Experimental study of 136Nd at high angular momentum

Nuclear Physics A350 (1980) 190 - 204; Not to be reproduced

by photoprint

@

North-Holland Publishing Co., Amsterdam

or microfilm without written permission

from the publisher

EXPERIMENTAL STUDY OF 13‘jNd AT HIGH ANGULAR MOMENTUM l M. M. ALGONARD +, Y. EL MASRI ++, I. Y. LEE *, F. S. STEPHENS, M. A. DELEPLANQUE ** and R. M. DlAMOND Nuclear Science Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720, USA Received

12 July 1979

(Revised

31 July 1980)

The y-ray multiplicities following 1ooMo(40Ar, .uny)Nd have been studied by several methods. The measured width of the multiplicity distribution and the shape of the multiplicity spectrum as a function of transition energy suggest a broad region of feeding into the 4n channel. The dependence of the multiplicity on transition energy, for the sum of all reaction channels and for only the 4n reaction channel, is well reproduced by a calculation which suggests that the products become deformed rotors at spins above 30h.

Abstract:

E

NUCLEAR REACTIONS 1ooMo(40Ar, xny), E = 170 MeV; messured y-ray multiplicities versus E Y 136Nd deduced effective moment of inertia. Enriched targets.

1. Introduction Heavy-ion induced reactions are known to bring to the compound system large amounts of angular momentum. However, the amount actually remaining in evaporation residues is limited by particle emission, or by fission or deep inelastic processes. Recent studies of 40Ar-induced reactions in various targets have shown ‘) that this angular momentum is a maximum (h 60h) for residual nuclei with atomic number Z = 5CL70. Hence these nuclei are favorable for the study of behavior at high spin. The continuum y-ray de-excitation of Te and Yb nuclei at the edges of this Zregion have already been studied 2-4) and show an interesting behavior. In “j2Yb the (yrast) bump in the continuum y-ray spectrum, due to collective rotational transitions, is well pronounced and its edge shifts towards higher energies with an * ’ ” t **

This work was supported by Division of Nuclear Physics of the US Department of Energy. Present address: Centre d’Etudes Nucltaires de Bordeaux Gradignan, 33170 Gradignan, France. Present address: Institut de Physique Corpusculaire, Louvain la Neuve, Belgium. Present address: Oak Ridge National Laboratory, Oak Ridge, TN 37830. Present address: Institut de Physique Nucltaire, 91406 Orsay. France. 190

M. M. AIPonard et al. / 13’Nd

191

increase in bombarding energy. This strongly suggests that the transition energies and the spins of the higher collective states are related through the usual expression for rotational states : E, = ;;

(41-2),

where E, is the y-ray transition energy and 9 is the effective moment of inertia. The 1’ 8Te results indicate that the collective y-ray bump in that nucleus only develops above a bombarding energy such that more than 30h are brought into the nucleus. This is supported by the calculations of Anderson et al. 5, of the potential energy surfaces (or shapes) for different angular momenta, which indicate an increase in deformation at about this spin region. These results suggested a study of Nd residual nuclei might be interesting for at least two reasons : their atomic number (Z = 60) is favorable for the highest angular momentum transfer to a residual compound nucleus, and they may be sensitive to shell effects because of their vicinity to a closed shell at 82 neutrons. The aim of this experiment was to undertake a study of the average multiplicities and effective moments of inertia of the Nd nuclei produced with 170 MeV 40Ar bombardment, and specifically of ’ 36Nd since the 4n reaction channel was dominant at the bombarding energy used. This faiorable cross section allowed a study of the y-ray multiplicity as a function of transition energy for that residual nucleus.

