- Email: [email protected]
The Coulomb break-up of 9Be
Physics Letters B 283 ( 1992) 27-31 North-Holland
PHYSICS LETTERS B
The Coulomb break-up of 9Be E.W. M a c d o n a l d , A.C. Shotter, D. B r a n f o r d , J. R a h i g h i 1, T. D a v i n s o n a n d N.J. D a v i s Department of Physics, Universityof Edinburgh, Edinburgh EH9 3JZ, UK
Received 14 January 1992
Kinematically complete data is presented on the break-up reaction t Z°Sn(gBe, 8B%.,.+ n ) 12OSng.s.at Eb~a,~= 90 MeV for several scattering angles inside the grazing angle. These data are compared with the predictions of a Coulomb break-up model. It is shown that the data can be understood in terms of the Coulomb model provided some account is taken of the interactions of the breakup fragments with the target. Analysis of the 9Be break-up data, using radio-isotope measurements of the 9Be (~', n) cross-section, indicates that for this photo-disintegration reaction there is probably a significant direct component to the threshold cross-section, in addition to a threshold resonance at 1.69 MeV.
It has now been well established that there exists a non-sequential break-up mechanism for VLi projectiles scattered off heavy targets such as 96Zr, 12°Sn and 2°Spb [ 1-4]. The original discovery of the non-sequential mechanism was made by Shorter et al. [ 1 ] while studying the reaction 2°Spb(TLi, t t + t ) . This discovery stimulated much interest and further work [ 4 - 6 ] , such that there now exists an extensive dataset on the 7Li non-sequential reaction. Shorter et al. proposed an explanation of the non-sequential yield in terms of a Coulomb direct break-up model [2 ]. The central feature of this model is that the 7Li projectile is excited directly from its ground state into continuum a + t states by the projectile-target Coulomb interaction. At forward scattering angles, the direct Coulomb break-up model is very successful at reproducing both the shape and magnitude of the experimental energy spectra [2]. Recent calculations [ 7 ] have extended the Coulomb model to include, in a simplifed fashion, the effect of nuclear final state interactions (FSIs) between the break-up fragments and the target. These new calculations have demonstrated that the Coulomb model can explain the magnitude of the non-sequential yield for all measured angles up to the grazing angle. (Beyond the grazing
Permanent address: Esfahan Nuclear Technology Centre, Esfahan, Iran.
angle, the assumptions of the Coulomb model are not valid. ) Interest in break-up reactions has recently grown due to the possibility of using such reactions to extract radiative capture cross-sections. Clearly, if break-up reactions are to be used in this manner, it is important to test the Coulomb model on other breakup reactions and in particular to explore the new ideas regarding the role of final state interactions in the break-up process. The break-up of 9Be into the 8Be + n channel is a good reaction to study because this reaction has a high predicted Coulomb break-up cross-section due to its low Q-value ( - 1 . 6 6 6 MeV) and high E1 effective charge (ZsBe/A,Be -- Z , / A n = 0.5). Furthermore, there exists high-quality 9Be(•, n) p h o t o - n e u t r o n data [8,9], which means that Coulomb break-up cross-sections can be accurately calculated for the 9Be--,8Be+n reaction and that the Coulomb model can therefore be stringently tested by an experimental measurement of this reaction. In this letter, we shall present the results of an experimental study of the break-up reaction ~2°Sn(gBe, 8 B e + n ) . The measured break-up cross-sections will be compared with the predictions of the Coulomb model and the effect of final state interactions on the 9Be break-up process will be investigated. The experimental work discussed here was undertaken at the nuclear structure facility (NSF) of Dar-
0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
27
Volume 283, number 1,2
PHYSICS LETTERS B
esbury Laboratory. The NSF was used to provide a beam of 90 MeV 4 + 9Be nuclei. This beam was directed on self-supporting targets of ~2°Sn with areal densities of ~ 690 g g / c m 2. The experimental apparatus consisted o f a high efficiency 8Be telescope and a cluster of six liquid-scintillator neutron detectors. The 8Be telescope had an effective solid-angle of 8.5 msr for 80 MeV 8Beg.~. nuclei [ 10,11 ]. The cluster of neutron detectors was placed at a distance of 2 m from the target, and the neutron energies were measured by the time offlight method. For 10 MeV neutrons, a neutron energy resolution of ~ 1 MeV was achieved. Using this apparatus, event-by-event data was collected on the reaction ~2°Sn(gBe, S B e + n ) at a beam energy o f 90 MeV. A typical coincidence spectrum is shown in fig. 1. This spectrum gives the SBeg.~+ n coincidence yield as a function of the SBe and neutron kinetic energies "~. To guide the identification of different reaction processes, several kinematic loci have been plotted in fig. 1. The curve labelled E, = 0 . 0 cor*~ The SBeg.~ events were identified by first calculating the centre of mass energy of the two break-up ct particles. An energy window was then placed on the region corresponding to the break-up of the ground-state of SBe. In fact, most ct+ct events fell within this window. Any ct + ct events from other channels, e.g. 9Be-+ 5He + cc were insignificant within this window [ 10,11 I.
