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Inelastic scattering of tritons and protons from 210Pb
Nuclear
Physics Al62 (1971) l-l
Not to be reproduced
by photoprint
1; @
North-Holland
Publishing
or microfilm without written permission
Co., Amsterdam from the publisher
INELASTIC SCATTERING OF TRITONS AND PROTONS FROM “‘Pb C. ELLEGAARD Carnegie-Mellon
and P. D. BARNES
University,
Pittsburgh,
Pennsylvania
t
E. R. FLYNN Los Alamos
Scientific
Laboratory,
Los Alamos,
New Mexico t
and
G. J. IGO University
of California,
Los Angeles
and Los Alamos
Received 8 October
Scientific
Laboratory
t
1970
Abstract:
A search for collective states in 210Pb has been conducted utilizing inelastic scattering of 20 MeV tritons and 20.5 MeV protons. In the triton scattering, cross sections were obtained for levels at 0.795, 1.87 and 2.83 MeV. The 0.795 level is a known 2+ level. It is excited with a cross section of one-half of that observed for the first 2+ level of 206Pb under identical conditions. The two other states are assigned as 30 states. The cross sections obtained for these two levels are approximately 8 and ) of the cross section found in the (t, t’) reaction for the first 3- state of 2osPb. In the proton scattering, the above results are confirmed and several other levels observed. The results are compared with DWBA calculations.
E
NUCLEAR REACTIONS ‘lOPb(t, t’), (p, p’), E, = 20.0 MeV, EI, = 20.5 MeV; measured a(&, 19),u(&, 8). 210Pb deduced levels, J, Z, L. Enriched target.
1. Introduction The inelastic scattering process preferentially excites collective states in nuclei and has often been used to locate such states. Inelastic scattering from nuclei in the lead region has been systematically studied by many groups using a variety of projectiles: protons loa), deuterons ‘3 6), tritons ‘), alpha particles *, “) 1 6O [ref. ‘“)I and electrons 11*‘*). The results of the inelastic scattering from the doubly closed shell nucleus *‘*Pb show as dominant features a strongly excited 3- state at 2.6 MeV, a strongly excited 5- state at 3.2 MeV and at higher energies some less strongly excited but still collective 2’, 4+ and 6+ states. The dominant features of inelastic scattering from nuclei in the vicinity of “*Pb are strongly excited states or multiplets of levels near the same energy as the strongly excited states in “*Pb. This corresponds to excitation of the core with the configuration of the extra particles or holes left unchanged. In addition there are in these neighboring nuclei states at lower excitation energy corresponding to the degrees of freedom of the extra particles or holes. Notably in doubly even nuclei the lowest state is a collective 2+ state. t Work supported by the Atomic Energy Commission February
197 1
2
C. ELLEGAARD
et al.
The above-mentioned multiplets, as exemplified by the doublet at 2.6 MeV in ‘*‘Pb [refs. “-“)I and the septuplet at 2.6 MeV in **%i [refs. ‘*6*9, ‘“)I, are well described [refs. “*“)I by assuming a weak coupling between the hole or particle and the 3vibrational state of the core. Inelastic scattering is not possible on ‘*‘Pb but a measurement ’ “) of the lifetime of the J$- state at 1.422 MeV indicates that it contains a large admixture of core excitation. Thus ‘09Pb appears significantly different from the above-mentioned isotopes in that a large part of the 3- core excitation is found far away from 2.6 MeV. This is however accurately explained 13*14S16)by the coupling between the neutron in the j, state and the 3- vibration, with the same model that describes the close multiplets in the other cases. In ‘l*Pb there are two neutrons in the same shell as the single neutron in ‘*‘Pb. It is expected “) that this will produce a similar strong coupling between particle states and core states. The present work is a study of the inelastic scattering of 20 MeV tritons and 20.5 MeV protons from ‘l*Pb. The main results are the observation of a splitting of the collective octupole strength and the measurement of the B(E2) value for the lowest 2+ state. There are some shortcomings in the quality of the experimental data because of the radiation hazards involved in using the 210Pb target. However the results as quoted here are reliable within the accuracies quoted. 2. Experiment A ‘l*Pb target was bombarded with beams of 20 MeV tritons and 20.5 MeV protons from the Los Alamos three-stage tandem accelerator facility. The scattered particles were analysed in a broad-range magnetic spectrometer I*) and recorded on photographic plates. The resulting triton and proton spectra are shown in figs. 1 and 2. 2.1. TARGET
The 210Pb target was a 240 pg,/cm2 metal deposit on a 50 pg/cm’ carbon backing. The preparation of this target by isotopic separation has been described elsewhere ’ “). The target is isotopically very pure but it has a relatively large content of light impurities. Peaks from these impurities are easily identified by their shift in energy as a function of angle. The content of some impurities is large enough to make inelastic scattering on these nuclei important. This creates an extra background in the spectra but all significant peaks have been identified as arising from “*Pb or from known levels in the main impurities. At the time the triton exposures were made approximately 5 “/, of the “*Pb had decayed into 206Pb(210Pb @!z 210Bi fl>z ‘l*Po ‘?Y?$! ‘06Pb). No trace of peaks arising from 206Pb was observed in the inelastic scattering or other reactions observed simultaneously 20). This is as expected because most of the 206Pb nuclei should recoil oui of the target. The earlier proton exposures also show no contamination from decay products.
3
zloPW,0, (PtP’) EXCITATION
Ii0
ii5
ENERGY
)
( MeV
Ii5
Ii0 DISTANCE
ALONG
130 PLATE
135
140
(cm)
Fig. 1. Triton spectrum from the *r’Pb(t, t ’ ) *lOPb* reaction at 66”. The three peaks labeled 0.795, 1.872 and 2.839 are the three main peaks for which angular distributions were obtained. Numbers in parentheses indicate peaks observed only at this angle but located at energies where peaks are observed in the (p, p’) spectra. At other angles they are obscured by impurity peaks or general background level. Peaks marked by chemical symbol and mass number arise from known levels in the indicated nucleus.
