Tensor Analysing Powers for 7Li Induced
Transfer Breakup Reactions
N. J. Davis , R. P. Ward , K. Rusek† , N. M. Clarke , G. Tungate ,
J. A. R. Griffith , S. J. Hall , O. Karban , I. Martel-Bravo ,
J. M. Nelson , J. Gómez-Camacho‡ , T. Davinson§ , D. G. Ireland§ ,
K. Livingston§ , E. W. Macdonald§ , R. D. Page§ , P. J. Sellin§ ,
C. H. Shepherd-Themistocleous§ , A. C. Shotter§ and P. J. Woods§
£
School of Chemistry and Physics, Keele University, Keele, Staffordshire ST5 5BG, England
†
Department of Nuclear Reactions, The Andrzej Sołtan Institute for Nuclear Studies,
Hoża 69, 00-681 Warsaw, Poland
££
School of Physics and Astronomy, University of Birmingham,
Edgbaston, Birmingham B15 2TT, England
‡
Departmento de Física Atómica, Molecular y Nuclear, Facultad de Física,
Universidad de Sevilla, Aptdo. 1065, 41080 Sevilla, Spain
§
Department of Physics and Astronomy, University of Edinburgh,
Mayfield Road, Edinburgh EH9 3JZ, Scotland
Abstract. The tensor analysing power T20 has been measured for the 120 Sn(7 Li,8 Be 2α 119 In and
α d121 Sn transfer breakup reactions at 70 MeV bombarding energy. Coupled
channels and continuum discretized coupled channels calculations, incorporating a detector phase
space correction, were found to give good agreement with the data.
120 Sn(7 Li,6 Li
INTRODUCTION
Transfer breakup reactions are of particular interest because they combine two processes,
nucleon transfer and breakup, which are now relatively well understood in isolation.
However there has been little published on such transfer breakup reactions. Lithium-7
induced transfer breakup reactions are of relevance to studies of nuclei having cluster
structures and to radioactive beam studies where fragmentation is likely. Coupled channels (CC) calculations have been found to describe transfer reactions very well and more
recently continuum discretized coupled channels (CDCC) calculations have been very
successful in describing breakup reactions [1]. The challenge is to thoroughly test these
calculations with the more complex transfer breakup reactions.
EXPERIMENT
The analysing power T20 was measured for transfer breakup reactions resulting from
beam on a 120 Sn target. Data were
heavy ion collisions induced by a 70 MeV 7 Li
obtained for the 120 Sn(7 Li,8 Be
2α 119 In proton pickup and 120 Sn(7 Li,6 Li
α
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
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d121Sn neutron stripping reactions. The experimental procedure was described earlier
by Davis et al. [1].
RESULTS
Data
For the 120 Sn(7 Li,8 Be 2α 119 In reaction spectra were reconstructed corresponding
to breakup via the 0 ground state of 8 Be. The unresolved ground 92 and 0.31 MeV
12 first excited states of 119 In were found to be populated strongly in these spectra. For
the 120 Sn(7 Li,6 Li α d121 Sn reaction spectra were reconstructed corresponding to
breakup via the 2.18 MeV 3 state of 6 Li. These latter spectra were observed to contain
three strong structures corresponding to the unresolved ground 32 , 0.006 MeV 112
first excited and 0.06 MeV 12 second excited states and many unresolved states
around 1.2 MeV and 2.7 MeV in 121 Sn. Many of the states contributing to the two latter
structures have uncertain or unknown spin-parities, rendering the analysis of that data
difficult or impossible. Thus, data for those two structures will not be presented here but
will be reported elsewhere [2].
Calculations
CC and CDCC calculations were performed, using version FRXP.18 of the code
FRESCO [3], for the 120 Sn(7 Li,8 Be 2α 119 In and 120 Sn(7 Li,6 Li
α d121 Sn re120
7
8
119
actions, respectively. For the Sn( Li, Be 2α ) In reaction the entrance channel optical potential was that of Cook [4] and the exit channel optical potential was determined
from single folding using an empirical α + 120Sn optical potential [5] and 8 Be α α
cluster wavefunctions with a Gaussian shaped binding potential. The 8 Be ground state
was assumed to be weakly bound, by just 0.01 MeV, and the potential depth was adjusted
to reproduce this. For the 120 Sn(7 Li,6 Li α d)121 Sn reaction the entrance channel optical potential was that of Cook [4] and the exit channel optical potential was determined
from single folding using empirical α 120 Sn [5] and d120 Sn [6] optical potentials and
CDCC 6 Li α d wavefunctions [7] calculated using the α d binding potential proposed by Kubo and Hirata [8]. Spectroscopic amplitudes were obtained from Cohen and
Kurath [9] and Turkiewicz et al. [10]. The coupling schemes used are shown in Figures 1
and 2.
