The neutron magic numbers N=16, 20 & 28 for neutron rich exotic nuclei, as probed by

1. The neutron magic numbers N=16, 20 & 28 for neutron rich exotic nuclei, as probed by nucleon transfer with radioactive beams Wilton Catford University of Surrey, UK Thank you to all my collaborators who made it possible to perform the experiments reported in this talk SURREY, PAISLEY, LIVERPOOL, YORK, BIRMINGHAM, DARESBURY with LPC CAEN, ORSAY, SACLAY, GANIL, SANTIAGO, TRIUMF

2. Learning about nuclear structure using single neutron transfer reactions with reaccelerated radioactive beams Wilton Catford University of Surrey, UK • those new magic numbers that appear all the time in PRL • How nucleon transfer helps us to understand structure evolution • Some details that affect how we need to design experiments • Examples of current experimental apparatus: TIARA, SHARC • Some examples of recent results in the neutron rich neon region Thank you to all my collaborators who made it possible to perform the experiments reported in this talk SURREY, PAISLEY, LIVERPOOL, YORK, BIRMINGHAM, DARESBURY with LPC CAEN, ORSAY, SACLAY, GANIL, SANTIAGO, TRIUMF

3. 1950’s 1960’s 1967 208Pb(d,p)209Pb Deuteron beam + target Tandem + spectrometer >1010pps (stable) beam Helpful graduate students

4. STABLE NUCLEI RADIOACTIVE 1990’s 2000’s…….. 1950’s 1960’s 1967 208Pb(d,p)209Pb 1998 d(56Ni,p)57Ni 1999 p(11Be,d)10Be Rehm ARGONNE Fortier/Catford GANIL

5. 1p3/2 1p3/2 1p3/2 1p3/2 Exotic Exotic Stable Stable Utsuno et al., PRC,60,054315(1999) Monte-Carlo Shell Model (SDPF-M) Exotic Stable N=20 N=20 Note: This changes collectivity, also… Removing d5/2 protons (Si O) gives relative rise in n(d3/2)

6. 1s 1/2 0d 5/2 A. SINGLE PARTICLE STATES – EXAMPLE Example of population of single particle state: 21O 0d 3/2 energy of level measures this gap 1s 1/2 Jp = 3/2+ 0d 5/2 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… x 1/2+ Jp = 3/2+ 2+ We measure how the two 3/2+ states share the SP strength when they mix

7. SINGLE PARTICLE STATES – SPLITTING 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 Plot: John Schiffer

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. USING RADIOACTIVE BEAMS in INVERSE KINEMATICS (d,p) from 180° to forward of 80° (d,t) forward of 45° INCIDENT BEAM The energies are only weakly dependent on mass of the beam so a general purpose array can be utilised (d,d) just forward of 90°

11. Target Changing Mechanism Barrel Si 36 < lab < 144  Beam VAMOS Forward Annular Si 5.6 < lab < 36  Backward Annular Si 144 < lab < 168.5 

12. combining transfer and gamma-ray decays gives a rich insight into the structure Leaping ahead to preview results horizontal axis = gamma-ray energy with doppler correction applied vertical axis = energy populated in (d,p) as calculated from proton angle and energy 25Na (d,p) 26Na

13. 26Na had been studied a little, beforehand (N=15, quite neutron rich) negative parity 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 CX FUSION-EVAP positive parity

14. 2014/2015 TIARA 24Ne + d 25Ne + p 100,000 pps t1/2 = 3.38 min 20O 10,000 pps t1/2 = 13.51 s 26Ne < 3000 pps t1/2 = 197 ms

16. TIARA+MUST2+VAMOS+EXOGAM @ SPIRAL/GANIL PURE 25Ne re-accelerated beam at pps, 10.A MeV isotopically pure beam, CIME at SPIRAL/GANIL 26Ne (SPIRAL) ~10 A MeV 3000 pps Focal Plane: 1 mg/cm2

17. Results from a (d,p) experiment to study 25Ne W.N. Catford et al., PRL 104, 192501 (2010) GAMMA RAY ENERGY SPECTRA FIX E_x EXCITATION E_x FROM PROTONS

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

19. TIARA+MUST2+VAMOS+EXOGAM @ SPIRAL/GANIL 80% 15N3+ Focal Plane: 1 mg/cm2

20. New Experimental Results:d(20O,p)21O and (d,t) and (d,d)‏ 20O(d,p)21O TIARA (d,p)‏ BOUND STATES 20O 21O TIARA 19O VAMOS 20O(d,d*)20O 20O(p,p*)20O TIARA Unbound MUST2 A. Ramus et al. Ph.D. Paris XI