EXCITATION
ENERGY
4
5
t Me’4
) 2
3
f
!
15
“‘Pb
(
p,p’l
EP
*
20.5
9
=
63’
Mev
i0
25 OISTANCE
Fig. 2. Proton spectrum from the ‘l”Pb(p, numbers correspond to levels in *rOPb as number of the impurity nucleus from which 7 correspond to the 0.795 MeV,
ALONG
30 PLATE
lcml
p ’) zXOPb* reaction at 63”. Peaks marked with boldface given in table 1. Other peaks are marked with the mass they arise from known excited states. Peaks nos. 1,4 and 1.869 MeV and 2.828 MeV levels respectively.
4
C. ELLEGAARD
et al.
2.2. EXPOSURES AND ABSOLUTE YIELDS
Exposures of approximately 6000 PC and 900 ,uC were made at 6” intervals from 70” forward for protons and from 66” forward for tritons. Because of the increasing intensity of peaks from the lighter impurities and the increasing number of slit-scattered particles, the proton spectra could not be analysed further forward than 28”. For the triton spectra the slit-scattering was unusually high, as may be seen in fig. 1, and the spectra could be analysed no further forward than 48”. No attempt to repeat the triton data was made because of the radiation hazards and the possible scattering chamber contamination. At the angles between 48” and 66” reliable cross sections were obtained for the three main triton peaks that are discussed in the next section, The relative normalization of the different exposures was obtained by monitoring the number of elastically scattered particles in a CsI(TI) scintillation counter located at a forward angle. For the triton exposures the absolute cross section was obtained by scanning the peaks corresponding to elastic scattering at 60” and 66” in the short exposures. The absolute cross section for elastic scattering of tritons from ‘l”Pb is assumed to be the same as for zosPb. This cross section has been measured 2i) at the same energy (20.0 MeV) to an accuracy of 5 ‘A. The uncertainty in the absolute cross section for the triton exposures is estimated to be + 15 o/0with 10 ‘A arising from the uncertainty in scanning the intense peaks. For the proton exposures the absolute cross section could not be obtained in the same direct way because the peaks corresponding to elastic scattering were too intense to be scanned. However a normalization was obtained by the following two methods: (i) The cross section of the first 2+ state was normalized to give the cross section predicted by distorted wave Born approximation (DWBA) calculations (subsect. 3.1.2) assuming the value of j?” to be the one obtained from the triton data. (ii) An absolute scale for the cross section was obtained in the work 19) on the “‘Pb(p d)‘09Pb reaction which was recorded at the same time as the (p, p’) reaction. Here th; absolute values for the cross section were obtained by setting the differential cross section for populating the 2152 keV level jn the “‘Pb(p, d)‘09Pb’ reaction equal to the cross section obtained z”) in the reaction ‘O’Pb(p, d)“‘Pb(O). The first method involves a DWBA calculation with the uncertainties inherent in such a calculation. The second method involves assumptions about the structure of the 2152 keV level in 209Pb. These assumptions are not likely to introduce any serious error. The two methods agree within 30 %. With most emphasis on the second method an absolute scale is obtained for the angular distributions of fig. 4. 3. Experimental results and analysis Table 1 lists the energy levels observed in the (t, t’) and (p, p’) experiments. Because the ground state peaks were too intense to be scanned in all of the proton spectra, the energy scale for the (p, p’) results was normalized to give an excitation energy
5
210Pbk0, (P,P’)
of 0.795 MeV for the first excited state, in accordance with the (t, t’) results and the results of refs. 23124). TABLE 1 Excitation energy (MeV) Peak no. (proton spect.)
Previous experiments
L
Decay ‘) of ““Tl
zOsPb(t, p) (P, P’) &lo keV
(t, t’) &15 keV
13 MeV “)
20 MeV “)
0 1 2 3
0
4
1.869
5
2.215
6
0.795 d) 1.095 1.192
0 0.795 (1.086)
0 2 4 6
1.872
3
(5)
2.518
(4)
0 0.804 1.099 1.117 1.281 1.806 1.876 2.012 2.048 2.222 2.420 2.460 2.522
2.909
0 0.795 1.094 1.193 1.273 1.799 1.869 2.004 2.037 2.214 2.412 2.454 2.516 2.529 2.701 2.791 2.823 2.861 2.900
3.155
3.151
2.706 7
2.828
2.839
3
8
3.069
(3.085)
2
9
3.194
10 11 12 13 14
4.080 4.128 4.185 4.285 4.390
15 16 17
5.396 5.445 5.492
(3.209)
(4.093)
2.833
0 0.795 1.09 1.17
1.85 1.95, 2.00
2.40
2.58
2.93, 3.03, 3.07
4
2 2 (4)
3.227 3.314 3.457 3.575 3.628 3.673 3.707 3.880 3.913 4.077 4.144
3.309
4.265 4.390 4.685
‘) See ref. 2z). “) See ref. 23). ‘) See ref . *‘+). *) Normalized to give the same excitation energy as the (t, t’) results and refs. 23*24).
C. ELLEGAARD
6
3.1. ANGULAR
al.
et
DISTRIBUTIONS
3.1.1. Tritons. Fig. 3 shows the angular distributions of the three main peaks in the triton spectra. The 0.795 MeV level has previously been assigned ‘“) as a 2’ level. For comparison we have plotted the cross section for excitation of the first 2+ level of ‘06Pb in the (t, t’) reaction under identical conditions ‘). The 2+ in ‘l*Pb is excited with very nearly half the strength of that of the 2+ in “‘Pb. This is also the ratio / “‘Pb
(t,t’)
E,
20
30
40
50
= 20.0NIeV
60
70
t DEGREES I
ANGLE
Fig. 3. Angular distributions from the 2t0Pb(t t’)2toPb* reaction (full circles and squares). For comparison the angular ~stributions from td IcsPb(t, t’)+“*Pb(3-) and Z06Pb(t, t’)“06Pb(2+) reactions at the same energy (open circles) are shown.
