Recent Progress in Nuclear Physics Studies through Spins and Nuclear Moments

P.F. ManticaChemistry and NSCLMichigan State UniversityEast Lansing, MI 48824mantica@msu.edu

SPIN2006October 3, 2006

Outline of Talk

• Nuclear spin polarization from intermediate energy reacitons– Nucleon removal reactions– Nucleon pick-up reactions

• Ground state magnetic moments of mirror nuclei– 35K-35S and nuclei with small Sp values – 57Cu-57Ni and shell breaking of doubly-magic

56Ni• Excited-state g factors in even-even nuclei

– Application of transient field to fast beams– Shape transition in the neutron-rich sulfur

isotopes

Magnetic Moments and Nuclear Structure

Since the electromagnetic interaction has a simple and well-known structure, the study of nuclear moments is an effective means for testing nuclear wave functions.

Nuclear magnetic dipole moment:

= <I,M=I|z|I,M=I>

For a nucleon in a shell-model orbit:

neutron823proton585

01

21

121

..

gg

jgggj

s

ssp

1s1/2

1p3/2

1p1/2

1d5/2

2s1/2

1d3/2

1f7/2

1f5/2

28

2028

502p3/2

2p1/2

1g9/2

1g7/2

2d5/2

protons1s1/2

1p3/2

1p1/2

1d5/2

2s1/2

1d3/2

1f7/2

28

2028

50 1g9/2

1g7/2

2d5/2

neutrons

1f5/22p3/2

2p1/2

Magnetic Moments and Mirror Nuclei

If isospin is a good quantum number

The summed moments of mirror nuclei, those nuclei that differ simply by exchange of protons and neutrons, can be directly related to the expectation value of the isoscalar magnetic moment.

JiJi

ii 30

JiT

z iTT,T,Jz

012

Isospin, T , is a quantum number that arises from the identical treatment of protons and neutrons due to the charge independence of nuclear forces. The z-component of isospin, Tz = (N – Z)/2, is a measure of the neutron–proton asymmetry in the nucleus.

38.0)()( JTTTT zz

Isoscalar Spin Expectation Values:T = 1/2 Mirror Partners

17N-17Ne

Spin

exp

ecta

tion

val

ue

1.0

-1.0

0.0

1.5

Known Ground-State Moments

35K, Tz = -3/2

57Cu, Tz = -1/2

Spin Polarization via Fragmentation(nucleon removal)

• Fragments collected off the central beam axis.

• Polarization as large as 20% for 12B fragments at wings of momentum distribution.

• In initial experiments no spin polarization detected at the peak of the momentum yield curve.

• Provides a means for

measuring ground state dipole moments of exotic nuclei.

Asahi et al., Phys. Lett. B251, 488 (1990)

Details of the Kinematical Model

y

z x

Beam

k = (k , k , k )x y z

R = (X, Y, Z)

TargetProjectile

-k / pfx

L

defProjectile- rest fram e

Target

sincos RkRk xyz

LP z /When = 0

Rkyz

00 ppatP

When 0

defLx pk 0

00 ppatP

Nucleon Pick-up Reactions

Pfaff et al., Phys. Rev. C51, 1348 (1995)Souliotis et al., Phys. Rev. C46, 1383 (1992)

18O (E = 80 MeV/nucleon) tPFF ppp outgoing projectile

parttarget

nucleon

0.960

0.965

0.970

0.975

0.980

0.985

19O 18N 17C

AlTa

<p/A

> F/<

p/A>

beam

Fermi

P

PPF

FF

F pApA

AAp 1

From momentum conservation, the data to the left are consistent with the nucleon picked up with the Fermi momentum 230 MeV/c oriented along the direction of the projectile motion

37K Spin Polarization150 MeV/A 36Ar on Be target

Reaction:

36Ar + p 37K

37K fragments implanted into a KBr crystal

T1/2 (37K) = 1.23 sQ+EC (37K) = 6.1 MeV

Polarization monitored by pulsed magnetic field method

Maximum polarization observed when separator tuned just off the peak production of 37K