21. BOUND STATES:d(20O,t)19O (pick-up)‏ Full strengthfor0d5/2and1s1/2measured ! Jπ= 5/2+ C2S=4.76(94) 1s1/2 =2.04(39) 0d5/2 =6.80(100) A. Ramus PhD. Thesis Universite Paris XI Sum Rules: M. Baranger et al., NPA 149, 225 (1970) Jπ= 1/2+ C2S=0.50(11) v1s1/2 partially occupied in 20O : correlations

22. TIARA+MUST2+VAMOS+EXOGAM @ SPIRAL/GANIL PURE 26Ne (SPIRAL) ~10 A MeV 3000 pps Focal Plane: 1 mg/cm2

23. N=17 ISOTONES Shell model predictions vary wildly for fp intruders Systematics show region of dramatic change 27Ne Predictions 7/2never seen 3/2 known 27Ne IS THE NEXT ISOTONE

24. 27Ne BOUND STATES The target was 1 mg/cm2 CD2 (thick, to compensate for 2500 pps) Known bound states were selected by gating on the decay gamma-ray (and the ground state by subtraction) 3/2 3/2+ In these case, the spins were already known. The magnitude was the quantity to be measured.

25. 27Ne UNBOUND STATES EXCLUDE MISSING MOMENTUM • 27Ne results • level with main f7/2 strength is unbound • excitation energy measured • spectroscopic factor measured • the f7/2 and p3/2 states are inverted • this inversion also in 25Ne experiment • the natural width is just 3.5  1.0 keV

26. N=17 ISOTONES 1.80 7/2 0.76 3/2 27Ne17 4.03 ISOTOPE CHAINS 3.33 1.80 0.76 27Ne 25Ne Mg Ne d3/2 level is 2.030 25Ne

27. 27Ne 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 29Mg, 25Ne also • so we need to understand • why an ad hoc lowering • of the fp-shell by 0.7 MeV • is required by the data!

28. The Next Step… p 3/2 f 7/2 d 3/2 25Na (d,p) 26Na odd-odd final nucleus High density of states Gamma-gating needed s 1/2 d 5/2 neutrons protons

29. TIGRESS ISAC2

30. SHARC at ISAC2 at TRIUMF Christian Diget ~ 3 x 107pps

31. SHARC chamber (compact Si box) TIGRESS TRIFOIL @ zero degrees BEAM Bank of 500 preamplifiers cabled to TIG10 digitizers TIGRESS WILTON CATFORD, SURREY

33. Data from d(25Na,p)26Na at 5 MeV/A using SHARC at ISAC2 at TRIUMF Gemma Wilson, Surrey cascade decays ground state decays Excitation energy deduced from proton energy and angle Doppler corrected (b=0.10) gamma ray energy measured in TIGRESS

34. If we gate on a gamma-ray, then we bias our proton measurement, if the gamma detection probability depends on the proton angle. And it does depend on the proton angle, because the gamma-ray correlation is determined by magnetic substate populations. However, our gamma-ray angular coverage is sufficient that the integrated efficiency for gamma detection remains very similar and the SHAPE of the proton angular distribution is unchanged by gating.

35. PRELIMINARY PRELIMINARY

39. FUTURE: • We have experiments planned with 16C, 64Ge at GANIL & 28Mg and others at TRIUMF • Many other groups are also busy! T-REX at ISOLDE, ORRUBA at ORNL etc • New and extended devices are planned for SPIRAL2, HIE-ISOLDE and beyond Designed to use cryogenic target CHyMENE and gamma-arrays PARIS, AGATA… A development of the GRAPA concept originally proposed for EURISOL.

40. TSR@ISOLDE • Existing storage ring • Re-deploy at ISOLDE • Thin gas jet targets • Light beams will survive • Increased luminosity • Supported by CERN • In-ring initiative led by UK • Also linked to post-ring • helical spectrometer electron capture limit multiple scattering limit 12C6+ Circumference 55.4m

41. The neutron magic numbers N=16, 20 & 28 for neutron rich exotic nuclei, as probed by nucleon transfer with radioactive beams Wilton Catford University of Surrey, UK Thank you to all my collaborators who made it possible to perform the experiments reported in this talk SURREY, PAISLEY, LIVERPOOL, YORK, BIRMINGHAM, DARESBURY with LPC CAEN, ORSAY, SACLAY, GANIL, SANTIAGO, TRIUMF