of 8” or the B(E2) value of the states
W3’8210= 0.50+0.15. @F2), 06 In terms of single-particle units G
=
1
WA) igjzq
(3+Aj2 =
4n(21+1)
z2p2
1’
the 2+ of zo6Pb has 4S8) G, = 7. The 2” of ‘l*Pb thus has G2 = 3.5i_1.0. The two other strongly excited states are compared in fig. 3 with the results for the first 3- state of ‘*‘Pb. Experience from the other lead isotopes suggests that there should be a 3- state with an intensity equal to that found in 208Pb and it should be found near 2.6 MeV. The only states strongly excited near this energy are 1.87 MeV and 2.83 MeV levels. They have similar angular distributions, different from that of
I
210Pb(t, 0, (P,P') the 2+ level. The next collective
states observed
in the ‘OsPb spectrum
and 4+ levels, but they are down by a factor of 10 in intensity
unlikely that either of the two strong peaks should be associated It is concluded that the two levels are both 3- states. They account sity observed in “*Pb and share this intensity in the ratio 2 : 1. This yields: B(E3)1.s,
are the 5-, 2+
from the 3-, so it is with these states. for the full inten-
= 0.6510.15,
B(E3)20spb B(E3),.s,
= 0.35&0.10,
B(E3)2os,, or, using an average value 3*4.8,11.12) of G3(208Pb) G3 (1.87)=
23+5,
G,(2.83)
= 35.5 = 12*4.
These 3- assignments are substantiated below by the proton data. 3.1.2. Protons. Fig. 4 shows the angular distributions obtained in the (p, p’) experiment. They are compared with distributions calculated in the DWBA, using the code DWUCK 25). The parameters used in the calculations are from Becchetti and Greenlees ‘“) and are given in table 2. The parameters were checked for inelastic scattering by comparing calculated angular distributions with proton scattering data at 24 MeV on “*Pb [ref. 4)]. These fits are also good, giving greater confidence in the present results. The first three states have previously been assigned 24) as 2+, 4+ and 6+ states. There are not many data points because the peaks constantly lie among the peaks from elastic scattering from impurities. There is however nothing inconsistent with these assignments. The next two distributions shown are for the two states assigned as 3- from the triton data. These show more clearly angular distributions corresponding to L = 3. The DWBA calculations yield the following values of (j33)2 and G3: 0.0075 f0.0025,
(P3K37
=
(p3);.83
= 0.0060+0.0020,
G,(1.87)
= 21+7,
G,(2.83)
= 16f5.
and
These values are within the uncertainties of the values obtained from the (t, t’) results and the sum of the G3 values is equal to the G3 value of “‘Pb. The main difference from the triton results is that the intensity ratio is 1 : 1.3, where the tritons showed a ratio of 1 : 2, the ratios being better determined than the absolute values. DWBA calculations show that the (p, p’) and (t, t’) cross sections have very little Q-dependence in the energy range of the two states. A possible source of this discrepancy is that in this energy region there are resonances in the proton channel. This is especially true for the state at 2.83 MeV where the outgoing proton has an
8
C. ELLEGAARD
et al.
energy of 17.5 MeV, which is where the strong di and gS resonances are found 27). This may well change the intensity for this state, It is not clear what might happen to the angular distribution although this is usually determined principally by the Ltransfer. However the fact that it shows an L = 3 distribution is taken as evidence for the correctness of the 3- assignment. Thus the proton data gives good support to the Ep = 20.5
2’0Pb ( p,p’ )
MeV
loo
2.5t8we;‘f--7.,__,__2_~_
t
#6
_, -
El
100
100
I. 192 hwv
2 *
#3
t
Y
l-
L=6 i
x7
’t
L=3
L=2
i
L.
0
20
40
60
0
1 40
20
4.185 100
60
MIV
loo * I5 + t t
t
- #I2
+1+*, 100- 4.285~~V-t<,_,_-: x 13 100 -
i 100
4.390mcv t #
20
60
40
0
distributions
*
40
20
ANGLE
TABLE
58.2
6
1.17
et 0.75
W” _____1.8
5.445 x
Mev
16
I
t
’
t
+++ t
t
+
60
#
17
0
+ ,
I
I,
5.492mev
+
t
20
40
60
(DEGREES)
p’) *lOPb* reaction.
of protons from the “‘Pb(p, DWBA fits to the data.
Optical-model VII
4
14
LABORATORY
Fig. 4. Angular
t
+
LOO
L=4
0
(L.4)
The curves are
2
parameters for (p, p’)
w,r“I -~ 37.2
0
1.32
Units are in fm and MeV. “) W, for DWUCK = 4x W,, of ref. 26). b, Inclusion of the spin-orbit term of ref. 26) made no visibie change.
a1
rc
v,,,.b,
0.66
1.2
0
210Pb(t, 0, (P,P’)
9
two 3- assignments, but the ratio of the fi2 values should be taken from the triton data where no resonances are expected. Of the other states there are two relatively strong 2+ states at 4.0 and 4.1 MeV, and two probable 4+ states at 3.2 and 4.3 MeV. The state at 2.2 MeV is the only one that has a shape like an L = 5. One expects to see a 5- excitation at or below 3.2 MeV, but this peak is one that stands out very much more strongly in the proton spectrum than in the triton spectrum and because of protons resonances this assignment may not be meaningful. 4. Discussion Fig. 5 shows a summary of some of the results of inelastic scattering in the lead region, mentioned in the introduction, together with the results of the present paper. COLLECTIVE
EXCITATIONS
2+
3208Pb
206Pb
207P b I
I
I
I
209 3
20gPb
2 ?
&&--y -J-l 4321043210 EXCITATION
ENERGY
(Mel’)
Fig. 5. Distribution of collective excitations in some nuclei in the lead region including a summary of the present work. The heights of the bars indicate the relative magnitudes of the B(EA) values, with the same scale for the different nuclei but different scale for 3- and 2+ states.