2. Experimental procedure The experiment was carried out at the 88” Cyclotron of the Lawrence Berkeley Laboratory with a 170 MeV 40Ar beam. This energy (known to better than 1 MeV) was selected so as to bring in the maximum angular momentum for the compound nucleus and still yield the 4n channel as the dominant reaction. A target of “‘MO (2 mg/cm’) on a lead backing (N 7 mg/cm2) was used. The target thickness was chosen as a compromise between furnishing a yield (counting rate) necessary for the triple coincidence measurement and still keeping the energy spread of the beam in such a target at a tolerable level. The experimental set-up is shown in fig. 1. Three 7.6 x 7.6 cm NaI detectors were located in the reaction plane at O”,40° and 80°, respectively, to the beam axis and at 60 cm from the target. A Ge(Li) detector (50 cm3) was at - 70” and at 6 cm from the target. A multiplicity filter, composed of six 7.6 x 7.6 cm NaI(T1) detectors, was set just upstream of the target, symmetric around the beam axis, like a “halo”. Coincidence events between the Ge(Li) detector and any of the three in-plane NaI (IP NaI) counters were recorded event by event on magnetic tape. The identification of the IP NaI involved was performed by recording a separate time signal (TAC) between each of these three counters and the Ge(Li) detector. These time-to-amplitude

192

M. M. AIPonard et al. I 13’jNd

33

NaI (0’)

1~

ONaI(40”)

4-J Nal(80”)

Fig. 1. Experimental set-up.

spectra were used to : (a) select prompt events from delayed ones, and (b) distinguish, by time-of-flight, the desired y-ray pulses in the NaI counters from neutrons. For each coincidence event between the Ge(Li) detector and one of the IP NaI counters, we also recorded the number of NaI counters (0 to 6-fold) in the multiplicity filter found within 70 ns coincidence. From the coincidence requirement between the Ge(Li) and the IP NaI detectors we are able to construct continuum NaI y-spectra associated with an individual reaction channel by gating on discrete y-lines in the Ge(Li) detector from the desired evaporation residue. Fig. 2 shows a typical Ge(Li) spectrum for the “‘Mo+~‘A~ reaction at 170 MeV; it is dominated mainly by the discrete y-lines which are products of the 4n reaction channel. A typical NaI pulse-height spectrum generated from gates set on the 4n lines in the coincident Ge(Li) detector is shown in the lower part of fig. 3. The true energy distribution of these continuum y-rays is obtained from this raw spectrum using a modification of an unfolding procedure designed by Mollenauer 6). This unfolded spectrum (upper part of fig. 3), when properly normalized, allows the determination of the average y-ray multiplicity, R,, of the 4n reaction channel as well as the effective moment of inertia of 136Nd at high angular momenta. The additional coincidence requirement with the multiplicity filter can lead to the determination of the average y-multiplicities observed in each of the IP NaI detectors as a function of the y-ray energies (E,). This can be done either for the sum of the open channels at a specific beam energy, or for only one channel by setting appropriate gates in the Ge(Li) detector. Similar studies with the multiplicity

193

M. M. AIPonard et al. / ‘36Nd I

I

I

I

I

'O"Mo+ 4oAr 4.103

3.103 In 5 8 2.103

600

Energy

(keV)

Fig. 2. Ge(Li) spectrum (- 700) from “‘MO + 40Ar reaction at 170 MeV bombarding energy in prompt coincidence with any of the in-plane NaI detectors.

filter can be performed on the discrete y-lines in the Ge(Li) spectrum instead of the IP NaI spectra leading to the average multiplicity and its second moment for each reaction channel observed. The coincidence events were recorded on a ModComp IV computer and the singles spectra of the Ge(Li) detector were recorded on an XC-660 computer. Dead-time corrections for both acquisitions were made by using a pulser generator triggered by delayed pulses from the Ge(Li) detector itself.

3. Analysis and results 3.1. AVERAGE

MULTIPLICITY

AND CONTINUUM

ANISOTROPY

(IP NaI METHOD)

The average multiplicity AT7in the 4n” reaction channel was deduced from the analysis of the y-ray spectra of the IP NaI in coincidence with the 4n y-lines in the Ge(Li) according to the method described in ref. 2). The average multiplicity is given by : R, N l+Z (2) I$& ’ where $ is the total number of singles events in the Ge(Li) detector corresponding to the 4n channel gate set for the coincident events, $ is the number of gated coincidence events in the IP NaI counter, and E is the absolute efficiency of the IP NaI.

