Perspectives and limitations of 2p and 2n knockout reactions

1

• Perspectives and limitations of 2p and 2n
  knockout reactions
• 1st Int.Workshop on Quasi-free Scattering with
  Radioactive Ion Beams, ECT Trento, 7-11
  April 2008

Jeff Tostevin, Department of Physics Faculty of
Engineering and Physical Sciences University of
Surrey, United Kingdom
2
Acknowledge the ongoing (growing) collaboration
K.P. Siwek B.M. Sherrill J.R. Terry D.
Weisshaar K. Yoneda H. Zwahlen
P. Adrich D. Bazin B.A. Brown C.M. Campbell J.M.
Cook D.-C. Dinca A. Gade T. Glasmacher P.G.
Hansen S. McDaniel W.F. Mueller A. Obertelli
Y. Utsuno
3
Towards 2N spectroscopy of rare isotope beams
Outline Knockout mechanism (i) Sudden two
nucleon (2N) removal from fast fragmentation
beams, (ii) the parameter selection scheme
where input as taken/guided by theory, (iii)
recent results and status check, (iv) limitations
but still early days. Interest (i) assessing
shell model wave functions and interactions, (ii)
shell gaps 2N correlations, as revealed by
inclusive and partial cross sections, -2N
momentum distributions
4
2N removal at beam energies gt 100 MeV/nucleon
9Be
light nuclear
target
1
2
fast spectator
c
Experiments are inclusive (with respect to the
target final states). Residue final state
measured using gamma rays, whenever possible
and momenta (p//) of the residues.Cross sections
are large and they include both Stripping
(inelastic/absorptive) and diffractive (elastic)
interactions of the removed nucleon(s) with the
target
5
2N removal removal of deficient species - direct
n
p
Spherical Hartree Fock density (SkX)
6
Energetics 2p knockout 38Si ? 36Mg
?1p
indirect 2p KO
2.80(64)
?
18.60
?
39.24
36Mg
1n KO
?1p
4.38
?
?2p
5.29
?
38Si
7
Sudden removal from the residue as a spectator
Core/residue state is assumed a spectator so
reaction probes the two nucleon overlap and (in
general) there are several coherent active 2N
configurations overlap determined by the two
nucleon amplitudes (TNA)
8
Target drills out a cylindrical volume at the
surface
(i) Cross section will be sensitive to the
spatial correlations of pairs of nucleons near
surface (ii) No spin selection rule (for S0
versus S1 pairs). Reaction mechanism (iii) We
can gain first expectation of the extent to which
we are sensitive to correlations by looking at
the 2N overlaps in this sampled volume
z
9
Sudden 2N removal from the mass A residue
Sudden removal residue momenta probe the
summed momenta of pair in
the projectile rest
frame
A
laboratory frame and
Projectile rest frame
and component equations
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Look at momentum content of sampled volume
2
1
z
Probability of a residue with parallel momentum ?A
J. A. Tostevin, EPJ Special Topics 150, 67 (2007)
RNB7 Proceedings
11
Antisymmetrized 28Mg ? 26Ne removal of
uncorrelated
4
2
0
J.A. Tostevin, SENUF 06, JPG Conference series
2006
12
Coherence of shell model correlations
28Mg (Z12, N 16) ? 26Ne(0)
13
Two nucleon KO J-dependence of p//
28Mg (?2p) 82.3 A MeV
4
2
Residue momentum probability
0
14
Two proton knockout from 38Si ? 36Mg(0,2)
38Si (?2p) 83 A MeV
Theory Expt. 0 56 58(7) 2
44 42(7)
0
Residue momentum distribution
2
dp/p1.66
A. Gade, JAT et al., to be published
15
Two neutron knockout from 22Mg ? 20Mg(0,2)
22Mg (?2n) 75.1 A MeV
0
Expt. 0 84 2 16
Residue momentum distribution
A. Gade, JAT et al., to be published
2
16
Now include all 2N absorption mechanisms
core survival and nucleon removal
2N stripping
1N stripped 1N diffracted
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The diffractive/stripping contributions
nucleon 2 absorbed
nucleon 1 survives, but can be bound to c or
unbound ?
nucleon 1 (1c) unbound (1c) bound
18
Sudden removal eikonal model cross sections
J.A. Tostevin et al., PRC 70 (2004) 064602 and
PRC 74 (2006) 064604.
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Sudden removal eikonal model cross sections
1
2
A
At any given facility, and a programme of
measurements (with essentially fixed energy per
nucleon) and a given target then only two things
change for different exotic beams (1) the core
target interaction, (2) the nuclear structure

