- Email: [email protected]
Inelastic scattering of 185 MeV protons from light nuclei
Nuclear Physics 69 (1965) 81--102; (~) North-Holland Publishing Co., Amsterdam Not to
bc reproduced by photoprint or microfilm without writt¢n p¢rmisslon from the publisher
INELASTIC SCATTERING FROM
O F 185 M e V P R O T O N S
LIGHT NUCLEI
D. HASSELGREN, P. U. RENBERG, O. SUNDBERG and G. TIBELL The Gustaf Werner Institute, University of Uppsala, Uppsala, Sweden Received 23 December 1964 Abstract: Differential cross sections have been measured for scattering of 185 MeV protons from excited levels of the seven light nuclei LP, Li', Be9, B1°, B11, C 12 and 016. The energy analysis of the inelasticallyscattered protons has been performed in a magnetic spectrometer giving a resolution of 0.4--0.5 MeV (full width at half maximum) of peaks in the energy spectra. The measurements cover an angular region of 3°.5~,5°.5 in the laboratory system and excitation energies up to 30 MeV. For 31 peaks in the energy spectra angular distributions are presented. Excitation energies and in some cases intrinsic widths are given for a total of 68 levels excited in this experiment. The results are compared with those of previous experiments using incoming protons of about the same energy and, in a few cases, with theoretical analyses of inelastic proton scattering NUCLEAR. REACTIONS s, 'Li, 9Be, 10, liB, 1~C, 1SO(p, p,), E = 185 MeV; measured tr(Ep, 0). Deduced levels, _P. Enriched 6Li, I°B, lXB targets.
I
I
1. Introduction A t energies o f 15-50 M e V the a n g u l a r d i s t r i b u t i o n s o b t a i n e d in inelastic p r o t o n scattering are r a t h e r sensitive to spins a n d parities o f the excited levels. I n fact, the q u a n t u m n u m b e r s o f m a n y levels have been d e t e r m i n e d as a result o f such experiments. A t a b o m b a r d i n g energy o f 100-200 M e V the a n g u l a r d i s t r i b u t i o n s also s h o w a b e h a v i o u r characteristic o f the t r a n s i t i o n f r o m the g r o u n d state o f the t a r g e t n u cleus. This has been d e m o n s t r a t e d b y M a r i s a n d T y r r n in t h e o r e t i c a l w o r k on inelastic p r o t o n scattering 1). A t these energies c o m p a r a t i v e l y little structure is o b served in the a n g u l a r d i s t r i b u t i o n s a n d b r o a d l y s p e a k i n g t w o types o f curves are o b t a i n e d ; e.g. one with a d i p in the f o r w a r d direction a n d t h e o t h e r rising t o w a r d s smaller scattering angles. T h e y b o t h decrease with increasing angle. I n f a v o u r a b l e cases the p o s i t i o n o f the m a x i m u m o f the f o r m e r t y p e o f a n g u l a r d i s t r i b u t i o n gives i n f o r m a t i o n o n the m u l t i p o l a r i t y o f the electric t r a n s i t i o n involved. T y p i c a l e x a m p les o f such a n g u l a r d e p e n d e n c e are o b t a i n e d in the cases o f excited levels w h i c h decay t o the g r o u n d state via p u r e E2 a n d M1 transitions, respectively. S o m e o f the m o r e i m p o r t a n t studies o f inelastic p r o t o n scattering f r o m c o m p l e x nuclei at energies a b o u t 100-200 M e V p e r f o r m e d to d a t e are listed in table 1. I n m o s t cases m e a s u r e m e n t s have also been m a d e on heavier nuclei, b u t here we restrict o u r 81
D. HASSELGREN e t aL
82
selves to the lp shell region. The energy resolution listed indicates full width at half m a x i m u m ( F W H M ) of a peak in the energy spectrum without extra broadening due to thick targets, intrinsic widths of the levels studied, etc. It is obvious that the resolution in energy is a figure of merit for such experiments and sets a definite limit to what can be achieved regarding information on nuclear levels. TABLE I
Summary of some experiments on inelastic proton scattering at energies between 96 and 185 MeV Ref.
2)
Bombarding energy (MeV)
4)
96-t-2 96-4-2 185-4-< 1 1854- < 1 135 and 95
6)
155+0.5
3)
Target nuclei
Method of energy analysis
c 12 Li, Be, B, C, N, O CTM, 016 Li, Bee, B, N 14 Clz Lie, Li7, Bee, B1°, B11, C12
range telescope range telescope magnetic spectrometer magnetic spectrometer total absorption magnetic spectrometer
Energy resolution (FWHM, MeV) 3.0 3.0 1.8 1.8 3.4 0.8
In table 1 the error in bombarding energy refers to the spreadin energy of the incoming protons rather than to any uncertainty in the absolute value of this energy. At this institute a high resolution magnetic spectrometer which gives an overall resolution in inelastic proton scattering of 0.30 MeV has recently been developed 6). H o w much of that figure results from the spread in the extracted proton beam energy is not known but the contribution is probably less than 0.25 MeV. It was therefore thought worthwhile to repeat and extend the measurements previously performed by Tyr~n and Maris 3). We report here the results obtained for scattering f r o m Li e, Li 7, Be 9, B 1o, B11, C12 and 016 in the angular range 3°.5 to 45°.5 (laboratory system). In two previous publications 7, 8) preliminary results have been given for the 7.66 MeV level in C 12 and for all of the nuclei studied except Li 7. After a description of the experimental arrangements and procedure the results are given in the f o r m of energy spectra and angular distributions for resolved peaks. The results are discussed briefly and compared with previously published data as well as with some theoretical predictions.
2. Experimental Arrangements A schematic drawing of the lay-out of the experiment is presented in fig. 1. The external, unpolarized proton beam of the synchrocyclotron passes two focussing magnets, two bending magnets and one adjusting magnet before striking the target which is placed in a chamber connected to the vacuum tank of the magnetic spectrometer. A circular collimator, 20 m m in diam., is placed in the cyclotron tank in order to
INELASTIC
PROTON
83
SCATTERING
=o "O
.> O
t I
it3
I
• ... ~....:
-.,
•- i ° .-..... • •. °o
~
i':"" •
"
E-
.;~.~ )V-';-'+.~ J ~
o
°
E to.
/+.~
0~ ,.r-
0~
.o
...'.-
~~
\
E o ,.2
84
D. HASSELGRENet
al.
m a k e the b e a m better defined g e o m e t r i c a l l y at the target. T h e b e a m cross section at the t a r g e t p o s i t i o n is a l m o s t circular with a d i a m e t e r o f a b o u t 2.5 m m . A s e c o n d circular c o l l i m a t o r j u s t before t h e t a r g e t prevents p r o t o n s scattered off t h e M y l a r w i n d o w s o f the p r o t o n v a c u u m t u b e a n d the scattering c h a m b e r f r o m entering t h e MeV 0.40
0.35.
0.30-
90
95
¢00
105 ¢rn R
Fig. 2. Experimentally measured energy resolution (FWHM) versus distance R from exit pole boundary to energy channel defining counters. The straggling in energy loss is subtracted but not the energy spread of the incoming beam. The diagram is taken from ref. 6). TABLE 2 Target specifications for all the nuclei investigated in this experiment Target
LP Lie Li T Li7 Be9 B1° Btt Bu C 12 Ct6 Ole(H~O) OX6(HaO) OX6(DIO)
Isotopic purity (~o) 95.6 95.6 92.5 92.5 100.0 92.3 81.2 98.6 98.9 98.9 99.8 99.8 99.8
Thickness (g/era2)
0.078 0.233 0.064 0.129 0.423 0.185 0.071 O.126 O.156 0.206 0.34 0.21 0.14
Straggling (FWHM, MeV) 0.18 0.32 0.16 0.22 0.40 0.28 O.17 0.22 0.26 0.30 0.4 0.3 0.25
m a g n e t . Its d i a m e t e r is k e p t large e n o u g h so t h a t the b e a m will pass freely t h r o u g h it, n o r m a l l y 30 m m . T h e inset o f fig. 1 also shows a third, one-sided, straight c o l l i m a t o r , which was used f o r scattering angles larger t h a n 7 ° . This shield m a k e s it i m p o s s i b l e for p r o t o n s in the direct b e a m to enter the m a g n e t after scattering f r o m t h e exit wind o w o f the c h a m b e r . T h e solid angle in scattering f r o m the target is defined b y a recta n g u l a r c o l l i m a t o r p l a c e d j u s t outside the fringe o f the m a g n e t i c field.
INELASTIC PROTON SCATTEKING
85
The n = 0 magnetic spectrometer will be fully described in a later publication 6). With the solid angle used in this experiment (1.17 x 10-3 sr), the transmission is 100 % according to the orbits calculated from field measurements. The total opening angle is 2°.3. The scattered protons are detected in a double two-fold coincidence telescope system with six energy channels. The whole set-up of detectors is mounted on a support which can be moved along the direction of the protons leaving the magnet. For each nucleus and scattering angle, the focal distance has been calculated, and fig. 2, taken from ref. 6), shows how the experimental energy resolution (FWHM) changes with the distance R, between magnet exit and detector. Table 2 gives the details of the targets used in the experiment. The boron powder was packed in containers of Mylar foils, 25 pm thick. The same thickness of foils was used for the water targets which were surrounded by a second layer of Mylar foils to prevent vacuum leaks. By using ordinary and heavy water as 016 targets in different angular regions the peak due to scattering from hydrogen or deuterium did not cause difficulties in resolving the inelastic peaks from oxygen. The 5 mm Li6 target was wrapped in A1 foils, 50 #m thick. The incident beam is monitored with a counter telescope, which consists of two plastic scintillation counters, and is directed towards the target (see fig. 1).
3. Experimental Procedure 3.1. PROTON BEAM The size and position of the incident beam spot were frequently checked by exposing photographic paper. Fine adjustments were performed with the steering magnet shown in fig. 1. 3.2. TARGET The target was placed in vacuum and rotated in such a way that its normal formed an angle, with respect to the incoming beam, equal to half the scattering angle. In this geometry the target contribution to the broadening of peaks in the energy spectra comes primarily from straggling. 3.3. SPECTROMETER AND DETECTOR SYSTEM For each target and scattering angle the detectors were placed in the position giving the best energy resolution. For the first six crystals, this position corresponds to the image plane of the magnet. The energy spectrum was run from a little above the elastic peak and down in steps of about 0.4 MeV. As yet there is no accurate absolute measurement of the magnetic field, and the energy calibration is obtained by means of well-known peaks in some of the spectra. At frequent intervals during each recording of an energy spectrum the target was removed by means of a remotely controlled target changer and the background
86
D. HASSELGREN e t al.
measured. In the cases where the targets were not self-supporting a dummy target consisting only of the foils was used in the background measurements. Except for the smallest scattering angles this background was negligibly small over the whole spectrum. 4. Evaluation of Data and Discussion of Errors
In this section some of the problems involved in converting the raw data into the final energy spectra and angular distributions are discussed. 4.1. ENERGY CALIBRATION Since the magnetic field has not yet been measured in absolute units, we used the information obtained in the spectra from nuclei with well separated and accurately known energy levels to calibrate the energy scale. The elastic and first inelastic peak in carbon with a separation 9) of 4.433 MeV is one example, and there are several others among the nuclei studied here. The uncertainty in locating any peak varies very much from case to case and is reflected in the errors assigned to the excitation energies quoted in the next subsection. Another resaon for error differences is the fact that the excitation energies have been obtained by averaging over different numbers of energy spectra. The minimum error has been estimated to be 0.I MeV. 4.2. ABSOLUTE CROSS SECTIONS For a constant number of protons striking the target and constant solid angle the proportionality factor between peak areas in the energy spectra and differential cross sections for scattering will vary with target and scattering angle. To get a direct measurement of the cross section one also needs to know the eliicieney o f the system. For reasons discussed below we have chosen to use the method of comparison with well-known proton-proton cross sections. The target thickness can be determined to an accuracy of a few percent except for the water targets where bubbling could not be prevented. However, the cross sections for 016 could be determined directly by comparison with peaks obtained in scattering from the hydrogen in the water targets. The energy channel width is calculated from the parameters of the spectrometer. It varies between 0.15 and 0.17 MeV for the smaller scattering angles but goes down to 0.10 MeV for the lightest nucleus Li 6 at the largest angle (45°.5). Various methods for determining the areas under the peaks have been tried. F r o m well separated peaks in the energy spectra one can construct a standard curve with might also be used for resolving more complicated structures. However, it was found possible to use triangles for this purpose without introducing systematic errors. Rough estimates of the intrinsic widths of excited levels have been obtained by simple comparison with peaks known to have a line width equal to the experimental energy resolution. In so doing we have assumed that the intrinsic width and the experimental energy resolution add quadratically to give the resultant width of a peak in the spectrum.