194

M. M. AIPonard et al. / L36Nd

Energy

fMeV)

Fig. 3. Bottom: Sum of the three IP NaI spectra in coincidence with the main 4n y-ray lines in the Ge(Li) detector: squares are raw data and dots are unfolded data. Top: Ratio of the 0” to 80” NaI unfolded (and Doppler-shifted) spectra.

According to this method the raw y-ray spectra of the IP NaI are unfolded ‘j) to construct the true energy distribution. The average multiplicity (a,) was calculated from the summation of the three IP NaI spectra and the sum of all the events observed in the normalized unfolded coincidence spectrum for an energy > 340 keV (to account for this cut off near some discrete line energies in 136Nd one unit was added for the final MYvalue). No correction for the angular correlation has been made since for the extreme possibilities of either El or E2 transitions this summation is nearly equivalent (within 5 “/,) to the true yield (A, of the angular correlation). Because multiple events, where more than one IP NaI detector fired at a given time, were electronically suppressed, the average multiplicity was corrected (< 6 %) for these losses. This method gives a mean multiplicity in the 4n channel, R, = 24+ 3 (errors estimated from the precision in the unfolding procedure, statistical uncertainties, etc. . .). Comparison of the unfolded spectra from. the IP NaI at O” (Doppler corrected) and at SO0 gives the anisotropy of the continuum gamma rays. Calculations ‘) show that the beam y-y correlation with the Ge(Li) detector at -700 is similar to

M. M. Alionard et al. / 136Nd

195

the usual beam-y distribution for high angular momentum: i.e. the 0°/800 ratio is about 1.6 for stretched E2 radiations and about 0.6 for stretched dipole radiations. The experimental values observed are shown in fig. 3. Between 1 and 2 MeV in the bump region, the anisotropy suggests a dominance of stretched E2(Z -+ Z-2) transitions. The nearly isotropic angular distribution observed above N 2 MeV is consistent with the expectations for a statistical cascade. Also, as expected *), this region yields an exponential decrease of the intensity with the increase in y-ray energy. These data are in agreement with previous work 2); however, the anisotropy observed at low energy (< 1 MeV) is lower than expected and will be discussed further.

3.2. AVERAGE

MULTIPLICITY

(HALO METHOD)

Another way to measure the average multiplicity is to observe the number of events in some xny lines (4n for example) in the Ge(Li) detector in coincidence with a given number (p-fold) of the six NaI detectors of the multiplicity filter as well as one of the IP NaI detectors. Fig. 4 shows Ge(Li) spectra corresponding to the 1 - to 5fold coincidence requirement. The average multiplicity in a given channel is computed

I

3 Fold

-1

-4002 4 Fold

s s

I 2 Fold

- 200 5 Fold

400

800

-

0

Energy CkeV)

Fig. 4. Ge(Li) y-spectrum in l- to Sfold coincidence with the 6 NaI detectors of the multiplicity fdter.

M. M. Alionard et al.

196

I ‘36Nd

from a combination of the counts observed in the different p-folds as described in ref. ‘). To take account of the coincidence required with the IP NaI, one unit was added to the final R, value. The second moment of the multiplicity distribution is also determined (w = J(M’) -(IV)‘). This method led to a mean value of R, = 27+ 2 for the 4n reaction channel. Table 1 shows the average multiplicities for the 5n, 4n and 3n reaction channels and the corresponding width obtained for the 4n channel; the statistics are too poor in the other reaction channels to determine the width of their multiplicity distributions. In order to see if there were any target thickness effect in the determination of R, and its distribution, we repeated this experiment using only the Ge(Li) and the multiplicity filter, but with a 1 mg/cm’ self-supporting target. These results are also presented in table 1. Although the multiplicity could be lower for the 2 mg/cm2 target (lower mean bombarding energy), all the values agree with the IP NaI measurement within their uncertainty. This could be expected from a crude calculation of the AZ, and hence AM, spread (assuming a rigid rotor), due to the target thickness. This estimate leads to AM, about two times smaller than the actually measured FWHM (2.35 w). 3.3. AVERAGE

MULTIPLICITY

AS A FUNCTION

OF THE y-RAY ENERGY

Using the Halo-method (sect. 3.2) applied to the unfolded spectra of the IP Nal, one can calculate the average multiplicity as a function of the y-ray energy (i.e.

