Single nucleon transfer between p-shell nuclei around 10 MeV/u - for nuclear astrophysics
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Transcript of Single nucleon transfer between p-shell nuclei around 10 MeV/u - for nuclear astrophysics
Single nucleon transfer between p-shell nuclei around 10 MeV/u
- for nuclear astrophysics
Livius TracheCyclotron Institute, Texas A&M University
ATLAS workshop 2009
User Group Meeting
Argonne, IL, Aug 8-9, 2009
Techniques used to determine (p,) reaction rates
• Work at TAMU on nuclear astrophysicsA) indirect methods (p- or n-transfer)B) RNBs or stable beams
• Lessons learned:1. Seek the relevant quantities (ex: SF vs ANC)2. Model or parameter independent3. Combination of methods is useful – availability
important4. Need more in terms of supportive information for
reliable calculations: theories, models (and codes), effective n-n interactions, systematics … → still need good stable beam data OMP
MARS group at Texas A&M University
Indirect methods for transfer reactions with stable and unstable beams
Major accomplishments:– ANC technique firmly established for transfer reactions
• Proton transfer for 7Be(p, 11C(p,)12N, 12N(p, )13O, 13N(p, )14O, 14N(p, )15O
• neutron transfer and mirror symmetry for ANC – (7Li,8Li) for (7Be,8B) → 7Be(p, )8B ( S17)
– (22Ne,23Ne) for (22Mg,23Al) →22Mg(p,)23Al
– (17O,18O) for (17F,18Ne) →17F(p, )18Ne
• Optical Model Potentials for nucleus-nucleus collisions from double-folding procedure using JLM eff inter. Needed in DWBA. Established with stable beams and tested for RNBs: 7Be, 8B, 11C, 12N, 13N, 17F, …
• Advances in Trojan-horse method (extrap to E=0 and electron screening effects)
Extracting spectroscopic factors or ANCs
Transfer reaction B+d→A+a peripheral (absorption)
• Transfer matrix element:
• Cross section in terms of the ANCs:
22 2
2( ) ( ) A A d d
A A
A
d
A d d
d
A dBp
DWl j l j
Bpl j apl jl j apl j bd b
C Cd
proton-nucleus also peripheral
( )2
, ( )ABpp C
ANC - independent on binding potential geometry!OMP knowledge crucial for reliable absolute values!
( ) ( )A df Bp ap iM I V I
I CW r
rBpA
r R
BpA l Bp Bp
Bp
Bp NA
,
( )12
2
Depend on geom (r0,a) of proton-binding potential < 20-40%
Depend on OMP* n Factors !!!
= studied at TAMU
Ne-Na cycleCNO, HCNO
12C 13C
13N 15N
15O
14N
17O
17F
16O
18F
18O14O
19Ne18Ne
13O
11C
12N
8B
7Be
9C 10C
10B
11N
11B9B
8Be
22Ne21Ne
9Be
23Na
17Ne
16F15F
22Na20Na
24Al23Al 25Al
24Mg23Mg22Mg21Mg20Mg
19Na
19F
20Ne
25Si24Si 26Si
15C14C
27Al26Al
28Si27Si 29Si
26Mg25Mg
27P26P 28P 30P29P 31P
28S27S 29S 31S30S 32S
32Ar31Ar 33Ar 35Ar34Ar 36Ar
31Cl30Cl 32Cl 34Cl33Cl 35Cl
34S33S
March 2009
etc.
= planned
12O
16Ne
22Al
23Si
25P
21Al
30Si
(p,n) possible
stable
used at TAMU
(p,2n) possible
21Na
also 38Ca, 46V, 57Cu, 62Ga, …
14F
Transfer r.
RNB
Cross sections for (p,) from p-transfer reactions with RNB from MARS
12 C
12 N
Melamine target
(Faraday Cup)
E - det . (PSSD)
Er - det .
