Shell-Model Calculation in Analyses of 35-MeV (p,n) Reactions

CNS University of TokyoMarch 5, 2005Orihara H.,

Shell-Model wave functions play a significant role in interpretation of the 35-MeV (p,n) reaction.Cross-section magnitudes, their q-dependence, and reaction mechanism of the (p,n) reaction strongly depend on individual single particle wave functions involved.

As such, study of the 35-MeV (p,n) reaction gives a good place to test a shell-model calculation.

H. OriharaTohoku Institute of Technology

In this report, we discuss five (p,n) reactions covering p-, sd-, and fp-nuclei.

12C(p,n)12N reaction concentrating on 0+ → 0+ transition40Ar(p,n)40K reaction concentrating on 0+ → 0+ transition40Ca(p,n)40Sc reaction concentrating on 0+ → 0- transition 58Ni(p,n) 58Cu reaction concentrating on 0+ → 1+ transition70Zn(p,n) 70Ga reaction concentrating on 0+ → 1+ transition

In a microscopic DWBA analysis

Zj ′j =OBTDj ′j TiTizΔTΔTz |TfTfz(2ΔT +1)

(2 ji +1)(2Tf +1)

OBTDj ′j = ′j ||| a ′j+ aj

ΔT ,ΔJ||| j

B(GT) = Z j ′j ′j ||στ || jgAgV

j ′j∑

2

dσ (p,n)dΩ ∝ Zj ′j ′j || (στ)Vστ f (r) || j

j ′j∑

2

Unambiguous evidence for the knockout-exchange effect observed in the 12C(p,n)12N(2.44 MeV, 0+)

101

102

103

6 8 10 12 14 16

COUN

TS/2

0keV

Neutron Energy (MeV)

12C(p,n)12NEp=35 MeV0 deg

2.44MeV,0+

1.19MeV,2+

gs,1+0+→ 0+

10-2

10-1

100

0 40 80 120 160

CRO

SS S

ECTI

ON

(mb/

sr)

c. m. Angle (deg)

12C(p,n)12NEp= 35MeVEX=0.0 MeV

total

1[1,1]

ΔJ[ΔL,ΔS]= 1[0,1]1[2,1]

0+ 1+

10-4

10-3

10-2

10-1

0 40 80 120 160

0[0,0]

CRO

SS S

ECTI

ON

(mb/

sr)

c. m. Angle (deg)

12C(p,n)12NEp= 35MeVEX=2.44MeV

0+ 0+ total

ΔJ[ΔL,ΔS]= 0[1,1]

Particle-hole

configuration0+ → 0+ 0+ → 1+

1p1/2 ← 1p1/2 -0.45989 -0.04406

1p1/2 ← 1p3/2 - -0.71360

1p3/2 ← 1p1/2 - -0.32507

1p3/2 ← 1p3/2 0.33419 -0.06326

1d3/2 ← 1d3/2 0.00048 0.00025

1d3/2 ← 1d5/2 - -0.00238

1d3/2 ← 2s1/2 - -0.00031

1d5/2 ← 1d3/2 - -0.00036

1d5/2 ← 1d5/2 -0.00771 -0.0041

2s1/2 ← 1d3/2 - 0.00021

2s1/2 ← 2s1/2 -0.00005 -0.00031

Calculated by the codeOXBASH in full p- and sd-shell model spacewith SPSDMWK inter-action

Comparative Study of the (p,n) Reactions on 40Ca and 40Ar for the 1.6 MeV-State in the A=40 Isobar Triplet

. .

Excitation Energy in 40K (MeV) 8 6 4 2 0 -2

Coun

ts/5

0keV

40

200

160

120

80

0

40Ar(p,n)40Kθlab. = 15degEp = 35 MeV

0.0

0, 4

-; 0.

030,

3-

0.80

0, 2

-0.