INELASTIC PROTON SCATTERING
87
The real background as obtained in the target-removed measurements was normally very small and without structure. However, due to effects such as multiple scattering in the target, high density of levels in the target nucleus and the onset of various knockout reactions, all spectra will show a more or Iess smooth level over which peaks corresponding to strongly excited levels are superimposed. To subtract this "background" is the most delicate part in the determination of the cross section. The procedure adopted here has been to draw a smooth curve under the peaks, joining as well as possible the structureless parts of the spectrum and to subtract this level before determining the areas. Previously the number of protons striking the target for a certain number of monitor counts was determined by means of irradiation of polystyrene foils 7, a). Several checks have now been made on the consistency of these results. In some cases like Li, Be and C the elastic cross sections have been accurately measured at this energy xo). Those results differed in a systematic way slightly from the ones obtained in this experiment. However, the monitor could also be calibrated by scattering from CH and using the well-known proton-proton cross section ~o). In this way the elastic cross sections in the two measurements agreed completely. Since the latter method avoids the difficulty of determining the efficiency of the spectrometer-detector system, it was considered more reliable and has been used in the present work. The overall uncertainty in the absolute cross sections becomes about 10 ~o, slightly less for Li 6, Be 9, C 12 and 016 and slightly more for Li 7, B x° and B H. 5. Results and Discussion
Figs. 3-9 show energy spectra obtained at one scattering angle for each of the seven nuclei studied. They have been chosen to exhibit the most prominent peaks in the region of excitation energies covered. The angular distributions of the cross sections for resolved levels are presented in figs. 10-18. In fig. 20 the experimental results are collected to show which states are excited to a measurable degree in the scattering of 185 MeV protons. The results are presented with an attempt to correlate observed peaks in the energy spectra with previously published experimental data regarding the level schemes of the nuclei concerned. We also compare our results with those obtained in similar experiments and with some theoretical analyses. The solid lines in figs. 3-17 only serve as guides for the eye, whereas the curves of figs. 18 and 19 are calculated theoretically. 5.1. THE Lie NUCLEUS (figs. 3, 10 and 11) Four inelastic levels of Li 6 have been seen in this experiment and the angular distributions obtained are shown in figs. 10 and 11. The peaks at 2.2+0.1 and 3.6+0.1 MeV are easily resolved and can obviously be identified with the well-known 9) levels at 2.184 and 3.560 MeV, respectively. The corresponding transitions to the ground state are known to be E2 and MI.
88
D.
HASSELGREN et a L
8000
L i 6 15 = 6000
t 4000
° o°°
2O0O
°°
00o
i
o
~
o =oooo oooOoOOoo °°°°°°° I
to
8
I
6
I
I
,6
'~
2
0
xl/m
t
Eexc(MeV]
Fig. 3. Energy spectrum at 15 ° (lab system) for inelastic scattering of 185 MeV protons from LP (target thickness 0.233 g/cm=). The statistical errors are comparable to or smaller than the size of the experimental points.
; 500
Li ~ 25 o 1000
5OO
o~Ooo~OoOOooOoOO~o°°°0°°oJ !
t
12
f
I
10
I
I
8
I
00000000~1
8
2
0 Eexc(MeV]
Fig. 4. F.nergy spectrum at 25 ° (lab system) for inelastic scattering oi" 185 M e V protons from L i v (target thickness 0.064 g/cm=). The errors shown are statistical.
1500
BeS
25 o
°O~o o°
,00 °
I
18
I
I
I,~
I
I
12
I
I
10
I
I
8
i
o
o °°
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°%°
r
°o
!
OooooO0oi I
I
6
I
I
4
2
Eexc (MeV)
Fig. 5. Energy spectrum at 25 ° (lab system) for inelastic scattering of 185 M e V protons from Be °. The errors shown are statistical.
INELASTIC
89
SCATTERING
PROTON
As is seen f r o m the figures the angular distributions for the peaks at 4.4-t-0.2 and 5.4+0.2 MeV very closely resemble the one obtained for the 2.2 MeV peak. The level listed in ref. 9) at 4.52 MeV is reported to be about 600 keV broad, to have zero isospin (T = 0) and spin-parity 2 +. Since we observe an intrinsic width for the peak at 4.4+0.2 MeV of about 0.6 MeV the identity seems clear.
3000
B Io 2 0 °
u~
"~
2000
~000
ioooo oooo¢~ooOoOOOoOOOo oo I
I
I
18
I
.o.o
o OooOooOooooOt~°°°Ooo
I
16
/
°o° o
1
t
I
I
12
14
I
00°°%
I
I
I
8
tO
I
I
6
oOOO° O~)O
I
:; ~" 1
i
2
Z
0 Eexc (MeV)
Fig. 6. Energy spectrum at 20o (lab system) for inelastic scattering of 185 MeV protons from Bx°. The errors shown are statistical. i
i
i
i
i
i
i
i
i
,
i
i
i
i
,
1
i
i
1500
"~
B"
10"
1ooo
"*I-~ 500
!
*******************************~**
I6
14
12
I0
,~ Y2
oo°*
8
6
,~
2
0
Eexc(Meg)
Fig. 7. Energy spectrum at l0 ° (lab system) for inelastic scattering of 185 MeV protons from a Bu target of 98.6 ~o isotopic purity. The errors shown are statistical. Regarding the peak observed at 5.4+_.0.2 MeV it appears more difficult to obtain a clear identification. The peak is about 1 MeV wide and the angular distribution suggests an E2 transition. Two excited states are known 9) in this region: a sharp level at 5.35 MeV (T = 1) and a broad one at 5.5 MeV (T = 0, J~ -- 1+). Considering the large width of this peak in the spectrum it seems probable that the level at 5.5 MeV is excited. At higher excitation energies a structure is seen around 7 MeV suggesting the observation of two different levels, one at about 6.5 MeV for smaller angles and one at
D . HASSELGREN e t al.
90
~
i
I
i
•
~
•
oo
g % d'
%o o
o
o
~
o
8
0
# o
~o
o
~e
%
m
~
o
I
I
J
I
(sj/un qJe) 30o0 ,o#p
(sl!un 'qJe) 3POP DTP
i
~
i
~
•.- [ .
Lug
o
g-
[
.o
# oo oo <>o
~.~
°o
%
o? o
~
g. °° o
00 o o o
i g
?
,e. o o o o
I
( s l ! u n "qJe) 3PLOP ~2P
~,8 e
o
% %
( s l t u n "q~e) 3PUP .
i
o
0
91
INELASTIC PROTON SCATTERING
,ot
Li 6 3 6 t O I MeV 4.4+-02MeV
6.0 4.0 E
~1~ ~.o~
" 5,4• tO.2 MeV
-YO .cj¸. E
~1~ 2,0 T
10
J
20
,o
Jo
~
O;og
I0
Fig. 10. Angular distributions for the second I 85 andthirdpeak observed in the Li 6 (p,p)Li reaction at 185 MeV (lab system).
20
40
30
e l°ab
Fig. 11. Angular distributions for the first and fourth peak observed in the LP(p, p') LP* reaction at 185 MeV (lab system). i
i
8.o
i
F
Be9 2 3 5 + O.l lvleV
6.to
LiT
4.6+-0.1HeV
~0
6.65 + 0 2 MeV 50
~
.
L.
T
" 40
~l~ 4.0 -o~
10 ./ 2.0
2.0 [0
10
20
30
40
toO'*-b
Fig. 12. Angular distributions for the second and fourth peak observed in the LiV(p,p')LF * reaction at 185 MeV (lab system).
10
20
30
40
9 ~0b
Fig. 13. Angular distributions for the first three peaks observed in the Be°(p, p')Be 9. reaction at 185 MeV (lab system).
92
D. HASSELGRENet aL
approximately 7.5 MeV for angles over 20 °. The maximum cross section comes at 18 ° and is 0.4 mb/sr.
Bt°
~o
~ ~ .~ .,~o~
V
6.l+-0.1MeV
~I~ 2.0
~0 20
30
~0
e ~a b
Fig. 14. Angular distributions for two of the peaks observed in the BI°(p, p')B 1°* reaction at 185 MeV (lab system). i
(a)
t
i
(b)
Bit
Bn
20
2.2t0.I I~V
~
~
~
5 95 tOlSIvleV
0.5'
0
(c)
J
20
3O
o
etab
~0
Bit
3o
5. I t O.15MeV ~? 6.8t0.I MeV
E 20
0
I0
lab
i
IO
20
Fig. 15. Angular distribution for the first peak (a) for two of the peaks (b) and for the third and fourth peak (c) observed in the Bll(p, p')B 11. reaction at 185 MeV (lab system).
30 OObla ~0
In comparing the data of ref. 5) and those presented here, we find some notable discrepancies. The cross sections for the first two peaks at 2.2 and 3.6 MeV are about 50 ~o lower for 185 than for 155 MeV protons. Furthermore, the angular distribution presented in ref. 5) for the 3.6 MeV peak shows a marked departure from the smooth
93
INELASTIC PROTON SCATTERING
i
(a)
i
Ci 2
(b)
~ 4.4 tO.l MeV ;? 15.15+-0.1 MeV
~0
cl 2
;? ZestO.l MeV 4 9.7.~O. 15MeV
50
.~ 4.o
1.5
E ~E
10
2.0
0.5
f
~0
I
I0
20
(c)
30
8
o
10
lab 40
30
(d)
C~2
0.6
20
C 12
~? 12.?*-0.2MeV
~, le.2*- O3 MeV
2O
16.1+0.2 MeV
O°lab . ~0
~ .
? 19.3 +-02 MeV
E 0~ 1.0
0,2
I
,
tO
20
20 0 °lab
I0
20
0 olab ~0
30
Fig. 16. Angular distributions for two of the peaks (a and c), for the second and third peak (b) and for two peaks in the giant resonance region (d) observed in the C12(p, p')C 1=* reaction at 185 MeV (lab system). 50
i
(b) ~a~
~
0 t6'
0 ~e
l~
6.15"-0. l /4eV z os±o.ls Mw
T
t.5
'5.3'o.2t~v 187+-02MeV-
30
"~
to
2O ~5
~0
10
20
30
,$0
9
o lab
I0
I
I
20
30
O°lab dO
Fig. 17. Angular distributions for the first two peaks (a) and for three of the peaks (b) observed in the OXS(p, p')O 16. reaction at 185 MeV (lab system).
94
u.
HASSELGP-,EN
e t al.
exponential form obtained here (fig. 10). Theoretical calculations 15) aimed at fitting the 155 M e V results are shown in fig. 19 together with the experimental results obtained here. As has been remarked by Jackson and Mahalanabis 15) the new exi
~5
r
i
i
I
0 I6
i
ll5~-O21vleV (exp.points) •
0
theoretical curve tl.9 MeV)
(Erikson
13.1t0.2 M e V (exp points)
ta
theoretical
2.0
(Erikson
curve
t2.8 MeV)
E ;
05
\
/ ~ '-
~0
[\\
4
i,.+
I0
2O
3O
-.t
(b)
•
o 40 0 lab
I
z
tO
20
#
30
e°
tab
Fig. 18. Theoretical curve for a (2-, T = 0) state at 11.9 MeV (a) and for a (2-, T = 1) state at 12.8 MeV (b) in Oze as calculated by Erikson 22), compared with experimental points from this experiment. i
i
i
i
l
Li 6
3,6"-0.1MeV E~p. poin:s
8.0
t
Theoretlcol curve~
6.0
t i
4.0
~t~
i. . . . b=2.24 fm ,150);-b=[6Ofm
d{Morfedwa~e~°) . . . .
b=224 frn
,I
2.0
10
20
30
40
O~ab
Fig. 19. The 3.6 M e V peak in LP compared with theoretical predictions from ref. 15). perimental results tend agreement with elastic A calculation o f the performed by Erikson points presented in fig.
to favour a larger value for the length parameter b, in better electron scattering results. angular distribution to be expected at our energy has been 15). Also in this case the agreement with the experimental 19 was quite satisfactory.
