Trends in SingleParticle Energies from Transfer Reactions

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Trends in Single-Particle Energies from Transfer
Reactions

• S.J.Freeman, J.P.Schiffer, J.A.Clark,
  C.M.Deibel,
• A.M.Howard, B.P.Kay, A.Parikh, P.D.Parker,
• D.Sharp and C.Wrede
• University of Manchester, Argonne National
  Laboratory and Yale University

HELIOS Collaboration Western Michigan University
, Argonne National Laboratory and University of
Manchester
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Single-particle structure exotic nuclei
Single-particle structure is at the root of much
of low energy nuclear physics. Drives shape
changes, collective modes etc.
Well-grounded expectations that the character of
single-particle nature will be radically changed
in exotic systems
Quantitative measurements of single-particle
nature of states are absolutely necessary to make
definitive comment on s.p. evolution.E.g. 41Ca
structure.
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Single-Particle Transfer
Single-step process avoiding excitation of
core. Cross section dependent on entrance/exit
channels and single-particle nature of bound
state via the spectroscopic factor.
Requires(i) cross sections (ii) large direct
yield (iii) modelling of entrance/exit channels
and bound state wave functions.
Issues(i) experimental errors, esp.
systematic.(ii) well-matched transfer, low CN /
multistep contributions.(iii) choices in optical
and BS potentials.
Comparison of isolated measurements is fraught
with difficulty!
Absolute spectroscopic factors (from transfer
reactions) often noted as having questionable
meaning.
Relative spectroscopic factors can ameliorate
many worries if consistent experimental,
analytical and DWBA methods are used across all
nuclides of interest.
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Experimental Details

• (a,3H/3He) reactions and inverses large Q,
  favouring high-L transfer
• up to 50 MeV alpha particles from Yale tandem on
  targets, usually supported by thin carbon foils.
• Ions identified/analysed in Yale Split Pole
  Spectrograph with gas-filled focal plane
  detector.
• Rutherford scattering enable extraction of
  scattering measured absolute cross section.
• Measurements at near peak yield and at angles
  sensitive to differences in angular distributions.

Keeping an eye on systematic errors same
aperture, same integrator scale, monitor target
thickness
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Protons outside Z50 in Sb Isotopes
Protons outside closed shells. Sn cores are
fairly stable. No indications of shape changes.
g7/2 and h11/2 single-proton states?
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Protons Outside Z50 Tensor Interaction
Tensor interaction neutron ?h11/2 (jgt) filling
in Sn cores with increasing A attractive effect
on proton ?g7/2 (jlt) repulsive effect on proton
?h11/2 (jgt)
?h11/2
?h11/2
?g7/2
proton
neutron
Main driver of the shifts appears to be the
tensor part of the interaction. Otsuka et al.
Phys. Rev. Lett. 95, 232502 (2005)
Calculations based on ??? meson exchange added
to other mean-field effects estimated from a
Woods-Saxon potential
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Neutrons Outside N82
N82(a,3He) _at_ 51MeV
Each high-L transfer has TWO significant
fragments due to particle-core coupling 0 ?
h9/2 mixes with 2? f7/2 0 ? i13/2 mixes with
3?? f7/2
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Neutrons Outside N82
0 ? h9/2 with 2? f7/2 matrix element155
keV0 ? i13/2 with 3?? f7/2 matrix element
671 keVMatrix elements constant to 3 across
all targets.extent of mixing depends mainly on
separation of unperturbed states
Protons are filling mainly ?1g7/2 ( and
?2d5/2)Beyond Z64 start to fill ?1h11/2
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Neutron Holes in N82
N82(3He,a) _at_ 34 MeV
If consistent explanation, tensor-driven trends
should also arise for hole statesneutron holes
in h11/2 and g7/2 as protons fill mainly ?1g7/2 (
and ?2d5/2). Surprising asymmetry in
fragmentation across N82.
Some older data available on subset of targets
but no tables of cross sections! Three point
distributions with (3He,a) beginning to get
difficult. Suffering a little from other strong
reaction groups on focal plane. Plan to use
(p,d) reactions to supplement information.
Implement a blocker where possible.
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Neutrons Outside N50
If consistent explanation, tensor-driven trends
should reverse, even in stable systemsneutrons
in h11/2 and g7/2 as protons fill fp shell
(mainly jlt) followed by g9/2 (jgt).
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Charged particles in a Solenoid
Potentially high angle-energy acceptance.
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Resolution 75 keV
Commissioning run d(12B,p) _at_ 6.75 MeV/u inflight
radioactive beam, 107-8 pps, 1 T, proton energies
0.5-3 MeV, Si recoil detector.
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Conclusions

