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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
The 30Mg(t, p)32Mg “Puzzle” Revisited!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
Outline!
Short Introduction
The 30Mg(t,p)32Mg Reaction Fortune’s analysis The “Puzzle” Revisited Three-level Mixing
Energies, wavefuntions, and cross-sections Summary
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
“Classic” magic numbers are generally correct only for stable and near stable isotopes Experimental studies of new exo:c isotopes has provided insight on the important role play by the tensor and 3-‐body forces in the changes in shell structure and collec:vity: A delicate balance between the monopole field and correla3ons.
Evolu:on of Shell Structure and Collec:vity R.V.F Janssens, Nature, Vol. 435, 2005.
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
“Classic” magic numbers are generally correct only for stable and near stable isotopes Experimental studies of new exo:c isotopes has provided insight on the important role play by the tensor and 3-‐body forces in the changes in shell structure and collec:vity: A delicate balance between the monopole field and correla3ons.
Evolu:on of Shell Structure and Collec:vity R.V.F Janssens, Nature, Vol. 435, 2005.
N=20 Island of Inversion
32Mg, at the center of this region, has been a subject of intense work for many years, both experimental and theore3cal. à Much evidence has been obtained for the existence of deformed ground states.
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
“Classic” magic numbers are generally correct only for stable and near stable isotopes Experimental studies of new exo:c isotopes has provided insight on the important role play by the tensor and 3-‐body forces in the changes in shell structure and collec:vity: A delicate balance between the monopole field and correla3ons.
Evolu:on of Shell Structure and Collec:vity R.V.F Janssens, Nature, Vol. 435, 2005.
N=20 Island of Inversion
32Mg, at the center of this region, has been a subject of intense work for many years, both experimental and theore3cal. à A clear fingerprint : Rota3onal ground state band
Cf. Heather Crawford’s talk
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
The 30Mg(t,p)32Mg reaction!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
The 30Mg(t,p)32Mg reaction!
E(02+) = 1058(2) keV!
!σ(g.s.) = 10.5(7) mb!σ(02
+) = 6.5(5) mb !!σ(02
+)/σ(g.s.) = 0.62(6)!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
The 30Mg(t,p)32Mg “puzzle”!
| 0gs+ >=α | sph > +β | def >
α 2 ≈ 0.8 β 2 ≈ 0.2
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
A paradigm shift: 2-Level to 3-Level Mixing J!
Guided by shell model we consider the need for 3 configurations to describe the low-energy structure in 32Mg.!
Caurier, Nowacki, Poves PRC 90, 0914302 (2014). -‐-‐ SDPF-‐U-‐MIX interac3on
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
!Construct a mixing matrix of the form:!!!!!!!!Take e0 (0p0h) = 1.4 MeV, e2 (2p2h) = 0.2 MeV, and e4 (4p4h) = 0.0 MeV.!!Diagonalize to extract energies and 0+ wavefunctions of the form:!
3-Level Mixing!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
Diagonalization Solution!
• Constrain Vmixing by matching to experimental E(02+) = 1058(2) keV!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
Diagonalization Solution!
SDPF-‐U-‐MIX interac3on
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
Cross-Section Analysis!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
32Mg:!
T0,2 & T2,4! T0,0 & T2,2!
Cross-Section Analysis!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
Cross-Section Ratio and the 30Mg Wavefunction!
V [MeV]0.2 0.3 0.4 0.5 0.6 0.7 0.8
Mg
|0p0
h> F
ract
ion
30
0.8
0.9
1 + 10m/ + 20
m
00.10.20.30.40.50.60.70.80.91• Constrain the 30Mg ground
state wavefunction based on the cross-section ratio !
σ(02+)/σ(g.s.) = 0.62(6)!
• 32Mg is dominated by 2p2h and 4p4h components (>95%) while 30Mg is predominantly 0p0h, in agreement with experiment !
(W. Schwerdtfeger et al., Phys. Rev. Lett. #103, 012501 (2009).)!
!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
Sum Rule!
V (MeV)
Total
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
A Spectrum of Solutions!
• Shell model prefers a 30Mg ground state more consistent with 80% 0p0h – within 3-level model small modifications to the initial e0, e2 and e4 can yield a consistent solution sets!
3-level model robustly confirms 2p2h/4p4h dominated 32Mg, at the center of the Island of Inversion !
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
A comment on the mixing matrix elements!
< 0p0h |V | 2p2h >=< 2p2h |V | 4p4h >=V
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
A comment on the mixing matrix elements!
< 0p0h |V | 2p2h >=< 2p2h |V | 4p4h >=V
< npnhJ |V | (n+ 2)p(n+ 2)hJ >∝< 0p0h0+ |V | 2p2h0+ >
< 2p2h |V | 4p4h >≈< 0p0h |V | 2p2h > /2Gerace and Green, NPA 93, 110 (1967)
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
A comment on the mixing matrix elements!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
A comment on the mixing matrix elements!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
Inclusion of the third state, namely 4p4h configura:on resolves the “puzzle” of 32Mg discussed by Fortune, and the ground state emerges naturally as dominated at the 95% level by intruder (2p2h and 4p4h) configura:ons. Within a simple three-‐level model, self-‐consistent solu:ons exist that provide good agreement with the experimental excita:on energy of the 0+2 state, the cross-‐sec:on ra:o and the summed cross-‐sec:ons with a reasonable value for the cross-‐sec:on for transfer of two sd neutrons. These scenarios also indicate a 30Mg ground-‐state dominated by the 0p0h component, in line with experimental evidence and shell-‐model expecta:ons .
Summary!
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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!
Office of Science
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Contract No. DE-‐AC02-‐05CH11231 (LBNL), by the U.S. NSF Grant No. PHY-‐1404442, and by the Spanish Ministry of Ciencia e Innovacion under Grant FPA2014-‐57196 and Program Centros de Excelencia Severo Ochoa -‐ SEV-‐2012-‐0249.
Acknowledgements!