LIVING WITH TRANSFER AS AN EXPERIMENTAL SPECTROSCOPIST

WILTON CATFORD

TRENTO WORKSHOP 4-8 Nov 13FROM 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

1p3/21p3/2

StableExotic

1p3/21p3/2

StableExotic

Utsuno et al., PRC,60,054315(1999)Monte-Carlo Shell Model (SDPF-M)

N=20

N=20

Exotic Stable

Removing d5/2 protons (Si O)

gives relative rise in n(d3/2)

Note:This changescollectivity,also…

Example of population of single particle state: 21O

0d 5/21s 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 nucleonThis nucleon enters a vacant orbitalIn principle, we know the orbital wavefunction and the reaction theory

But not all nuclear excited states are single particle states…

0d 5/21s 1/2

energy of level measures this gap

Jp = 3/2+

Jp = 3/2+

2+

x 1/2+

We measure how the two 3/2+ statesshare the SP strength when they mix

A. SINGLE PARTICLE STATES – EXAMPLE

SINGLE PARTICLE STATES – SPLITTING

Plot: John Schiffer

If we want to measure the SPE,splitting due to level mixingmeans that all componentsmust be found, to measure the true single particle energy

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 statesAlso 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)

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 changesIn 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 momentumand the theory is tractable.

Calculated differential cross sections show that 10 MeV/A is good (best?)

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+24Negs

USD

0.63

In 25Ne we used gamma-gamma coincidencesto distinguish spinsand go beyond orbital AMFIRST QUADRUPLE COINCIDENCE (p-HI-g-g )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 p = –

= 1

( = 3)7/2 –

3/2 –

0.73

0.75

W.N. Catford et al., PRL 104, 192501 (2010)

25Ne 27Ne

27Ne17

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

ISOTOPECHAINS

Mg Ne

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=15Odd d5/2 proton 25Ne statesProbe p-n interaction across N=20

25Na (d,p) 26Na

CX FUSION-EVAP

26Na 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

positiveparity

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 FactorShell 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

WILT

ON

CAT

FORD

JU

NE

2008

Spectroscopic FactorShell 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 theassumed potential well or other structure model

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

WILT

ON

CAT

FORD

JU

NE

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

u(r)

V(r)

REMARKS ABOUT INTERPRETING (d,p) TRANSFER

Geometry Correlations Desire Relatives

Peripheral: forward angles, lower energies

Eb defines the wavefunction asymptoticsIndependence

of the ANCon geometryGeometry

Dependenceof high energy (d,p)

on geometry

Is the effective well geometryeven the same for all orbitals?

(coupled channels treatments address this)

surfaceregion

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 viaSHORTRANGEcorrelations

MY ANSWER:

WEIGHTED Ex 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 Ex S.P. energies(traditional approach)

Must use SM SF’s (not quenched)

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 notequal 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

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 quenchingmeasured with transfer SF’s ? As much as for knockout?

If not, what about astrophysics ?

Formalism used in present work

Ground state

Excited statesUSDA/USDB

Excited statesGXPF1A

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 interactionsExtraction of structure information

SFEXP=SFSM

BOUND STATES: d(20O,t)19O (pick-up)

A. Ramus PhD. Thesis Universite Paris XI

C2S=4.76(94)

C2S=0.50(11)

0d5/2 =6.80(100)

1s1/2 =2.04(39)

Jπ= 1/2+

Jπ= 5/2+

Sum Rules:M. Baranger et al., NPA 149, 225 (1970)

v1s1/2 partially occupied in 20O : correlations

Full strength for 0d5/2 and 1s1/2 measured !

Updates on the different trends from transfer and knockout

Slide credit: Jenny Lee

26Ne(d,t)25Ne 26Ne(p,d)25Neg.s. 1/2+ g.s. 1/2+

1.703 5/2+ 1.703 5/2+

3.300 5/2+

First 5/2+

Second excited 5/2+

GAMMA ENERGY

26Ne(d,tg)25Ne

1701 keV

1600 keV

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

INDIVIDUAL DECAY SPECTRA OF EXCITED 5/2+ STATES

JEFFRY THOMAS, SURREY

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 TRANSFER AS AN EXPERIMENTAL SPECTROSCOPIST

WILTON CATFORD

TRENTO WORKSHOP 4-8 Nov 13FROM NUCLEAR STRUCTURE TO PARTICLE-TRANSFER REACTIONS AND BACK