To make a reasonable comparison of data with prediction, the detector configuration
used for the breakup fragments needs to be considered. The 8 Be case is the simplest
because the 8 Be is in its ground state so L 0 for the breakup. The L 0 breakup
gives an isotropic distribution of α fragment directions in the centre of mass of the 8 Be.
A direct measurement of T20 for the transfer breakup reaction is consequently made
because it does not matter where the detectors are placed relative to the reaction plane.
The 6 Li case is somewhat more complicated because the 6 Li is in the 2.19 MeV 3
excited state. This is known to be a pure L 2 α d cluster state, so L 2 breakup
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2+
1/2-
3/2-
0+
7
Li + 120 Sn
FIGURE 1. Coupling scheme for 120 Sn(7 Li,8 Be
the projectile/ejectile.
119
2α
In + 8Be
119 In CC
calculations. The spin-parities refer to
3+
1/2-
3/2-
1+
7
FIGURE 2. Coupling scheme for
refer to the projectile/ejectile.
Li + 120 Sn
121
120 Sn(7 Li,6 Li
α
Sn +6 Li
d121 Sn
CDCC calculations. The spin-parities
of the state with no L 4 admixture can be assumed to a very good approximation.
The L 2 breakup will result in an anisotropic fragment distribution and a consequent
phase space effect due to detector positions. A technique was therefore developed to take
this into account, as described previously by Davis et al. [1], by which the measured
analysing powers Tkq are modelled by a combination of the calculated polarization
transfer coefficients Xkqk¼ q¼ with tensors Ik¼ q¼ which are related to the detector geometry.
DISCUSSION AND CONCLUSIONS
Calculations for the 120 Sn(7 Li,8Be
2α 119 In reaction are compared with the data in
Figure 3. The data agree very well with the calculation assuming population of the 119 In
ground state. The calculation assuming population of the 119 In first excited state is very
different and does not reproduce the data. This is perhaps an indication that only the
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0.8
T20
0.6
0.4
0.2
0.0
10
20
30
40
–0.2
–0.4
θc.m.
FIGURE 3. Results of CC calculations for the 120 Sn(7 Li,8 Be 2α 119 In reaction compared with data.
The solid and dotted lines assume population of the 119 In 92 ground state and 0.31 MeV 12 first
excited state, respectively.
ground state is significantly populated by the reaction.
Calculations without the detector phase space correction for the 120 Sn(7 Li,6 Li
α d121 Sn reaction assuming population of the ground 32 , 0.006 MeV 112 and
0.06 MeV 12 states are shown with the unresolved data in Figure 4. Good agreement
is not achieved, although it could be argued on the basis of these calculations alone
that the calculation for the 12 state, being predominantly negative, represents the data
better than the calculations for the other two states, which are predominantly positive.
Calculations with the detector phase space correction included are shown in Figure 5.
These illustrate the importance of the correction which leads to far better agreement
between the calculations and the data. They also lead to a different conclusion than
that arrived at from the uncorrected calculations alone, because once the correction is
included all three calculations are very similar and agree with the data equally well.
This means the relative contributions from the three states to the data are not important
in assessing the success of the calculations.
In conclusion, the results show that the calculations do well in reproducing T20
analysing power data in one of the first tests of CC and CDCC calculations for transfer
breakup reactions. A more detailed description of this study is in preparation [2].
ACKNOWLEDGMENTS
This work was supported in part by the Engineering and Physical Sciences Research Council of the United Kingdom and by the State Committee for Scientific
Research (KBN) of Poland.
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1.0
T 20
0.5
0.0
-0.5
-1.0
-1.5
0
10
20
Center of mass angle (degrees)
30
FIGURE 4. Results of CDCC calculations without detector phase space correction for the
120 Sn(7 Li,6 Li
α d121 Sn reaction. The dotted, solid and dashed lines assume population of the 121 Sn
32 ground state, the 112 state at 0.006 MeV and the 12 state at 0.06 MeV, respectively.
1.0
T 20
0.5
0.0
-0.5
-1.0
-1.5
0
10
20
Center of mass angle (degrees)
30
FIGURE 5. Results of CDCC calculations including detector phase space correction for the
120
Sn(7 Li,6 Li α d121 Sn reaction. The dotted, solid and dashed lines assume population of the 121 Sn
32 ground state, the 112 state at 0.006 MeV and the 12 state at 0.06 MeV in 121 Sn, respectively.
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