What can we learn from transfer, and how is best to do it? Wilton Catford University of Surrey A Single Particle States; Changing magic no.’s B How reactions can study this physics 14th CNS INTERNATIONAL SCHOOL C Practicalities; Inverse Kinematics D Experimental setups E Results & Perspectives Univ of Tokyo 26 Aug – 1 Sep 2015 SATURN HST/ IR 1998, TETHYS VOYAGER2 1981, URANUS HST/ IR 1986

Lecture notes: written version University of Surrey Guildford United Kingdom Adelaide South Australia INPC 11-16 September 2016* Lecture notes: written version http://personal.ph.surrey.ac.uk/~phs1wc/transfer/catford-euroschool-transfer-revised.pdf or the more correct reference is: Catford, W. N. (2014). Chapter 3: Lecture Notes in Physics, 879 (1), 67-122. (Springer) http://www.springer.com/us/book/9783642451409 Some very useful notes on reaction theory, by Antonio Moro (Seville) at CERN 2014 school: https://indico.cern.ch/event/298890/contribution/0/attachments/562278/774562/course-notes.pdf homepage for the school with hyperlinks: https://indico.cern.ch/event/298890/timetable/#20140422 * http://www.physics.adelaide.edu.au/cssm/workshops/inpc2016/

Motivation: nuclear structure reasons for transfer What quantities we actually measure What reactions can we choose to use? What is a good beam energy to use? Inverse Kinematics Implications for Experimental approaches Example experiments and results 14th CNS INTERNATIONAL SCHOOL Univ of Tokyo 26 Aug – 1 Sep 2015

THEORY at CNS SHELL MODEL CRIB low energy 2 MeV/A (nuclear astrophysics) BIG RIPS high energy >100 MeV/A SHARAQ Many young (!!) and distinguished researchers! GRAPE Ge gamma ray array NEW PROJECT: slowed down beams at RIBF 10 MeV/A

THESE LECTURES – EXPERIMENTS THAT NEED (as shown later) FAIRLY LOW ENERGIES… FIRST ACCELERATOR → MAKE RADIOACTIVITY → ION SOURCE → RE-ACCELERATE → 5-10 MeV/A (Future: CNS slowed beams at RIBF) SECOND ACCELERATOR PRODUCTION EXPERIMENT FIRST ACCELERATOR

Nucleon Transfer using Radioactive Beams: results and lessons from the TIARA and TIARA+MUST2 experiments at SPIRAL WILTON CATFORD, University of Surrey, UK W.N. Catford, N.A. Orr, A. Matta, B. Fernandez-Dominguez, F. Delaunay, C. Timis, M. Labiche, J.S. Thomas, G.L. Wilson, S.M. Brown, I.C. Celik, A.J. Knapton et al.

Results from SHARC+TIGRESS at ISAC2/TRIUMF C.Aa. Diget, B.R. Fulton, S.P. Fox R. Wadsworth WNC, G.L. Wilson, A. Matta, S.M. Brown, I.C. Celik, G.J. Lotay G. Hackman, A.B. Garnsworthy, S. Williams C. Pearson, C. Unsworth and the TIGRESS collaboration N.A. Orr, F. Delaunay, N.L. Achouri Boston2 F. Sarazin J.C. Blackmon C. Svensson R.A.E. Austin

SINGLE PARTICLE STATES in the SHELL MODEL: Changes – tensor force, p-n Residual interactions move the mean field levels Magic numbers “migrate”, changing stability, reactions, collectivity… Similarly… proton filling affects neutron orbitals

(d, ) p SINGLE PARTICLE STATES in the SHELL MODEL: Probing the changed orbitals and their energies…

(d, ) p SINGLE PARTICLE STATES in the SHELL MODEL: As we approach the dripline, we also have to worry about the meaning and theoretical methods for probing resonant orbitals in the continuum…

Changing shell structure and collectivity at the drip line J.Dobaczewski et al., PRC 53 (1996) 2809

p n 22O (23O) 28Si (29Si) 24Ne (25Ne) ? N=16 / N=20 / N=28 Development 0s, 1p 0d5/2 1s1/2 0d3/2 0f7/2 p n 22O (23O) 28Si (29Si) empty 24Ne (25Ne) ? N=14 (N=15) 1/2+ is g.s. in 25Ne – can measure 3/2+ energy directly and also 7/2– and 3/2– in 25Ne, using (d,p) on 24Ne 1p3/2 T. Otsuka et al.

