Neutron Proton Pairing

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The (3He,p) Reaction to Study np Pairing in
NZ Nuclei
A. O. Macchiavelli Lawrence Berkeley National
Laboratory
Many thanks to R.MClark , P.Fallon
Workshop on Theory and Experiment Intersections
in Modern Nuclear Structure ECT -
Trento, Italy - April 23-27th, 2007
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Everything you need to know about pairing in
nuclei
D.M. Brink and R.A. Broglia Nuclear
Superfluidity Pairing in Finite
Systems Cambridge University Press, 2005
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Outline

• Brief Introduction
• Current status of np pairing
• BE differences
• Ground states of odd-odd NZ nuclei
• Rotational properties
• The (3He,p) transfer reaction with radioactive
  beams
• Pairing vibrations near 40Ca and 56Ni
• Proof of principle
  
• The 44Ti(3He,p) reaction
• Discussion of systematics
• Summary and conclusions
• Future work and Other topics
• If time permits or over coffee
• Interesting results from a single j shell model

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• Gap in the excitation spectra of even-A nuclei
• Odd-even mass differences
• Rotational moments of inertia

Relevance to other finite Fermion systems such as
3He clusters, Fermi-gas condensates, quantum
dots, metal clusters, .
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2D Even-even gap
D Odd-Even mass difference
2D Odd-odd to Even-even mass difference
AZN
A1ZN1
A2ZN2
A2(Z1)N1
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Pair gaps from mass differences
BM Vol 1 page 170
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Pair gaps from rotational properties
12 A-1/2
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NP PAIRING
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T1, L0, S0
T0, L0, S1 Deuteron-like pairs
Tz0
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NZ nuclei, unique systems to study np
correlations As you move out of NZ nn
and pp pairs are favored Role of isoscalar (T0)
and isovector (T1) pairing Large spatial
overlap of n and p Pairing vibrations (normal
system Pairing rotations (superfluid
system) Does isoscalar pairing give rise to
collective modes? What is (are) the
smoking-gun(s)?   Binding energy differences
Ground states of odd-odd self-conjugate
nuclei   Rotational properties moments of
inertia, alignments   Two-particle transfer
cross-sections
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Neutron - Proton pair blocking

• Use binding energy differences to test for the
  presence and character
• of pair correlations.

Must compare states with the same isospin!! For
T 0 states Use the even-even NZ neighbors as
a reference For T 1 states Use the even-even
isobaric analogs as a reference
(c.f. P.Vogel NPA 662 (2000) 148)
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• T0 states give a pair gap