For the L = 3 excitations there is a pronounced splitting of the collective strength in ‘l”Pb in contrast to the small splitting of the lighter nuclei. For the L = 2 excitations the low-energy 2+ level of “‘Pb has half the strength of that of the 2+ level in 206Pb. At higher energy we see two states near the energy of the 2+ level in “*Pb, each with about half the strength of the first 2+ level of “*Pb. The normalization for
10
C. ELLEGAARD
et al.
these states is obtained from the known strength of the low 2+ level [from (t, t’)], and by assuming DWBA calculations to be valid for the analysis of the (p, p’) cross sections. The ‘lOPb isotope is primarily different from the other Pb isotopes in that the strength of the collective 3- state is split and shifted. The difference arises from the nature of the levels available to the extra particles or holes. In ‘i”Pb the low-lying particle orbits have high spins and both positive and negative parity. Thus states of spin 3- and 5- can be generated with the consequence that these states mix with and change the properties of the core excited states. In particular a particle in the g, orbit and a particle in the j, orbit will form a 3- state very close to the 3- core state at 2.6 MeV. Hamamoto 17) has calculated the mixing of these 3- states and predicts a level at 2.11 MeV with 84 % of the 3- strength of “‘Pb and a level at 3.31 MeV with 25 % of the ‘08Pb strength. Both states are predicted slightly high in energy but otherwise the agreement with the (t, t’) experiment is very good. The agreement with the (p, p’) is poorer. In the lighter lead isotopes the low-lying orbits are all of low spins. They cannot make up a 3- state and thus the core excited state is left unperturbed. Instead there are relatively more low-lying combinations giving spin and parity 2+, thus, for example, giving the low-lying 2+ level of 206Pb more larg,- components and making it more collective than in ‘i”Pb. This difference is indicated by a comparison of the shellmodel calculations for 206Pb by True and Ford 29) and for ‘i”Pb by Redlich 30). In neither case is the lowest 2+ state predicted as collective as it is found experimentally but the predicted amount of configuration mixing is substantially greater for “‘Pb than for ‘i”Pb. Increased collectivity is suggested for the 2+ level in ‘i”Pb by the multipole pairing calculations of Bbs and Broglia 31), although also here core polarization is ignored. In the “‘Pb(t, p)210 Pb experiment of ref. 23) an enhancement was observed in the population of the lowest 2+ level of a factor of 3.0 over that predicted for a pure This again indicates that substantial configuration mixing occurs (g,)9 : + configuration. for this level. Similar, although smaller, enhancement was noted for the (t, p) reaction to the 4+ state. The 6+ state at 1.192 MeV and the 8+ state at 1.281 MeV are found to be populated as almost pure (gg)2 states. This can account for the small cross section found for the 6+ level. We gratefully acknowledge the excellent scanning by the scanning groups of the Los Alamos Laboratory and Carnegie-Mellon University and the able assistance of the operators at the Los Alamos tandem accelerator. We also thank B. Dropesky the for preparing the 210Pb target and S. Orbeson for his assistance in obtaining data.
210Pb(t, 0, @, P’)
II
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)
S. Hinds, H. Marchant, J. H. Bjerregaard and 0. Nathan, Phys. Lett. 20 (1966) 674 J. C. Hafele and R. Woods, Phys. Lett. 23 (1966) 579 A. Scott and M. Fricke, Phys. Lett. 20 (1966) 654 G. Vallois, J. Saudinos, 0. Beer, M. Gendrot and P. Lopato, Phys. Lett. 22 (1966) 659; G. Vallois, thesis, Saclay (1968) R. K. Jolly, E. K. Lin and B. L. Cohen, Phys. Rev. 128 (1962) 2292 B. Elbek et al., to be published E. R. Flynn, data on inelastic scattering analysed only for the purpose of present comparisons 5. Alster, Phys. Rev. 141 (1966) 1138; Phys. Lett. 25B (1967) 459 R. A. Broglia, J. S. Lilley, R. Perazzo and W. R. Phillips, Phys. Rev. Cl (1970) 1508 J. P. Schiffer, D. G. Fleming, H. E. Gove and J. Hertet, Bull. Am. Phys. Sot. 12 (1967) 655; Phys. Rev. Lett. 23 (1969) 488 H. Crannell, R. Helm, H. Kendall, J. Oesen and M. Yearin, Phys. Rev. 123 (1961) 923 G. A. Peterson and J. F. Ziegler, Phys. Lett. 21 (1966) 543 B. R. Mottelson, Proc. Int. Conf. on nuclear structure, ed. J. Sanada, Tokyo, 1967 I. Hamamoto, Nucl. Phys. Al26 (1969) 545 C. Ellegaard, J. Kantele and P. Vedelsby, Phys. Lett. 25B (1967) 512 C. Ellegaard, J. Kantele and P. Vedelsby, Nucl. Phys. Al29 (1969) 113 1. Hamamoto, to be published, preprint J. Borggreen, B. Elbek and L. Perch Nielsen, Nucl. Instr. 24 (1963) 1 G. Igo, E. R. Flynn, B. J. Dropesky and P. D. Barnes, submitted to Phys. Rev. C. Ellegaard, P. D. Barnes and E. R. Flynn, to be published E. R. Flynn, D. D. Armstrong, J. G. Beery and A. G. Blair, Phys. Rev. 140 (1968) 1142 J. H. Bjerregaard, 0. Hansen, 0. Nathan, L. Vistisen, R. Chapman and S. Hinds, Nucl. Phys. All3 (1968) 484 P. D. Barnes, E. R. Flynn and G. Igo, to be published P. Weinzierl, E. Ujlaki, G. Preinreich and G. Eden, Phys. Rev. 134 (1964) B257 P. D. Kunz, DWUCK, private communication F. D. Becchetti and G. W. Greenlees, Phys. Rev. 182 (1969) 1190 N. Stein, C. A. Whitten and D. A. Bromley, Phys. Rev. Lett. 20 (1968) 113 C. A. Whitten, N. Stein, G. E. Holland and D. A. Bromley, Phys. Rev. 188 (1969) 1941 W. W. True and K. W. Ford, Phys. Rev. 109 (1958) 1675 M. G. Redlich, Phys. Rev. 138 (1965) B544 D. Bbs and R. Broglia, submitted to Phys. Rev.
