Investigation of Single-Particle Structure in 26Na using thenew SHARC Array

Gemma Wilson

Investigation of Single-Particle Structure in 26Na using thenew SHARC Array
25Na (d,p) 26Na

p3/2
f7/2
d3/2
s1/2

Multiplets:
π(d5/2)⊗ʋ(p3/2)⟶(1,2,3,4)-

odd-odd final nucleus
High density of states

d5/2
protons

neutrons

Gamma-­‐ga.ng	  neededMigration of levels as nuclei become more exotic, normalised to 7/2- energy
2

7/23/2-

N=20 gap

3/2+-2

N=16 gap
1/2+-4Na-6
1614

12108

Atomic number, ZDashed line: N=15Solid line: N=173/2-, N=157/2-, N=153/2+, N=151/2+, N=153/2-, N=177/2-, N=173/2+, N=17Na, Z=1121O, N=1323O, N=156Relative energy (MeV)

0SHARC•Upstream box of 4 DSSSDs•Downstream box of up to 4 dE-E
•Upstream CD of 4 DSSSDs• Downstream of SHARC• 4 clovers at 90˚, 4 at 135˚
• 10µm scintillation foil with active area
• Full BGO suppressionof 40mm x 40mm
• Each clover has 32-fold segmentation• Mounted with 30µm Al foil to stop
fusion evaporation products

TIGRESS Trifoil

Experimental Setup
SHARC
Downstream box
Elastically scattered p and dd(25Na,p)26Na at TRIUMF
Beam: 3x107 pps,
5 AMeV 25Na from ISAC IITIGRESS
8 x HPGe
resolution anddecay scheme

CD detector
ejected protons(CD2)n target
0.5mg/cm2
SHARC
Upstream box

TrifoilTags recoil events
All beam goes throughejected protons

30µm Al foil
Catches fusion evaporation
products from carbon

Use of Trifoil for vetoing γ rays
407026Na511 keV

Ungated974 keV25Na ` ïTrifoil gated1509

837 keV
25Na ` ï

26

1266
031
P CN233
Na1612 keV
25Na ` ï

1806026
Na

Data from one clover. Doppler correction and addback applied.

signal to background ratio improved by a factor of 10•67% detection efficiency of γ rays from 26Na[1]•[1] G.W. et al., J. Phys. Conf. Ser. 381, 012097 (2012)

Analysis

Trifoil gatedAnalysis

Decays straight to theground state

Trifoil gated

324
151

233.3 2+
233

Using the Ex vs Eγ plot to identify γ rays

406.5 2+407

[1]82.5 1+151 keV

4000

0 3+233 keV

26Na

3500

407 keVCounts/1 keV

3000
2500
2000

174 keV

1500

419 keV

324 keV

1000
50000100200300

E (keV)[1] Sangjin Lee et al., Phys. Rev. C 73, 044321 (2006)

400

500

Eγ/keV151

233

233.3 2+82.5 1+

4000

0 3+

3500

26Na

Counts/1 keV

3000
2500
2000

174 keV

1500

419 keV

1000
500
00324

Using the Ex vs Eγ plot to identify γ rays

406.5 2+
407

[1]

100

200

300

400

500

E (keV)

151

233

233.3 2+82.5 1+

4000

0 3+

3500

26Na

Counts/1 keV

300025002000

174 keV

1500

419 keV

1000
500
00324

Using the Ex vs Eγ plot to identify γ rays

406.5 2+407

[1]100200300

400500E (keV)

E*
407
233
82gs



151

233

233.3 2+82.5 1+

4000

0 3+

3500

26Na

Counts/1 keV

3000
2500
2000

174 keV

1500

419 keV

1000
500
00324

Using the Ex vs Eγ plot to identify γ rays

406.5 2+
407

[1]

100

200

300

400500E (keV)

E*
407
233
82gs

Angular distributions
7 states in 26Na with a ground-state decay branch analysed• Proton angular distributions extracted from γ-ray gating•ℓ-transfer deduced from proton angular distributions•

Theoretical cross-sections calculated using ADWA Johnson-Soper
method (R.C. Johnson and P.J.R. Soper, Phys. Rev. C. 1, 976 (1970))• For states with no angular distribution extracted, Jπ assignments
inferred from the N=15 isotone, 28Al
•233-keV state:
1dm/d1 (mb/Sr)

dm/d1 (mb/Sr)

1

0.1

0.01

0.001

s1/2
0306090elab (°)

