Probing the evolution of shell structure with in-beam spectroscopy

Alexandra Gade

National Superconducting Cyclotron Laboratory

and

Department of Physics and Astronomy

at Michigan State University, East Lansing, Michigan 48824

Outline

• One-nucleon exchange (HI-induced) and N=30 in neutron-rich Ar and S nuclei … or the structure beyond N=28

• Two-proton knockout towards N=40 … or mounting evidence for intruder configurations near N=40

• Nuclear structure at N=50 … news on the collectivity of Se and Ge

Experimental approach –In-beam -ray spectroscopy

exotic beam

targetreacted

beam

v/c=0.3-0.4

-Particle spectroscopy

Identification of the reaction residues

Momentum distributions

Scattering angle

- -ray spectroscopy

Identify the final state

Tag the inelastic process

Target position

Focal plane

• Experimental task: Quantify changes encountered in rare isotopes and measure observables that are calculable and can serve to discriminate between theories

Inverse-kinematics, HI-induced nucleon-

exchange reactions with fast beams: 9Be(48K,48Ar+ )X and 9Be(46Cl,46S+ )X

Reaching nuclei with more neutrons than the primary and secondary beams

• 48Ca primary beam

• 110 x 103 48K per second secondary

projectile beam (pure)

• 6 x 103 46Cl per second secondary

projectile beam (purity exceeding 98%)

• 376 mg/cm2 9Be reaction target

• Inclusive cross sections: 48Ar: =0.13(1)mb (~1 out of 310,000) 46S: =0.057(6)mb (~1 out of 700,000)

A. Gade et al., Phys. Rev. Lett. 102, 182502 (2009)

True needle in haystack problem

Reaching closer to the driplines

Inverse-kinematics, HI-induced

nucleon exchange reactions with fast

beams: 9Be(48K,48Ar+ )X

Narrow momentum distribution in agreement with 2-body reaction and observations by G.A. Souliotis et al., PRC 46, 1383 (1992)

A. Gade et al., Phys. Rev. Lett. 102, 182502 (2009)

Gamma-ray spectroscopy closer to the neutron dripline

Inverse-kinematics, HI-induced

nucleon exchange reactions with fast

beams

Nuclei with more neutrons than the

beam can be produced at cross

sections sufficient for -ray

spectroscopy

48Ar: transitions in agreement with A. Navin et al., PRL 101, 032501 (2008) Deep-inelastic scattering at GANIL

A. Gade et al., Phys. Rev. Lett. 102, 182502 (2009)

Region around the key nucleus 42Si -The role of N=30

Status

• Sizeable Z=14 sub-shell gap from cross sections in one- and two-proton knockout at NSCL J. Fridmann et al., Nature 435, 922 (2005); PRC 74, 034313 (2006)

• First in-beam -ray spectroscopy of 42Si at GANIL revealed low-lying 2+ state B. Bastin, S. Grevy et al., PRL 99, 022503 (2007)

• New effective interaction in the sd-fpvalence space, SDPF-U, one version for Z>14 and one version for Z ≤ 14 (essential for the description of 42Si (N=28): monopole shift (fp shell gap) and pairing modifications) F. Nowacki and A. Poves, PRC 79, 014310 (2009)

Question: What is the influence of the monopole shift and pairing modifications on N=30?

N=28N=20 N=22 N=24

Systematics of 2+1 states in comparison to shell model

SDPF-NR interaction: S. Nummela et al., PRC 63, 044316 (2001)

SDPF-NR

• 2+ of 40,42Si too high by 400 and 700 keV, respectively,

• 46S too high relative to 44S

2+1 2+

1

Implement pairing and shell gap modifications step-by-step with linear Z-dependent interpolation

Shell modelpairing modification

SDPF-NR2

• 2+ of 42Si still too high

• 44S too low

SDPF-NR2

• SDPF-NR for Ca (Z=20)

• J=0+ fp-shell matrix elements Vnn (pairing) reduced by 15% for Z=14; Z-dependent, linear interpolation for Z=16,18