Groh et al., PRL 90, 202502 (2003)

Spin Polarization via Nucleon Pickup

tPFF ppp outgoing projectile

parttarget

nucleonAt the peak of the momentum distribution,<pF> = p0, <pPF> = pbeam, and <pt> = pFermispin polarization is positive

Lz increases linearly with K

Coupled Cyclotron Facility Layout

• Experimental apparatus: • 4π-Array (N2), • 92-inch chamber (N3), • S800 magnetic spectrograph (S3)• segmented Ge-array for -ray Doppler shift correction• Si-strip-CsI array for high efficiency charged particle coincidence

experiments• Superconducting “sweeper” magnet for n-coincidences at 0

degrees• Modular neutron array (MONA) for high-efficiency neutron

detection• Gas stopping and Penning trap

Dipole Magnet for Nuclear Moment Measurements• A small dipole magnet will be located in the S1 vault for

nuclear moment measurements.– magnet gap = 10 cm – capability for catcher cooling– Bmax = 5000 Gauss – improved PMT performance at– optional vacuum chamber high B fields

Mantica et al., NIM A422, 498 (1999)

Nuclear Magnetic Resonance

• Energy of magnetic substates

E = mIgNB• Energy difference

between adjacent substates

E = gNB• Typical transition

energyE = (1)(5e-27 J/T)(0.1 T)

E = 5e-26 Jradiofrequency region!

Measure β angular distributions:θcos1)θ( 1PAW

Science Motivation for (35K)• Highest mass mirror pair for T=3/2 nuclei

Test of isospin symmetry in heavier nuclei• Proton separation energy of 35K only ~78 keV

Nuclide lies very near proton drip line• Systematic variation of T=3/2 mirror moments

Minamisono et al., PRL 69, 2058 (1992)

Sp = 140 keV

Isoscalar Spin Expectation Values:T = 1/2,3/2 Mirror Partners

17N-17Ne

Spin

exp

ecta

tion

val

ue

1.0

-1.0

0.0

1.5

Magnetic Moment of 35K

L = 600±10 kHz

35K in KBr

g(35K) = 0.261±0.004

rf sweeps between 520 and 620 kHz • based on previous measurement of g(35K) = 0.24(2)*• H0 = 3012 G• FM = ±10 kHz, H1 ~ 2 G

*Schafer et al., PRC 57, 2205 (1998)

Mertzimekis et al., PRC 73, 024318 (2006)

The 35K-35S mirror pair is the heaviest T=3/2 system studied to date. The isoscalar spin expectation value

<> = -0.284±0.040 agrees well with T=1/2 systematics

Isoscalar Spin Expectation Values:T = 1/2,3/2 Mirror Partners

17N-17Ne 35S-35K

Spin

exp

ecta

tion

val

ue

1.0

-1.0

0.0

1.5

Buck-Perez Plot for T = 3/2 Nuclides

Buck, Merchant, and Perez, PRC 63, 037301 (2001)

Plot of gp v. gn extracted for mirror moments shows linear trend with slope and intercept

nn

pp

gGgG

000.1199.1

102.0001.1096.0122.1

np gg

016.0052.1010.0148.1

T = 1/2

T = 3/2

Theory

and results are similar, even though T=3/2 nuclei near the proton drip line

Science Motivation for (57Cu)

• Highest mass mirror pair for T=1/2 nucleiTest of isospin symmetry in heavier nuclei

• Single-proton configuration outside “doubly-magic” 56Ni

Excellent test case for comparison with shell-model predictions

• Systematic variation of Cu magnetic moments shows unexpected behavior

Golovko et al., Phys. Rev. C70 014312 (2004).

Copper-57 = Nickel-56 + proton

57Cu Results

Minamisono et al., PRL 96, 102501 (2006).

The new (57Cu) shows a positive deviation from the systematic trend of the heavier Cu magnetic moments, however, the value is still significantly smaller than theoretical estimates.

