the mg(t, p) mg “puzzle” revisited · nuclear structure 2016 – knoxville, tn, usa! july...

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Nuclear Structure 2016 – Knoxville, TN, USA!July 24-29, 2016!

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The 30Mg(t, p)32Mg “Puzzle” Revisited!

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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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“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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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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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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The 30Mg(t,p)32Mg reaction!

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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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The 30Mg(t,p)32Mg “puzzle”!

| 0gs+ >=α | sph > +β | def >

α 2 ≈ 0.8 β 2 ≈ 0.2

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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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!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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Diagonalization Solution!

•  Constrain Vmixing by matching to experimental E(02+) = 1058(2) keV!

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Diagonalization Solution!

SDPF-‐U-‐MIX interac3on

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Cross-Section Analysis!

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32Mg:!

T0,2 & T2,4! T0,0 & T2,2!

Cross-Section Analysis!

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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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Sum Rule!

V (MeV)

Total

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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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A comment on the mixing matrix elements!

< 0p0h |V | 2p2h >=< 2p2h |V | 4p4h >=V

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< 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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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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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!

the mg(t, p) mg “puzzle” revisited · nuclear structure 2016 – knoxville, tn, usa! july...

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