2+1 2+

1

Shell modelfp shell gap

SDPF-NR3

• 2+ of 40,42Si good

• 44S much too low

SDPF-NR3

• SDPF-NR for Ca (Z=20), SDPF-NR2 for Z=14,16,18

• Lowering the neutron p1/2 and p3/2 orbits by 1 MeV for Z=14; Z-dependent, linear interpolation for Z=16,18

2+1 2+

1

Shell modelconclusion

Outcome for the systematic of 2+1 states

• The modifications needed to describe 42Si – SDPF-NR3 – fail for 44S and 46Ar (linear interpolation does not work, no smooth change in the effective interaction, rather a sudden change – in agreement with the findings by Nowacki and Poves)

• The description of the N=30 isotones improves, but the N=30 isotones are much less impacted by the changes that drive structure 42Si

• While SDPF-NR overpredicts the 2+ energy of 48Ar and 46S by 136 keV and 282 keV, respectively, SDPF-NR3 moderately lowers these energies and gives better agreement (now within 51 keV and 86 keV)

A single effective interaction valid in the sd-pf shell is still a challenge

Motivation – Another “Island of Inversion” around N=40?

• Beta decay to 64,66Fe [M. Hannawald et al., PRL 82, 1391 (1999)]

• Beta decay to 60-63Cr [O. Sorlin et al., EPJ A 16, 55 (2003)]

• Rotational band built on 9/2+ in 55,57Cr [A. Deacon et al., PLB 622, 151 (2005)]

• Low-lying 9/2+ isomer in 59Cr at 503 keV with possibly oblate deformation[S. J. Freeman et al., PRC 69, 064301 (2005)]

• Large deformation of 62Cr [N. Aoi et al., J. Phys.: Conf. Ser. 49, 190 (2006), PRL 102, 012502 (2009)]

The attractive monopole part of the tensor force ( f7/2 - f5/2 ) weakens as protons are removed from f7/2. The f5/2 orbit shifts up in energy and the gap between the f5/2 and g9/2 orbits is reduced, allowing neutron occupancy of the intruder g9/2 orbit already for nuclei with fewer than 40 neutrons

T. Otsuka et al., PRL 95 232502 (2005)

The experiment

• One-proton knockout from 67Co and 69Co 66Fe and 68Fe

• Two-proton knockout from 66Fe, 68Ni and 70Ni 64Cr, 66Fe and 68Fe

• Inclusive cross section for the production of 64Cr from 66Fe

-ray spectroscopy of 66Fe and 68Fe

Projectile beam energies between 72-84 MeV/u

P. Adrich et al., PRC 77, 054306 (2008)

Iron isotopes – N=40

P. Adrich et al., PRC 77, 054306 (2008)

4+ 2+ and 2+ 0+

transitions in agreement with the measurement of M. Hannawald et al., PRL 82, 1391 (1999)

In a single-particle picture, the removal of 2 protons from f7/2can populate states with spins from 0+, 2+, 4+ and 6+

Iron isotopes – N=42

P. Adrich et al., PRC 77, 054306 (2008)

Observation of excited states in 68Fe

A structural change between Ni and Fe at N=40

P. Adrich et al., PRC 77, 054306 (2008)

The direct two-proton knockout probes the overlap of the wave functions of the projectile ground state and the residues’ final state. Small cross section structural change (reduced overlap) between the ground state and final state configurations in 66Fe and 64Cr

A possible explanation …thanks to K. Sieja and F. Nowacki

http://www.nscl.msu.edu/~brown/ECT-2009/pdf/29-7-Sieja.pdf

Intermediate-energy Coulomb excitation of 82Ge and 84Se

• Se and Ge isotopes have rich nuclear structure

• Shape coexistence rules from A ~ 70 to N=Z

• Most neutron-rich Se and Geaccessible for experiments are around N=50 – north of double-magic 78Ni

Collectivity at N=50 – Shell ModelWork in progress

• N=50 Se and Ge isotones emerge as very useful to guide effective interactions!