120

0.1

0.01

d3/2

s1/2150d3/2

1800.001
030

6090elab (°)

120150180

233-keV state:1dm/d1 (mb/Sr)

dm/d1 (mb/Sr)

10.1

0.01

0.1

0.01

s1/2

d3/2

s1/20.001
030

6090
elab (°)

120150d3/20.001
1800306090
elab (°)

12015018010101

1
dm/d1 (mb/Sr)

dm/d1 (mb/Sr)

407-keV state:

0.1

0.01

0.1

0.01

s1/2

d3/2

s1/20.001
030

6090
elab (°)

120150d3/21800.001
030

6090
elab (°)

120150180

233-keV state:
1dm/d1 (mb/Sr)

dm/d1 (mb/Sr)

10.1

0.01

0.10.01

d 407-keV
s1/2s direct measurements of the 233-dor
There have been no previous
3/2+ [1,2]states;
theyhave
onlybeen
previously
deducedtobe20.001
0.001
03060901201501800306090120150180
1/2

3/2

elab (°)

elab (°)[1] Sangjin Lee et al., Phys. Rev. C 73, 044321 (2006) -14C(14C,d)407-keV state:
26Mg(3H, 3He)26Na[2] 10K.I. Pearce et al., Phys. Rev C 35, 5 (1987)
101
dm/d1 (mb/Sr)

dm/d1 (mb/Sr)

10.1

0.01

0.1

0.01

s1/2

d3/2

s1/20.001
0306090elab (°)

120150d3/21800.001
0306090elab (°)

120150180

Substate populations over proton CM angle for a 2.2 MeV state in 26Na
0.4

s1/2 20.2

m=2
m=1
m=0+

p3/2 40.16

0.3

m=4
m=3
m=2
m=1
m=0W(m)

W(m)

0.12
0.2

0.1

00.04

0102030

CM (°)

4050

d3/2 4
0.16

060

0.2+

m=4
m=3
m=2
m=1
m=00102030

CM (°)

4050

f7/2 6

0.12W(m)

0.12
W(m)

0.0860-m=6m=5
m=4
m=3m=2m=1
m=00.08

0.08
0.04
0.04
00102030

CM (°)

40506000102030

CM (°)

405060The γ-ray angular distribution varies as a function of proton angle, so proton
angular distributions are distorted if extracted with the requirement of a γ ray.
The effect is calculated by integrating the calculated γ-ray angular distribution
for each proton angle over the range of the TIGRESS detectors.

Comparison of proton angular distributions withand without a γ-ray gate
10dσ/dΩ (mb/Sr)

10.10.233 2+, s1/2 M10.233 2+, s1/2 gated
0.407 2+, d3/2 M1
0.407 2+, d3/2 gated
2.2 4-, p3/2 E1
2.2 4-, p3/2 gated
2.2 6-, f7/2 E3
2.2 6-, f7/2 gated

0.01

0.001

020406080

100120140160180

θlab (°)

Gating does not affect the shape of the angular distribution, but the size of thecross section. The spectroscopic factor is recovered by correcting for themeasured γ-ray efficiency.

Proton angular distributions

110.13509 keV

=13134 keV

=12225 keV

=22118 keV

=20.11806 keVd/d (mb/Sr)

0.01

=20.1

0.01

10.1

10.01

0.1407 keV

=00.01

1

10.1
0.1
0.01233 keV
4060

80

100

lab (°)

120

=0140160

0.011804060

80

100

lab (°)

120

140

160

180

Theoretical cross-sections calculated using TWOFNR, using the zero-range ADWA
method[1].
[1] R.C. Johnson and P.J.R. Soper, Phys. Rev. C 1, 976 (1970)

2+ 4072+ 2331+3+1119*

2.4

1446*
3134 66.4
2727 33.62771 41.02853 25.02620 34.0100 3509

2427

323 12.4
174

1+ 15072020 52.3
2427 47.7

4+ 21182193 ~1002118 100

4+ 2225

1786 <20~100 1274

5.8 419

This work
2565

233 57.1
151 42.9820
1806 75.1

3+ 1806
2225 94.2<10 1102

Branching ratios
in red1573 18.3

26Na
794 46.9

2185 20.4

2078 32.7

3205 100

1406 19.2

612 49.4

2797 31.3

4303 (5-)

407 85.2

Energies in keV
1400 6.65011 (3-,4-)4915 (6-)