T0 States
T 1 states give no pair gap
c.f. P.Vogel NPA 662 (2000) 148
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Two ingredients
Isovector pairing gap DT1
Symmetry energy ES(T)
Even-even T0
E0 _________________________________________ Odd-
odd T0 E0 2DT1 ES(0) T1 E0 0
ES(1) _________________________________________
Even-even T1 E0 2DT1 ES(1) ______________
___________________________ Odd-even T1/2 E0
DT1 ES(1/2)
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Coriolis effects
jw 2D
T0, J1 Deuteron-like pairs
T1, J0
Is there any difference in their response to
rotational motion?
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Detailed spectroscopy from GAMMASPHERE Microball
Neutron Array FMA data Resolve discrepancies
in yrast and near yrast bands Differential
Doppler shift measurements indicate different
shapes for the bands in 72Kr
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No clear cut evidence for delayed
alignments Difficult issue, shape degrees of
freedom need to be understood
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Recent work by Ramon Wyss et al. on decay
properties of 73Kr and 75Rb may suggest the
development of dynamical T0 pairing collectivity
at high spins.
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Quasideuteron alignment
J(1) (MeV-1)
w(keV)
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Low level density near the ground state Gap like
in even-even nuclei
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quasideuteron
J1
J large B(M1) J- small B(M1)
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The smoking gun?
Two particle transfer reactions like (t,p) or
(p,t), where 2 neutrons are deposited or picked
up at the same point in space provide an specific
tool to probe the amplitude of this collective
motion. The transition operator ltfaaigt will
be proportional to the pair density of the
nucleus.
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Collective pairing vibrations near closed shells
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Study binding energies around closed shells (40Ca
and 56Ni) T0 Energy comparable with single
particle separation - low collectivity. T1
Energy consistent with collective excitations.
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(3He,p) Transfer Reactions
L0 transfer forward peaked
Measure the np transfer cross section to T1 and
T0 states Both absolute s(T0) and s(T1) and
relative s(T0) / s(T1) tell us about the
character and strength of the correlations
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R.Chasman
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(3He,p) Transfer Reactions in Reverse Kinematics
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(3He,p) Transfer Reactions in Reverse Kinematics
Lawrence Berkeley National Laboratory, Argonne
National Laboratory , Western Michigan
University and Rutgers University Collaboration
Degrader 10mg/cm2
46V
44Ti
106 /sec From ATLAS
FMA
3He
Au
Si detector 500m 16x16 1sr
Gas cell 100mg/cm2
20 counts/day
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Proof of principle
Lawrence Berkeley National Laboratory, Argonne
National Laboratory , Western Michigan
University and Rutgers University Collaboration
Faraday Cup
Monitor
To FMA
Beam
Au degrader
Si detectors
Gas Cell
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Nucl.Phys. A80 (1966)
Nucl.Phys. A116 (1968)
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The 242 MeV 44Ti Beam
Purchase 100mCi of 44Ti from LANL 20k Some
Chemistry Tandem Ion-Source
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The 242 MeV 44Ti Beam
44Ti / 44Ca 2.5 ? Need FMA selection
FMA Settings 107MeV, A44, q20
33S 44Ca 44Ti
E Monitor _at_ 0o X1800 Attenuator
1.1 x 106 44Ti/sec
E vs DE(IC)
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A46 (44Ti, 3He,p ? 46V)
Ring
Proton E (10keV)
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Systematic of (3He,p) and (t,p) reactions in
stable NZ nuclei
????
Phonon Limit (n1) s0-gt1 From 40Ca
Single-particle estimate (spin)x(3He)x(LS -gt jj)
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R.Chasman - ANL
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Summary and Conclusions
Rotational Properties
Ground State Binding Energies (pair gaps)
Energies of T0 T1 states in NZ nuclei
Excitation spectra near shell gaps (pair
vibrations)
Evidence for full isovector T1 pairing
(nn,np,pp) - charge independence. BE differences
can be described by an appropriate combination of
the symmetry energy and the isovector pairing
energy. No evidence for a T0 deuteron-like
pairing condensate in NZ nuclei. The T0 states
in an odd-odd NZ nucleus can be characterized as
a seniority 2 state (as in any other odd-odd
nucleus). ( Single-l and single-j shell models
capture the most relevant ingredients of pairing
correlations. They appear to support these
findings.)
The smoking gun ? (3He,p) reaction in inverse
kinematics Successful run with 44Ti
What is next??
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HELIOS at ANLB.Back, J.P.Schiffer, A.Wuossma et
al.
Recoil detector
Target
Downstream Si array
Upstream Si array
Beam axis
Solenoid
Schematic design
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Improved resolution for (d,p)
Q Value
Ep vs q
DE50 keV Dq1o
Ep (MeV)
qp (deg)
DE50 keV DZ1mm
Ep vs Z
Ep (MeV)
Zp (cm)
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• 56Ni at ANL or ORNL
• 72Kr at TRIUMF

Can we use np knockout?

• Measure snp with S800 and GRETINA and determine
  exclusive cross-section to 0 and 1 ground
  states.
• Use secondary NZ beams, 44Ti, 56Ni, etc.
• With 100mgr/cm2 target, 10 gamma-efficiency and
  s 1mb
• we would need 103 particles/sec !!

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Other topics in Paring in Nuclei
Pairing in weakly bound systems

• Opportunity to study the density dependence of
  nucleon pairing is provided by two neutron halo
  nuclei.

Pairing Phase Transition in Neutron Rich Nuclei
(t,p) and (p,t) reactions near 78Ni and 132Sn
doubly magic nuclei
Giant Pairing Vibration
Elementary mode of excitation, not yet
discovered. Use weakly bound projectiles such as
6He to avoid Q-value mismatch
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Thank You!
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Single l-shell model
SU(4)
x G1/(G1G0)
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Here is where the action is
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What about spin-orbit?
l-s ls
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Single-j shell model
and L0 matrix elements
l-s ls
Vls
Vls 0 l-shell Vls j-shell
Use OXBASH B.A.Brown et al., MSU Report 524
(1998)
V x V T1,J0 (1-x) V T0,J1
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the action is now at lower xs
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and more interesting
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Ground state has aligned spins!!!
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This happens as the JJ coupling sets in
Obviously not the case in nuclei, but can it be
tested in mixed fermion traps?
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Two particles
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Thank You Again!