1. 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

2. Lecture notes: written version
University of Surrey
Guildford
United Kingdom
Adelaide
South Australia
INPC September 2016*
Lecture notes: written version
or the more correct reference is:
Catford, W. N. (2014). Chapter 3: Lecture Notes in Physics, 879 (1), (Springer)
Some very useful notes on reaction theory, by Antonio Moro (Seville) at CERN 2014 school:
homepage for the school with hyperlinks: *

3. 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

4. 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

5. 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

6. 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.

7. 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

8. 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

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

10. (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…

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

12. 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.

13. 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, (2006).
T. Otsuka et al., Phys. Rev. Lett. 87, (2001).

14. 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.

15. 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)

16. 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 20 16 16
23O from USD and Stanoiu PRC 69 (2004) and Elekes PRL 98 (2007)
25Ne from TIARA, W.N. Catford et al. Eur. Phys. J. A, 25 S1 251 (2005)

17. 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

18. 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

19. 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

20. 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

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

22. with increasing angle
John Schiffer, Argonne

23. 1950’s
1960’s
Pb(d,p)209Pb
Deuteron beam + target
Tandem + spectrometer
>1010 pps (stable) beam
Helpful graduate students

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