891,

5-

1.64

4, 0

+

2.29

0, 1

+

4.38

4, 0

+(IA

S)

1.96

0, 2

+

0+→ 0+

10-3

10-2

10-1

100

101

0 20 40 60 80 100 120 140

Micro J=0Macro IASdata

40Ar(p,n)40KEp = 35 MeVEx = 4.384MeV

c.m. Angle (deg)

CRO

SS S

ECTI

ON

(mb/

sr)

Δ

10-3

10-2

10-1

0 20 40 60 80 100 120 140CR

OSS

SEC

TIO

N (m

b/sr

)

c.m. Angle (deg)

40Ar(p,n)40KEp = 35 MeVEx = 1.65MeV

Calculated by the code OXBASH in full sd- and pf-shellmodel space with SDPFMWK interaction

40Ar(p,n) 40K reaction 40Ca(p,n)40Sc

reaction

T=2, 0+, #1

(4.384MeV, IAS)

T=1, 0+, #1

(1.644MeV)

T=1, 0+, #1

πd5/2,νd

5/2-1 - - -0.00287

πs1/2,νs

1/2-1 - - 0.00171

πd3/2,νd

3/2-1 0.49140 -0.48943 0.08224

πf7/2,νf7/2-1 0.35782 0.34697 -0.05505

πf5/2,νf5/2-1 0.00106 -0.00060 0.00165

πp3/2,νp

3/2-1 0.00111 -0.00052 -0.00301

πp1/2,νp

1/2-1 0.00022 -0.00001 -0.00155

A candidate of 0+ → 0- transition based onshell-model calculation

ConfigurationOBTD

0+ → 0- #1

1d5/2 ← 1f5/2 -0.00235

1d3/2 ← 2p3/2 -0.01013

2s1/2 ← 2p1/2 -0.00360

1f5/2 ← 1d5/2 0.02550

2p3/2 ← 1d3/2 0.85414

2p1/2 ← 2s1/2 0.05207

1501209060300.001

.01

.1

1

CROS

S SE

CTIO

N (m

b/sr

)c.m. Angle (deg)

40Ca(p,n)40ScEp = 35 MeV

2.38 M eV

3.05 M eV

0+ 4-

0+ 3-

Differential cross sections for neutrons leading to the 2.18-, 2.38- and 3.05-MeV states in 40Sc. Curves are DWBA predictions.

58Ni(p,n) 58Cu Reaction

0

20

40

60

80

100

024681012

Counts/25keV B

in

Ex(MeV) in58Cu

58Ni(p,n)58CuEp=35 MeVθ

lab = 0 deg

1.05

8MeV

, 1+ gs,

1+0.

203M

eV,

0+

10-2

10-1

100

101

0 20 40 60 80 100 120

IAS(Jon,Best-fit)data

58Ni(p,n)58CuEp=35 MeV

0.203MeV, IAS

c.m. Angle (deg)

CROSS SECTION (mb/sr)

10-3

10-2

10-1

100

0 20 40 60 80 100 120

1+#2*0.6data

58Ni(p,n)58CuEp=35 MeV

Ex= 1.058MeV

c.m. Angle (deg)

CROSS SECTION (mb/sr)

10-3

10-2

10-1

100

0 20 40 60 80 100 120

1+#1data(58Ni:gs,1+)

58Ni(p,n)58CuEp=35 MeV

0.0MeV

CROSS SECTION (mb/sr)

c.m.Angle (deg)

Reduction of the Gamow-Teller MatrixElement for the β-Decay in

7 0Ga -7 0Zn by the 35-MeV (p ,n )Reaction on 70Zn

For determination of ft-value by β-decay,precise determination of the branching ratio is essential.

1

10

100

1000

02468101214

70Zn(p,n)70GaEp=35 MeV

lab=20degθ

Coun

ts/2

5keV

Excitation Energy (MeV) in 70Ga

IAS, 8.26MeV

gs0+ 1+

10-2

10-1

100

0 20 40 60 80 100 120

CRO

SS S

ECTI

ON

(mb/

sr)

c.m. Angle (deg)

70Zn(p,n)70GaEp=35 MeV

IASEx=8.26 MeV

0+ 1+Ground State

€

ft =6170

B(GT) gVgA

2

log ft = 4.56 ± 0.06.

€

B(GT : 1+ → 0 +) =13

< N >

dσdΩ

0+→1+ , peak

1T0⋅ dσdΩ

IAS, peak

H. Orihara et al.,Phys. Lett.B539(2002)40

Summary:For (p,n) reaction at Ep=35MeV,cross-section magnitudes, their q-dependence, andreaction mechanism of the (p,n) reaction stronglydepend on individual single particle wave functionsinvolved.

Reasinable explanations for experimental evidencesin nuclei extending p-, sd, and ligh pf-shell nucleihave been obtained by the present shell-modelwave functions.

More reliable wave functions are strongly awaitedfor those of 58Ni and heavier nuclei.