Betty Tsang, NSCL/MSU

China Atomic Energy Insstitute, March, 2006

Neutron Spectroscopic Factors from Transfer Reactions

Nucleon

knockout

Gade, PRL 93, 042501 (2004)

(e,e’p)

Lapikas, NPA 553, 297c (1993)

Transfer Reactions

NSCL

Lansing

Detroit

Ann Arbor

NSCL@MSU

NSCL

Engineering

Tennis, etc.

NSCL@MSU

Biochemistry

NSCL

Biomedical & Physical Sciences

Plant Biology

Plant Science Greenhouses

Chemistry

Law

Engineering

Tennis, etc.

Performing Arts

A national user facility for rare isotope research and education in nuclear science, astro-nuclear physics, accelerator physics, and societal applications

~300 employees, ~ 50 undergraduate and ~ 50 graduate students, 24 faculty(as of March 05)

User group of over 600 CCF users

The National Superconducting

Cyclotron Laboratory@Michigan State University

National Superconducting Cyclotron Laboratory

K500

World’s first superconducting cyclotron (1982)

K1200World’s most powerful

superconducting cyclotron (1989)

A1900

Coupled Cyclotron Facility (2000)

Mass separator

Magic number

N=2

N=10

N=20

Maria Goeppert-Mayer & Hans

Jensen, 1963 Noble Prize

winners for the Nuclear Shell

Model.

Spectroscopic Factors:

measure the single

particle structure of the

valence nucleons.

0 1 23 4

5 6

7 8

9 10

111213

14

1516

17181920

2122

2324

25262728

2930

3132

33343536

3738394041

424344

45464748

49505152

535455

56

5758

59

H (1)He (2)Li (3)

Be (4) B (5) C (6) N (7)

O (8) F (9)

Ne (10)Na (11)

Mg (12)Al (13)Si (14) P (15)

S (16)Cl (17)

Ar (18) K (19)

Ca (20)Sc (21)

Ti (22) V (23)

Cr (24)Mn (25)

Fe (26)Co (27)

Ni (28)Cu (29)

Zn (30)Ga (31)

Ge (32)As (33)

Se (34)Br (35)Kr (36)Rb (37)

Sr (38) Y (39)

Zr (40)Nb (41)

Mo (42)Tc (43)

Ru (44)Rh (45)Pd (46)Ag (47)

Cd (48)In (49)

Sn (50)Sb (51)

Te (52) I (53)

Xe (54)

3 reaction++ 12C

p process:14O+ 17F+p17F+p 18Ne18Ne+ …

rp process:41Sc+p 42Ti

+p 43V

+p 44Cr44Cr 44V+e++ne44V+p …

Astrophysics Network calculations

• Need nuclear reaction

rates and spectroscopic

factors

Measurements of Spectroscopic Factors

Nucleon

knockout

Gade, PRL 93, 042501 (2004)

(e,e’p)

Lapikas, NPA 553, 297c (1993)

Transfer Reactions

(p,d) & (d,p) reactions

0

200

400

600

50's 60's 70's 80's 90's 2000-

Number of papers published

Decade

# o

f pap

ers

Spectroscopic factors from transfer reactions

Pros:

We know the exact state of the

nucleon transferred.

Good understanding of the

experimental technique and

reaction theory (DWBA).

Lots of data from past 40 years.

Cons:

Do we measure the “absolute”

spectroscopic factors?

Data appear to give inconsistent

results

One of the important techniques

to understand the structure of the

nuclei including rare isotopes

RM

EX

jl

d

dd

d

S

)(

)(

,

A(d,p)B B(p,d)A

• Published spectroscopic factors show large fluctuations from analysis to analysis

Spectroscopic Factors from literaturesExample: 1p1/2 neutron SF in 13C = 12C+n

RM

EX

gs

d

dd

d

S

)(

)(

Liu et al, PRC 69, 064313 (2004)

Basic assumptions

of DWBA

The reaction is dominated by 1-step direct transfer.

Elastic scattering is the main process in the entrance and

exit channels.

A(d,p)B B(p,d)A

TDWBA = <Apf|V|Bdi>

DWBA

EX

jl

d

dd

d

S

)(

)(

,

Murillo, NPA579,125 (1994)

SF=0.99

Ed=16 MeV

14C(d,p)15CGoss, PRC12,1730 (1975)Ed=14 MeV

SF=0.88

Cecil, NPA255,345 (1975)Ed=17 MeV

SF=1.03

The data differ by factor

of 2 but SF’s are nearly

the same by varying the

input parameters!!