TABLE

I

““‘Mo+~~A~ (170 MeV): average multiplicities and relative cross sections A, ’

q ‘1

xn channel

Second moment IP Nal method

4n

3n 5n 6n all charm

24k3

Halo method 27k2 26k2 “) 28+3 b, 30&3 l9*2

5.4* 1.2 5.6* 1.5 S.O+ 2.6

(E, > 2.4 MeV) (NaI) 25+4

erei ? 82k4

20+2 56-1-3 8-&2 25+3 23k3 “) 22k3 ‘)

’ See text for definition of methods used. Errors quoted include an absolute efficiency uncertainty. “) Experiment with only a Ge(Li) multiplicity filter coincidence requirement using a 2 mg/cm2 target. ‘) Same as “) but with a 1 mg/cm’ target. ‘) See subsect. 3.2 and fig. 5. d, From singles y-lines yield; errors include a 5 0/0relative efficiency uncertainty.

M. M. AIPonard et al. 1 ls6Nd

197

Fig. 5. Bottom: Energy spectrum of the 3 IP NaI detectors in coincidence with one NaI detector in the multiplicity filter and the 4n y-lines in the Ge(Li) detector. Top: Multiplicity spectrum of the 3 IP NaI: dots are all open channels and squares are 4n reaction channel only.

channel number) by analyzing the number of events observed in each channel for each p-fold coincidence of the multiplicity filter ‘). This analysis was made in two ways: (a) without any selection on the reaction channel, yielding a mean multiplicity for all the open channels; and (b) gating on the 4n y-lines in the Ge(Li) detector, which gives 8, values for the 4n channel only. In the latter case, because of the triple coincidence requirement, the statistics are quite poor for the high y-ray energies. Fig. 5 presents a comparison of the multiplicities for all the open reaction channels (solid dots) with the 4n channel (open squares) averaged over five channels above 1.2 MeV. These values result from the summation of the three IP NaI spectra. The multiplicity spectra are quite similar whether the 4n reaction channel only is selected, or ail the reaction channels are taken into account. This feature is mostly due to the dominance of the 4n reaction cross section over the other reactions, as can be seen in the last column of table 1 where the relative cross sections of the xn channels are quoted. However, at low energy (below I MeV) the inclusion of the 5n contribution, which is the other main component in this reaction, results in a smaller mean multiplicity than for the 4n channel alone. A prominent feature of these multiplicity spectra is the existence of a peak for which the maximum multiplicity is nearly 30 and is located at E,, cv 2 MeV which is the upper edge of the bump region of the collective E2 transitions.

M.

19x

M. Al&onard et al. / “‘Nd

In column 5 of table 1, we present the average of these multiplicities for the energy region EY > 2.4 MeV (beyond the collective bump). Because of the low statistics in this energy region, the errors are somewhat larger; however, these mean multiplicity values compare quite well with the average multiplicity in the 4n reaction channel. This is not surprising, since the statistical y-rays are thought to be a measure of the average y-ray multiplicity (per event) and, as already mentioned, the reaction is dominated by the 4n exit channel. 3.4. EFFECTIVE