3509 4-3134 3-2855 2-2193

2+ 4072+ 2331+3+1119*

2.4

1446*
3134 66.4
2727 33.6

2771 41.02853 25.02620 34.0

3134 3-2855 2-794 46.9

2185 20.4

2078 32.7***
100 3509

2427

323 12.4
1741+ 1507

2020 52.3
2427 47.7

4+ 21182193 ~1002118 100

4+ 2225

1786 <20~100 1274

5.8 419

This work
2565

233 57.1
151 42.9820
1806 75.1

3+ 1806
2225 94.2<10 1102

Branching ratios
in red1573 18.3

26Na
3205 100*
1406 19.2

612 49.4

2797 31.3

4303 (5-)

407 85.2

Energies in keV
1400 6.6*5011 (3-,4-)4915 (6-)

2193*3509 4-* Negativeparitystates

Final Spectroscopic Factorssdpf model space with 0.7 MeV reduction
between the sd- and pf-shells

This work
E* (MeV)coupling

S.F. ± ~20%

Jπ

3.512

p3/2

0.54

4-

3.613

p3/2

0.43

4-

3.136

p3/2

0.10

3-

3.377*

p3/2

0.15

3-

2.226

d3/2

0.43

4+

1.648

d3/2

0.59

4+

2.119

d3/2

0.22

4+

1.807

d3/2

0.22

3+

1.247

d3/2

0.32

3+

0.407

s1/2

0.34

2+

0.231

s1/2

0.19

2+

0.233

s1/2

0.14

2+

0.05

s1/2

0.22

2+

E* (MeV) coupling S.F. ± ~20%

*This state also has an f7/2 component, S.F. = 0.17Jπ

Findings - calculations• Identified key states in 26Na for comparison with the shell model. In this region, theshell model is having to reproduce negative-parity states at relatively low energies, andwith the ν(d3/2) orbital giving states lower than the 7/2.
• SPDF-M calculations previously failed in this region (27Ne), which motivated WBP.
WBP-M found good agreement for positive and negative parity levels, and it predicts
the multiplet spitting for the proton-neutron coupling well. Spectroscopic factors arewell produced. WBP-M also worked for 25Ne[1] and 27Ne[2] with a 0.7 MeV shift.
• Full 1 ω s-p-sd-pf WBP-M calculations now being finalised for 26Na, as presented for27Ne. We are finding that the SF comparisons are unaffected, and the shift of 0.7 MeV

is appropriate again.
• Calculations also done for the isotone 28Al, and a shift was also needed.

The states identified in 26Na are key for shell-modelcomparisons[1] W.N. Catford, et al. Phys. Rev. Lett. 104, 192501 (2010)[2] S.M. Brown, et al. Phys. Rev. C 85, 011302 (2012)

Findings - future work

• Technique of gating on a γ ray to extract proton angular distributions works well.
Subsequent analysis showing that large angular coverage for γ rays is proving to beeffective at giving negligible distortion of the proton differential cross-sections.
• Future: Complete 26Na analysis with further SF analysis for cascade decays ofstates and to extract the weaker states. Extend to 29Mg (N=17) to measure SFs
for lowest levels and identify further single-particle strength that is predicted to befound higher in energy (approved at TRIUMF)

Collaborators
W.N. Catford, S.M. Brown, A. Matta
N.A. Orr, N.L. Achouri
G. Hackman, A.B. Garnsworthy, S.J. Williams, C. Pearson, R. Churchman,
M. Djongolov, C. Unsworth and the TIGRESS collaboration

C.Aa. Diget, B.R. Fulton, S.P. Fox, R. Wadsworth

H.C. Boston, A.J. Boston,
L. Harkness, R. Ashley

F. Sarazin

C. Svensson

J.C. Blackmon

R.A.E. Austin

Trifoil gatedGating technique
Statedecay tothe g.s.

Background - general case

Findings
The energies of the negative parity states in 26Na agree with predictions, towithin ~100 keV when the gap between the sd- and pf-shells was reduced
by 0.7 MeV relative to WBP in the s-p-sd-pf calculation
This systematic lowering of the shell gap was also applicable in the study of
25Ne[1] and 27Ne[2]As previously seen in 25Ne [1], we see the ν(d3/2) states ~0.5 MeV higher
than predicted than WBP (which uses USD in the sd-shell)

These findings should motivate improvements to the shell modelinteractions to remove the need for ad hoc adjustments of single particle
levels[1] W.N. Catford, et al. Phys. Rev. Lett. 104, 192501 (2010)[2] S.M. Brown, et al. Phys. Rev. C 85, 011302 (2012)