Physics Al62 (1971) l-l
Not to be reproduced
by photoprint
1; @
North-Holland
Publishing
or microfilm without written permission
Co., Amsterdam from the publisher
INELASTIC SCATTERING OF TRITONS AND PROTONS FROM “‘Pb C. ELLEGAARD Carnegie-Mellon
and P. D. BARNES
University,
Pittsburgh,
Pennsylvania
t
E. R. FLYNN Los Alamos
Scientific
Laboratory,
Los Alamos,
New Mexico t
and
G. J. IGO University
of California,
Los Angeles
and Los Alamos
Received 8 October
Scientific
Laboratory
t
1970
Abstract:
A search for collective states in 210Pb has been conducted utilizing inelastic scattering of 20 MeV tritons and 20.5 MeV protons. In the triton scattering, cross sections were obtained for levels at 0.795, 1.87 and 2.83 MeV. The 0.795 level is a known 2+ level. It is excited with a cross section of one-half of that observed for the first 2+ level of 206Pb under identical conditions. The two other states are assigned as 30 states. The cross sections obtained for these two levels are approximately 8 and ) of the cross section found in the (t, t’) reaction for the first 3- state of 2osPb. In the proton scattering, the above results are confirmed and several other levels observed. The results are compared with DWBA calculations.
E
NUCLEAR REACTIONS ‘lOPb(t, t’), (p, p’), E, = 20.0 MeV, EI, = 20.5 MeV; measured a(&, 19),u(&, 8). 210Pb deduced levels, J, Z, L. Enriched target.
1. Introduction The inelastic scattering process preferentially excites collective states in nuclei and has often been used to locate such states. Inelastic scattering from nuclei in the lead region has been systematically studied by many groups using a variety of projectiles: protons loa), deuterons ‘3 6), tritons ‘), alpha particles *, “) 1 6O [ref. ‘“)I and electrons 11*‘*). The results of the inelastic scattering from the doubly closed shell nucleus *‘*Pb show as dominant features a strongly excited 3- state at 2.6 MeV, a strongly excited 5- state at 3.2 MeV and at higher energies some less strongly excited but still collective 2’, 4+ and 6+ states. The dominant features of inelastic scattering from nuclei in the vicinity of “*Pb are strongly excited states or multiplets of levels near the same energy as the strongly excited states in “*Pb. This corresponds to excitation of the core with the configuration of the extra particles or holes left unchanged. In addition there are in these neighboring nuclei states at lower excitation energy corresponding to the degrees of freedom of the extra particles or holes. Notably in doubly even nuclei the lowest state is a collective 2+ state. t Work supported by the Atomic Energy Commission February
197 1
2
C. ELLEGAARD
et al.
The above-mentioned multiplets, as exemplified by the doublet at 2.6 MeV in ‘*‘Pb [refs. “-“)I and the septuplet at 2.6 MeV in **%i [refs. ‘*6*9, ‘“)I, are well described [refs. “*“)I by assuming a weak coupling between the hole or particle and the 3vibrational state of the core. Inelastic scattering is not possible on ‘*‘Pb but a measurement ’ “) of the lifetime of the J$- state at 1.422 MeV indicates that it contains a large admixture of core excitation. Thus ‘09Pb appears significantly different from the above-mentioned isotopes in that a large part of the 3- core excitation is found far away from 2.6 MeV. This is however accurately explained 13*14S16)by the coupling between the neutron in the j, state and the 3- vibration, with the same model that describes the close multiplets in the other cases. In ‘l*Pb there are two neutrons in the same shell as the single neutron in ‘*‘Pb. It is expected “) that this will produce a similar strong coupling between particle states and core states. The present work is a study of the inelastic scattering of 20 MeV tritons and 20.5 MeV protons from ‘l*Pb. The main results are the observation of a splitting of the collective octupole strength and the measurement of the B(E2) value for the lowest 2+ state. There are some shortcomings in the quality of the experimental data because of the radiation hazards involved in using the 210Pb target. However the results as quoted here are reliable within the accuracies quoted. 2. Experiment A ‘l*Pb target was bombarded with beams of 20 MeV tritons and 20.5 MeV protons from the Los Alamos three-stage tandem accelerator facility. The scattered particles were analysed in a broad-range magnetic spectrometer I*) and recorded on photographic plates. The resulting triton and proton spectra are shown in figs. 1 and 2. 2.1. TARGET
The 210Pb target was a 240 pg,/cm2 metal deposit on a 50 pg/cm’ carbon backing. The preparation of this target by isotopic separation has been described elsewhere ’ “). The target is isotopically very pure but it has a relatively large content of light impurities. Peaks from these impurities are easily identified by their shift in energy as a function of angle. The content of some impurities is large enough to make inelastic scattering on these nuclei important. This creates an extra background in the spectra but all significant peaks have been identified as arising from “*Pb or from known levels in the main impurities. At the time the triton exposures were made approximately 5 “/, of the “*Pb had decayed into 206Pb(210Pb @!z 210Bi fl>z ‘l*Po ‘?Y?$! ‘06Pb). No trace of peaks arising from 206Pb was observed in the inelastic scattering or other reactions observed simultaneously 20). This is as expected because most of the 206Pb nuclei should recoil oui of the target. The earlier proton exposures also show no contamination from decay products.
3
zloPW,0, (PtP’) EXCITATION
Ii0
ii5
ENERGY
)
( MeV
Ii5
Ii0 DISTANCE
ALONG
130 PLATE
135
140
(cm)
Fig. 1. Triton spectrum from the *r’Pb(t, t ’ ) *lOPb* reaction at 66”. The three peaks labeled 0.795, 1.872 and 2.839 are the three main peaks for which angular distributions were obtained. Numbers in parentheses indicate peaks observed only at this angle but located at energies where peaks are observed in the (p, p’) spectra. At other angles they are obscured by impurity peaks or general background level. Peaks marked by chemical symbol and mass number arise from known levels in the indicated nucleus.
EXCITATION
ENERGY
4
5
t Me’4
) 2
3
f
!