J.A. Tostevin, G. Podolyák et al., PRC 70 (2004)
064602.
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Effective interactions Folding models
Double folding
B
A
Single folding
B
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Reaction description is rather robust -
quantitative
Residue-target interaction is highly absorptive
at gt100 MeV/u with a range fixed by the residue
and target sizes. This is encoded within the
double folding model and is cross referenced to
These ion-ion interactions and their
S-matrices are calculated reliably using Glauber
methods using Hartree-Fock densities.
B.A. Brown et al., Phys. Rev. C65 (2001) 014612
22
Overlap function sensitivity Hartree Fock sizes
Rms radii of sp formfactors are the requirement
for determining the cross sections to high
precision We constrain to Hartree-Fock values
23
Sensitivity to s.p. orbitals correlation with
radii
24
Single particle radii other benchmarks
Can compare sp rms radii in selected cases in the
mass region under study with those used / deduced
in electron scattering e.g. Kramer et al.
NPA 679 267 (2001)
25
Our sensitivity is not to to the ANC
26
Correlated 28Mg ? 26Ne(0,2,4), 82.3 MeV/u
Data D. Bazin et al., PRL 91 (2003) 012501
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Knockout cross sections correlated case
28Mg ?26Ne(0, 2, 4 , 22) 82.3 MeV/u

Sigma (mb)


1
2
J.A. Tostevin et al., PRC 70 (2004) 064602, PRC
74 064604 (2006
28
Ratio of measured to calculated cross sections
J.A. Tostevin and B.A. Brown, PRC 74 064604
(2006), PRC 70 064602 (2004) Figure A. Gade
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Extent of the Island of Inversion to 36Mg?

• Insufficient yield for, e.g.
• secondary beam inelastic scattering
• 2) Parent for beta decay, 37Na, is particle
  unbound
• 3) can use 2p removal from n-rich (sd-shell)
  parent, 38Si

A. Gade et al, PRL 99, 072502 (2007)
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38Si(-2p) to 36Mg shell model and interactions?
Monte-Carlo shell model calculations SDPF-M
interaction of Utsono, Otsuka et al.
38Si

p
n
p
n
p
n
Measured cross sections and those calculated
assuming population of the 0hw components of the
final states by the direct 2p knockout reaction
mechanism
A. Gade et al, PRL 99, 072502 (2007)
31
Two nucleon stripping full p// calculations
0
2
28Mg (?2p) 82.3 A MeV
4
Full Approx
E.C. Simpson and J.A. Tostevin, in progress
32
Inclusive momentum distributions 28Mg (?2p)
28Mg (?2p) 82.3 A MeV
sum
0
4
2
E.C. Simpson and J.A. Tostevin, in progress
33
Exclusive momentum distributions 28Mg (?2p)
28Mg (?2p) 82.3 A MeV
4
counts
34
Inclusive momentum distributions 22Mg (?2n)
22Mg (?2n) 75.1 A MeV
Expt. 0 84 2 16
35
Limitations 2n from n-rich, e.g. 18C ? 17C, 16C
4.98
direct 2n KO
indirect 2n KO
?1n
0.73
?
4.91
16C
1n KO
4.18
17C
?1n
?2n
(sd)4
18C
36
Limitations 2n from n-rich, e.g. 19C ? 18C, 17C
4.91
?1n
indirect 2n KO
direct 2n KO
4.18
?
4.76
17C
1n KO
?1n
?2n
0.58
18C
(sd)5
19C
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Inclusive cross sections for -1n knockout
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Inclusive 1neutron KO - neutron rich carbons
E.C. Simpson and J.A. Tostevin, work in progress
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Inclusive 2n ko - the neutron rich carbons
indirect 2n KO
direct 2n KO
E.C. Simpson and J.A. Tostevin, in progress
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Status we are able to

• calculate two-nucleon removal within a parameter
  free model using specific shell model and
  systematic mean-field (spherical HF) structure
  information to set all important interaction and
  bound states ranges
• observe systematic renormalisation of (1N and)
  2N strength not yet understood quantitatively
  but already allows the identification of
  structure effects beyond these systematics
• have identified spectroscopic value of momentum
  distributions of -2N reactions and have a more
  complete calculation available

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Two proton knockout from 38Si ? 36Mg(0,2)
38Si (?2p) 83 A MeV
uncorrelated
38Si
36Mg
Residue momentum probability
2
0
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Required target-like sp overlaps are available
p
Microscopic overlap from Argonne 9- and 8-body
wave functions (Bob Wiringa et al.) available for
a 9Be target case
Normalised bound state in Woods-Saxon potential
well x (0.23)1/2 Spectroscopic factor
43
Removal strengths at the Fermi surface 2008
Shell M)
44
Antisymmetrized 28Mg ? 26Ne removal of
uncorrelated
4
2
0
J.A. Tostevin, SENUF 06, JPG Conference series
2006