Cu magnetic moments

Resonance Curve

(57Cu) = 2.00 ±0.05 N

Breaking of 56Ni core?The 57Cu-57Ni mirror pair is the heaviest T=1/2 system studied to date. The isoscalar spin expectation value:

<> = -0.78±0.031 deviates significantly from predictions that expect 56Ni to have double-magic character

Spin expectation values

Small magnetic moment of 57Cu ground state and negative spin expectation value for the A=57, T=1/2 mirror pair suggests that 56Ni is not a good doubly-magic core in 57Cu

Sulfur isotopes are in a region of changing structure for 20<N<28

g factors can give information on proton and neutron contribution to the wavefunction of the first excited 2+ state

Neutron-Rich S Isotopes: Rapidly Changing Structure

38S

40S

38S

40S

Sensitivity of g factors

• proton & neutron: g different in sign and magnitude

• Extreme single particle result:

826.3,0:586.5,1:

12)( 2

1

s

s

s

ggnggp

gggjg

d5/2

s1/2

d3/2

f7/2

sd shell+0.08

+5.59

+1.92

- 0.55

p3/2- 1.3

• Protons in sd shell,with Z=16 subshell closure at stability

• Single-particle structure influenced by shell gaps: f7/2 gap, s1/2-d3/2 gap

355 mg/cm2 Au target for intermediate-energy Coulomb excitation (with spin alignment)

110 mg/cm2 Fe target, at room temperature. Magnetized by external electromagnet

40 MeV/u

20 MeV/u

~5 MeV/uProjectiles:

38S: 105 pps E(2+)=1292 keV (2+)= 4.9 ps

40S 104 pps E(2+)= 903 keV (2+)= 20 ps

-rays

gBTF

No B applied B appliedExcited-state spin precesses while traversing the magnetized foil

High velocity transient field technique

Transient field endstation

Doppler corrected spectra (=40o). Correction performed event-by-event using particle energy measured in phoswich detector.

Gamma-ray angular distribution in projectile frame, corrected for Lorentz boost.

nucnuc

lab dd

2

2

)cos1(1

38,40S results

g (2+ ; 38S) = +0.13(5)g (2+ ; 40S) = -0.02(6)

Using BTF parametrizationand from double ratios,g factors were extracted.

(radioactive)

(stable)

gp(theory) gn(theory) g(theory) g(experiment)38S +0.298 -0.301 -0.0026 +0.13(5)40S +0.276 -0.241 +0.035 -0.02(6)

g(2+) results: 38,40S

Davies et al., PRL 96, 112503 (2006).

SummaryBeta-NMR spectroscopy at the NSCL

• Spin polarization observed for proton pick-up reactions at fragmentation energies

• New data for spin expectation values of T=3/2 and T=1/2 nuclides

Transient field method on fast fragments• Fast-fragment g(2+) measurements

successfully performed at the NSCL• Lifetimes as short as 1-2 ps are accessible• TF measurements with rates as low as 104

particles per secondOther areas under development

• TDPAD on high-spin isomers near 68Ni• Development of NQR methods at the NSCL

CollaboratorsPolarization via Nucleon Pickup• A.D. Davies, D.E. Groh, S.N. Liddick, T.J. Mertzimekis,

J.S. Pinter, W.F. Rogers, A.E. Stuchbery, and B.E. Tomlin

Magnetic Moment of 35K• A.D. Davies, D.E. Groh, S.N. Liddick, T.J. Mertzimekis,

and B.E. TomlinMagnetic Moment of 57Cu• A.D. Davies, M. Hass, T. J. Mertzimekis, K. Minamisono,

J. Pereira, W.F. Rogers, J. Stoker, B. Tomlin, and R. R. Weerasiri

g(2+) of 38,40S• A. Becerril, C.M. Campbell, J.M. Cook, P.M. Davidson,

A.D. Davies, D.C. Dinca, A. Gade, S.N. Liddick, T.J. Mertzimekis, W.F. Mueller, A. Stuchbery, J.R. Terry, B.E. Tomlin, A.N. Wilson, K. Yoneda, and H. Zwahlen

Supported in part by NSF PHY-01-10253 and NSF PHY-99-83810