDY STRUCTURE Use transfer reactions to identify strong single-particle states, measuring their spins and strengths Use the energies of these states to compare with theory Refine the theory Improve the extrapolation to very exotic nuclei Hence learn the structure of very exotic nuclei N.B. The shell model is arguably the best theoretical approach for us to confront with our results, but it’s not the only one. The experiments are needed, no matter which theory we use. N.B. Transfer (as opposed to knockout) allows us to study orbitals that are empty, so we don’t need quite such exotic beams.

27. LIVING WITH TRANSFER AS AN EXPERIMENTAL SPECTROSCOPIST WILTON CATFORD TRENTO WORKSHOP 4-8 Nov 13 FROM NUCLEAR STRUCTURE TO PARTICLE-TRANSFER REACTIONS AND BACK