• Work in progress, B.A. Brown with input from M. Honma et al: Where are the very different predictions for the B(E2) values for the N=50 Ge and Se originating from in the different effective interactions?

JUN45: M. Honma, T. Otsuka et al., PRC 80, 064323 (2009)jj4xyz: Interactions from B.A. Brown, used in D. Verney et al., PRC 76, 054312 (2007)

Collectivity in the Se and Ge isotopic chains – Mean field

• CHFB-5DCH describes well the trend beyond A=74 but overpredictsthe B(E2) values towards the N = Z line

• HFB-17 approximately reproduces the trend for Ge heavier than A=70 but overpredictsthe collectivity towards N=Z as well. The Se chain is not well described.

CHFB-5DCH: J.-P. Delaroche, M. Girod, et al., PRC 81, 014303 (2010)HFB-17: S. Goriely et al., PRL 102, 152503 (2009)

Excitation of 4+ states in the inelastic scattering off 9Be?!

… why are Se and Ge so different?

• Inelastic and proton scattering on the stable selenium isotopes 74−82Se revealed that the 2+1states are excited the strongest, followed by the first 3− and, at markedly less cross section, higher-lying 2+ states and the 4+1level.

• One might expect 9Be-induced scattering to yield a similar population pattern, however, it seem that in 84Se+9Be the 4+1state is more strongly excited than the 3− state.

An old discussion - hexadacapole degrees of freedom in Se isotopes

• From inelastic scattering of polarized protons on 74−82Se Matsuki et al. present indications for a static or dynamic hexadecapole shape transition that occurs between the light (74,76,78Se) and heavier (80,82Se) selenium isotopes and point out that the hexadecapole degree of freedom plays an important role in the selenium isotopes.

• Ogino et al. find the hexadecapole strength fragmented strongly for 74−82Se.The transition strength to the 4+1 state was found to be weak except for the case of 82Se where a transition strength of almost 3 spu was measured for the first 4+ state.

S. Matsuki et al., Phys. Rev. Lett. 51, 1741 (1983).K. Ogino, Phys. Rev. C 33, 71 (1989).

To be finished soon …

• Origin of the difference in the SM effective interactions at N=50 for Se and Ge (B. A. Brown with input from M. Honma et al.)

• Why are the 4+ states excited with very different cross sections for the Se and Ge N=50 isotones?

• In general, population of excited states beyond the first 2+ in inelastic scattering induced by a 9Be target (collaboration with J. A. Tostevin, Surrey)

… but for now “Work in Progress”

• The role of N=30 in the region around 42Si?

• N=30 isotones are much less impacted by the changes that drive structure 42Si

• Effective interaction changes suddenly (Z-dependent interpolation failed)

• In-beam -ray spectroscopy following HI-induced nucleon exchange reactions may provide access to nuclei previously thought out of reach

• Evidence for a significant structural change between 66Fe and 64Cr (N=40)

Sensitivity of two-nucleon knockout to wave-function overlaps

• Nuclear structure at N=50, the role of Ge and Se – Shell-model interactions disagree and puzzling excitation of a 4+ state … work in progress – stay tuned.

Summary and outlook

A collaborative effort

P. Adrich

T. Baugher

D. Bazin

J. M. Cook

C. Aa Diget

A. Gade

T. Glasmacher

G.F. Grinyer

S. McDaniel

A. Ratkiewicz

K. P. Siwek

K. Walsh

D. Weisshaar

J. A. Tostevin

B. A. Brown

T. Otsuka

M. Honma

A collaborative effort

P. Adrich

T. Baugher

D. Bazin

J. M. Cook

C. Aa Diget

A. Gade

T. Glasmacher

G.F. Grinyer

S. McDaniel

A. Ratkiewicz

K. P. Siwek

K. Walsh

D. Weisshaar

J. A. Tostevin

B. A. Brown

T. Otsuka

M. Honma