15
“‘Pb
(
p,p’l
EP
*
20.5
9
=
63’
Mev
i0
25 OISTANCE
Fig. 2. Proton spectrum from the ‘l”Pb(p, numbers correspond to levels in *rOPb as number of the impurity nucleus from which 7 correspond to the 0.795 MeV,
ALONG
30 PLATE
lcml
p ’) zXOPb* reaction at 63”. Peaks marked with boldface given in table 1. Other peaks are marked with the mass they arise from known excited states. Peaks nos. 1,4 and 1.869 MeV and 2.828 MeV levels respectively.
4
C. ELLEGAARD
et al.
2.2. EXPOSURES AND ABSOLUTE YIELDS
Exposures of approximately 6000 PC and 900 ,uC were made at 6” intervals from 70” forward for protons and from 66” forward for tritons. Because of the increasing intensity of peaks from the lighter impurities and the increasing number of slit-scattered particles, the proton spectra could not be analysed further forward than 28”. For the triton spectra the slit-scattering was unusually high, as may be seen in fig. 1, and the spectra could be analysed no further forward than 48”. No attempt to repeat the triton data was made because of the radiation hazards and the possible scattering chamber contamination. At the angles between 48” and 66” reliable cross sections were obtained for the three main triton peaks that are discussed in the next section, The relative normalization of the different exposures was obtained by monitoring the number of elastically scattered particles in a CsI(TI) scintillation counter located at a forward angle. For the triton exposures the absolute cross section was obtained by scanning the peaks corresponding to elastic scattering at 60” and 66” in the short exposures. The absolute cross section for elastic scattering of tritons from ‘l”Pb is assumed to be the same as for zosPb. This cross section has been measured 2i) at the same energy (20.0 MeV) to an accuracy of 5 ‘A. The uncertainty in the absolute cross section for the triton exposures is estimated to be + 15 o/0with 10 ‘A arising from the uncertainty in scanning the intense peaks. For the proton exposures the absolute cross section could not be obtained in the same direct way because the peaks corresponding to elastic scattering were too intense to be scanned. However a normalization was obtained by the following two methods: (i) The cross section of the first 2+ state was normalized to give the cross section predicted by distorted wave Born approximation (DWBA) calculations (subsect. 3.1.2) assuming the value of j?” to be the one obtained from the triton data. (ii) An absolute scale for the cross section was obtained in the work 19) on the “‘Pb(p d)‘09Pb reaction which was recorded at the same time as the (p, p’) reaction. Here th; absolute values for the cross section were obtained by setting the differential cross section for populating the 2152 keV level jn the “‘Pb(p, d)‘09Pb’ reaction equal to the cross section obtained z”) in the reaction ‘O’Pb(p, d)“‘Pb(O). The first method involves a DWBA calculation with the uncertainties inherent in such a calculation. The second method involves assumptions about the structure of the 2152 keV level in 209Pb. These assumptions are not likely to introduce any serious error. The two methods agree within 30 %. With most emphasis on the second method an absolute scale is obtained for the angular distributions of fig. 4. 3. Experimental results and analysis Table 1 lists the energy levels observed in the (t, t’) and (p, p’) experiments. Because the ground state peaks were too intense to be scanned in all of the proton spectra, the energy scale for the (p, p’) results was normalized to give an excitation energy
5
210Pbk0, (P,P’)
of 0.795 MeV for the first excited state, in accordance with the (t, t’) results and the results of refs. 23124). TABLE 1 Excitation energy (MeV) Peak no. (proton spect.)
Previous experiments
L
Decay ‘) of ““Tl
zOsPb(t, p) (P, P’) &lo keV
(t, t’) &15 keV
13 MeV “)
20 MeV “)
0 1 2 3
0
4
1.869
5
2.215
6
0.795 d) 1.095 1.192
0 0.795 (1.086)
0 2 4 6
1.872
3
(5)
2.518
(4)
0 0.804 1.099 1.117 1.281 1.806 1.876 2.012 2.048 2.222 2.420 2.460 2.522
2.909
0 0.795 1.094 1.193 1.273 1.799 1.869 2.004 2.037 2.214 2.412 2.454 2.516 2.529 2.701 2.791 2.823 2.861 2.900
3.155
3.151
2.706 7
2.828
2.839
3
8
3.069
(3.085)
2
9
3.194
10 11 12 13 14
4.080 4.128 4.185 4.285 4.390
15 16 17
5.396 5.445 5.492
(3.209)
(4.093)
2.833
0 0.795 1.09 1.17
1.85 1.95, 2.00
2.40
2.58
2.93, 3.03, 3.07
4
2 2 (4)
3.227 3.314 3.457 3.575 3.628 3.673 3.707 3.880 3.913 4.077 4.144
3.309
4.265 4.390 4.685
‘) See ref. 2z). “) See ref. 23). ‘) See ref . *‘+). *) Normalized to give the same excitation energy as the (t, t’) results and refs. 23*24).
C. ELLEGAARD
6
3.1. ANGULAR
al.
et
DISTRIBUTIONS
3.1.1. Tritons. Fig. 3 shows the angular distributions of the three main peaks in the triton spectra. The 0.795 MeV level has previously been assigned ‘“) as a 2’ level. For comparison we have plotted the cross section for excitation of the first 2+ level of ‘06Pb in the (t, t’) reaction under identical conditions ‘). The 2+ in ‘l*Pb is excited with very nearly half the strength of that of the 2+ in “‘Pb. This is also the ratio / “‘Pb
(t,t’)
E,
20
30
40
50
= 20.0NIeV
60
70
t DEGREES I
ANGLE
Fig. 3. Angular distributions from the 2t0Pb(t t’)2toPb* reaction (full circles and squares). For comparison the angular ~stributions from td IcsPb(t, t’)+“*Pb(3-) and Z06Pb(t, t’)“06Pb(2+) reactions at the same energy (open circles) are shown.
