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LIVING WITH TRANSFER AS AN EXPERIMENTAL SPECTROSCOPIST

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LIVING WITH TRANSFERAS AN EXPERIMENTAL SPECTROSCOPIST

WILTON CATFORD

TRENTO WORKSHOP 4-8 Nov 13

FROM NUCLEAR STRUCTURE TO PARTICLE-TRANSFER REACTIONS AND BACK

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

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)

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

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

- 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)

But, in the presence of all these interesting issues, remember…

- 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.)

- 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.

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?)

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

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

- 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!

More on N=15

Odd d5/2 proton 25Ne states

Probe p-n interaction across N=20

25Na (d,p) 26Na

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

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

- Johnson-Soper Model: an alternative to DWBA that gives a simple prescription for taking into account coherent entangledeffects 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

WILTON CATFORD JUNE 2008

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

overlap integral

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

spectroscopic factor

REACTION MODEL FOR (d,p) TRANSFER – the ADWA

WILTON CATFORD JUNE 2008

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

Peripheral: forward angles, lower energies

Eb defines the wavefunction asymptotics

Independence

of the ANC

on geometry

Geometry

REMARKS ABOUT INTERPRETING (d,p) TRANSFER

Geometry Correlations Desire Relatives

Dependence

of high energy (d,p)

on geometry

surface

region

V(r)

u(r)

Is the effective well geometry

even the same for all orbitals?

(coupled channels treatments address this)

Must use SM SF’s (not quenched)

WEIGHTED ExS.P. energies

WEIGHTED ExS.P. energies

(traditional approach)

If the quenched SF’s are used

REMARKS ABOUT INTERPRETING (d,p) TRANSFER

Geometry Correlations Desire Relatives

States built in SM space

J states are mixed by residual interactions

… and are not pure SP states

J

mixing via

SHORT

RANGE

correlations

J

MY ANSWER:

- 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

WHAT DO WE WANT TO MEASURE?

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 ?

REMARKS ABOUT INTERPRETING (d,p) TRANSFER

Geometry Correlations Desire Relatives

THE SPECTROSCOPIC FACTOR HAS TWO (at least!) PROBLEMS:

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

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 ?

REMARKS ABOUT INTERPRETING (d,p) TRANSFER

Geometry Correlations Desire Relatives

ARE RELATIVE SF’s MORE ACCURATE THAN ABSOLUTE? … ALWAYS?

Formalism used in present work

M.B. Tsang and J. Lee et al., PRL 95, 222501 (2005)

SFEXP=SFSM

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

Ground state

USDA/USDB

Excited states

GXPF1A

Excited states

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

Updates on the different trends from transfer and knockout

Slide credit: Jenny Lee

Preliminary results for 26Ne(d,t)25Ne and also (p,d)

JEFFRY THOMAS, SURREY

26Ne(d,t)25Ne

26Ne(p,d)25Ne

g.s. 1/2+

g.s. 1/2+

26Ne(d,t)25Ne

GAMMA ENERGY

PRELIMINARY

Second excited 5/2+

1600 keV

1.703 5/2+

1.703 5/2+

First 5/2+

1701 keV

3.300 5/2+

INDIVIDUAL DECAY SPECTRA OF EXCITED 5/2+ STATES

- 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.

LIVING WITH TRANSFERAS AN EXPERIMENTAL SPECTROSCOPIST

WILTON CATFORD

TRENTO WORKSHOP 4-8 Nov 13

FROM NUCLEAR STRUCTURE TO PARTICLE-TRANSFER REACTIONS AND BACK