KNOCKOUT REACTIONS WITH RARE-ISOTOPE BEAMS

Spectroscopic factors and single-particle (unit) cross sections

Single-nucleon knockout: Bound and continuum states

Two-nucleon knockout: A new direct reaction

Absolute spectroscopic factors: What is the number of physical nucleons in a given shell-model state?

Nuclei with no bound states: 7He, 9He, 10Li

New Perspectives on pNew Perspectives on p--shell nucleishell nucleiMichigan State UniversityMichigan State University

July 22 July 22 -- 24, 200424, 2004

HALO AND CONTINUUM STATES

,

,

,

,

,

,

,

,

,

KNOCKOUT REACTION IN INVERSE KINEMATICS AT ENERGIES OF 60-100 MeV/nucleon

kA-1kA

k3

A A-1 Eγ

kA-1

CALCULATION OF THE CROSS SECTIONThe theoretical cross section for a given j channel is

where we define an empirical reduction factor relative to the shell model, describing the effect of contributions that go beyond effective-interaction theory. Initially is assumed to be unity.The single-particle cross sections are calculated in eikonal reaction theory, here for stripping. There is a similar expression for the contribution from diffraction dissociation.

Differential and integral partial cross sections, see:P.G. Hansen, Phys. Rev. Lett. 77, 1016 (1996)J.A. Tostevin, J. Phys. G 25, 735 (1999)K. Hencken, G. Bertsch and H. Esbensen, Phys. Rev. C 54, 3043 (1996)P.G. Hansen and J.A. Tostevin, Ann.Rev. Nucl. Part. Sci. 53, 219 (2003)

>−〈+

= ∑ ∫ jmSSjmbbjBj CNmnsp22 )1(d2

121),( πσ

),(1

2

n

NBjSC

AAR spifjsifj σσ

−=

sR

sR

The 11Be Halo

½-

½+

0.320

0.504

B(E1) =0.1 e2fm2

B(E1) =1.3 e2fm2

11Be

10Be+n

D.J. Millener et al., Phys Rev. C 28, 497 (1983)R. Anne et al., Nucl. Phys. A 575, 125 (1994)

SPECTROSCOPIC FACTORS IN THE 9Be(12Be,11Be+γ)X REACTION

Spectroscopic Factor0ħω 0+2ħω Exp.a)0 0.5 ≈1 (?)

≈0.3

2.18 0.8 0.37(6)

0 0.5 0.42(6)A. Navin et al., Phys Rev.Lett.85, 266 (2000)

1/2- -0.18

10Be+n

γ

5/2+ 1.28

Ghost States1/2+1/2-

1/2+ -0.50

SPECTROSCOPIC FACTORS IN THE 12C(11Li,10Li)X REACTION

Sexp1.01.90.1

H. Simon et al., Phys. Rev. Lett. 83 (1999) 496C.A. Bertulani and P.G. Hansen, to be published

PRECISION DETERMINATION OF THE SPECTROSCOPIC FACTOR IN THE 9Be(15C½+,14C0+)X REACTION

From 14C-gamma coinc. the branch to excited levels is 28.2(24)%

The inclusive cross section isσincl = 140.2(46) mb

(Average of two measurements)The gamma coincidences (left) give a ground state branch of 71.8(24)%

The resulting partial cross section is σ(0+) = 100.8(44) mb, which gives the spectroscopic factor

1.01(4)(5)

J.R. Terry et al., Phys. Rev. C, 69, 054306 (2004)

SPECTROSCOPIC FACTORS FROM SINGLE-NUCLEON KNOCKOUT AND COULOMB DISSOCIATION OF 0+⊗s1/2 STATES

T. Aumann et al., Phys. Rev. Lett. 84, 35 (2000)R. Palit et al., Phys. Rev. C 68, 034318 (2003)J.R. Terry et al., Phys. Rev. C, 69, 054306 (2004)T. Nakamura, to be publishedTheory (B.A. Brown), includes c-o-m correction

0

0.5

1

Spec

tros

copi

c Fa

ctor

0

0.5

1

11Be 15C

Nucl. Nucl. Theo.Coul.Theo.Coul.

TWO-PROTON KNOCKOUT FROM A NEUTRON-RICH NUCLEUS AT HIGH ENERGY IS A DIRECT REACTION

D. Bazin, B.A. Brown, C.M. Campbell, J.,A.Church, D.C. Dinca, J. Enders, A. Gade, T. Glasmacher, P.G. Hansen, W.F. Mueller, H. Olliver, B.C. Perry, B.M. Sherrill, J.R. Terry, J.A. Tostevin, Phys. Rev. Lett., 91, 012501 (2003)

Note: The theoretical problem is more involved here than for one-nucleon knockout. The cross section does not factorize! Coherence effects!