Changing Magic Numbers attractive p-n interaction tensor dominance Nuclei are quantum fluids comprising two distinguishable particle types… They separately fill their quantum wells… Shell structure emerges… Valence nucleons interact… This can perturb the orbital energies… The shell magic numbers for p(n) depend on the level of filling for the n(p) T. Otsuka et al., Phys. Rev. Lett. 97, 162501 (2006). T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001).

Changing Magic Numbers As the occupancy of the j> orbit d5/2 is reduced in going from (a) 30Si to (b) 24O, then the attractive force on j< d3/2 neutrons is reduced, and the orbital rises relatively in energy. This is shown in the final panel by the s1/2 to d3/2 gap, calculated using various interactions within the Monte-Carlo shell model.

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

SINGLE PARTICLE STATES – AN ACTUAL EXAMPLE excitation energy (MeV) 4.5 1.5 1.0 0.5 0.0 3.0 2.5 2.0 4.0 3.5 6 8 10 12 atomic number 1d3/2 1f7/2 27Mg 23O 25Ne Systematics of the 3/2+ for N=15 isotones (1d5/2)-1 2s1/2 removing d5/2 protons raises d3/2 and appears to lower the f7/2 Migration of the 3/2+ state creates N=16 from N=20 25Ne TIARA  USD modified 23,25O raise further challenges 21O has similar 3/2+-1/2+ gap (same d5/2 situation) but poses interesting question of mixing (hence recent 20O(d,p)@SPIRAL) 20 16 16 23O from USD and Stanoiu PRC 69 (2004) 034312 and Elekes PRL 98 (2007) 102502 25Ne from TIARA, W.N. Catford et al. Eur. Phys. J. A, 25 S1 251 (2005)

Changing Magic Numbers n 0d5/2 N=8 n 1s1/2 n 0f7/2 n 0p1/2 N=20 n 0d3/2 p 0p1/2 N=16 p 0p3/2 n 0p3/2 p 1s1/2 n 1s1/2 p 0d5/2 n 0d5/2 reduce Z, and N=8 gap is lost and N=6 opens reduce Z, and N=20 gap is lost and N=16 opens In the lighter nuclei (A<50) a good place to look is near closed proton shells, since a closed shell is followed in energy by a j > orbital. For example, compared to 14C the nuclei 12Be and 11Li (just above Z=2) have a reduced p (0p3/2) occupancy, so the N=8 magic number is lost. Similarly, compared to 30Si, the empty p (0d5/2) in 24O (Z=8) leads to the breaking of the N=20 magic number. Another possible extreme is when a particular neutron orbital is much more complete than normal. N=28 n 1p3/2 n 0f7/2 p 0d3/2 n 0d3/2 p 1s1/2 n 1s1/2 p 0d5/2 n 0d5/2 increase N, and Z=14 gap is lost and N=20 firms

Nuclear states are not in general pure SP states, of course For nuclear states, we measure the spin and energy and the magnitude of the single-particle component for that state (spectroscopic factor) Example: (relevant to one of the experiments)… 3/2+ in 21O

Example of population of single particle state: 21O 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+ 0d 5/2 1s 1/2 Jp = 3/2+ 2+ We measure how the two 3/2+ states share the SP strength when they mix

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

Neutron and Proton single-Particle States Built on 208 Pb Different Q-values Different target masses 53.75° - see next slide

with increasing angle John Schiffer, Argonne

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

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