INELASTIC PROTON SCATTERING
95
5.2. THE Li7 NUCLEUS (Figs. 4 and 12) Below an excitation energy of 10 MeV six peaks have been observed in the energy spectra from Li 7. The one at 4.6-t-0.1 MeV dominates in the whole angular region studied. It certainly corresponds to the level listed at 4.630 MeV (J" = ~ - ) in the literature 9, 11), which decays by an electric quadrupole transition. 23.4 t 0.4 ]
E.cMOV
22. f +-0.3 21.4 0.3
2I. t +-0.5 ] 20
23.4 +. 0.3
J
22.4 +- 0.7 ] J
] J
21.6 t 0.3
J
20.4 + 0.4 ]
20.2 +- 0,3 1.9.8 t 0.3
19.0 ; 0.4 ] J
19.3 : ~.Z ]
18.7 : 0.2
-
18,2 *. o 3
t;'.,~ *- 0.3 ~ 16.7 +- 0.3
]
1z8 ±
J
o3 J
1r. 1 t o.3 16.1 ~- 0.2 15.15 -+ 0.1
15-
1~'; "- 0.3 ~ 13.0+-0.3]
14.2 -* 0.,;
I3.0+0.2]
12.7+.0. 2
13.1+0-2
11.1+-0.6 I 0 6 .+ 0.4
10.4 +. 0.3
11.9 +-0.2 I1"2 +" 0"3 ~
lLO t O. 3 10. 5 -+ 0.2
10-
I5.3 +- 0.2
14.5 +- 0.4
11.5 +- 0 2
9.7 + 0.15
9.6~0.2]
8.95 ~- O. 15 8.5-
7.5
'//////////////, 5--
7e~o3] 6.65~0.2
7'9 ~- 0'3 ~ t
5.4 ~- 0.2 ]
5.5+.0.3]
4.4+-0.2]
~.610.
I
7.55+.0.15
7.4 ~__0.3
7.65+.0.1 Z05 +- 0.15
6.8+.01 6.5 +- 0.3
4.8 *-0.3
6. I +. 0.1 5.2 +- 0.2
J
&15 *. 0.1 5.1 t 0. I5 4.5 +. 0.1
4,~ +. 0.1
3.65 +-O. 2
3 . 6 +- 0,!
$.~ *- O.T
2.35 .+ 0.7
2.2 ~- 0. I5
2.2 "- 0.1
0.8 +- 0.2
0 . 5 +- 0 . I
OL/6
Li 7
Be 9
B tO
Bll
C12
0 16
Fig. 20. Excitation energies for the peaks observed in the inelastic scattering of 185 MeV protons from L P , Li 7, Be 9, B 1°, B 11, C 12 a n d 016. The vertical bars represent the measured intrinsic widths of the peaks. Widths smaller than 0.4 MeV are not shown.
For angles larger than 20 °, protons scattered from the well-known first excited state of Li 7 are seen at the lower energy end of the elastic peak. By using the information obtained from other nuclei about the shape of a pure peak it is possible to resolve the contribution from this level. The literature 9) value o f the excitation energy is 0.478 M e V and in the present experiment it was measured to lie at 0 . 5 + 0 . 1 MeV. The cross sections falls smoothly from a maximum value o f about 0.9 mb/sr at 200-25 ° .
96
D. HASSELGRENet aL
There is a small peak in the spectrum at 5.5+0.3 MeV with a width of about 0.4 MeV. It is not clearly resolved and thus is quite uncertain. The cross section never exceeds 0.5 mb/sr. A broad peak with an intrinsic width of about I MeV is observed at 6.65_+0.2 MeV. The angular distribution is shown in fig. 12. In ref. 9) a broad level is reported at 6.54 MeV and is certainly identical to the one excited here. Results H) for inelastic electron scattering from Li 7 give clear evidence for a level at 6.8+0.1 MeV (width 0.8 MeV) and indications of a state at 5.7__+0.1 MeV (width 0.5 MeV). There has been some doubt about the existence of the latter and as already mentioned the evidence presented here is quite weak. Two more peaks are seen in the energy spectra obtained here at 7.6_+0.3 and 9.6 + 0.2 MeV. For the former the maximum cross section is about 0.3 mb/sr and for the latter 0.4 mb/sr. They are both broader than the energy resolution of the apparatus. Two levels corresponding to these peaks are reported in the literature 9), one at 7.47 MeV (jz = ~r-) and the other at 9.6 MeV. Regarding levels with an excitation energy higher than 10 MeV it may be said that their cross sections all are less than 0.2 mb/sr. Since the experimental width of a peak in the energy spectrum was considerably larger than in the earlier 3) work at 185 MeV it is difficult to make direct comparisons except for a few well separated levels. In Li 7 a peak at 4.4+0.2 MeV was seen with an angular distribution dipped in the forward direction. It is apparently identical to the one seen in this experiment at 4.6_+ 0.1 MeV, but the cross section obtained here is almost twice as low. Some of the cross section in the earlier experiment, especially at small angles, probably came from the 3.6 MeV level in Li 6. In comparison with ref. 5) we have seen an additional peak in our experiment, namely the one at 5.5__+0.3 MeV. If real, it corresponds to a weakly excited level not listed in the compilations of ref. 9) but predicted by Clegg 12) and observed in inelastic electron scattering ~ ) . However, in the latter experiment it was recently given an alternative explanation, and in our case it probably needs further confirmation. Regarding the 0.478 MeV level some interesting results have recently been obtained by Mahalanabis la). She calculated the results to be expected in the scattering of 156 MeV protons and found a forward peaked angular distribution. Unfortunately we have not been able to follow the corresponding peak down to smaller angles. By studying the (p, p'y) reaction, Newton et aL 14) did obtain cross sections for this level down to 10°, which indicates an angular distribution resembling that of the 4.6 MeV state. 5.3. THE Be° NUCLEUS (Figs. 5 and 13) A great number of peaks have been observed in the energy spectra obtained in scattering from Be 9. Most of them are only weakly excited and not fully resolved. The angular distributions of the first three levels are presented in fig. 13. Their excitation energies have been found to be 2.35_+0.1, 4.8_+0.2 and 6.5+_0.3 MeV, respect-
INELASTIC PROTON SCATTERING
97
ively. Of these the second is somewhat broader than the experimental energy resolution whereas the third has an intrinsic width of 1.2+0.2 MeV. Except for the sharp state at 2.35 MeV which is listed in ref. 9) at 2.430 MeV (J~ = ~ - ) these peaks do not correspond to any well-known states in Be 9. However, recent experiments on proton 5) and electron 16) inelastic scattering have given similar results. The next three peaks are located at 7.9, 11.2 and 14.4 MeV (all with an error of ___0.3 MeV), respectively, and have been seen over the whole angular range covered. The angular distributions are quite flat with a maximum cross section of 0.5 mb/sr for the peak at 7.9 MeV and 0.3 mb/sr for the other two. The peak widths are compatible with intrinsic level widths between 0.5 and 1.0 MeV. In the latest compilation of ref. 9) four levels are listed in this region of excitation energies but the identity of the peaks obtained here is far from certain. At higher excitation energies five peaks have been seen at 16.7_+0.3, 17.44-0.3, 19.0_+0.4, 21.1 _+0.5 and 22.4_+0.7 MeV. The measurements have been extended to this energy region only for small angles and the maximum cross sections are 0.2, 0.3, 0.3, 0.5 and 0.3 mb/sr, respectively. The peaks seem to be quite wide and their existence is not established with any great certainty. However, they probably correspond to the structure seen at these energies (the giant resonance region) in (~,, n) reactions. For the 2.3 _+0.2 MeV peak in Be 9, seen by Tyr6n and Maris 3), both the angular distribution and the absolute magnitude of the cross section agree very well with our results (peak at 2.35_+0.1). On the other hand, the peak at 6.5 MeV which was expected to show some structure with improved energy resolution still appears as single in the present experiment. 5.4. THE B 1° NUCLEUS (Figs. 6 and. 14) As is seen from the spectrum presented in fig. 6 the dominating peak comes at about 6 MeV; its position has been measured to be 6.1 +0.1 MeV and there is no extra broadening. The angular distribution resembles very closely those obtained for the electric quadrupole transitions in the lighter nuclei. From what is known about the level scheme of B 1° it is not possible to identify this peak further. At 35 ° and 40 ° the elastic peak has a small bump located at 0.8___0.2 MeV which evidently corresponds to the known 9) level at 0.717 MeV (1 +, T = 0). It is weakly excited; the maximum cross section is about 0.1 mb/sr for these angles. Nothing is seen of the next level quoted in the literature 9) at 1.74 MeV (0 +, T = 1) but at 2.2_+0.15 MeV a peak appears with a maximum cross section at 20 ° of about 0.3 mb/sr. This then would be the 2.15 MeV level (1 +, T = 0) observed in a great number of nuclear reactions 9). The known state 9) at 3.59 MeV (2 +, T = 0) is found to be even more weakly excited. There is a peak in the energy spectrum at 3.65 4-0.2 MeV with a cross section which never exceeds 0.2 mb/sr. Before the dominating 6.1 MeV peak there is one at 5.2___0.2 MeV which has an angular distribution resembling that of the 2.2 MeV peak, both in shape and in absolute magnitude.