55 /30
l-
I
I
I
,
08~ , =@ Do-1;o k n-c
Luster
I
I
I
= 16 °
~,x(E =0.0
oIuf
"
I5-
~ 1o~
/ .
5 -
..
65
-1
c =0.024
~-0 02,.
• ...,..
Cr=0- 76
~
o -7 60
•
70
75
80
85
90
responds to quasi-elastic break-up, i.e. break-up in which the J:°Sn target nucleus is left in its ground state. Similarly, the curve labelled E, = 1.2, is the kinematic locus for the first excited ( 1.2 MeV) state of the target. The remaining curves are kinematic loci for SBe+n relative energies (er) of 0.024, 0.76 and 1.38 MeV. These relative energies were selected because they correspond to sequential break-up via the 1.69, 2.43 and 3.05 MeV states ofgBe respectively. The first point to note about the spectrum of fig. 1 is that quasi-elastic break-up is the dominant breakup channel. This was found to be true for all of the scattering angles at which measurements were made ( 13 °-23 ° ). There is however, an increase in the relative importance of inelastic break-up processes as the scattering angle increases. The lack of an enhancement of the yield along the ~r= 1.38 and ~,=0.76 curves indicates that sequential break-up via the 2.43 and 3.05 MeV states of OBe does not contribute strongly to the SBe + n coincidence yield. Most of the yield is concentrated at low relative energies (e~ < 0.5 MeV) and peaks in the region where the e,=0.024 MeV loci cross the quasi-elastic locus. Consequently, break-up via the 1.69 MeV state ofgBe could be contributing to the measured break-up yield. The distribution of the break-up yield along the quasi-elastic locus is seen more clearly in the pro_ jeered 8Be spectrum of fig. 2. This spectrum is created by placing a two-dimensional window on the quasi-elastic locus and then plotting the selected 8Beg.~ + n events as a function of the SBe kinetic energy. The limits used to define the window were: - 0 . 5 M e V < E , < 0 . 5 MeV. Fig. 2 emphasises the points made above, i.e. there is no clear evidence of breakup via the 2.43 MeV or 3.05 MeV states ofgBe, and the yield is concentrated at zero relative energy - the threshold of the '~Be +SBe+n reaction. The principal objective of the experiment described in this letter was to determine if the Coulomb break-up model is applicable to the break-up of ~Be. Within the framework of the Coulomb model, and assuming only E1 processes, the Coulomb break-up yield for '~Be is given by [ 2,12 ].
95
EeBe (HEY) Fig. 1. Coincidence yield for the break-up reaction ~2°Sn(gBe, 8Beg.~.+n) at Ebe~m= 90 MeV.
28
4 June 1992
(0, ~,) =
<) ,-vk= - (0, ~ ) , (1)
Volume 283, number 1,2
8Be-n
60
I
PHYSICS LETTERS B
reLat ive
I
I
(heY)
energy
I
I
I
50 4O
c 30
o co
2O
0%= 13. 5 ° e n=11 °
data
0%+= 13.2
°
10 0 65
I1~, I , & . J 70
80 75 E,~,, (MeV)
85
90
Fig. 2. Coincidence yield for the quasi-elastic break-up reaction ~2°Sn(gBe, 8B%s.+n)12°Sng.~. at Ebe, m=90 MeV. The smooth curve corresponds to the Coulomb calculation described in the text. Note that this curve has been normalised to the experimental curve. Therefore, only its shape is of significance, not its magnitude.