9.6 9.8 10 10.2 10.426Ne Parallel Momentum [GeV/c]

0

500

1000

σinc = 1.50(10) mb

Theory (0d)2

σth = 1.35 mb

TWO-PROTON KNOCKOUT CROSS SECTIONS FROM RESIDUE-GAMMA COINCIDENCES

28Mg →26Ne(0+, 2+, 4+) σ(in mb)

TWO-PROTON KNOCKOUT CROSS SECTIONS FROM RESIDUE-GAMMA COINCIDENCES

28Mg →26Ne(0+, 2+, 4+) σ(in mb)

D. Bazin et al., Phys. Rev. Lett., 91, 012501 (2003)J.A. Tostevin, G. Podolyák et al., in preparation

Note the destructive interference in the L=2 channel. This is reproduced in the new theory that combines sd-many-body wave functions with four-body eikonal reaction theory.

40

80

120

0 1 2 3Gamma Energy [MeV]

1.4838(7)%

2.0253(5)% 1.70

10(5)%

Iπ E σunc σth σexp0+ 0.00 0.39 0.53 0.70(15)2+ 2.02 0.48 0.16 0.09(15)4+ 3.50 0.87 0.52 0.58(9)2+ 3.72 - 0.22 0.15(9)

0 0.2 0.4 0.6 0.8 1Stheo/(2j+1)

0

0.2

0.4

0.6

0.8

1

1.2

S exp

/(2j

+1)

l = 0l = 1l = 2l = 3

Rs = 1.00

Rs = 0.65

Measured vs. Theoretical Spectroscopic Factors in Units

of the Maximum Sum-Rule Value

P.G. Hansen and B.M. Sherrill, Nucl. Phys. A 693, 133-168 (2001)

J. Enders, A. Bauer, D. Bazin, A. Bonaccorso, B.A. Brown, T. Glasmacher, P.G. Hansen, V.Maddalena, K.L. Miller, A. Navin, B.M. Sherrill and J.A. Tostevin, Phys. Rev. C 65, 034318 (2002).

P.G. Hansen and J.A. Tostevin, Annual Review of Nuclear and Particle Science 53, 219 (2003)

J.R. Terry et al. Phys. Rev. C, in press

Alexandra Gade et al., to be published

Update Feb. 2004

THE (e,e’p) REACTION FINDS REDUCTION FACTORS OF 0.6 - 0.7 RELATIVE TO MEAN-FIELD THEORY

W. Dickhoff and C. Barbieri, Prog. Nucl. Part. Sci., in press.G.J. Kramer, H.P. Blok and L. Lapikas, Nucl. Phys. A 679, 267 (2001).V.R. Pandharipande, I. Sick and P. deWitt Huberts, Revs.Mod.Phys. 69, 981 (1997).

REDUCTION FACTOR Rs FOR WEAKLY BOUND(Sp = 0.14 and 1.3 MeV) RADIOACTIVE NUCLEI

100 1000200 50050

Beam Energy [A MeV]

0

0.2

0.4

0.6

0.8

1

Red

uctio

n Fa

ctor

Rs

70 80

(8B,7Be) 0p3/2S = 0.137 MeV

(9C,8B) 0p3/2 1.296

D.Cortina-Gil et al., Phys. Lett. B 529, 36 (2002) and references thereinB.A. Brown, PGH, B.M. Sherrill and J.A. Tostevin, Phys. Rev. C 65, 061601 (2002)J.Enders et al., Phys. Rev. C 67, 064301 (2003)

Z

18

8

N14

Knockout of a d5/2 valence neutron from the N=14 nuclei 22O and 32Ar

Pote

ntia

l Dep

th [

MeV

]-10 -5 0 5 10

-60-50-40-30-20-100

-10 -5 0 5 10

0 2 4 6Radius [fm]

0 2 4 6Radius [fm]

0

0.2

0.4

0.6

Rad

ial d

istr.

[fm

-1]

32Ar22Oπ

π

π

π

ν

ν

ν

ν

21O 31Ar

Density distributions from Hartree-Fock calculations with the Skyrme-X interaction:B.A Brown, Phys. Rev. C 58, 220 (1998)

Sn =21.99(5) MeV

Sp =2.45 MeV

STRUCTURE: 31,32Ar are good sd-shell nuclei

Counts/11 keV

.

ef

ef

B(E2

)(

ef

m)

24

DSAM

[7]

(p,p

)[

9]

,

Coulomb

ex

.[

10]

Present

wor

k

Nakada

et

al

.[

8]

ee

l.