98
D. HASSELGREN et aL
In fig. 14 the angular distribution for the peak observed at 7.55-t-0.15 MeV is shown. It is evidently of the type found for the 3.6 MeV level of Li 6, which is known to decay by a pure MI transition. At higher excitation energies two more peaks have been found; like the one just mentioned above they are slightly broader than the line width of the experiment. They occur at I 1.0 __.0.3 and 13.0___0.3 MeV, respectively. Of these the lower has been seen only at a few angles and has a maximum cross section of 0.3 mb/sr. The higher one has been observed in the angular region 40-30 ° and reaches a maximum cross section of almost 0.8 mb/sr at 20 °. It is doubtful, however, if the peak is single or double, and therefore the angular distribution is not presented: In B ~° Jacmart et aL 5) have seen two peaks at 7.4+0.3 and 8.05+0.3 MeV where only one at 7.55+0.15 MeV was observed in the present experiment. This discrepancy is probably not serious, since we have based our energy assignment on the position of the peak at small angles where it was most dearly seen. 5.5. THE Bu NUCLEUS (Figs. 7 and 15) The first three peaks at 2.2___0.1, 4.5_+0.1 and 5.1_+0.15 MeV, respectively, are easily identified with known 9) levels reported to be 2.14 (½-), 4.46 ( { - ) and 5.03 (½- or { - ) MeV above the ground state of B 11. Their angular distributions are shown in fig. 15. As is the case for the following three peaks observed in the energy spectra their intrinsic widths are too small to be noticed in the present experiment. The peak at 6.8 _+0.1 MeV (fig. 15c) whose angular distribution has almost exactly the same shape as that for the peak at 4.5 MeV certainly corresponds to the level 9) at 6.76 MeV (probably -~-). In the angular region 80-25 ° we observe a peak at 7.4-t-0.3 MeV with a maximum cross section of less than 0.3 mb/sr, previously not seen in (p, p') experiments. There is a level reported 9) at 7.30 MeV (probably { - ) which might correspond to this peak. Around 9 MeV excitation energy several levels are known, and therefore no definite assignment can be given to the peak observed at 8.95+__0.15 MeV (fig. 15b). At about 9.8 MeV there is an indication of a peak with a maximum cross section of 0.2 mb/sr. It is seen between 15 ° and 25 °. In the 10.5__+0.2 MeV peak there is some evidence for an intrinsic width. It has been observed in the angular range 8o-40 ° and has a maximum cross section less than 0.4 mb/sr. Three more peaks have been observed in the energy spectra for B 11 at 11.9_+0.2, 13.0 + 0.2 and 14.5___0.4 MeV, respectively. Of these the first peak has been seen only for forward angles (4°-15 °) with a cross section less than 0.4 mb/sr, the second peak in the angular range 40-35 ° with a cross section of about 0.4 mb/sr and a fairly fiat angular distribution. The peak at 13.0 MeV seems to have an intrinsic width of about 0.4 MeV. The one remaining, at 14.5 MeV has only been observed at 15 °, 20 ° and 35 ° and yields a very small cross section, about 0.15 mb/sr. The present results for B 1~ agree very well with both ref. 5) and those of Newton
INELASTIC PROTON SCATTERING
99
et al. 17) with the possible exception of the peak at 2.2_+ 0.1 MeV which has a higher
cross section in ref. 17). It may also be noted that the 7.55 MeV peak in B 1° and the 9.0 MeV peak in B 11 probably were too close for separation in the earlier 3) work at 185 MeV in which a target of natural boron was used. This was particularly troublesome since these two peaks have very similar angular distributions. 5.6. T H E C TM N U C L E U S (Figs. 8 and 16)
In C 12 15 peaks have been seen in the energy spectra with widely varying cross sections. Some of these can be identified with well-known levels 9) and are listed in table 3. TABLE 3 Experimental results on some peaks observed in the energy spectra of C TM together with listed p r o p erties of the corresponding excited levels ~) Ex. energy (MeV) This exp. Listed value 4.4 q-0.1 7.65 4-0.1 9.7 4-0.15 12.7 4-0.2 15.154-0.1 16.1 4-0.2
4.433 7.656 9.64 12.71 15.11 16.11
Accepted value o f J,~ T 2+ 0+ 31+? 1+ 2+
0 0 0 0 1 1
Max. cross section d c q d ~ ( m b / s r ) at angle 5.6 0.9 1.2 0.35 4.7 0.28
18°.5 forward 23 ° 8°.5 forward 15°.5
The angular distributions for the peaks presented in table 3 are shown in figs. 16a-c. Since the preliminary report 7), which gave the angular distribution of the 7.65 MeV peak, more measurements have been made confirming the results reported there. At 10.6+0.4 and 11.1 +0.4 MeV two small peaks appeared; both of them were difficult to resolve clearly. The former has been seen from 4 ° to 40 ° with a maximum cross section of 0.35 mb/sr at 22 °, the latter has been observed in the angular region 20 ° to 30 ° and gives a somewhat larger cross section. An upper limit of 0.2 mb/sr can be set on the cross section for exciting a level at 14.2_+0.4 MeV, and it is seen only beyond the angles (about 20 °) where the 15.15 MeV peak has decreased to less than 5 ~o of its maximum. For the nine peaks discussed thus far no intrinsic width has been observed. The remaining peaks, located in the giant resonance region all have widths between 0.5-0.8 MeV. The angular distributions for the peaks observed in this region either have a maximum at an angle below 15 ° or are forward peaked. As an example fig. 16d shows the distributions for the peaks at 18.2_+0.3 and 19.3_+0.2 MeV. The existence of the peak at 20.4_+0.4 MeV is rather uncertain; it has been seen over the whole angular region with a cross section less than 0.5 mb/sr. The last three peaks (21.4+0.3, 22.1 ___0.3 and 23.1_+0.4 MeV) are to be considered as the most probable decomposition of the structure in the region 20.5-24 MeV. The angular
100
D. HASSELGRENet
aL
distributions of the first two are quite similar; they increase from about 0.2 mb/sr at 30 ° to approximately 1.0 mb/sr for angles below 10 °. The peak at 23.4___0.4 MeV finally has been observed f r o m 4°.5 to 20 ° and the cross section remains below 0.4 mb/sr. A few examples will be given here of the experimental and theoretical work on inelastic proton scattering from C 12. The agreement between the 155 MeV results s) and those of the present experiment is very good. Regarding the theoretical analyses, the work of Sanderson 1 s) bears directly on our data. The angular distributions for exciting several states in C 12 by 180 MeV protons have been calculated and compared with the results of ref. 3). Regarding the 9.63 MeV level the agreement still holds as far as the shape of the angular distribution is concerned but our cross sections are about half of those calculated. For the level at 15.1 MeV (1 +, T = 1) our cross section is the same as the theoretical value at 9 ° laboratory scattering angle but increases faster in the forward direction. In the giant resonance region two broad peaks were observed in the earlier work a), one at about 19 MeV and the other at 22 MeV. Sanderson compares the experimental cross sections obtained with the sum of contributions f r o m three T = 1 states in each group, plus one T = 0 level falling under the 22 MeV b u m p and two T = 0 states which contribute to the structure at 19 MeV. As seen from fig. 20 six peaks have now been observed in this region. Assuming that our peak at 18.2-t-0.3 MeV is the sum of contributions from Sanderson's levels at 18.2 ( 2 - , T = 1) and 18.7 MeV ( 1 - , T = 1) and, furthermore, that our peak at 19.3_+0.2 MeV corresponds to the one at 19.3 MeV ( 2 - , T = 1), the agreement is quite satisfactory between the angular distributions presented in fig. 15c and those calculated. Due to large uncertainties in the experimental data at the higher excitations (21-24 MeV) a detailed comparison is difficult. However, if we sum the cross sections from the peaks observed in this region the results will be quite close to that obtained by Sanderson i s). As a final remark concerning C 12 it may be noted that the essential features on the rather unique angular distribution found for the 7.65 MeV peak were reproduced in a preliminary calculation performed by Eriksson and Rinander 19). Following a suggestion by Brink 2o) they assumed the 0 + state at 7.656 MeV to be a monopole vibration characterized by a radius R = Ro(1 +ct), where ~ is a deformation parameter. 5.7. THE Ot6 NUCLEUS (Figs. 9, 17 and 18) The first two peaks observed in the spectra f r o m O 16 come at 6.15 + 0.1 and 7.05 + 0.15 MeV. Evidently each one of them might correspond to a mixture of contributions f r o m two well-known 9) levels 6.05 (0+), 6.13 ( 3 - ) and 6.92 (2+), 7.12 MeV ( 1 - ) respectively, all with isospin T = 0. Further separation is not easily attained with our bombarding energy. However, it has been shown 21) that by studying also the (p, p'?) reaction it is possible to get more detailed information about these peaks. This work is discussed below.
INELASTIC PROTON SCATTERING
101
The upper limit 9) of the cross section for exciting the states at 8.88, 9.59 and 9.85 MeV can be set to 0.1 mb/sr. In the angular region 15°-35 ° we have observed a peak at 10.4+_0.3 MeV. It is not clearly resolved and has a cross section at 20 ° of about 0.3 mb/sr. Fig. 18 presents the angular distributions for the peaks found at 11.5-t-0.2 and 13.1+_0.2 MeV. The dashed curves have been calculated theoretically 22). The angular distributions for the peaks at 15.3 +_0.2, 18.7 +_0.2 and 20.2 +_0.3 MeV are shown in fig. 17b. In the giant resonance region there are five more peaks, all with a cross section smaller than 0.4 mb/sr. The excitation energies can be found in fig. 20. Except for the peak at 17.8+_0.3 MeV this structure is visible preferably for angles below 20 ° but even there it is quite difficult to make an unambiguous decomposition. Some interesting differences have been obtained from the results of ref. a) because of the improved energy resolution. First of all t w o peaks now appear in the energy region 6-7 MeV, and it is quite clear that the earlier angular distribution is the sum of those presented in fig. 16a. In this connection it may be noted that by looking at the (p, p'v) reaction, Rowe et aL 21) have been able to give separate cross sections for three of the four levels involved. At 150 MeV proton energy and for a scattering angle of 25 ° they obtain 0.23+_0.14, 3.16+_0.11 and 0.88+_0.13 mb/sr for the levels at 6.05, 6.13 and 6.92 MeV, respectively. These values agree very well with our cross sections if our 6.15 MeV peak is considered as the sum of contributions from the first two levels in 016 . Finally, regarding the earlier 3) work at 185 MeV it seems that the previously observed peak at 12.5+_0.3 MeV in 016 now has been resolved into two components, namely those shown in fig. 18. As was mentioned above the curves in fig. 18 have been calculated by Erikson 22) for one state at 11.9 MeV (2-, T = 0) and one at 12.8 MeV (2-, T = 1). The authors wish to express their gratitude to the head of the Institute, Professor The Svedberg, and to Dr. H. Tyrfn for their kind interest in this work. The assistance of Messrs. A. Ingemarsson, S. Dahlgren and R. Gabrielsson during a considerable part of the experiment is gratefully acknowledged. We also wish to thank Dr. Arne Johansson for many valuable discussions. Miss D. Jackson, Mrs. J. Mahalanabis and Messrs. T. Erikson, T. A. Eriksson and G. Rinander have kindly informed us about the results of their theoretical analyses before publication. It is a pleasure to acknowledge the technical aid of the members of the cyclotron staff under Messrs. A Svanheden and B. Hemryd. Thanks are due to Mrs. A. Astr6m for preparing all graphs and to Mrs. L. Borgman for secretarial help. This work has been supported financially by the Swedish Atomic Research Council.
102
D. HASSELGRENet al.
References 1) 2) 3) 4) 5)
Th. A. J. Maris and H. Tyr6n, Nuclear Physics 3 (1957) 35 K. Strauch and F. Titus, Phys. Rev. 95, (1954) 854, 103 (1956) 200, 104 (1956) 191 H. Tyr6n and Th. A. J. Maris, Nuclear Physics 4 (1957) 637, 6 (1958) 82 J. M. Dickson and D. C. Salter, Nuovo Cim. 6 (1957) 235 J. C. Jacmart, J. P. Garron, M. Riou and C. Ruhla, Phys. Lett. 8 (1964) 269; J. C. Jacmart, Th~s¢, Universit6 de Paris (1964) 6) A. Johansson, A. Svanheden, U. Svanberg and H. Tyr6n, private commlmication 7) D. Hasselgren, P. U. Renberg, O. Sundberg and G. Tibell, Phys. Lett. 9 (1964) 166 8) D. Hasselgren et al., Comptes Rendus du Congr~s International de Physique Nucl6aire 1964, (CNRS, Paris, 1965) vol. II, p. 406 9) F. Ajzenberg-Selove and T. Lauritsen, Nuclear Physics 11 (1959) 1; T. Lauritsen and F. Ajzenberg-Selove, Nuclear Data Sheets, NRC 61-5 and 6 10) A. Johansson, U. Svanberg and P. E. Hodgson, Ark. Fys. 19 (1961) 541 11) M. Bernheim and G. R. Bishop, Phys. Lvtt. 5 (1963) 294; G. R. Bishop and M. Bernheim, Phys. Lett. 8 (1964) 48 12) A. B. Clegg, Nuclear Physics 33 (1962) 194 13) J. Mahalanabis, Ph. D. Thesis, submitted to the University of London (November 1964) unpublished 14) D. Newton et al., Prec. Phys. Soc. 79 (1962) 27 15) D. F. Jackson and J. Mahalanabis, Nuclear Physics 64 (1965) 97; T. Erikson, private communication 16) H. Nguyen Ngoc, M. Hers and J. Perez y Jorba, Nuclear Physics 42 (1963) 62 17) D. Newton, A. B. Clegg, G. L. Salmon and D. J. Rowe, Nuclear Physics Laboratory, University of Oxford, preprint (1963) 18) E. A. Sanderson, Nuclear Physics 35 (1962) 557 19) T. A. Eriksson and G. A. Rinander, private communication 20) D. M. Brink, private communication 21) D. J. Rowe, A. B. Clegg, G. L. Salmon and P. S. Fisher, Prec. Phys. Soc. 80 (1962) 1205 22) T. Erikson, Nuclear Physics 55 (1964) 497
bc reproduced by photoprint or microfilm without writt¢n p¢rmisslon from the publisher
INELASTIC SCATTERING FROM
O F 185 M e V P R O T O N S
LIGHT NUCLEI
D. HASSELGREN, P. U. RENBERG, O. SUNDBERG and G. TIBELL The Gustaf Werner Institute, University of Uppsala, Uppsala, Sweden Received 23 December 1964 Abstract: Differential cross sections have been measured for scattering of 185 MeV protons from excited levels of the seven light nuclei LP, Li', Be9, B1°, B11, C 12 and 016. The energy analysis of the inelasticallyscattered protons has been performed in a magnetic spectrometer giving a resolution of 0.4--0.5 MeV (full width at half maximum) of peaks in the energy spectra. The measurements cover an angular region of 3°.5~,5°.5 in the laboratory system and excitation energies up to 30 MeV. For 31 peaks in the energy spectra angular distributions are presented. Excitation energies and in some cases intrinsic widths are given for a total of 68 levels excited in this experiment. The results are compared with those of previous experiments using incoming protons of about the same energy and, in a few cases, with theoretical analyses of inelastic proton scattering NUCLEAR. REACTIONS s, 'Li, 9Be, 10, liB, 1~C, 1SO(p, p,), E = 185 MeV; measured tr(Ep, 0). Deduced levels, _P. Enriched 6Li, I°B, lXB targets.