where Zv is the target charge, v is the 9Be velocity, d(E~ (0, er) is the standard E1 Coulomb excitation orbital term and B(E1, er) is the reduced transition probability per unit er. The reduced transition probability can be determined from the 9Be( 7, n) photodisintegration cross-section, ay.,, via the relation: B(E1, ~ r ) -
9 ch 16~r3Eyu~.n(Ev),
(2)
where Ev=er-Q and Q is the Q-value for the 9Be-,SBe+n reaction ( Q = - 1.666 MeV). In the threshold region there have been several detailed measurements of the 9Be (7, n) photo-disintegration reaction [ 8,9,13,14 ]. One of the most accurate being the radio-isotope measurement of Fujishiro et al. [8,9 ]. Their data show an asymmetric peak in the 9Be (7, n) excitation function which rises sharply from less than 1 lab at the aBeg.s.+ n threshold to a maximum of 1.4 mb at 29 keV above the threshold. The width of the peak was found to be 100 keV (FWHM). The bremsstrahlung difference data of Jakobson [14] reveals similar structure in the 9Be(7, n) excitation function. Jakobson [14] also measured neutron angular distributions and found that the neutrons associated with the 1.69 MeV peak
4 June 1992
were emitted isotropically. This s-wave nature of the neutron emission is consistent with the threshold peak being due to a ~+ state in 9Be. The neutron time of flight measurements of Berman et al. [13] are in broad agreement with the other data on the 9Be (7, n ) reaction. Berman et al., however, found that the maximum of the threshold peak occurred at just 6 keV above the threshold. Although the threshold peak has been interpreted by several authors as being due to a resonance in 9Be, there has been some disagreement as to its origin. For example, Berman et al. [ 13 ] conclude that their data cannot be explained by the presence of a single -~+ level near the threshold, whereas Barker et al. [ 15,16 ] conclude that all of the existing data is consistent with a single ½+ level, 31 keV above threshold. In the opinion of the present authors, the contribution of direct processes to the 9Be (7, n) yield has not been given sufficient consideration. The direct transition from the ground-state of 9Be to continuum neutron s-states is an E1 transition with a high E1 effective-charge. Consequently, the cross-section for this transition should be significant. If there is a strong direct component to the 9Be(7, n) yield this will change the nature of the Coulomb break-up of9Be. A direct component will lead to direct break-up processes whereas a resonant component will lead to sequential break-up processes. For direct break-up processes, final state interactions (FSIs) between the break-up fragments and the target can have a crucial effect on the experimentally measured coincidence cross-section. For sequential break-up processes, however, FSIs are insignificant since the 9Be nucleus decays at ~ 290 fm from the target nucleus (using AE At~ h and AE~ 100 keV). Therefore, to take account of the effect of FSIs on the Coulomb break-up cross-section, it is necessary to know the relative strengths of the direct and sequential break-up processes, which means knowing the relative strengths of the direct and resonant components of the 9Be (7, n) yield. Unfortunately, this information is not yet available. Despite this fact, useful progress can still be made by first performing a Coulomb break-up calculation in which the effect of FSIs is ignored. This was done in the following manner. Eqs. ( 1 ) and (2) were used with the photo-disintegration data of Fujishiro et al. [8,9] to calculate Coulomb break-up cross-sections of the form (dZo-/dff29Be d~r) (0, Er) for 29
V o l u m e 283, n u m b e r 1,2
PHYSICS LETTERS B
the reaction 12°sn(gBe, 8 B e + n ) . These cross-sections were then used in a Monte Carlo simulation of the experimental configuration [ 17 ] to determine the shape and magnitude of the corresponding experimental spectra. The use of Monte Carlo techniques was essential in order to account for the effect o f the complex experimental geometry and efficiencies on the experimental spectra. The Monte Carlo simulation o f the 8Be projected energy spectrum has been plotted in fig. 2 as a smooth curve. This curve has been normalised to the experimental curve. Therefore, only its shape is o f significance, not its magnitude. It can be seen that a fair reproduction of the shape of the experimental spectrum has been achieved. A more important comparison, however, is that between the absolute magnitudes of the calculation and the data. In fig. 3 the cross-sections predicted by the no-FSl calculation (smooth curve) are plotted with the experimental cross-sections (triangular data-points). The calculated cross-sections are considerably greater than the experimental cross-sections at all angles for which data was collected. This observation does not necessarily mean that the Coulomb break-up model is in-
3000
I
I
I
I
2500 L
200o vE
c~1500
looo x
0
/~
-\
500
0
J 0
,
,
5
lO
15
20
25
Lsb
• e+. [degrees)
Fig. 3. Double differential cross-sections for the quasi-elastic break-up reaction ' 2°Sn(gBe, 8Beg.s.+ n ) J2°Sngs.at E~am---90 MeV. These cross-sections correspond to the case 0,he= On. The triangular data-points are the experimental cross-sections. The solid curve corresponds to the no-FS1 Coulomb break-up calculation described in the text. The two dashed curves, labelled A and B, are produced by multiplying the solid curve by the reduction factors X~ and )(2, respectively. 30
4 J u n e 1992