[93]

suka

et

al

.[

94]

Brown

[103]

5/2+

0.95

0.40(6)

1.61

0.00

1/2+

3/2+

30Cl + p

C2Sth

0.08

0.37

4.1231Ar

πd3/2 νd3/2πd5/2 νd3/2

GTR

The Giant Gamow-Teller Resonance in the Beta Decay of 32Ar:T. Björnstad et al., Nucl. Phys. A 443, 283 (1985)

E.K. Warburton and B.A. Brown, PRC 46, 923 (1992)

1.74

0.94

Eth(g’A/gA)2 = 0.49(5)

MOMENTUM DISTRIBUTION AND CROSS SECTION FOR THE 9Be(32Ar, 31Ar)x REACTION

Counts/11 keV

.

.

ef

ef

B(E2

)(

ef

m)

24

DSAM

[7]

(p,p

)[

9]

,

Coulomb

ex

.[

10]

Present

wor

k

Nakada

et

al

.[

8]

ee

l.

[93]

Ot

suka

et

al

.[

94]

Brown

[103]

Alexandra Gade, D. Bazin, B.A. Brown, C.M. Campbell, J.A. Church, D.C. Dinca, J. Enders, T. Glasmacher, P.G. Hansen, Z. Hu, K.W. Kemper, W.F. Mueller, H. Olliver, B.C. Perry, L.A. Riley, B.T. Roeder, B.M. Sherrill, J.R. Terry, J.A. Tostevin and K.L. Yurkewicz, Phys. Rev.Lett, 93, 042501 (2004)

σexp = 10.4(13) mbTheory:C2S = 4.12σsp = 9.92 mb

Rs = 0.24(4)(4)10 10.2 10.4

31Ar Momentum [GeV/c]

0

10

20

30

40

50

Eve

nts/

bin

31Ar

l = 0

l = 2

.

THE 9Be(22O,21O)X REACTION

5/2+

1.33

2.19

3.15

3.81

0.00

1/2+

3/2+

5/2+

20O + n

C2S0.14

0.03

0.23

5.2221O

Sn = 6.85(6) MeVMeasured inclusive cross sectionGANILa) 51 MeV/nucleon: 120(14) mbGSIb) 938 MeV/nucleon: 70(9) mb

Rs = 0.70(6)

a) E. Sauvan et al. Phys. Lett B 491,1 (2000)

b) T. Aumann and B. Jonson, personal communication (2004)

REDUCTION FACTOR Rs vs. SEPARATION ENERGY

0 5 10 15 20 25Nucleon Separation Energy [MeV]

0

0.2

0.4

0.6

0.8

1

Red

uctio

n Fa

ctor

Rs

-n-p

22O

32Ar

15C

B.A. Brown, PGH, B.M. Sherrill and J.A. Tostevin, Phys. Rev. C 65, 061601 (2002)J.Enders et al., Phys. Rev. C 67, 064301 (2003)A. Gade et al., Phys. Rev. Lett. 93, 042501 (2004)K. Miller et al., to be publishedJ.R. Terry et al., Phys. Rev. C, 69, 054306 (2004)

ABSOLUTE SPECTROSCOPIC FACTORS FOR KNOCKOUT REACTIONS ON LIGHT p-SHELL NUCLEI. COMPARISON WITH

THE VARIATIONAL MONTE-CARLO METHODa)

Initial State Final State Spectroscopic FactorPJTb) VMCa) Exp. Method Ref.

7Li(3/2-) 6He(0+,2+) 1.15 0.55 0.58(3) (e,e’p) (c)8B(2+) 7Be(3/2-,1/2-) 1.44 1.27 1.23(6) Knockout (d)9C(3/2-) 8B(2+) 1.03 1.11 0.85(6) Knockout (d)

a) S.C. Pieper and R.B Wiringa, Annu. Rev. Nucl. Part. Sci. 51, 53 (2001); R. B.Wiringa, personal communication.

b) With the p-shell PJT interaction. Includes the center-of-mass correction. B.A. Brown, Prog. Part. Nucl. Phys. 47, 517 (2001).

c) L. Lapikás, J. Wesseling and R.B. Wiringa, Phys. Rev. Lett. 82, 4404 (1999).d) B.A. Brown, PGH, B.M. Sherrill and J.A. Tostevin, Phys. Rev. C 65, 061601

(2002); J.Enders et al., Phys. Rev. C 67, 064301 (2003).