I
I
1. Introduction A t energies o f 15-50 M e V the a n g u l a r d i s t r i b u t i o n s o b t a i n e d in inelastic p r o t o n scattering are r a t h e r sensitive to spins a n d parities o f the excited levels. I n fact, the q u a n t u m n u m b e r s o f m a n y levels have been d e t e r m i n e d as a result o f such experiments. A t a b o m b a r d i n g energy o f 100-200 M e V the a n g u l a r d i s t r i b u t i o n s also s h o w a b e h a v i o u r characteristic o f the t r a n s i t i o n f r o m the g r o u n d state o f the t a r g e t n u cleus. This has been d e m o n s t r a t e d b y M a r i s a n d T y r r n in t h e o r e t i c a l w o r k on inelastic p r o t o n scattering 1). A t these energies c o m p a r a t i v e l y little structure is o b served in the a n g u l a r d i s t r i b u t i o n s a n d b r o a d l y s p e a k i n g t w o types o f curves are o b t a i n e d ; e.g. one with a d i p in the f o r w a r d direction a n d t h e o t h e r rising t o w a r d s smaller scattering angles. T h e y b o t h decrease with increasing angle. I n f a v o u r a b l e cases the p o s i t i o n o f the m a x i m u m o f the f o r m e r t y p e o f a n g u l a r d i s t r i b u t i o n gives i n f o r m a t i o n o n the m u l t i p o l a r i t y o f the electric t r a n s i t i o n involved. T y p i c a l e x a m p les o f such a n g u l a r d e p e n d e n c e are o b t a i n e d in the cases o f excited levels w h i c h decay t o the g r o u n d state via p u r e E2 a n d M1 transitions, respectively. S o m e o f the m o r e i m p o r t a n t studies o f inelastic p r o t o n scattering f r o m c o m p l e x nuclei at energies a b o u t 100-200 M e V p e r f o r m e d to d a t e are listed in table 1. I n m o s t cases m e a s u r e m e n t s have also been m a d e on heavier nuclei, b u t here we restrict o u r 81
D. HASSELGREN e t aL
82
selves to the lp shell region. The energy resolution listed indicates full width at half m a x i m u m ( F W H M ) of a peak in the energy spectrum without extra broadening due to thick targets, intrinsic widths of the levels studied, etc. It is obvious that the resolution in energy is a figure of merit for such experiments and sets a definite limit to what can be achieved regarding information on nuclear levels. TABLE I
Summary of some experiments on inelastic proton scattering at energies between 96 and 185 MeV Ref.
2)
Bombarding energy (MeV)
4)
96-t-2 96-4-2 185-4-< 1 1854- < 1 135 and 95
6)
155+0.5
3)
Target nuclei
Method of energy analysis
c 12 Li, Be, B, C, N, O CTM, 016 Li, Bee, B, N 14 Clz Lie, Li7, Bee, B1°, B11, C12
range telescope range telescope magnetic spectrometer magnetic spectrometer total absorption magnetic spectrometer
Energy resolution (FWHM, MeV) 3.0 3.0 1.8 1.8 3.4 0.8
In table 1 the error in bombarding energy refers to the spreadin energy of the incoming protons rather than to any uncertainty in the absolute value of this energy. At this institute a high resolution magnetic spectrometer which gives an overall resolution in inelastic proton scattering of 0.30 MeV has recently been developed 6). H o w much of that figure results from the spread in the extracted proton beam energy is not known but the contribution is probably less than 0.25 MeV. It was therefore thought worthwhile to repeat and extend the measurements previously performed by Tyr~n and Maris 3). We report here the results obtained for scattering f r o m Li e, Li 7, Be 9, B 1o, B11, C12 and 016 in the angular range 3°.5 to 45°.5 (laboratory system). In two previous publications 7, 8) preliminary results have been given for the 7.66 MeV level in C 12 and for all of the nuclei studied except Li 7. After a description of the experimental arrangements and procedure the results are given in the f o r m of energy spectra and angular distributions for resolved peaks. The results are discussed briefly and compared with previously published data as well as with some theoretical predictions.
2. Experimental Arrangements A schematic drawing of the lay-out of the experiment is presented in fig. 1. The external, unpolarized proton beam of the synchrocyclotron passes two focussing magnets, two bending magnets and one adjusting magnet before striking the target which is placed in a chamber connected to the vacuum tank of the magnetic spectrometer. A circular collimator, 20 m m in diam., is placed in the cyclotron tank in order to
INELASTIC
PROTON
83
SCATTERING
=o "O
.> O
t I
it3
I
• ... ~....:
-.,
•- i ° .-..... • •. °o
~
i':"" •
"
E-
.;~.~ )V-';-'+.~ J ~
o
°
E to.
/+.~
0~ ,.r-
0~
.o
...'.-
~~
\
E o ,.2
84
D. HASSELGRENet
al.
m a k e the b e a m better defined g e o m e t r i c a l l y at the target. T h e b e a m cross section at the t a r g e t p o s i t i o n is a l m o s t circular with a d i a m e t e r o f a b o u t 2.5 m m . A s e c o n d circular c o l l i m a t o r j u s t before t h e t a r g e t prevents p r o t o n s scattered off t h e M y l a r w i n d o w s o f the p r o t o n v a c u u m t u b e a n d the scattering c h a m b e r f r o m entering t h e MeV 0.40
0.35.
0.30-
90
95
¢00
105 ¢rn R
Fig. 2. Experimentally measured energy resolution (FWHM) versus distance R from exit pole boundary to energy channel defining counters. The straggling in energy loss is subtracted but not the energy spread of the incoming beam. The diagram is taken from ref. 6). TABLE 2 Target specifications for all the nuclei investigated in this experiment Target
LP Lie Li T Li7 Be9 B1° Btt Bu C 12 Ct6 Ole(H~O) OX6(HaO) OX6(DIO)
Isotopic purity (~o) 95.6 95.6 92.5 92.5 100.0 92.3 81.2 98.6 98.9 98.9 99.8 99.8 99.8
Thickness (g/era2)
0.078 0.233 0.064 0.129 0.423 0.185 0.071 O.126 O.156 0.206 0.34 0.21 0.14
Straggling (FWHM, MeV) 0.18 0.32 0.16 0.22 0.40 0.28 O.17 0.22 0.26 0.30 0.4 0.3 0.25
m a g n e t . Its d i a m e t e r is k e p t large e n o u g h so t h a t the b e a m will pass freely t h r o u g h it, n o r m a l l y 30 m m . T h e inset o f fig. 1 also shows a third, one-sided, straight c o l l i m a t o r , which was used f o r scattering angles larger t h a n 7 ° . This shield m a k e s it i m p o s s i b l e for p r o t o n s in the direct b e a m to enter the m a g n e t after scattering f r o m t h e exit wind o w o f the c h a m b e r . T h e solid angle in scattering f r o m the target is defined b y a recta n g u l a r c o l l i m a t o r p l a c e d j u s t outside the fringe o f the m a g n e t i c field.
INELASTIC PROTON SCATTEKING
85
The n = 0 magnetic spectrometer will be fully described in a later publication 6). With the solid angle used in this experiment (1.17 x 10-3 sr), the transmission is 100 % according to the orbits calculated from field measurements. The total opening angle is 2°.3. The scattered protons are detected in a double two-fold coincidence telescope system with six energy channels. The whole set-up of detectors is mounted on a support which can be moved along the direction of the protons leaving the magnet. For each nucleus and scattering angle, the focal distance has been calculated, and fig. 2, taken from ref. 6), shows how the experimental energy resolution (FWHM) changes with the distance R, between magnet exit and detector. Table 2 gives the details of the targets used in the experiment. The boron powder was packed in containers of Mylar foils, 25 pm thick. The same thickness of foils was used for the water targets which were surrounded by a second layer of Mylar foils to prevent vacuum leaks. By using ordinary and heavy water as 016 targets in different angular regions the peak due to scattering from hydrogen or deuterium did not cause difficulties in resolving the inelastic peaks from oxygen. The 5 mm Li6 target was wrapped in A1 foils, 50 #m thick. The incident beam is monitored with a counter telescope, which consists of two plastic scintillation counters, and is directed towards the target (see fig. 1).
3. Experimental Procedure 3.1. PROTON BEAM The size and position of the incident beam spot were frequently checked by exposing photographic paper. Fine adjustments were performed with the steering magnet shown in fig. 1. 3.2. TARGET The target was placed in vacuum and rotated in such a way that its normal formed an angle, with respect to the incoming beam, equal to half the scattering angle. In this geometry the target contribution to the broadening of peaks in the energy spectra comes primarily from straggling. 3.3. SPECTROMETER AND DETECTOR SYSTEM For each target and scattering angle the detectors were placed in the position giving the best energy resolution. For the first six crystals, this position corresponds to the image plane of the magnet. The energy spectrum was run from a little above the elastic peak and down in steps of about 0.4 MeV. As yet there is no accurate absolute measurement of the magnetic field, and the energy calibration is obtained by means of well-known peaks in some of the spectra. At frequent intervals during each recording of an energy spectrum the target was removed by means of a remotely controlled target changer and the background
86
D. HASSELGREN e t al.
measured. In the cases where the targets were not self-supporting a dummy target consisting only of the foils was used in the background measurements. Except for the smallest scattering angles this background was negligibly small over the whole spectrum. 4. Evaluation of Data and Discussion of Errors
In this section some of the problems involved in converting the raw data into the final energy spectra and angular distributions are discussed. 4.1. ENERGY CALIBRATION Since the magnetic field has not yet been measured in absolute units, we used the information obtained in the spectra from nuclei with well separated and accurately known energy levels to calibrate the energy scale. The elastic and first inelastic peak in carbon with a separation 9) of 4.433 MeV is one example, and there are several others among the nuclei studied here. The uncertainty in locating any peak varies very much from case to case and is reflected in the errors assigned to the excitation energies quoted in the next subsection. Another resaon for error differences is the fact that the excitation energies have been obtained by averaging over different numbers of energy spectra. The minimum error has been estimated to be 0.I MeV. 4.2. ABSOLUTE CROSS SECTIONS For a constant number of protons striking the target and constant solid angle the proportionality factor between peak areas in the energy spectra and differential cross sections for scattering will vary with target and scattering angle. To get a direct measurement of the cross section one also needs to know the eliicieney o f the system. For reasons discussed below we have chosen to use the method of comparison with well-known proton-proton cross sections. The target thickness can be determined to an accuracy of a few percent except for the water targets where bubbling could not be prevented. However, the cross sections for 016 could be determined directly by comparison with peaks obtained in scattering from the hydrogen in the water targets. The energy channel width is calculated from the parameters of the spectrometer. It varies between 0.15 and 0.17 MeV for the smaller scattering angles but goes down to 0.10 MeV for the lightest nucleus Li 6 at the largest angle (45°.5). Various methods for determining the areas under the peaks have been tried. F r o m well separated peaks in the energy spectra one can construct a standard curve with might also be used for resolving more complicated structures. However, it was found possible to use triangles for this purpose without introducing systematic errors. Rough estimates of the intrinsic widths of excited levels have been obtained by simple comparison with peaks known to have a line width equal to the experimental energy resolution. In so doing we have assumed that the intrinsic width and the experimental energy resolution add quadratically to give the resultant width of a peak in the spectrum.