MOMENTS

OF INERTIA

The moment of inertia I in a ground-state rotational band of a deformed nucleus is related to the y-transition energy (E;) which connects two states with respective spin values I and i- 2 by eq. (1). In fig. 6 we show the usual backbending type of plot of 2Y/h2 against (h~)~, the square of the rotational frequency (approximated by $!$). Results for the discrete transitions between the lower spin states up to I” - 14* [ref. to)] are shown in dots for 136Nd and in open circles for its isotone ‘34Ce. Both nuclei do show a sharp backbend around spin I = 10. Although several methods have been derived to calculate the moment of inertia for higher spin states, as shown in ref. 2), these methods have limited applicability to 136Nd because in this case the backbending region goes up to around 900 keV and the feeding region extends down to - 1.15 MeV and also because the angular distribution observed at low energy (fig. 3) indicates a component which is not stretched E2 (this could be due to a large dipole component of the continue transitions as already observed in other nuclei [see for example ref. ““)]). However an

140

sphere A=i36L_

rd

_

I 1.0

I 0.5 (?i w )* b4eV21

Fig. 6. Values of W/h2 for ‘36Nd extracted from discrete y-lines (dots) and from the edge of the bump; open circles are from the discrete y-lines of the isotone 13“Ce.

M. M. AlPonard et al. / “‘Nd

199

estimate of the effective moment of inertia can be obtained for the high-spin region at the extreme end of the collective bump. If the nucleus is rotational and there is no anomaly in this high-spin region, this energy corresponds to the highest angular momentum in the residual nucleus. Some previous multiplicity experiments, as described in ref. “), using “‘MO targets and 4oAr beam energies from 150 to 185 MeV, have shown that the limitation in angular momentum for the fusion of the “‘MO + 40Ar system occurs only at 185 MeV. Hence we assumed no angular momentum limitation in the 4n channel, besides we assumed that the maximum angular momentum brought into the compound system l&,. leads to the maximum angular momentum in the 4n channel. This last assumption is supported by the mean multiplicity value in the 3n channel (N 3 units above the 4n mean multiplicity) and the 3n cross section (small versus the 4n cross section). The l&, value is deduced from the bombarding energy at mid-target: in = 0.219R JKE;,~ 1max

(3)

where(Ln.

is c.m. bombarding energy, V is the Coulomb barrier, p the reduced mass of target (A,) and projectile (A& and R the sum of the nuclear radii: R = 1.16 (&+X4$+2). The maximum angular momentum in the 4n evaporation residue was taken to be 1max= 0.81,& to account for the angular momentum loss due to particle evaporation. This l,,, value corresponds to the highest spin states i.e. to the y-ray energy at the end of the collective bump. Then the effective moment of inertia extracted using relation (1) leads to 29/h’ = 104 + 14 MeV- ‘. Because of the above assumptions there is a 10-15 % uncertainty in the angular momentum estimate leading to the quoted uncertainty. This result is also shown in fig. 6, where it can be seen to ap preach the diffuse rigid-sphere value r2) (29/h2 = 105 MeV- ‘). The derivation of this result assumes a rotational collective motion; in this spin region this assump tion is supported by the analysis of the energy dependence of the multiplicity (sect. 4). The 136Nd behavior appears similar to that of ‘62Yb[ref. ‘)I and of ’ “Te[ref. “)I, both for the continuum y-ray spectrum with a well-pronounced collective bump, as with the similarity of the moment of inertia to the diffuse sphere estimate. The spectral bump indicates a rotational behavior, and hence a deformed nucleus at high spin; this agrees with calculations for Te [ref. ‘)I and Nd [ref. ‘“)I so one might expect that the effective moment of inertia at high spin would be larger than the diffuse rigid-sphere value. That does not appear to be true in either case. However, the difference is probably less than the errors in the experimental values.

4. Multiplicity dependence on y-ray energy We will consider the observed multiplicity dependence on y-ray energy first for the sum of all the reaction channels and then for the 4n reaction channel alone.