TWOFNR (Tostevin)

Soper-Johnson

Adiabatic

Approximation to take

care of d-break-up

effects.

Use global p and n

optical potential with

standardized parameters

(CH89)

n-potential : Woods-

Saxon shape ro=1.25 fm

& ao=0.65; depth

adjusted to experimental

binding energy.

Include finite range &

non-locality corrections

12C(d,p)13Cgs

SF=0.75+0.10

SF(SM) = 0.62

Liu et al, PRC 69, 064313 (2004)

The spectroscopic factors deduced in a systematic and consistent way show that we can extract spectroscopic factors within the measurement uncertainties.

Apply the technique to a large data set

Liu et al, PRC 69, 064313 (2004)

Systematic extraction of SF’s

g.s. n-spectroscopic factors for 80 nuclei

Use 3-body

adiabatic model

calculations,

with one set of

input parameters

through-out

(Hui Ching Lee)

Z=3 Li 6, 7, 8, 9Z=4 Be 9, 10, 11Z=5 B 10, 11, 12Z=6 C 12, 13, 14, 15Z=7 N 14, 15, 16Z=8 O 16, 17, 18, 19Z=9 F 19, 20Z=10 Ne 21, 22, 23Z=11 Na 24Z=12 Mg 24, 25, 26, 27Z=13 Al 27, 28Z=14 Si 28, 29, 30, 31Z=15 P 32Z=16 S 32, 33, 34, 35, 37Z=17 Cl 35, 36, 37, 38Z=18 Ar 36, 37, 38, 39, 40Z=19 K 39, 40, 41, 42Z=20 Ca 40, 41, 42, 43, 44, 45, 47, 48, 49Z=21 Sc 45, 46Z=22 Ti 46, 47, 48, 49, 50, 51Z=23 V 51Z=24 Cr 50, 51, 52, 53, 55

Tsang et al, PRL 95, 222501 (2005)

Sn 80 nuclei

(p,d) : S+ 47 nuclei

(d,p) : S- 56 nuclei

(p,d) & (d,p) 18 nuclei

A+pB+d S+

B+dA+p S-

Equivalent processes S+ = S-

18 nuclei

Self consistency checks

Assign uncertainties

Quality Control ?

80 nuclei from Li to Cr (~ 430 angular distributions)

20 % uncertainties for

each measurement

Comparison with Endt’s best SF values for single nucleon

transfer reaction in A=21-44 region

Endt’s SF:

uncertainty : 25% [(p,d),

(d,p), (d,t), (3He, )]

50 % for (d,p)

and (p,d) reactions only)

removal of normalization

uncertainties

mainly based on

communication with authors

Our SF :

uncertainty : < 20 %

re-analysis by consistent

method and parameters

reproduced easily

g.s. n-spectroscopic factors for 80 nuclei

For 3-body

adiabatic model

calculations,

use one set of input

parameters

through-out

(Hui Ching Lee)

Z=3 Li 6, 7, 8, 9Z=4 Be 9, 10, 11Z=5 B 10, 11, 12Z=6 C 12, 13, 14, 15Z=7 N 14, 15, 16Z=8 O 16, 17, 18, 19Z=9 F 19, 20Z=10 Ne 21, 22, 23Z=11 Na 24Z=12 Mg 24, 25, 26, 27Z=13 Al 27, 28Z=14 Si 28, 29, 30, 31Z=15 P 32Z=16 S 32, 33, 34, 35, 37Z=17 Cl 35, 36, 37, 38Z=18 Ar 36, 37, 38, 39, 40Z=19 K 39, 40, 41, 42Z=20 Ca 40, 41, 42, 43, 44, 45, 47, 48, 49Z=21 Sc 45, 46Z=22 Ti 46, 47, 48, 49, 50, 51Z=23 V 51Z=24 Cr 50, 51, 52, 53, 55

nS

12

11

j

nS

IPM (Austern, pg 291)For n even

For n odd

Textbook Example:

Extracted spectroscopic factors for Ca isotopes, 40Ca – 48Ca

A IPM

40 4

41 1

42 2

43 3/4

44 4

45 1/2

46 6

47 1/4

48 8

Double magic40Ca (closed proton

and neutron shells)

spherical core

Valence

neutrons for 41Ca-48Ca in good

single particle state

Comparison with Independent Particle Model (IPM)

for Ca isotopes, 40Ca – 48CaTsang et al, PRL 95, 222501 (2005)

Comparison with Independent Particles Model for 80 nucleiTsang et al, PRL 95, 222501 (2005)

Z=3 Li 6, 7, 8Z=4 Be 9, 10, 11Z=5 B 10, 11, 12Z=6 C 12, 13, 14, 15Z=7 N 14, 15, 16Z=8 O 16, 17, 18, 19Z=9 F 19, 20Z=10 Ne 21, 22, 23Z=11 Na 24Z=12 Mg 24, 25, 26, 27Z=13 Al 27, 28Z=14 Si 28, 29, 30, 31Z=15 P 32Z=16 S 32, 33, 34, 35, 37Z=17 Cl 35, 36, 37, 38Z=18 Ar 36, 37, 38, 39, 40, 41Z=19 K 39, 40, 41, 42Z=20 Ca 40, 41, 42, 43, 44, 45, 47, 48, 49Z=21 Sc 45, 46Z=22 Ti 46, 47, 48, 49, 50, 51Z=23 V 51Z=24 Cr 50, 51, 52, 53, 55

60 SF from shell model (Oxbash).

Good agreement with most isotopes

Tsang et al, PRL 95, 222501 (2005)

Measurements of Spectroscopic Factors

(e,e’p)

Nucleon

knockout

Lapikas, NPA 553, 297c (1993)Gade, PRL 93, 042501 (2004)

Transfer Reactions

Tsang et al, PRL 95, 222501 (2005)

Comparison of Spectroscopic Factors

Nucleon

knockout

(e,e’p)

Nucleon

knockout

SF(JLM)<SF(CH) by 15%

SF depends on geometries of the n-wave functions.

Liu et al, PRC 69, 064313 (2004)

Systematic extraction of SF’s

Reduction of spectroscopic factors

1. Constrain n-wavefunction with HF calculations 15%

reduction; HF calc’s give target densities.

2. Use JLM potentials 15% reduction.

3. Procedure allows evaluations of rare isotopes

SF(HF)~0.7*SF(conv)

Comparison of spectroscopic factors

p-richn-rich

11C

22O

32Ar

34Ar

40Ca

49Ca

p-SF

DS=Sp-Sn

n-SF

DS=Sn-Sp

Comparisons with SF from other reactions

p-richn-rich

11C

22O

32Ar

34Ar

40Ca

Constraining the n-wave function and target densities with HF calculations and

JLM potentials results in reduction of SF values

Reduction is similar in magnitude in (e,e’p) & knockout with large fluctuations.

The DS (or n-separation energy) dependence is questionable for stable nuclei.

Clear dependence is seen in very asymmetric nuclei in knockout reactions.

46Ar Approved

experiment to

measure (p,d)

reactions in

inverse

kinematics

with 46Ar & 34Ar beams

The High Resolution Array•Flexible easily reconfigured array with 20 independent telescope (can be expanded).

•High resolution:

<0.2 at 50 cm.

–High resistivity silicon; DE35 keV FWHM, per signal.

4x CsI(Tl) 4cm

32 strips (front, 2mm pitch)

Beam

Si-DE 65 m

32 strips v (front)

Si-E 1.5 mm

pixel

32 strips h. (back)

deSouza, IU

16 Slot

Motherboard.

HiRA Electronics (WU+SIU)

ASIC: Application Specific Integrated Circuit

16 Channel chip

HiRA Electronics Setup Behind

Detectors in Vacuum Chamber

02023: Summation of 8 telescopes after

gain-matched. (32x8 strips & 4x8 CsI)

02019 - Resonance spectroscopy of

molecular states in 12Be & 14Be(Oct 05)

The S800 Spectrograph

Inverse kinematics with

radioactive ion beams

p+34Ar 33Ar+d

The S800 Spectrograph

34Ar beamCH2 target

33Ar

d

Inverse kinematics with

radioactive ion beams

p+34Ar 33Ar+d

Transfer ReactionsPast (IPM)

Present (LB_SM)

Stable nuclei

Future

Radioactive nuclei

Z>24 nuclei;

excited states;

proton

spectroscopic

factors etc.