INELASTIC PROTON SCATTERING
87
The real background as obtained in the target-removed measurements was normally very small and without structure. However, due to effects such as multiple scattering in the target, high density of levels in the target nucleus and the onset of various knockout reactions, all spectra will show a more or Iess smooth level over which peaks corresponding to strongly excited levels are superimposed. To subtract this "background" is the most delicate part in the determination of the cross section. The procedure adopted here has been to draw a smooth curve under the peaks, joining as well as possible the structureless parts of the spectrum and to subtract this level before determining the areas. Previously the number of protons striking the target for a certain number of monitor counts was determined by means of irradiation of polystyrene foils 7, a). Several checks have now been made on the consistency of these results. In some cases like Li, Be and C the elastic cross sections have been accurately measured at this energy xo). Those results differed in a systematic way slightly from the ones obtained in this experiment. However, the monitor could also be calibrated by scattering from CH and using the well-known proton-proton cross section ~o). In this way the elastic cross sections in the two measurements agreed completely. Since the latter method avoids the difficulty of determining the efficiency of the spectrometer-detector system, it was considered more reliable and has been used in the present work. The overall uncertainty in the absolute cross sections becomes about 10 ~o, slightly less for Li 6, Be 9, C 12 and 016 and slightly more for Li 7, B x° and B H. 5. Results and Discussion
Figs. 3-9 show energy spectra obtained at one scattering angle for each of the seven nuclei studied. They have been chosen to exhibit the most prominent peaks in the region of excitation energies covered. The angular distributions of the cross sections for resolved levels are presented in figs. 10-18. In fig. 20 the experimental results are collected to show which states are excited to a measurable degree in the scattering of 185 MeV protons. The results are presented with an attempt to correlate observed peaks in the energy spectra with previously published experimental data regarding the level schemes of the nuclei concerned. We also compare our results with those obtained in similar experiments and with some theoretical analyses. The solid lines in figs. 3-17 only serve as guides for the eye, whereas the curves of figs. 18 and 19 are calculated theoretically. 5.1. THE Lie NUCLEUS (figs. 3, 10 and 11) Four inelastic levels of Li 6 have been seen in this experiment and the angular distributions obtained are shown in figs. 10 and 11. The peaks at 2.2+0.1 and 3.6+0.1 MeV are easily resolved and can obviously be identified with the well-known 9) levels at 2.184 and 3.560 MeV, respectively. The corresponding transitions to the ground state are known to be E2 and MI.
88
D.
HASSELGREN et a L
8000
L i 6 15 = 6000
t 4000
° o°°
2O0O
°°
00o
i
o
~
o =oooo oooOoOOoo °°°°°°° I
to
8
I
6
I
I
,6
'~
2
0
xl/m
t
Eexc(MeV]
Fig. 3. Energy spectrum at 15 ° (lab system) for inelastic scattering of 185 MeV protons from LP (target thickness 0.233 g/cm=). The statistical errors are comparable to or smaller than the size of the experimental points.
; 500
Li ~ 25 o 1000
5OO
o~Ooo~OoOOooOoOO~o°°°0°°oJ !
t
12
f
I
10
I
I
8
I
00000000~1
8
2
0 Eexc(MeV]
Fig. 4. F.nergy spectrum at 25 ° (lab system) for inelastic scattering oi" 185 M e V protons from L i v (target thickness 0.064 g/cm=). The errors shown are statistical.
1500
BeS
25 o
°O~o o°
,00 °
I
18
I
I
I,~
I
I
12
I
I
10
I
I
8
i
o
o °°
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°%°
r
°o
!
OooooO0oi I
I
6
I
I
4
2
Eexc (MeV)
Fig. 5. Energy spectrum at 25 ° (lab system) for inelastic scattering of 185 M e V protons from Be °. The errors shown are statistical.
INELASTIC
89
SCATTERING
PROTON
As is seen f r o m the figures the angular distributions for the peaks at 4.4-t-0.2 and 5.4+0.2 MeV very closely resemble the one obtained for the 2.2 MeV peak. The level listed in ref. 9) at 4.52 MeV is reported to be about 600 keV broad, to have zero isospin (T = 0) and spin-parity 2 +. Since we observe an intrinsic width for the peak at 4.4+0.2 MeV of about 0.6 MeV the identity seems clear.
3000
B Io 2 0 °
u~
"~
2000
~000
ioooo oooo¢~ooOoOOOoOOOo oo I
I
I
18
I
.o.o
o OooOooOooooOt~°°°Ooo
I
16
/
°o° o
1
t
I
I
12
14
I
00°°%
I
I
I
8
tO
I
I
6
oOOO° O~)O
I
:; ~" 1
i
2
Z
0 Eexc (MeV)
Fig. 6. Energy spectrum at 20o (lab system) for inelastic scattering of 185 MeV protons from Bx°. The errors shown are statistical. i
i
i
i
i
i
i
i
i
,
i
i
i
i
,
1
i
i
1500
"~
B"
10"
1ooo
"*I-~ 500
!
*******************************~**
I6
14
12
I0
,~ Y2
oo°*
8
6
,~
2
0
Eexc(Meg)
Fig. 7. Energy spectrum at l0 ° (lab system) for inelastic scattering of 185 MeV protons from a Bu target of 98.6 ~o isotopic purity. The errors shown are statistical. Regarding the peak observed at 5.4+_.0.2 MeV it appears more difficult to obtain a clear identification. The peak is about 1 MeV wide and the angular distribution suggests an E2 transition. Two excited states are known 9) in this region: a sharp level at 5.35 MeV (T = 1) and a broad one at 5.5 MeV (T = 0, J~ -- 1+). Considering the large width of this peak in the spectrum it seems probable that the level at 5.5 MeV is excited. At higher excitation energies a structure is seen around 7 MeV suggesting the observation of two different levels, one at about 6.5 MeV for smaller angles and one at
D . HASSELGREN e t al.
90
~
i
I
i
•
~
•
oo
g % d'
%o o
o
o
~
o
8
0
# o
~o
o
~e
%
m
~
o
I
I
J
I
(sj/un qJe) 30o0 ,o#p
(sl!un 'qJe) 3POP DTP
i
~
i
~
•.- [ .
Lug
o
g-
[
.o
# oo oo <>o
~.~
°o
%
o? o
~
g. °° o
00 o o o
i g
?
,e. o o o o
I
( s l ! u n "qJe) 3PLOP ~2P
~,8 e
o
% %
( s l t u n "q~e) 3PUP .
i
o
0
91
INELASTIC PROTON SCATTERING
,ot
Li 6 3 6 t O I MeV 4.4+-02MeV
6.0 4.0 E
~1~ ~.o~
" 5,4• tO.2 MeV
-YO .cj¸. E
~1~ 2,0 T
10
J
20
,o
Jo
~
O;og
I0
Fig. 10. Angular distributions for the second I 85 andthirdpeak observed in the Li 6 (p,p)Li reaction at 185 MeV (lab system).
20
40
30
e l°ab
Fig. 11. Angular distributions for the first and fourth peak observed in the LP(p, p') LP* reaction at 185 MeV (lab system). i
i
8.o
i
F
Be9 2 3 5 + O.l lvleV
6.to
LiT
4.6+-0.1HeV
~0
6.65 + 0 2 MeV 50
~
.
L.
T
" 40
~l~ 4.0 -o~
10 ./ 2.0
2.0 [0
10
20
30
40
toO'*-b
Fig. 12. Angular distributions for the second and fourth peak observed in the LiV(p,p')LF * reaction at 185 MeV (lab system).
10
20
30
40
9 ~0b
Fig. 13. Angular distributions for the first three peaks observed in the Be°(p, p')Be 9. reaction at 185 MeV (lab system).
92
D. HASSELGRENet aL
approximately 7.5 MeV for angles over 20 °. The maximum cross section comes at 18 ° and is 0.4 mb/sr.
Bt°
~o
~ ~ .~ .,~o~
V
6.l+-0.1MeV
~I~ 2.0
~0 20
30
~0
e ~a b
Fig. 14. Angular distributions for two of the peaks observed in the BI°(p, p')B 1°* reaction at 185 MeV (lab system). i
(a)
t
i
(b)
Bit
Bn
20
2.2t0.I I~V
~
~
~
5 95 tOlSIvleV
0.5'
0
(c)
J
20
3O
o
etab
~0
Bit
3o
5. I t O.15MeV ~? 6.8t0.I MeV
E 20
0
I0
lab
i
IO
20
Fig. 15. Angular distribution for the first peak (a) for two of the peaks (b) and for the third and fourth peak (c) observed in the Bll(p, p')B 11. reaction at 185 MeV (lab system).
30 OObla ~0
In comparing the data of ref. 5) and those presented here, we find some notable discrepancies. The cross sections for the first two peaks at 2.2 and 3.6 MeV are about 50 ~o lower for 185 than for 155 MeV protons. Furthermore, the angular distribution presented in ref. 5) for the 3.6 MeV peak shows a marked departure from the smooth
93
INELASTIC PROTON SCATTERING
i
(a)
i
Ci 2
(b)
~ 4.4 tO.l MeV ;? 15.15+-0.1 MeV
~0
cl 2
;? ZestO.l MeV 4 9.7.~O. 15MeV
50
.~ 4.o
1.5
E ~E
10
2.0
0.5
f
~0
I
I0
20
(c)
30
8
o
10
lab 40
30
(d)
C~2
0.6
20
C 12
~? 12.?*-0.2MeV
~, le.2*- O3 MeV
2O
16.1+0.2 MeV
O°lab . ~0
~ .
? 19.3 +-02 MeV
E 0~ 1.0
0,2
I
,
tO
20
20 0 °lab
I0
20
0 olab ~0
30
Fig. 16. Angular distributions for two of the peaks (a and c), for the second and third peak (b) and for two peaks in the giant resonance region (d) observed in the C12(p, p')C 1=* reaction at 185 MeV (lab system). 50
i
(b) ~a~
~
0 t6'
0 ~e
l~
6.15"-0. l /4eV z os±o.ls Mw
T
t.5
'5.3'o.2t~v 187+-02MeV-
30
"~
to
2O ~5
~0
10
20
30
,$0
9
o lab
I0
I
I
20
30
O°lab dO
Fig. 17. Angular distributions for the first two peaks (a) and for three of the peaks (b) observed in the OXS(p, p')O 16. reaction at 185 MeV (lab system).
94
u.
HASSELGP-,EN
e t al.
exponential form obtained here (fig. 10). Theoretical calculations 15) aimed at fitting the 155 M e V results are shown in fig. 19 together with the experimental results obtained here. As has been remarked by Jackson and Mahalanabis 15) the new exi
~5
r
i
i
I
0 I6
i
ll5~-O21vleV (exp.points) •
0
theoretical curve tl.9 MeV)
(Erikson
13.1t0.2 M e V (exp points)
ta
theoretical
2.0
(Erikson
curve
t2.8 MeV)
E ;
05
\
/ ~ '-
~0
[\\
4
i,.+
I0
2O
3O
-.t
(b)
•
o 40 0 lab
I
z
tO
20
#
30
e°
tab
Fig. 18. Theoretical curve for a (2-, T = 0) state at 11.9 MeV (a) and for a (2-, T = 1) state at 12.8 MeV (b) in Oze as calculated by Erikson 22), compared with experimental points from this experiment. i
i
i
i
l
Li 6
3,6"-0.1MeV E~p. poin:s
8.0
t
Theoretlcol curve~
6.0
t i
4.0
~t~
i. . . . b=2.24 fm ,150);-b=[6Ofm
d{Morfedwa~e~°) . . . .
b=224 frn
,I
2.0
10
20
30
40
O~ab
Fig. 19. The 3.6 M e V peak in LP compared with theoretical predictions from ref. 15). perimental results tend agreement with elastic A calculation o f the performed by Erikson points presented in fig.
to favour a larger value for the length parameter b, in better electron scattering results. angular distribution to be expected at our energy has been 15). Also in this case the agreement with the experimental 19 was quite satisfactory.