correct. Instead, for the following reasons, it may provide evidence that there is a significant direct component to the 9Be break-up yield. Firstly, direct break-up processes are subject to FSIs and, for the close-geometry system used in the present work, FSIs will always tend to reduce the measured break-up cross-sections. Secondly, the reduction factor due to FSIs should increase with scattering angle (since the impact parameter decreases). This is consistent with fig. 3 since the ratio of the no-FSI calculation to the experimental data increases with angle. In order to explore the above hypothesis further, it is necessary to estimate the magnitude of the FSI reduction factor and its dependence on scattering angle. This was carried out by using the FSI model that Shotter et al. developed in order to explain the direct break-up reaction o f 7Li [ 7]. In this model, the overlap of the wave-function of the break-up fragments with the target nucleus is first determined. A strong absorption potential is then used for the field o f the target nucleus to calculate the reduction factor - it being assumed that if the projectile and target overlap, the nuclear interaction will deflect or absorb at least one fragment and therefore significantly reduce the probability that both fragments are detected. By considering two geometrical extremes for the overlap it is possible to define two limiting reduction factors, Xj and X 2. For the J2°Sn(9Be, 8Be + n ) reaction these limiting reduction factors were calculated using the method discussed in ref. [7]. Since only the direct component of the Coulomb break-up yield is effected by FSIs, only this component should be multiplied by the FSI reduction factor. However, as discussed above, the relative strength of the direct component is unknown. In order to progress we shall assume that all o f the Coulomb yield is direct in nature, and then compare the result of this assumption with the experimental data. For this case, of a pure direct Coulomb yield, the predicted break-up cross-sections are obtained by multiplying the no-FSl cross-sections by the reduction factors X~ and X2. The resulting curves have been plotted in fig. 3 and are labelled A and B respectively. All o f the experimental data points lie between the two extreme limits of the FSI model. The fact that the inclusion of FSIs in the theoretical calculation is consistent with the experimental data provides evidence that FSIs are significant and therefore that a substantial direct break-up component is present. If
Volume 283, number 1,2
PHYSICS LETTERS B
this interpretation o f the data is correct, then by considering the extreme reduction factor X1 it is apparent that at least ~ 70% o f the C o u l o m b yield is direct in nature. O f course, the large difference between the two limiting reduction factors means that it is possible that an appreciable resonant c o m p o n e n t is also present, but the data suggest that direct processes are d o m i n a n t . The angular distributions o f fig. 3, and the relationship o f the d a t a points to them, b e a r a striking resemblance to the results presented by Shotter in fig. 3 o f ref. [ 7 ] for the break-up reaction 12°Sn (7Li, c t + t ) . F o r this reaction, the direct break-up mechanism was u n a m b i g u o u s l y identified a n d the experimental d a t a points were found to lie between the two FSI limits of a C o u l o m b break-up calculation in just the same way that the present d a t a lie between the FSI limits. A n o t h e r argument in support of the presence of a direct yield is that the shape of the 8Be projected energy spectra are observed to change with scattering angle [ 11 ]. This change in shape can be readily u n d e r s t o o d for direct break-up reactions in terms o f the effect o f FSIs on the energy and trajectory o f the break-up fragments. In conclusion, it has been shown that the break-up reaction 12°Sn(9Be, 8Beg.s.+n ) 120Sng.s can be understood in terms o f a C o u l o m b break-up model i f a significant fraction o f the break-up yield is direct in nature and if the effect o f final state interactions between the break-up fragments and the target nucleus are included in the model. The experimental cross-sections, the shape o f the projected energy spectra and the change in shape o f these spectra with scattering angle all suggest that direct C o u l o m b break-up plays an i m p o r t a n t role in the break-up of 9Be. If indeed this is correct, then there probably exists a significant direct component to the threshold cross-section of the ~Be (7, n) photo-disintegration reaction, in addition to a threshold resonance at 1.69 MeV. An interesting test o f these hypotheses would be the m e a s u r e m e n t of the 9Be break-up cross-section at scattering angles
4 June 1992
forward o f the angles measured in this work. Finally, this work demonstrates the i m p o r t a n c e of taking account o f final state interactions when considering direct processes. In particular, if Coulomb break-up data is to be used to extract photo-fission data, as mentioned above, then the role o f FSIs must be fully understood first.
References
[ 1] A.C. Shoner, A.N. Bice, J.M. Wouters, W.D. Rae and J. Cerny, Phys. Rev. Lett. 46 (1981) 12. [2] A.C. Shoner, V. Rapp, T. Davinson, D. Branford, N.E. Sanderson and M.A. Nagarajan, Phys. Rev. Lett. 53 (1984) 1539. [3] A.C. Shotter, V. Rapp, T. Davinson and D. Branford, J. Phys. G 14 (1988) L169. [4] H. Utsunomiya et al., Phys. Lett. B 211 (1988) 24. [ 5 ] D.K. Srivastava, D.N. Basu and H. Rebel, Phys. Len. B 206 (1988) 391. [6] G. Baur and M. Weber, Nucl. Phys. A 504 (1989) 352. [7] A.C. Shorter, J. Phys. G 15 (1989) L41. [ 8 ] M. Fujishiro, T. Tabata, K. Okamoto and T. Tsujimoto, Can. J. Phys. 60 (1982) 1672. [9 ] M. Fujishiro, K. Okamoto and T. Tsujimoto, Can. J. Phys. 61 (1983) 1579. [ 10] E.W. Mcdonald, A.C. Shotter, D. Branford, J. Rahighi, T. Davinson, N.J. Davis and J. Yorkston, A high efficiency 8Be detector, to be submitted to Nucl. Instrum. Methods. [ 11 ] E.W. Macdonald, Ph.D Thesis, University of Edinburgh 1988, unpublished. [12] K. Alder and A. Winther, Electromagnetic excitation (North-Holland, Amsterdam, 1975 ). [13] B.U Berman, R.L. Van Hemert and C.D. Bowman, Phys. Rev. 163 (1967) 958. [14] M.J. Jakobson, Phys. Rev. 123 (1961 ) 229. [ 15] F.C. Barker and B.M. Fitzpatrick, Aust. J. Phys. 21 (1968) 415. [ 16 ] F.C. Barker, Can. J. Phys. 61 ( 1983 ) 1371. [ 17 ]EW. Macdonald, General purpose Monte-Carlo simulation code for break-up reactions, UNIMONTE (University of Edinburgh 1988 ), unpublished.