• Careful and consistent systematic transfer
  studies reveal trends in high-j particle states
  orbitals outside N82 and Z50 which are
  quantitatively consistent with expectations of
  the tensor interaction.
• Currently working on hole states and case where
  sense of the trend should reverse to extend
  monotonic trends in particle states studied so
  far.
• HELIOS should be an extremely useful device for
  transfer studies in inverse kinematics,
  particularly with radioactive beams.

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Away from Stable Systems Go North or East!
No measurements of N83 spectroscopic factors
other than the current results on stable solid
targets..
The systematics for the lowest energy states show
a distinct turn around at Z64 perhaps this is
where ?1g7/2 is full and ?1h11/2 starts to be
occupied and reverses the effects of the tensor
shifts on neutron states?
But Z64 is where the 0 ? i13/2 is expected to
be closest to 3?? f7/2
Difficult radioactive beams
Similar expected reversal far from stability in
Sb when neutron Fermi surface moves from jgt to jlt.
Impossibly neutron-rich radioactive beams
Modifed Gogny Otsuka et al. Phys. Rev. Lett. 97,
162501 (2006)
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Neutrons outside stable N50 targets
Proton Fermi surface moves from fp shell (mainly
jlt) to g9/2 (jgt) and any tensor-driven shifts in
neutron states should alter direction. Maybe
hints of this in the trends of the lowest-lying
7/2 and 11/2 states BUT fragmentation is
strong and spectroscopic factors need attention
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Explanations?
Difficult to understand conventionally. No single
potential appears describe the separation of
these states as a function of neutron
number.Green line Woods-Saxon model with depth
adjusted to the BE of ?g7/2
Sn cores are very stable.agree with all usual
indicators of deformation small, similar.
g7/2 and h11/2 single-proton states?
N82 cores are somewhat stable.Woods-Saxon
cannot reproduce crossing of lowest 9/2- and
13/2 states.
h9/2 and i13/2 single-neutron states?
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Protons Outside Z50 Results
DWBA using standard optical and bound-state
parameters, give good reproduction of angular
distributions Single common normalization across
all isotopes and L transfers chosen to sum to
unityS differ significantly from older (d,p) work
Lowest 7/2 and 11/2- across stable Sb isotopes
have constant spectroscopic factors, and appear
to be of near single-particle-like ph11/2 and
pg7/2 character (to within usual caveats). More
careful analysis shows the trend in the centroid
of strength closely follows that of the lowest
states.
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Trends in centroid energies
Centroids for the high-j neutron states show
similar, but less pronounced variation to the
lowest states of the right spin-parity.
Experimental proton occupancy from transfer
reactions
Protons are filling mainly ?1g7/2 AND ?2d5/2
As with trends in Sb nuclei, this could be due to
a tensor interaction between these neutron states
and valence protons.
Wildenthal, Newman and Auble, Phys.Rev.C3, 1199
(1971)
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Predictions of Tensor Interaction
Combining with the experimental proton occupancy
from transfer reactions
QUALITATIVE EFFECTSProtons are filling mainly
?1g7/2 AND ?2d5/2 ?1g7/2 (jlt) ? ?i13/2 (jgt)
should be ATTRACTIVE?1g7/2 (jlt) ? ?h9/2 (jlt)
should be REPULSIVE ? separation should
DECREASE with Z?2d5/2 (jgt) should have
opposite, but smaller effect in the neutron
states due to the reduced radial overlapOverall
expect states to move closer with Z.
?i13/2
?h9/2
QUANTITATIVE EFFECTSUsing the ??? meson
exchange ?i13/2 ?h9/2 separation changes
by -0.180 MeV per additional ?1g7/2 proton0.04
MeV per additional ?2d5/2 proton
Good overall reproduction of the experimental
trends.effects of the tensor interaction appear
to be a rather common feature.
Otsuka, private communication