200

M. M. Al&ward

et al. 1 13’Nd

4.1. ALL REACTION CHANNELS

An interpretation of the dependence observed for multiplicity as a function of y-ray energy is given in ref. 4). We have used the same general description with some minor variations. The total cross section (0) is the sum of the evaporation residue cross section (a,3 and the fission and deep-inelastic cross section (ani); we neglect the transfer reaction cross section in this analysis. As already mentioned (sects. 3 and 4) at 170 MeV bombarding energy there is no angular momentum limitation in the production of the evaporation residues. This means that fission and deepinelastic processes are negligeable compared to fusion. Hence cr 2: rr,, and the maximum angular momentum Z&:,,brought into the system is directly related to the maximum spin (I,,,,,) in the residual nucleus. To account for particle evaporation and the fact that not all collisions lead to fusion, Z,,, is empirically taken to be Z,,, N O,S&,, with Z,$, deduced from the bombarding energy at mid-target according to eq. (3). In order to smooth the cut-off in the cross section distribution we used the following relations: (I = nA2 c (21+ l)T,_(Z) 1

with rl(Z) = [lfexp

(I-Z)/W’]-’

and W’ = 0.1 Z. The evaporation residue de-excitation was assumed to occur through several types of y-rays, as described in ref. ‘): (a) Statistical y-rays whose energies are independent of spin; four statistical y-rays were taken into account. (b) Collective rotational y-rays; states ranging from spin I, up to I,,,,, lead to rotational transitions with their energies given by E, = (h2/2Y)(4 Z-2). The moment of inertia was taken as*the rigid-sphere value in this analysis, in accordance with fig. 6. (c) Non-correlated y-rays, that is, transitions with no strong correlation between the spin and the transition energy; for each spin these transitions were distributed in a triangular shape leading to more transitions for the lowest energies, the height and base of this triangle were adjusted to the data to reproduce the down slope of the MY spectrum at low energy. These non-correlated y-rays occur between states ranging from spin Z, down to the ground state and compete between Z, and Z, with the rotational y-rays. The division between rotational and non-correlated transitions is taken to be a linearly increasing fraction between Zi and Z2. Since the transitions may not be pure stretched E2 transitions, a parameter (P) was introduced to give the proportion of dipoles. The resulting multiplicity then is +Z (I+ P). Results of this analysis for the system looMo + 40Ar at 170 MeV bombarding

hi. hf. Alhonard et al. / ‘36Nd

‘oaMP

10 -

r 0

201

+ 4Dctr

all channels

I 1.

t

I

I

2.

3.

4. Ex(McV)

Fig. 7. Multiplicity versus y-ray transition energy for all open channels. (a) Fit of the experimental data (dots) with a) I,,,,, = 52 and Z, = 30, Z, = 44, P = 0.1 for the non-correlated y-rays. (b) same as (a) but assuming only a rotational y-ray cascade. (c) same as (a) but with Z,, = 38.

energy (160 MeV at mid-target) are presented in fig. 7. The maximum angular momentum should be increased by one unit in order to fit the peak of the multiplicity distribution. The dashed curve (b) in fig. 7 is obtained assuming that all the nonstatistical transitions are rotational. From comparison with the data (dots), one can see that the position of the high-energy side of the multiplicity peak above 2 MeV is reproduced, which means that in this high-spin region, the effective moment of inertia is nearly the rigid-sphere value, in agreement with the dete~ination of the previous section. While the values calculated for the multiplicity in the 1 to 2.5 MeV energy agree with the experimental data, the values are too low both in the low energy (< 1 MeV) and high energy (> 3 MeV) part of the spectrum. The peak of the multiplici~ distribution reflects the region of rotational transitions confo~ing to the rigid-rotor relation (1). The high energy part (> 3 MeV) of the multiplicity spectrum yields the mean value of the multiplicity for all the open channels. In order to increase the multiplicity at low y-ray energies (and hence the mean value) the presence of non-correlated y-ray transitions must be introduced. This leads to a better fit (curve a of fig. 7) for f, = 30, I, = 44 and P = 0.1. Since in our hypothesis the rotational transitions occur only above spin I,, its value is determined from the start of the multiplicity bump. The value of Z2 is determined by the fitting to the non-correlated region of the spectrum. In order to check the consistency of our analysis, we have compared multiplicity data from ref. “) for the same system, but at 160 MeV bombarding energy (153 MeV at mid-target). Keeping the same set of parameters for the best fit at 170