INELASTIC PROTON SCATTERING
95
5.2. THE Li7 NUCLEUS (Figs. 4 and 12) Below an excitation energy of 10 MeV six peaks have been observed in the energy spectra from Li 7. The one at 4.6-t-0.1 MeV dominates in the whole angular region studied. It certainly corresponds to the level listed at 4.630 MeV (J" = ~ - ) in the literature 9, 11), which decays by an electric quadrupole transition. 23.4 t 0.4 ]
E.cMOV
22. f +-0.3 21.4 0.3
2I. t +-0.5 ] 20
23.4 +. 0.3
J
22.4 +- 0.7 ] J
] J
21.6 t 0.3
J
20.4 + 0.4 ]
20.2 +- 0,3 1.9.8 t 0.3
19.0 ; 0.4 ] J
19.3 : ~.Z ]
18.7 : 0.2
-
18,2 *. o 3
t;'.,~ *- 0.3 ~ 16.7 +- 0.3
]
1z8 ±
J
o3 J
1r. 1 t o.3 16.1 ~- 0.2 15.15 -+ 0.1
15-
1~'; "- 0.3 ~ 13.0+-0.3]
14.2 -* 0.,;
I3.0+0.2]
12.7+.0. 2
13.1+0-2
11.1+-0.6 I 0 6 .+ 0.4
10.4 +. 0.3
11.9 +-0.2 I1"2 +" 0"3 ~
lLO t O. 3 10. 5 -+ 0.2
10-
I5.3 +- 0.2
14.5 +- 0.4
11.5 +- 0 2
9.7 + 0.15
9.6~0.2]
8.95 ~- O. 15 8.5-
7.5
'//////////////, 5--
7e~o3] 6.65~0.2
7'9 ~- 0'3 ~ t
5.4 ~- 0.2 ]
5.5+.0.3]
4.4+-0.2]
~.610.
I
7.55+.0.15
7.4 ~__0.3
7.65+.0.1 Z05 +- 0.15
6.8+.01 6.5 +- 0.3
4.8 *-0.3
6. I +. 0.1 5.2 +- 0.2
J
&15 *. 0.1 5.1 t 0. I5 4.5 +. 0.1
4,~ +. 0.1
3.65 +-O. 2
3 . 6 +- 0,!
$.~ *- O.T
2.35 .+ 0.7
2.2 ~- 0. I5
2.2 "- 0.1
0.8 +- 0.2
0 . 5 +- 0 . I
OL/6
Li 7
Be 9
B tO
Bll
C12
0 16
Fig. 20. Excitation energies for the peaks observed in the inelastic scattering of 185 MeV protons from L P , Li 7, Be 9, B 1°, B 11, C 12 a n d 016. The vertical bars represent the measured intrinsic widths of the peaks. Widths smaller than 0.4 MeV are not shown.
For angles larger than 20 °, protons scattered from the well-known first excited state of Li 7 are seen at the lower energy end of the elastic peak. By using the information obtained from other nuclei about the shape of a pure peak it is possible to resolve the contribution from this level. The literature 9) value o f the excitation energy is 0.478 M e V and in the present experiment it was measured to lie at 0 . 5 + 0 . 1 MeV. The cross sections falls smoothly from a maximum value o f about 0.9 mb/sr at 200-25 ° .
96
D. HASSELGRENet aL
There is a small peak in the spectrum at 5.5+0.3 MeV with a width of about 0.4 MeV. It is not clearly resolved and thus is quite uncertain. The cross section never exceeds 0.5 mb/sr. A broad peak with an intrinsic width of about I MeV is observed at 6.65_+0.2 MeV. The angular distribution is shown in fig. 12. In ref. 9) a broad level is reported at 6.54 MeV and is certainly identical to the one excited here. Results H) for inelastic electron scattering from Li 7 give clear evidence for a level at 6.8+0.1 MeV (width 0.8 MeV) and indications of a state at 5.7__+0.1 MeV (width 0.5 MeV). There has been some doubt about the existence of the latter and as already mentioned the evidence presented here is quite weak. Two more peaks are seen in the energy spectra obtained here at 7.6_+0.3 and 9.6 + 0.2 MeV. For the former the maximum cross section is about 0.3 mb/sr and for the latter 0.4 mb/sr. They are both broader than the energy resolution of the apparatus. Two levels corresponding to these peaks are reported in the literature 9), one at 7.47 MeV (jz = ~r-) and the other at 9.6 MeV. Regarding levels with an excitation energy higher than 10 MeV it may be said that their cross sections all are less than 0.2 mb/sr. Since the experimental width of a peak in the energy spectrum was considerably larger than in the earlier 3) work at 185 MeV it is difficult to make direct comparisons except for a few well separated levels. In Li 7 a peak at 4.4+0.2 MeV was seen with an angular distribution dipped in the forward direction. It is apparently identical to the one seen in this experiment at 4.6_+ 0.1 MeV, but the cross section obtained here is almost twice as low. Some of the cross section in the earlier experiment, especially at small angles, probably came from the 3.6 MeV level in Li 6. In comparison with ref. 5) we have seen an additional peak in our experiment, namely the one at 5.5__+0.3 MeV. If real, it corresponds to a weakly excited level not listed in the compilations of ref. 9) but predicted by Clegg 12) and observed in inelastic electron scattering ~ ) . However, in the latter experiment it was recently given an alternative explanation, and in our case it probably needs further confirmation. Regarding the 0.478 MeV level some interesting results have recently been obtained by Mahalanabis la). She calculated the results to be expected in the scattering of 156 MeV protons and found a forward peaked angular distribution. Unfortunately we have not been able to follow the corresponding peak down to smaller angles. By studying the (p, p'y) reaction, Newton et aL 14) did obtain cross sections for this level down to 10°, which indicates an angular distribution resembling that of the 4.6 MeV state. 5.3. THE Be° NUCLEUS (Figs. 5 and 13) A great number of peaks have been observed in the energy spectra obtained in scattering from Be 9. Most of them are only weakly excited and not fully resolved. The angular distributions of the first three levels are presented in fig. 13. Their excitation energies have been found to be 2.35_+0.1, 4.8_+0.2 and 6.5+_0.3 MeV, respect-
INELASTIC PROTON SCATTERING
97
ively. Of these the second is somewhat broader than the experimental energy resolution whereas the third has an intrinsic width of 1.2+0.2 MeV. Except for the sharp state at 2.35 MeV which is listed in ref. 9) at 2.430 MeV (J~ = ~ - ) these peaks do not correspond to any well-known states in Be 9. However, recent experiments on proton 5) and electron 16) inelastic scattering have given similar results. The next three peaks are located at 7.9, 11.2 and 14.4 MeV (all with an error of ___0.3 MeV), respectively, and have been seen over the whole angular range covered. The angular distributions are quite flat with a maximum cross section of 0.5 mb/sr for the peak at 7.9 MeV and 0.3 mb/sr for the other two. The peak widths are compatible with intrinsic level widths between 0.5 and 1.0 MeV. In the latest compilation of ref. 9) four levels are listed in this region of excitation energies but the identity of the peaks obtained here is far from certain. At higher excitation energies five peaks have been seen at 16.7_+0.3, 17.44-0.3, 19.0_+0.4, 21.1 _+0.5 and 22.4_+0.7 MeV. The measurements have been extended to this energy region only for small angles and the maximum cross sections are 0.2, 0.3, 0.3, 0.5 and 0.3 mb/sr, respectively. The peaks seem to be quite wide and their existence is not established with any great certainty. However, they probably correspond to the structure seen at these energies (the giant resonance region) in (~,, n) reactions. For the 2.3 _+0.2 MeV peak in Be 9, seen by Tyr6n and Maris 3), both the angular distribution and the absolute magnitude of the cross section agree very well with our results (peak at 2.35_+0.1). On the other hand, the peak at 6.5 MeV which was expected to show some structure with improved energy resolution still appears as single in the present experiment. 5.4. THE B 1° NUCLEUS (Figs. 6 and. 14) As is seen from the spectrum presented in fig. 6 the dominating peak comes at about 6 MeV; its position has been measured to be 6.1 +0.1 MeV and there is no extra broadening. The angular distribution resembles very closely those obtained for the electric quadrupole transitions in the lighter nuclei. From what is known about the level scheme of B 1° it is not possible to identify this peak further. At 35 ° and 40 ° the elastic peak has a small bump located at 0.8___0.2 MeV which evidently corresponds to the known 9) level at 0.717 MeV (1 +, T = 0). It is weakly excited; the maximum cross section is about 0.1 mb/sr for these angles. Nothing is seen of the next level quoted in the literature 9) at 1.74 MeV (0 +, T = 1) but at 2.2_+0.15 MeV a peak appears with a maximum cross section at 20 ° of about 0.3 mb/sr. This then would be the 2.15 MeV level (1 +, T = 0) observed in a great number of nuclear reactions 9). The known state 9) at 3.59 MeV (2 +, T = 0) is found to be even more weakly excited. There is a peak in the energy spectrum at 3.65 4-0.2 MeV with a cross section which never exceeds 0.2 mb/sr. Before the dominating 6.1 MeV peak there is one at 5.2___0.2 MeV which has an angular distribution resembling that of the 2.2 MeV peak, both in shape and in absolute magnitude.