of 8” or the B(E2) value of the states
W3’8210= 0.50+0.15. @F2), 06 In terms of single-particle units G
=
1
WA) igjzq
(3+Aj2 =
4n(21+1)
z2p2
1’
the 2+ of zo6Pb has 4S8) G, = 7. The 2” of ‘l*Pb thus has G2 = 3.5i_1.0. The two other strongly excited states are compared in fig. 3 with the results for the first 3- state of ‘*‘Pb. Experience from the other lead isotopes suggests that there should be a 3- state with an intensity equal to that found in 208Pb and it should be found near 2.6 MeV. The only states strongly excited near this energy are 1.87 MeV and 2.83 MeV levels. They have similar angular distributions, different from that of
I
210Pb(t, 0, (P,P') the 2+ level. The next collective
states observed
in the ‘OsPb spectrum
and 4+ levels, but they are down by a factor of 10 in intensity
unlikely that either of the two strong peaks should be associated It is concluded that the two levels are both 3- states. They account sity observed in “*Pb and share this intensity in the ratio 2 : 1. This yields: B(E3)1.s,
are the 5-, 2+
from the 3-, so it is with these states. for the full inten-
= 0.6510.15,
B(E3)20spb B(E3),.s,
= 0.35&0.10,
B(E3)2os,, or, using an average value 3*4.8,11.12) of G3(208Pb) G3 (1.87)=
23+5,
G,(2.83)
= 35.5 = 12*4.
These 3- assignments are substantiated below by the proton data. 3.1.2. Protons. Fig. 4 shows the angular distributions obtained in the (p, p’) experiment. They are compared with distributions calculated in the DWBA, using the code DWUCK 25). The parameters used in the calculations are from Becchetti and Greenlees ‘“) and are given in table 2. The parameters were checked for inelastic scattering by comparing calculated angular distributions with proton scattering data at 24 MeV on “*Pb [ref. 4)]. These fits are also good, giving greater confidence in the present results. The first three states have previously been assigned 24) as 2+, 4+ and 6+ states. There are not many data points because the peaks constantly lie among the peaks from elastic scattering from impurities. There is however nothing inconsistent with these assignments. The next two distributions shown are for the two states assigned as 3- from the triton data. These show more clearly angular distributions corresponding to L = 3. The DWBA calculations yield the following values of (j33)2 and G3: 0.0075 f0.0025,
(P3K37
=
(p3);.83
= 0.0060+0.0020,
G,(1.87)
= 21+7,
G,(2.83)
= 16f5.
and
These values are within the uncertainties of the values obtained from the (t, t’) results and the sum of the G3 values is equal to the G3 value of “‘Pb. The main difference from the triton results is that the intensity ratio is 1 : 1.3, where the tritons showed a ratio of 1 : 2, the ratios being better determined than the absolute values. DWBA calculations show that the (p, p’) and (t, t’) cross sections have very little Q-dependence in the energy range of the two states. A possible source of this discrepancy is that in this energy region there are resonances in the proton channel. This is especially true for the state at 2.83 MeV where the outgoing proton has an
8
C. ELLEGAARD
et al.
energy of 17.5 MeV, which is where the strong di and gS resonances are found 27). This may well change the intensity for this state, It is not clear what might happen to the angular distribution although this is usually determined principally by the Ltransfer. However the fact that it shows an L = 3 distribution is taken as evidence for the correctness of the 3- assignment. Thus the proton data gives good support to the Ep = 20.5
2’0Pb ( p,p’ )
MeV
loo
2.5t8we;‘f--7.,__,__2_~_
t
#6
_, -
El
100
100
I. 192 hwv
2 *
#3
t
Y
l-
L=6 i
x7
’t
L=3
L=2
i
L.
0
20
40
60
0
1 40
20
4.185 100
60
MIV
loo * I5 + t t
t
- #I2
+1+*, 100- 4.285~~V-t<,_,_-: x 13 100 -
i 100
4.390mcv t #
20
60
40
0
distributions
*
40
20
ANGLE
TABLE
58.2
6
1.17
et 0.75
W” _____1.8
5.445 x
Mev
16
I
t
’
t
+++ t
t
+
60
#
17
0
+ ,
I
I,
5.492mev
+
t
20
40
60
(DEGREES)
p’) *lOPb* reaction.
of protons from the “‘Pb(p, DWBA fits to the data.
Optical-model VII
4
14
LABORATORY
Fig. 4. Angular
t
+
LOO
L=4
0
(L.4)
The curves are
2
parameters for (p, p’)
w,r“I -~ 37.2
0
1.32
Units are in fm and MeV. “) W, for DWUCK = 4x W,, of ref. 26). b, Inclusion of the spin-orbit term of ref. 26) made no visibie change.
a1
rc
v,,,.b,
0.66
1.2
0
210Pb(t, 0, (P,P’)
9
two 3- assignments, but the ratio of the fi2 values should be taken from the triton data where no resonances are expected. Of the other states there are two relatively strong 2+ states at 4.0 and 4.1 MeV, and two probable 4+ states at 3.2 and 4.3 MeV. The state at 2.2 MeV is the only one that has a shape like an L = 5. One expects to see a 5- excitation at or below 3.2 MeV, but this peak is one that stands out very much more strongly in the proton spectrum than in the triton spectrum and because of protons resonances this assignment may not be meaningful. 4. Discussion Fig. 5 shows a summary of some of the results of inelastic scattering in the lead region, mentioned in the introduction, together with the results of the present paper. COLLECTIVE
EXCITATIONS
2+
3208Pb
206Pb
207P b I
I
I
I
209 3
20gPb
2 ?
&&--y -J-l 4321043210 EXCITATION
ENERGY
(Mel’)
Fig. 5. Distribution of collective excitations in some nuclei in the lead region including a summary of the present work. The heights of the bars indicate the relative magnitudes of the B(EA) values, with the same scale for the different nuclei but different scale for 3- and 2+ states.
For the L = 3 excitations there is a pronounced splitting of the collective strength in ‘l”Pb in contrast to the small splitting of the lighter nuclei. For the L = 2 excitations the low-energy 2+ level of “‘Pb has half the strength of that of the 2+ level in 206Pb. At higher energy we see two states near the energy of the 2+ level in “*Pb, each with about half the strength of the first 2+ level of “*Pb. The normalization for
10
C. ELLEGAARD
et al.
these states is obtained from the known strength of the low 2+ level [from (t, t’)], and by assuming DWBA calculations to be valid for the analysis of the (p, p’) cross sections. The ‘lOPb isotope is primarily different from the other Pb isotopes in that the strength of the collective 3- state is split and shifted. The difference arises from the nature of the levels available to the extra particles or holes. In ‘i”Pb the low-lying particle orbits have high spins and both positive and negative parity. Thus states of spin 3- and 5- can be generated with the consequence that these states mix with and change the properties of the core excited states. In particular a particle in the g, orbit and a particle in the j, orbit will form a 3- state very close to the 3- core state at 2.6 MeV. Hamamoto 17) has calculated the mixing of these 3- states and predicts a level at 2.11 MeV with 84 % of the 3- strength of “‘Pb and a level at 3.31 MeV with 25 % of the ‘08Pb strength. Both states are predicted slightly high in energy but otherwise the agreement with the (t, t’) experiment is very good. The agreement with the (p, p’) is poorer. In the lighter lead isotopes the low-lying orbits are all of low spins. They cannot make up a 3- state and thus the core excited state is left unperturbed. Instead there are relatively more low-lying combinations giving spin and parity 2+, thus, for example, giving the low-lying 2+ level of 206Pb more larg,- components and making it more collective than in ‘i”Pb. This difference is indicated by a comparison of the shellmodel calculations for 206Pb by True and Ford 29) and for ‘i”Pb by Redlich 30). In neither case is the lowest 2+ state predicted as collective as it is found experimentally but the predicted amount of configuration mixing is substantially greater for “‘Pb than for ‘i”Pb. Increased collectivity is suggested for the 2+ level in ‘i”Pb by the multipole pairing calculations of Bbs and Broglia 31), although also here core polarization is ignored. In the “‘Pb(t, p)210 Pb experiment of ref. 23) an enhancement was observed in the population of the lowest 2+ level of a factor of 3.0 over that predicted for a pure This again indicates that substantial configuration mixing occurs (g,)9 : + configuration. for this level. Similar, although smaller, enhancement was noted for the (t, p) reaction to the 4+ state. The 6+ state at 1.192 MeV and the 8+ state at 1.281 MeV are found to be populated as almost pure (gg)2 states. This can account for the small cross section found for the 6+ level. We gratefully acknowledge the excellent scanning by the scanning groups of the Los Alamos Laboratory and Carnegie-Mellon University and the able assistance of the operators at the Los Alamos tandem accelerator. We also thank B. Dropesky the for preparing the 210Pb target and S. Orbeson for his assistance in obtaining data.
210Pb(t, 0, @, P’)
II
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)
S. Hinds, H. Marchant, J. H. Bjerregaard and 0. Nathan, Phys. Lett. 20 (1966) 674 J. C. Hafele and R. Woods, Phys. Lett. 23 (1966) 579 A. Scott and M. Fricke, Phys. Lett. 20 (1966) 654 G. Vallois, J. Saudinos, 0. Beer, M. Gendrot and P. Lopato, Phys. Lett. 22 (1966) 659; G. Vallois, thesis, Saclay (1968) R. K. Jolly, E. K. Lin and B. L. Cohen, Phys. Rev. 128 (1962) 2292 B. Elbek et al., to be published E. R. Flynn, data on inelastic scattering analysed only for the purpose of present comparisons 5. Alster, Phys. Rev. 141 (1966) 1138; Phys. Lett. 25B (1967) 459 R. A. Broglia, J. S. Lilley, R. Perazzo and W. R. Phillips, Phys. Rev. Cl (1970) 1508 J. P. Schiffer, D. G. Fleming, H. E. Gove and J. Hertet, Bull. Am. Phys. Sot. 12 (1967) 655; Phys. Rev. Lett. 23 (1969) 488 H. Crannell, R. Helm, H. Kendall, J. Oesen and M. Yearin, Phys. Rev. 123 (1961) 923 G. A. Peterson and J. F. Ziegler, Phys. Lett. 21 (1966) 543 B. R. Mottelson, Proc. Int. Conf. on nuclear structure, ed. J. Sanada, Tokyo, 1967 I. Hamamoto, Nucl. Phys. Al26 (1969) 545 C. Ellegaard, J. Kantele and P. Vedelsby, Phys. Lett. 25B (1967) 512 C. Ellegaard, J. Kantele and P. Vedelsby, Nucl. Phys. Al29 (1969) 113 1. Hamamoto, to be published, preprint J. Borggreen, B. Elbek and L. Perch Nielsen, Nucl. Instr. 24 (1963) 1 G. Igo, E. R. Flynn, B. J. Dropesky and P. D. Barnes, submitted to Phys. Rev. C. Ellegaard, P. D. Barnes and E. R. Flynn, to be published E. R. Flynn, D. D. Armstrong, J. G. Beery and A. G. Blair, Phys. Rev. 140 (1968) 1142 J. H. Bjerregaard, 0. Hansen, 0. Nathan, L. Vistisen, R. Chapman and S. Hinds, Nucl. Phys. All3 (1968) 484 P. D. Barnes, E. R. Flynn and G. Igo, to be published P. Weinzierl, E. Ujlaki, G. Preinreich and G. Eden, Phys. Rev. 134 (1964) B257 P. D. Kunz, DWUCK, private communication F. D. Becchetti and G. W. Greenlees, Phys. Rev. 182 (1969) 1190 N. Stein, C. A. Whitten and D. A. Bromley, Phys. Rev. Lett. 20 (1968) 113 C. A. Whitten, N. Stein, G. E. Holland and D. A. Bromley, Phys. Rev. 188 (1969) 1941 W. W. True and K. W. Ford, Phys. Rev. 109 (1958) 1675 M. G. Redlich, Phys. Rev. 138 (1965) B544 D. Bbs and R. Broglia, submitted to Phys. Rev.