202

M. M. AlPonard el al. I L36Nd

MeV, changing only I,,,,, to 38, we have calculated curve c) in fig. 7. This is in satisfactory agreement with the data (some minor adjustment of 9 would be necessary for a better Iit). The I, and Z2 values used in the calculations suggest that the Nd nuclei have appreciable numbers of non-correlated y-rays involved in their continuum cascades and that the competition of rotational y-transitions starts only at w 30h. This was expected from the angular distribution observed at low energy in 136Nd (fig. 3) which suggested a mixture of dipole and quadrupole transitions. This is partly supported by the calculations of Pomorski et al. ’ 3, of the potential energy surfaces in the full (/I, r) plane for various angular momenta in lz8* 134. 14’Nd nuclei. Whereas they calculate that the lighter Nd are prolate and well deformed up to spin 60h, 14’Nd starts from an ablate shape, becomes prolate at 20h up to 40h with a very small deformation, then the deformation increases and 14’Nd is triaxial for spins between 50 to 60A (the maximum spin values in our experiment). From these results as well as experimental data on the odd 135, ’ 37Nd Cref. ‘“)I, an intermediate situation is expected for our case where mainly ’ 35, ’ 36* ’ 37Nd nuclei were produced. An additional consideration is that the 5n and 3n cross sections leading to ’ 35*’ 37Nd are 70 “/ and 25 y0 as large as the 4n cross section; from them a nonnegligible contribu:on of dZ = I (Ml + E2) transitions is expected, at least below 1 MeV [ref. 14)]. For these transitions we have Z?, = (h2/2.Y92Z, instead of relation (I). 4.2. 4n CHANNEL

The multiplicity spectrum as a function of the y-transition energy for a specific reaction channel is expected to be different from the multiplicity spectrum due to all open channels, since only some partial Z-waves will contribute instead of the total range from 0 to ZmaX. Some modifications were made to the formalism used in subsect.. 4.1 to calculate this multiplicity spectrum. In order to account for only the 4n channel and its corresponding l-window, the Z-summation in the cr cross section has to be truncated. This l-window leads to a sum on spin values (I) between Zminand ZmaX;we used I,,, = 2 (R,(4n)4+ w) and Zmin= I,,,,,-4w where w equals the second moment of M, in table 1. The ofd cross section was set to zero since, for the 4n channel at this bombarding energy, fission and deep-inelastic events do not contribute to the measured M,. Also, the non-correlated y-transitions were not included in order to minimize the number of parameters. The calculated M, spectrum for Zmin= 34 and I,,,,, = 54 is presented in fig. Sa in a pure rotor assumption for ’ 36Nd. These Z-values correspond to the experimental average multiplicity observed in the 4n reaction channel (li;i, = 26). The shape of the M, spectrum is well reproduced but the M, values are too high. In order to have

M. M. Manard

2.

et al.1 136Nd

4.

Eg

203

(MeV)

Fig. 8. Multiplicity versus y-ray transition energy for thepn reaction channel. Dots are experimental data and the smooth curves are fits through these data: (a) for I,,,., = 54, Imin= 34; (b) for I,,, = 51, I,,,, = 31, (see text for more detail).

a better agreement with the experiment these f-values need to be decreased to I&, = 31 and I,., = 51 (tig. 8b), the width of the reaction channel being kept constant. This decrease of 3 units in I-values corresponds to a change of 1.5 unit in multiplicity which is comparable to the uncertainties quoted in table 1. Assuming a rigid-body (diffuse sphere) moment of inertia (29/h’ = 105 MeV-I), the yrast line ~lculation leads to E, = 2 MeV for MY = 30 at the peak, in agreement with experiment. The maximum value observed, n/r, N 30, corresponds to I,,, = 52, also in agreement with results from subsect. 4.1. The main feature of this M, spectrum in the 4n channel is the existence of a peak at ‘V 2 MeV. The curve slopes down on either side towards the mean value of the multiplicity observed in the 4n channel (Hy = 27). The y-ray energy where the peak has decreased to 8, = 27 gives an indication for the lower ‘limit of the feeding region, Ey N 1.2 MeV, and the experimen~l second moment of the m~tiplicity reproduces quite well the width of the l-window for the 4n reaction channel.