12 C
12 N
Melamine target
(Faraday Cup)
E - det . (PSSD)
.
12C @23 MeV/uH2 cryotarget
12N @12 MeV/u99% pure, 4 mm diaMelamine target
Four telescopesystem (“the cross”):E – PSD 65, 110 m E – 500 m
Example 12N @12 MeV on N6C3H6 and C
• Primary beam: 12C @ 23 MeV/u 150 pnA• Secondary beam: 12N @12 MeV/u 2x105 pps
• Elastic cm =8-60 deg.• Fit OMP from folding JLM– no param adjust!• Transfer 14N(12N,13O)13C – fit w. DWBA extract ANC• 12N(p,)13O rate evaluated from ANC
A. Banu et al., PRC 79, 025805 (2009) C2p1/2
(13O g.s.)=2.53±0.30 fm-1
1/ 2
2pC
Details and problemsEnergy resolution (bad!)Beam res. 1-2% 2-4 MeV
angular resolution (limited!)Beam res. 0.8 – 2 deg!
Ang distr → ANC → astrophys S-factor → react rate
Wide systematics loosely bound stable p-shell nuclei
Semi-microscopic double folding potentialsfor nucleus-nucleus collisions
• HFB densities (to best match the surfaces)• tried various effective interactions (M3Y, DDM3Y, JLM, etc…)• Settled for JLM• Smearing w. range parameters tV=1.2 fm, tW=1. 75 fm• Renormalizations needed Nv, Nw
• JLM - uses eff inter of Jeukenne, Lejeune and Mahaux (PRC 16, 1977)• n-nucleus Bauge ea (PRC 58, 1998):
– energy and density dependent– independent geometry for real and imaginary potentials– normalization independent of partners– reproduces ELASTIC and TRANSFER data
• Checked for loosely bound p-shell nuclei stable beams ~ 10 MeV/u– Found Nv=0.37(2) Nw=1.0(1), tV=1.20 fm, tW=1. 75 fm
• Extended to RNB: 7Be, 8B, 11C, 12N, 13N, 17F on 12C, 14N targets
212121 ),,,()()()( rRrssEvrrrdrdRV eff
Double folding procedure:
( ) ( , ) ( , )VV W WU r V r i WtN rN t
Works for transfer reactionsJLM works for a range of energies
E/A=15-50 MeV/u
JLM works for elastic & transfer
Works for RNBs
J. Blackmon ea,
PRC 73, 034606 (2005)
G. Tabacaru ea,
PRC 73, 025808 (2006)
7Be on melamine
A. Azhari ea,PRL 82, 3960 (1999)
12N on melamineTAMU exps @ 12 MeV/u
A. Banu ea,
PRC 79, 025805 (2009)
Optical Model Potentials for Nucleus-Nucleus collisions
for RNBs ~ 10 MeV/u
Essential to make credible DWBA calc needed in transfer r.
Have established semi-microscopic double folding using JLM effective interaction:
• Established from exps with stable loosely bound p-shell nuclei: 6,7Li, 10B, 13C, 14N … @ 10 MeV/u
• Parameters: renormalization coeff. • Predicts well elastic scatt for RNBs:
•7Be, 8B, 11C, 12N, 13N, 17F• 7-10% uncertainty in DWBA calc
L. Trache ea, PRC 61 (2000)F Carstoiu ea PRC 70 (2004)OMP: need extension to sd-shell:
•Work on stable projectiles at TAMU
•RNB of good quality – ATLAS ?!
•Energy and angular resolution
Trojan-horse with RNB ?!
TECSA - simulations• Texas-Edinburgh-Catania Silicon Array• To work alone at MARS or coupled with MDM after upgrade (TRIBF?!)• “Flat” detector has better angular resolution, but less coverage.• “Lampshade” detector has more angular coverage but trickier angular resolution
(solid angle).
BT Roeder – MC simulations, Sep 2008
Future