Possibilities for Nuclear Physics at the Madrid Tandem Hans O. U. Fynbo Department of Physics and Astronomy University of Aarhus, Denmark Nuclear physics and astrophysics of light nuclei A=9 and A=12 Studies at CERN of the CSIC group What could be done at a tandem?
Nuclear chart N = Z ?
A=9 and A=12 Nuclei –“Exact” A-body calculations possible for A 12 (soon) Shell-model states Molecular-cluster states –Break-up mechanism not fixed by kinematics How does three particles tunnel? Fundamental QM problem –Crucial for bridging the A=5 and A=8 gaps in Big Bang and Stellar nuclear synthesis.
Ab-initio Monte-Carlo calculations for A 12
Model Predictions (eff. Int.)
Some recent model predictions Nucl. Phys. A679 (2001) 393. (R. Guardiola) Resonating group calculation J. Phys. G27 (2001) Variational Calculation Phys. Rev. C62 (2000) Ab-initio no-core shell-model Phys. Rev. Lett. 84 (2000) Ab-initio no-core shell model Phys. Rev. C61 (2000) U( +1) group theory for triangular states Phys. Rev. Lett. 81 (1998) Antisymmetrised molecular dynamics (AMD) Nucl. Phys. A618 (1997) 55. Cluster model Phys. Lett. B389 (1996) 631. Coordinate space Fadeev approach. 12 C not a closed chapter of nuclear physics
The triple- reaction rate
Break-up to Multi-particle Final States Initial state X: Some (nuclear) state Final state Y: Three (or more) particles E, X Y : a+b+c Energy (ab) + c Direct (ab) + c Sequential 12 C * 8 Be gs + 31 Cl * 30 S+p 29 P+2p (ab) + c ? 12 C * 8 Be(2+)+ a+(bc) 9 B 8 Be+p, 5 Li+ p
Questions E, E, ? -Often difficult to Measure Spin-parity? - Selection rules The structure of the state? -Cluster states -Many-body states The mechanism of the break-up? -Sequential or direct? -Importance of different channels Relation to state structure What is : Assymptotic Spectra -Observable -Energy and angular correlations
0,2 + 8 Be+ C 11 B+p ++++ Width Decay Structure E level /MeVJJ level 8 Be (0 + ) 8 Be (2 + )7.6542(15) (1.0) eV>96%<4% 9.641(5) (5) keV>96%<4% 10.3(3) (7) MeV>90%<10% (25) (25)keVStrongYes (16) (25)keVNoYes (6) (2.8) eVNoYes (17) (40)keVNoYes (15) (15)keV17(4)%83(4)% (3) (1.3) eVNoYes
Breakup of the 12.71MeV state Balamuth, Zurmuhle and Tabor Phys. Rev. C10 (1974) 975 A.A. Korshenninikov Sov. J. Nucl. Phys. 52 (1990) 827 R-matrix based sequential break-up with order-of-emission interference Hyperspherical Harmonics expansion. Simultaneous emission. SAME DATA !!
CERN
–Modern segmented Si-Detectors Large Solid Angle –detect all particles High Segmentation –no summing Previous studies using this setup 31 Ar 2p Nucl. Phys. A677 (2000) 38 9 C 2 p Nucl. Phys. A692 (2001) N 3 Under analysis R.R.Betts IL NOUVO CIMENTO 110A (1997) 975 ISOL beam Low energy isotope separated beam Can be stopped in C-foil Well-defined source –Modern segmented Si-Detectors Large Solid Angle –detect all particles High Segmentation –no summing
L. Fraile
12 C from the -decay of 12 B Latest evaluation 1990 Region probed by -decay 0 +, 1 +,2 + Region probed by delayed -emission
Dalitz plot for 3 E1E1 E2E2 E3E3 Dalitz plot = E /Q = (E +2 E )/Q Q
Simultaneous stepwise Data The 12.71MeV state: Dalitz plots Phase space E1E1 E2E2 E3E3 Dalitz plot
Stepwise Simultaneous
T - 8 Be -- 8 Be Coulomb interaction between 1 st and 2 nd emitted s neglected !!!! PRL 20 (1968) 1178 Classical calculation No ang.mom. Included Need unphysical S
Stepwise FSI Coulomb
Towards the Astrophysical Region 0 + state 2 + state 0 + state including interference with ghost anomaly
The triple- reaction rate
The -decay of 12 N Unpublished data from Heidelberg from 1978 (Schwalm) Main experimental problems are Energy loss in target Summing Evidence for new state near 13MeV
”13 MeV” state Broad state “Invisible” in reaction experiments “Invisible” in single spectrum
Unbound states in 9 B from 9 C -decay
-decay summary Selection rules pick out specific states among possibly many (spin + isospin) Particles from breakup of unbound states fed in the decay emitted from rest Point source Thin host -> reduced energy loss Certain states cannot be produced Time structure of events can be very peaked Yield is often very limited Very restricted access to beam
10 B( 3 He,p3 ) Peaks in p-spectrum State in 12 C Peaks in -spectrum State in 9 B
10 B( 3 He,p3 ) 10 Be( 3 He,n3 )... EE EpEp EpEp 1966
6 Li( 6 Li,3 ) Reaction mechanism FSI Coulomb effects EE EE 1968
9 Be ( 3 He,3 ) Reaction mechanism FSI Coulomb effects 8 Be (0 + ) EE EE 1965
13 C( 3 He,4 ) Also : 7 Li (d,n ), 10 Be( 3 He,n ), 6 Li ( 3 He,p ) EE EE 1965
Experiments at the MADRID tandem? Latest evaluation Nucl. Phys. A506 (1990) 11 B(d,p) 12 B 11 B(d,n) 12 C* 13 C( 3 He 12 C* 10 B( 3 He,p) 12 C* 11 B(p,) 12 C* P( 11 B,) 12 C* 10 B( 3 He,n) 12 N 3 He( 9 Be,) 12 C*
Summary To study exotic short lived nuclei new effective detector arrays have been developed New analysis methods A number of reactions suitable for tandems exist which were last visited >30 years ago. Huge potential for extracting interesting and very relevant information on light nuclei.