31
PHYSICS LETTERS B
The Coulomb break-up of 9Be E.W. M a c d o n a l d , A.C. Shotter, D. B r a n f o r d , J. R a h i g h i 1, T. D a v i n s o n a n d N.J. D a v i s Department of Physics, Universityof Edinburgh, Edinburgh EH9 3JZ, UK
Received 14 January 1992
Kinematically complete data is presented on the break-up reaction t Z°Sn(gBe, 8B%.,.+ n ) 12OSng.s.at Eb~a,~= 90 MeV for several scattering angles inside the grazing angle. These data are compared with the predictions of a Coulomb break-up model. It is shown that the data can be understood in terms of the Coulomb model provided some account is taken of the interactions of the breakup fragments with the target. Analysis of the 9Be break-up data, using radio-isotope measurements of the 9Be (~', n) cross-section, indicates that for this photo-disintegration reaction there is probably a significant direct component to the threshold cross-section, in addition to a threshold resonance at 1.69 MeV.
It has now been well established that there exists a non-sequential break-up mechanism for VLi projectiles scattered off heavy targets such as 96Zr, 12°Sn and 2°Spb [ 1-4]. The original discovery of the non-sequential mechanism was made by Shorter et al. [ 1 ] while studying the reaction 2°Spb(TLi, t t + t ) . This discovery stimulated much interest and further work [ 4 - 6 ] , such that there now exists an extensive dataset on the 7Li non-sequential reaction. Shorter et al. proposed an explanation of the non-sequential yield in terms of a Coulomb direct break-up model [2 ]. The central feature of this model is that the 7Li projectile is excited directly from its ground state into continuum a + t states by the projectile-target Coulomb interaction. At forward scattering angles, the direct Coulomb break-up model is very successful at reproducing both the shape and magnitude of the experimental energy spectra [2]. Recent calculations [ 7 ] have extended the Coulomb model to include, in a simplifed fashion, the effect of nuclear final state interactions (FSIs) between the break-up fragments and the target. These new calculations have demonstrated that the Coulomb model can explain the magnitude of the non-sequential yield for all measured angles up to the grazing angle. (Beyond the grazing
Permanent address: Esfahan Nuclear Technology Centre, Esfahan, Iran.
angle, the assumptions of the Coulomb model are not valid. ) Interest in break-up reactions has recently grown due to the possibility of using such reactions to extract radiative capture cross-sections. Clearly, if break-up reactions are to be used in this manner, it is important to test the Coulomb model on other breakup reactions and in particular to explore the new ideas regarding the role of final state interactions in the break-up process. The break-up of 9Be into the 8Be + n channel is a good reaction to study because this reaction has a high predicted Coulomb break-up cross-section due to its low Q-value ( - 1 . 6 6 6 MeV) and high E1 effective charge (ZsBe/A,Be -- Z , / A n = 0.5). Furthermore, there exists high-quality 9Be(•, n) p h o t o - n e u t r o n data [8,9], which means that Coulomb break-up cross-sections can be accurately calculated for the 9Be--,8Be+n reaction and that the Coulomb model can therefore be stringently tested by an experimental measurement of this reaction. In this letter, we shall present the results of an experimental study of the break-up reaction ~2°Sn(gBe, 8 B e + n ) . The measured break-up cross-sections will be compared with the predictions of the Coulomb model and the effect of final state interactions on the 9Be break-up process will be investigated. The experimental work discussed here was undertaken at the nuclear structure facility (NSF) of Dar-
0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
27
Volume 283, number 1,2
PHYSICS LETTERS B
esbury Laboratory. The NSF was used to provide a beam of 90 MeV 4 + 9Be nuclei. This beam was directed on self-supporting targets of ~2°Sn with areal densities of ~ 690 g g / c m 2. The experimental apparatus consisted o f a high efficiency 8Be telescope and a cluster of six liquid-scintillator neutron detectors. The 8Be telescope had an effective solid-angle of 8.5 msr for 80 MeV 8Beg.~. nuclei [ 10,11 ]. The cluster of neutron detectors was placed at a distance of 2 m from the target, and the neutron energies were measured by the time offlight method. For 10 MeV neutrons, a neutron energy resolution of ~ 1 MeV was achieved. Using this apparatus, event-by-event data was collected on the reaction ~2°Sn(gBe, S B e + n ) at a beam energy o f 90 MeV. A typical coincidence spectrum is shown in fig. 1. This spectrum gives the SBeg.~+ n coincidence yield as a function of the SBe and neutron kinetic energies "~. To guide the identification of different reaction processes, several kinematic loci have been plotted in fig. 1. The curve labelled E, = 0 . 0 cor*~ The SBeg.~ events were identified by first calculating the centre of mass energy of the two break-up ct particles. An energy window was then placed on the region corresponding to the break-up of the ground-state of SBe. In fact, most ct+ct events fell within this window. Any ct + ct events from other channels, e.g. 9Be-+ 5He + cc were insignificant within this window [ 10,11 I.
55 /30
l-
I
I
I
,
08~ , =@ Do-1;o k n-c
Luster
I
I
I
= 16 °
~,x(E =0.0
oIuf
"
I5-
~ 1o~
/ .
5 -
..
65
-1
c =0.024
~-0 02,.
• ...,..
Cr=0- 76
~
o -7 60
•
70
75
80
85
90
responds to quasi-elastic break-up, i.e. break-up in which the J:°Sn target nucleus is left in its ground state. Similarly, the curve labelled E, = 1.2, is the kinematic locus for the first excited ( 1.2 MeV) state of the target. The remaining curves are kinematic loci for SBe+n relative energies (er) of 0.024, 0.76 and 1.38 MeV. These relative energies were selected because they correspond to sequential break-up via the 1.69, 2.43 and 3.05 MeV states ofgBe respectively. The first point to note about the spectrum of fig. 1 is that quasi-elastic break-up is the dominant breakup channel. This was found to be true for all of the scattering angles at which measurements were made ( 13 °-23 ° ). There is however, an increase in the relative importance of inelastic break-up processes as the scattering angle increases. The lack of an enhancement of the yield along the ~r= 1.38 and ~,=0.76 curves indicates that sequential break-up via the 2.43 and 3.05 MeV states of OBe does not contribute strongly to the SBe + n coincidence yield. Most of the yield is concentrated at low relative energies (e~ < 0.5 MeV) and peaks in the region where the e,=0.024 MeV loci cross the quasi-elastic locus. Consequently, break-up via the 1.69 MeV state ofgBe could be contributing to the measured break-up yield. The distribution of the break-up yield along the quasi-elastic locus is seen more clearly in the pro_ jeered 8Be spectrum of fig. 2. This spectrum is created by placing a two-dimensional window on the quasi-elastic locus and then plotting the selected 8Beg.~ + n events as a function of the SBe kinetic energy. The limits used to define the window were: - 0 . 5 M e V < E , < 0 . 5 MeV. Fig. 2 emphasises the points made above, i.e. there is no clear evidence of breakup via the 2.43 MeV or 3.05 MeV states ofgBe, and the yield is concentrated at zero relative energy - the threshold of the '~Be +SBe+n reaction. The principal objective of the experiment described in this letter was to determine if the Coulomb break-up model is applicable to the break-up of ~Be. Within the framework of the Coulomb model, and assuming only E1 processes, the Coulomb break-up yield for '~Be is given by [ 2,12 ].
95
EeBe (HEY) Fig. 1. Coincidence yield for the break-up reaction ~2°Sn(gBe, 8Beg.~.+n) at Ebe~m= 90 MeV.
28
4 June 1992
(0, ~,) =
<) ,-vk= - (0, ~ ) , (1)
Volume 283, number 1,2
8Be-n
60
I
PHYSICS LETTERS B
reLat ive
I
I
(heY)
energy
I
I
I
50 4O
c 30
o co
2O
0%= 13. 5 ° e n=11 °
data
0%+= 13.2
°
10 0 65
I1~, I , & . J 70
80 75 E,~,, (MeV)
85
90
Fig. 2. Coincidence yield for the quasi-elastic break-up reaction ~2°Sn(gBe, 8B%s.+n)12°Sng.~. at Ebe, m=90 MeV. The smooth curve corresponds to the Coulomb calculation described in the text. Note that this curve has been normalised to the experimental curve. Therefore, only its shape is of significance, not its magnitude.
where Zv is the target charge, v is the 9Be velocity, d(E~ (0, er) is the standard E1 Coulomb excitation orbital term and B(E1, er) is the reduced transition probability per unit er. The reduced transition probability can be determined from the 9Be( 7, n) photodisintegration cross-section, ay.,, via the relation: B(E1, ~ r ) -
9 ch 16~r3Eyu~.n(Ev),
(2)
where Ev=er-Q and Q is the Q-value for the 9Be-,SBe+n reaction ( Q = - 1.666 MeV). In the threshold region there have been several detailed measurements of the 9Be (7, n) photo-disintegration reaction [ 8,9,13,14 ]. One of the most accurate being the radio-isotope measurement of Fujishiro et al. [8,9 ]. Their data show an asymmetric peak in the 9Be (7, n) excitation function which rises sharply from less than 1 lab at the aBeg.s.+ n threshold to a maximum of 1.4 mb at 29 keV above the threshold. The width of the peak was found to be 100 keV (FWHM). The bremsstrahlung difference data of Jakobson [14] reveals similar structure in the 9Be(7, n) excitation function. Jakobson [14] also measured neutron angular distributions and found that the neutrons associated with the 1.69 MeV peak
4 June 1992
were emitted isotropically. This s-wave nature of the neutron emission is consistent with the threshold peak being due to a ~+ state in 9Be. The neutron time of flight measurements of Berman et al. [13] are in broad agreement with the other data on the 9Be (7, n ) reaction. Berman et al., however, found that the maximum of the threshold peak occurred at just 6 keV above the threshold. Although the threshold peak has been interpreted by several authors as being due to a resonance in 9Be, there has been some disagreement as to its origin. For example, Berman et al. [ 13 ] conclude that their data cannot be explained by the presence of a single -~+ level near the threshold, whereas Barker et al. [ 15,16 ] conclude that all of the existing data is consistent with a single ½+ level, 31 keV above threshold. In the opinion of the present authors, the contribution of direct processes to the 9Be (7, n) yield has not been given sufficient consideration. The direct transition from the ground-state of 9Be to continuum neutron s-states is an E1 transition with a high E1 effective-charge. Consequently, the cross-section for this transition should be significant. If there is a strong direct component to the 9Be(7, n) yield this will change the nature of the Coulomb break-up of9Be. A direct component will lead to direct break-up processes whereas a resonant component will lead to sequential break-up processes. For direct break-up processes, final state interactions (FSIs) between the break-up fragments and the target can have a crucial effect on the experimentally measured coincidence cross-section. For sequential break-up processes, however, FSIs are insignificant since the 9Be nucleus decays at ~ 290 fm from the target nucleus (using AE At~ h and AE~ 100 keV). Therefore, to take account of the effect of FSIs on the Coulomb break-up cross-section, it is necessary to know the relative strengths of the direct and sequential break-up processes, which means knowing the relative strengths of the direct and resonant components of the 9Be (7, n) yield. Unfortunately, this information is not yet available. Despite this fact, useful progress can still be made by first performing a Coulomb break-up calculation in which the effect of FSIs is ignored. This was done in the following manner. Eqs. ( 1 ) and (2) were used with the photo-disintegration data of Fujishiro et al. [8,9] to calculate Coulomb break-up cross-sections of the form (dZo-/dff29Be d~r) (0, Er) for 29
V o l u m e 283, n u m b e r 1,2
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the reaction 12°sn(gBe, 8 B e + n ) . These cross-sections were then used in a Monte Carlo simulation of the experimental configuration [ 17 ] to determine the shape and magnitude of the corresponding experimental spectra. The use of Monte Carlo techniques was essential in order to account for the effect o f the complex experimental geometry and efficiencies on the experimental spectra. The Monte Carlo simulation o f the 8Be projected energy spectrum has been plotted in fig. 2 as a smooth curve. This curve has been normalised to the experimental curve. Therefore, only its shape is o f significance, not its magnitude. It can be seen that a fair reproduction of the shape of the experimental spectrum has been achieved. A more important comparison, however, is that between the absolute magnitudes of the calculation and the data. In fig. 3 the cross-sections predicted by the no-FSl calculation (smooth curve) are plotted with the experimental cross-sections (triangular data-points). The calculated cross-sections are considerably greater than the experimental cross-sections at all angles for which data was collected. This observation does not necessarily mean that the Coulomb break-up model is in-
3000
I
I
I
I
2500 L
200o vE
c~1500
looo x
0
/~
-\
500
0
J 0
,
,
5
lO
15
20
25
Lsb
• e+. [degrees)
Fig. 3. Double differential cross-sections for the quasi-elastic break-up reaction ' 2°Sn(gBe, 8Beg.s.+ n ) J2°Sngs.at E~am---90 MeV. These cross-sections correspond to the case 0,he= On. The triangular data-points are the experimental cross-sections. The solid curve corresponds to the no-FS1 Coulomb break-up calculation described in the text. The two dashed curves, labelled A and B, are produced by multiplying the solid curve by the reduction factors X~ and )(2, respectively. 30
4 J u n e 1992
correct. Instead, for the following reasons, it may provide evidence that there is a significant direct component to the 9Be break-up yield. Firstly, direct break-up processes are subject to FSIs and, for the close-geometry system used in the present work, FSIs will always tend to reduce the measured break-up cross-sections. Secondly, the reduction factor due to FSIs should increase with scattering angle (since the impact parameter decreases). This is consistent with fig. 3 since the ratio of the no-FSI calculation to the experimental data increases with angle. In order to explore the above hypothesis further, it is necessary to estimate the magnitude of the FSI reduction factor and its dependence on scattering angle. This was carried out by using the FSI model that Shotter et al. developed in order to explain the direct break-up reaction o f 7Li [ 7]. In this model, the overlap of the wave-function of the break-up fragments with the target nucleus is first determined. A strong absorption potential is then used for the field o f the target nucleus to calculate the reduction factor - it being assumed that if the projectile and target overlap, the nuclear interaction will deflect or absorb at least one fragment and therefore significantly reduce the probability that both fragments are detected. By considering two geometrical extremes for the overlap it is possible to define two limiting reduction factors, Xj and X 2. For the J2°Sn(9Be, 8Be + n ) reaction these limiting reduction factors were calculated using the method discussed in ref. [7]. Since only the direct component of the Coulomb break-up yield is effected by FSIs, only this component should be multiplied by the FSI reduction factor. However, as discussed above, the relative strength of the direct component is unknown. In order to progress we shall assume that all o f the Coulomb yield is direct in nature, and then compare the result of this assumption with the experimental data. For this case, of a pure direct Coulomb yield, the predicted break-up cross-sections are obtained by multiplying the no-FSl cross-sections by the reduction factors X~ and X2. The resulting curves have been plotted in fig. 3 and are labelled A and B respectively. All o f the experimental data points lie between the two extreme limits of the FSI model. The fact that the inclusion of FSIs in the theoretical calculation is consistent with the experimental data provides evidence that FSIs are significant and therefore that a substantial direct break-up component is present. If
Volume 283, number 1,2
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this interpretation o f the data is correct, then by considering the extreme reduction factor X1 it is apparent that at least ~ 70% o f the C o u l o m b yield is direct in nature. O f course, the large difference between the two limiting reduction factors means that it is possible that an appreciable resonant c o m p o n e n t is also present, but the data suggest that direct processes are d o m i n a n t . The angular distributions o f fig. 3, and the relationship o f the d a t a points to them, b e a r a striking resemblance to the results presented by Shotter in fig. 3 o f ref. [ 7 ] for the break-up reaction 12°Sn (7Li, c t + t ) . F o r this reaction, the direct break-up mechanism was u n a m b i g u o u s l y identified a n d the experimental d a t a points were found to lie between the two FSI limits of a C o u l o m b break-up calculation in just the same way that the present d a t a lie between the FSI limits. A n o t h e r argument in support of the presence of a direct yield is that the shape of the 8Be projected energy spectra are observed to change with scattering angle [ 11 ]. This change in shape can be readily u n d e r s t o o d for direct break-up reactions in terms o f the effect o f FSIs on the energy and trajectory o f the break-up fragments. In conclusion, it has been shown that the break-up reaction 12°Sn(9Be, 8Beg.s.+n ) 120Sng.s can be understood in terms o f a C o u l o m b break-up model i f a significant fraction o f the break-up yield is direct in nature and if the effect o f final state interactions between the break-up fragments and the target nucleus are included in the model. The experimental cross-sections, the shape o f the projected energy spectra and the change in shape o f these spectra with scattering angle all suggest that direct C o u l o m b break-up plays an i m p o r t a n t role in the break-up of 9Be. If indeed this is correct, then there probably exists a significant direct component to the threshold cross-section of the ~Be (7, n) photo-disintegration reaction, in addition to a threshold resonance at 1.69 MeV. An interesting test o f these hypotheses would be the m e a s u r e m e n t of the 9Be break-up cross-section at scattering angles
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forward o f the angles measured in this work. Finally, this work demonstrates the i m p o r t a n c e of taking account o f final state interactions when considering direct processes. In particular, if Coulomb break-up data is to be used to extract photo-fission data, as mentioned above, then the role o f FSIs must be fully understood first.
References
[ 1] A.C. Shoner, A.N. Bice, J.M. Wouters, W.D. Rae and J. Cerny, Phys. Rev. Lett. 46 (1981) 12. [2] A.C. Shoner, V. Rapp, T. Davinson, D. Branford, N.E. Sanderson and M.A. Nagarajan, Phys. Rev. Lett. 53 (1984) 1539. [3] A.C. Shotter, V. Rapp, T. Davinson and D. Branford, J. Phys. G 14 (1988) L169. [4] H. Utsunomiya et al., Phys. Lett. B 211 (1988) 24. [ 5 ] D.K. Srivastava, D.N. Basu and H. Rebel, Phys. Len. B 206 (1988) 391. [6] G. Baur and M. Weber, Nucl. Phys. A 504 (1989) 352. [7] A.C. Shorter, J. Phys. G 15 (1989) L41. [ 8 ] M. Fujishiro, T. Tabata, K. Okamoto and T. Tsujimoto, Can. J. Phys. 60 (1982) 1672. [9 ] M. Fujishiro, K. Okamoto and T. Tsujimoto, Can. J. Phys. 61 (1983) 1579. [ 10] E.W. Mcdonald, A.C. Shotter, D. Branford, J. Rahighi, T. Davinson, N.J. Davis and J. Yorkston, A high efficiency 8Be detector, to be submitted to Nucl. Instrum. Methods. [ 11 ] E.W. Macdonald, Ph.D Thesis, University of Edinburgh 1988, unpublished. [12] K. Alder and A. Winther, Electromagnetic excitation (North-Holland, Amsterdam, 1975 ). [13] B.U Berman, R.L. Van Hemert and C.D. Bowman, Phys. Rev. 163 (1967) 958. [14] M.J. Jakobson, Phys. Rev. 123 (1961 ) 229. [ 15] F.C. Barker and B.M. Fitzpatrick, Aust. J. Phys. 21 (1968) 415. [ 16 ] F.C. Barker, Can. J. Phys. 61 ( 1983 ) 1371. [ 17 ]EW. Macdonald, General purpose Monte-Carlo simulation code for break-up reactions, UNIMONTE (University of Edinburgh 1988 ), unpublished.
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