This study of the continuum y-ray spectrum from the de-excitation of Nd nuclei produced in the 40Ar induced reaction at 170 MeV has shown, as expected ‘), that the angular moments in these residual nuclei can be very high (I,,, N 52). The average multiplicity and the width of the multiplicity distribution in the 4n channel have been measured by two methods. We have deduced the effective moment of inertia of 136Nd at a spin N 5oh which is within 10 % of the rigid-body diffuse sphere estimate. Since 136Nd is near to a closed shell of nucleons, like “‘Te but unlike 162Yb, it might be expected with an increase in angular momentum, to

204

M. M. AIPonard et al. / lJ6Nd

behave more like “*Te. In fact, it shows a change-over to a deformed rotational behavior at spins above 30h similar to l1 8Te. Also the multiplicity versus E, curve for the 4n product (fig. 8) shows some structure which may be due to an anomaly in the moment of inertia at - 3%. However this structure is not strong enough to be concluding but it could be worthwhile to look at such structures in some more favorable nuclei. Although the study of the energy-dependent multiplicity of a given exit channel is quite time consuming, it appears worthwhile to pursue this kind of experiment in order to be able to look at the results of changing the bombarding energy and also the selected channel. In particular, one can obtain better insight into the nature of the collective and the non-collective (non-correlated) y-transitions observed, through angular distribution or polarization experiments. We are indebted to the operating crew of the 88” Cyclotron for providing the beam used in this study, and to Mr. Mon Lee and Mr. Don Lebeck for help with the electronics and the computer respectively. One of us (M.M.A.) would like to thank NATO for its fellowship.

References 1) J. 0. Newton, I. Y. Lee, R. S. Simon, M. M. Aleonard, Y. El Masri, F. S. Stephens and R. M. Diamond, Phys. Rev. Lett. 38 (1977) 810 2) R. S. Simon, M. V. Banaschik, R. M. Diamond, J. 0. Newton and F. S. Stephens, Nucl. Phys. A290 (1977) 253 3) R. S. Simon, R. M. Diamond, Y. El Masri, J. 0. Newton, P. Sawa and F. S. Stephens, Nucl. Phys. A313 (1979) 209 4) M. A. Deleplanque, I. Y. Lee, F. S. Stephens, R. M. Diamond and M. M. Aleonard, Phys. Rev. Lett. 40 (1978) 629 5) G. Anderson, S. E. Larson, G. Leander, P. MBller, S. G. Nilsson, I. Ragnarsson, S. Aberg, R. Bengtsson, J. Dudek, B. Nerlo-Pomorska, K. Pomorski and Z. Szymanski, Nucl. Phys. A268 (1976) 205 6) J. F. Mollenhauer, Phys. Rev. 127 (1962) 867 7) K. S. Krane and R. N. Steffen, Nucl. Data Tables 11 (1973) 351 8) J. R. Grover and J. Gillat, Phys. Rev. 157 (1967) 814 9) G. B. Hagemann, R. Broda, B. Herskind, M. Ishihara and S. Ogaza, Nucl. Phys. A245 (1975) 166 10) R. L. Bunting and J. J. Kraushaar, Nucl. Data Sheets 13 (1974) 191 11) J. 0. Newton, S. H. Die and G. D. Dracoulis, Phys. Rev. Lett. 40 (1978) 625 12) W. D. Myers, Nucl. Phys. A204 (1973) 465 13) K. Pomorski and B. Nerlo-Pomorska, Z. Phys. A2S3 (1977) 383 14) J. Gizon, A. Gizon, M. R. Maier, R. M. Diamond and F. S. Stephens, Nucl. Phys. A222 (1974) 557