98
D. HASSELGREN et aL
In fig. 14 the angular distribution for the peak observed at 7.55-t-0.15 MeV is shown. It is evidently of the type found for the 3.6 MeV level of Li 6, which is known to decay by a pure MI transition. At higher excitation energies two more peaks have been found; like the one just mentioned above they are slightly broader than the line width of the experiment. They occur at I 1.0 __.0.3 and 13.0___0.3 MeV, respectively. Of these the lower has been seen only at a few angles and has a maximum cross section of 0.3 mb/sr. The higher one has been observed in the angular region 40-30 ° and reaches a maximum cross section of almost 0.8 mb/sr at 20 °. It is doubtful, however, if the peak is single or double, and therefore the angular distribution is not presented: In B ~° Jacmart et aL 5) have seen two peaks at 7.4+0.3 and 8.05+0.3 MeV where only one at 7.55+0.15 MeV was observed in the present experiment. This discrepancy is probably not serious, since we have based our energy assignment on the position of the peak at small angles where it was most dearly seen. 5.5. THE Bu NUCLEUS (Figs. 7 and 15) The first three peaks at 2.2___0.1, 4.5_+0.1 and 5.1_+0.15 MeV, respectively, are easily identified with known 9) levels reported to be 2.14 (½-), 4.46 ( { - ) and 5.03 (½- or { - ) MeV above the ground state of B 11. Their angular distributions are shown in fig. 15. As is the case for the following three peaks observed in the energy spectra their intrinsic widths are too small to be noticed in the present experiment. The peak at 6.8 _+0.1 MeV (fig. 15c) whose angular distribution has almost exactly the same shape as that for the peak at 4.5 MeV certainly corresponds to the level 9) at 6.76 MeV (probably -~-). In the angular region 80-25 ° we observe a peak at 7.4-t-0.3 MeV with a maximum cross section of less than 0.3 mb/sr, previously not seen in (p, p') experiments. There is a level reported 9) at 7.30 MeV (probably { - ) which might correspond to this peak. Around 9 MeV excitation energy several levels are known, and therefore no definite assignment can be given to the peak observed at 8.95+__0.15 MeV (fig. 15b). At about 9.8 MeV there is an indication of a peak with a maximum cross section of 0.2 mb/sr. It is seen between 15 ° and 25 °. In the 10.5__+0.2 MeV peak there is some evidence for an intrinsic width. It has been observed in the angular range 8o-40 ° and has a maximum cross section less than 0.4 mb/sr. Three more peaks have been observed in the energy spectra for B 11 at 11.9_+0.2, 13.0 + 0.2 and 14.5___0.4 MeV, respectively. Of these the first peak has been seen only for forward angles (4°-15 °) with a cross section less than 0.4 mb/sr, the second peak in the angular range 40-35 ° with a cross section of about 0.4 mb/sr and a fairly fiat angular distribution. The peak at 13.0 MeV seems to have an intrinsic width of about 0.4 MeV. The one remaining, at 14.5 MeV has only been observed at 15 °, 20 ° and 35 ° and yields a very small cross section, about 0.15 mb/sr. The present results for B 1~ agree very well with both ref. 5) and those of Newton
INELASTIC PROTON SCATTERING
99
et al. 17) with the possible exception of the peak at 2.2_+ 0.1 MeV which has a higher
cross section in ref. 17). It may also be noted that the 7.55 MeV peak in B 1° and the 9.0 MeV peak in B 11 probably were too close for separation in the earlier 3) work at 185 MeV in which a target of natural boron was used. This was particularly troublesome since these two peaks have very similar angular distributions. 5.6. T H E C TM N U C L E U S (Figs. 8 and 16)
In C 12 15 peaks have been seen in the energy spectra with widely varying cross sections. Some of these can be identified with well-known levels 9) and are listed in table 3. TABLE 3 Experimental results on some peaks observed in the energy spectra of C TM together with listed p r o p erties of the corresponding excited levels ~) Ex. energy (MeV) This exp. Listed value 4.4 q-0.1 7.65 4-0.1 9.7 4-0.15 12.7 4-0.2 15.154-0.1 16.1 4-0.2
4.433 7.656 9.64 12.71 15.11 16.11
Accepted value o f J,~ T 2+ 0+ 31+? 1+ 2+
0 0 0 0 1 1
Max. cross section d c q d ~ ( m b / s r ) at angle 5.6 0.9 1.2 0.35 4.7 0.28
18°.5 forward 23 ° 8°.5 forward 15°.5
The angular distributions for the peaks presented in table 3 are shown in figs. 16a-c. Since the preliminary report 7), which gave the angular distribution of the 7.65 MeV peak, more measurements have been made confirming the results reported there. At 10.6+0.4 and 11.1 +0.4 MeV two small peaks appeared; both of them were difficult to resolve clearly. The former has been seen from 4 ° to 40 ° with a maximum cross section of 0.35 mb/sr at 22 °, the latter has been observed in the angular region 20 ° to 30 ° and gives a somewhat larger cross section. An upper limit of 0.2 mb/sr can be set on the cross section for exciting a level at 14.2_+0.4 MeV, and it is seen only beyond the angles (about 20 °) where the 15.15 MeV peak has decreased to less than 5 ~o of its maximum. For the nine peaks discussed thus far no intrinsic width has been observed. The remaining peaks, located in the giant resonance region all have widths between 0.5-0.8 MeV. The angular distributions for the peaks observed in this region either have a maximum at an angle below 15 ° or are forward peaked. As an example fig. 16d shows the distributions for the peaks at 18.2_+0.3 and 19.3_+0.2 MeV. The existence of the peak at 20.4_+0.4 MeV is rather uncertain; it has been seen over the whole angular region with a cross section less than 0.5 mb/sr. The last three peaks (21.4+0.3, 22.1 ___0.3 and 23.1_+0.4 MeV) are to be considered as the most probable decomposition of the structure in the region 20.5-24 MeV. The angular
100
D. HASSELGRENet
aL
distributions of the first two are quite similar; they increase from about 0.2 mb/sr at 30 ° to approximately 1.0 mb/sr for angles below 10 °. The peak at 23.4___0.4 MeV finally has been observed f r o m 4°.5 to 20 ° and the cross section remains below 0.4 mb/sr. A few examples will be given here of the experimental and theoretical work on inelastic proton scattering from C 12. The agreement between the 155 MeV results s) and those of the present experiment is very good. Regarding the theoretical analyses, the work of Sanderson 1 s) bears directly on our data. The angular distributions for exciting several states in C 12 by 180 MeV protons have been calculated and compared with the results of ref. 3). Regarding the 9.63 MeV level the agreement still holds as far as the shape of the angular distribution is concerned but our cross sections are about half of those calculated. For the level at 15.1 MeV (1 +, T = 1) our cross section is the same as the theoretical value at 9 ° laboratory scattering angle but increases faster in the forward direction. In the giant resonance region two broad peaks were observed in the earlier work a), one at about 19 MeV and the other at 22 MeV. Sanderson compares the experimental cross sections obtained with the sum of contributions f r o m three T = 1 states in each group, plus one T = 0 level falling under the 22 MeV b u m p and two T = 0 states which contribute to the structure at 19 MeV. As seen from fig. 20 six peaks have now been observed in this region. Assuming that our peak at 18.2-t-0.3 MeV is the sum of contributions from Sanderson's levels at 18.2 ( 2 - , T = 1) and 18.7 MeV ( 1 - , T = 1) and, furthermore, that our peak at 19.3_+0.2 MeV corresponds to the one at 19.3 MeV ( 2 - , T = 1), the agreement is quite satisfactory between the angular distributions presented in fig. 15c and those calculated. Due to large uncertainties in the experimental data at the higher excitations (21-24 MeV) a detailed comparison is difficult. However, if we sum the cross sections from the peaks observed in this region the results will be quite close to that obtained by Sanderson i s). As a final remark concerning C 12 it may be noted that the essential features on the rather unique angular distribution found for the 7.65 MeV peak were reproduced in a preliminary calculation performed by Eriksson and Rinander 19). Following a suggestion by Brink 2o) they assumed the 0 + state at 7.656 MeV to be a monopole vibration characterized by a radius R = Ro(1 +ct), where ~ is a deformation parameter. 5.7. THE Ot6 NUCLEUS (Figs. 9, 17 and 18) The first two peaks observed in the spectra f r o m O 16 come at 6.15 + 0.1 and 7.05 + 0.15 MeV. Evidently each one of them might correspond to a mixture of contributions f r o m two well-known 9) levels 6.05 (0+), 6.13 ( 3 - ) and 6.92 (2+), 7.12 MeV ( 1 - ) respectively, all with isospin T = 0. Further separation is not easily attained with our bombarding energy. However, it has been shown 21) that by studying also the (p, p'?) reaction it is possible to get more detailed information about these peaks. This work is discussed below.
INELASTIC PROTON SCATTERING
101
The upper limit 9) of the cross section for exciting the states at 8.88, 9.59 and 9.85 MeV can be set to 0.1 mb/sr. In the angular region 15°-35 ° we have observed a peak at 10.4+_0.3 MeV. It is not clearly resolved and has a cross section at 20 ° of about 0.3 mb/sr. Fig. 18 presents the angular distributions for the peaks found at 11.5-t-0.2 and 13.1+_0.2 MeV. The dashed curves have been calculated theoretically 22). The angular distributions for the peaks at 15.3 +_0.2, 18.7 +_0.2 and 20.2 +_0.3 MeV are shown in fig. 17b. In the giant resonance region there are five more peaks, all with a cross section smaller than 0.4 mb/sr. The excitation energies can be found in fig. 20. Except for the peak at 17.8+_0.3 MeV this structure is visible preferably for angles below 20 ° but even there it is quite difficult to make an unambiguous decomposition. Some interesting differences have been obtained from the results of ref. a) because of the improved energy resolution. First of all t w o peaks now appear in the energy region 6-7 MeV, and it is quite clear that the earlier angular distribution is the sum of those presented in fig. 16a. In this connection it may be noted that by looking at the (p, p'v) reaction, Rowe et aL 21) have been able to give separate cross sections for three of the four levels involved. At 150 MeV proton energy and for a scattering angle of 25 ° they obtain 0.23+_0.14, 3.16+_0.11 and 0.88+_0.13 mb/sr for the levels at 6.05, 6.13 and 6.92 MeV, respectively. These values agree very well with our cross sections if our 6.15 MeV peak is considered as the sum of contributions from the first two levels in 016 . Finally, regarding the earlier 3) work at 185 MeV it seems that the previously observed peak at 12.5+_0.3 MeV in 016 now has been resolved into two components, namely those shown in fig. 18. As was mentioned above the curves in fig. 18 have been calculated by Erikson 22) for one state at 11.9 MeV (2-, T = 0) and one at 12.8 MeV (2-, T = 1). The authors wish to express their gratitude to the head of the Institute, Professor The Svedberg, and to Dr. H. Tyrfn for their kind interest in this work. The assistance of Messrs. A. Ingemarsson, S. Dahlgren and R. Gabrielsson during a considerable part of the experiment is gratefully acknowledged. We also wish to thank Dr. Arne Johansson for many valuable discussions. Miss D. Jackson, Mrs. J. Mahalanabis and Messrs. T. Erikson, T. A. Eriksson and G. Rinander have kindly informed us about the results of their theoretical analyses before publication. It is a pleasure to acknowledge the technical aid of the members of the cyclotron staff under Messrs. A Svanheden and B. Hemryd. Thanks are due to Mrs. A. Astr6m for preparing all graphs and to Mrs. L. Borgman for secretarial help. This work has been supported financially by the Swedish Atomic Research Council.
102
D. HASSELGRENet al.
References 1) 2) 3) 4) 5)
Th. A. J. Maris and H. Tyr6n, Nuclear Physics 3 (1957) 35 K. Strauch and F. Titus, Phys. Rev. 95, (1954) 854, 103 (1956) 200, 104 (1956) 191 H. Tyr6n and Th. A. J. Maris, Nuclear Physics 4 (1957) 637, 6 (1958) 82 J. M. Dickson and D. C. Salter, Nuovo Cim. 6 (1957) 235 J. C. Jacmart, J. P. Garron, M. Riou and C. Ruhla, Phys. Lett. 8 (1964) 269; J. C. Jacmart, Th~s¢, Universit6 de Paris (1964) 6) A. Johansson, A. Svanheden, U. Svanberg and H. Tyr6n, private commlmication 7) D. Hasselgren, P. U. Renberg, O. Sundberg and G. Tibell, Phys. Lett. 9 (1964) 166 8) D. Hasselgren et al., Comptes Rendus du Congr~s International de Physique Nucl6aire 1964, (CNRS, Paris, 1965) vol. II, p. 406 9) F. Ajzenberg-Selove and T. Lauritsen, Nuclear Physics 11 (1959) 1; T. Lauritsen and F. Ajzenberg-Selove, Nuclear Data Sheets, NRC 61-5 and 6 10) A. Johansson, U. Svanberg and P. E. Hodgson, Ark. Fys. 19 (1961) 541 11) M. Bernheim and G. R. Bishop, Phys. Lvtt. 5 (1963) 294; G. R. Bishop and M. Bernheim, Phys. Lett. 8 (1964) 48 12) A. B. Clegg, Nuclear Physics 33 (1962) 194 13) J. Mahalanabis, Ph. D. Thesis, submitted to the University of London (November 1964) unpublished 14) D. Newton et al., Prec. Phys. Soc. 79 (1962) 27 15) D. F. Jackson and J. Mahalanabis, Nuclear Physics 64 (1965) 97; T. Erikson, private communication 16) H. Nguyen Ngoc, M. Hers and J. Perez y Jorba, Nuclear Physics 42 (1963) 62 17) D. Newton, A. B. Clegg, G. L. Salmon and D. J. Rowe, Nuclear Physics Laboratory, University of Oxford, preprint (1963) 18) E. A. Sanderson, Nuclear Physics 35 (1962) 557 19) T. A. Eriksson and G. A. Rinander, private communication 20) D. M. Brink, private communication 21) D. J. Rowe, A. B. Clegg, G. L. Salmon and P. S. Fisher, Prec. Phys. Soc. 80 (1962) 1205 22) T. Erikson, Nuclear Physics 55 (1964) 497