BEYOND THE NEUTRON DRIP LINE: THE OBSERVATION OF FINAL-STATE INTERACTIONS

L. Chen, B. Blank, B.A. Brown, M. Chartier, A. Galonsky, PGHand M. Thoennessen, Evidence for an l=0 ground state in 9He, Phys.Lett. B 505, 21 (2001).

M. Chartier, J.R. Beene, B. Blank, L. Chen, A. Galonsky, N. Gan, K.Govaert, P.G. Hansen, J. Kruse, V. Maddalena, M. Thoennessen, R.L. Varner, Identification of the Li-10 ground state, Phys. Lett. B 510, 24 (2001)

,,

,

BEYOND THE DRIP LINEIdentification of the 1s state in the unbound nuclear system 9He from the observation of final-state interactions in 8He+n following direct one- and two-proton knockout on 11Be

8 7 6 5 4 3 2Atomic Number Z

-14

-12

-10

-8

-6

-4

-2

0

2

E*- S

n [M

eV]

14N 13C 12B 11Be 10Li 9He15O

0 10r [fm]

0 10 20 30 40r [fm]

0 10 20r [fm]

15O

11Be

10Li0.5 MeV

1/2+

1/2-

7He

9Heas< -10 fm

`

RECENT EXPERIMENTS ON 7He(b) p(6He,6Li+γ)n

(c) 7Li(d,2He)7He

(a) 12C(8He,6He+n)X

(a) M. Meister et al., Phys. Rev. Lett. 88, 102501 (2002)

(b) G.V. Rogachev et al., Phys. Rev. Lett. 92, 232502 (2004)

(c) N. Ryezayeva et al., KVI Annual Report (2003)

Important contributions to this program came from:

T Aumann, D. Bazin, C.A. Bertulani, B.A. Brown, J. Enders, A. Gade, T. Glasmacher, V. Maddalena, W.F. Mueller, A. Navin, B. Sherrill, J.R. Terry, M. Thoennessen (National Superconducting Cyclotron Laboratory, Michigan State University), J.A. Tostevin(University of Surrey, U.K.)

Reviews:P.G. Hansen and B.M. Sherrill, Nucl. Phys. A 693, 133-168 (2001)P.G. Hansen and J.A. Tostevin, Annual Review of Nuclear and Particle Science 53, 219 (2003)

HALO AND CONTINUUM STATESKNOCKOUT REACTION IN INVERSE KINEMATICS AT ENERGIES OF 60-100 MeV/nucleonCALCULATION OF THE CROSS SECTIONSPECTROSCOPIC FACTORS IN THE 9Be(12Be,11Be+?)X REACTIONSPECTROSCOPIC FACTORS IN THE 12C(11Li,10Li)X REACTIONPRECISION DETERMINATION OF THE SPECTROSCOPIC FACTOR IN THE 9Be(15C½+,14C0+)X REACTIONSPECTROSCOPIC FACTORS FROM SINGLE-NUCLEON KNOCKOUT AND COULOMB DISSOCIATION OF 0+?s1/2 STATESTWO-PROTON KNOCKOUT FROM A NEUTRON-RICH NUCLEUS AT HIGH ENERGY IS A DIRECT REACTIONMeasured vs. Theoretical Spectroscopic Factors in Units of the Maximum Sum-Rule ValueTHE (e,e’p) REACTION FINDS REDUCTION FACTORS OF 0.6 - 0.7 RELATIVE TO MEAN-FIELD THEORYREDUCTION FACTOR Rs FOR WEAKLY BOUND(Sp = 0.14 and 1.3 MeV) RADIOACTIVE NUCLEISTRUCTURE: 31,32Ar are good sd-shell nucleiMOMENTUM DISTRIBUTION AND CROSS SECTION FOR THE 9Be(32Ar, 31Ar)x REACTIONTHE 9Be(22O,21O)X REACTIONREDUCTION FACTOR Rs vs. SEPARATION ENERGYABSOLUTE SPECTROSCOPIC FACTORS FOR KNOCKOUT REACTIONS ON LIGHT p-SHELL NUCLEI. COMPARISON WITH THE VARIATIONAL MONTE-CARLO METBEYOND THE DRIP LINEIdentification of the 1s state in the unbound nuclear system 9He from the observation of final-state inteRECENT EXPERIMENTS ON 7HeImportant contributions to this program came from: