A study of the 140Ce(d, p) and 142Nd(d, p) reactions at 19 MeV

Il.E.1:2.B

1

Nuclear Physics A238 (1975) 301-324; Not to be reproduced

by photoprint

@

North-Holland

Publishing

Co., Amsterdam

or microfilm without written permission from the publisher

A STUDY OF THE “‘Ce(d,

p) AND 14’Nd(d, p) REACTlONS AT 19 MeV

W. BOOTH, School of Physics,

S. WILSON

University

and

of Bradford,

Received

S. S. IPSON

Bradford

14 August

BD7 IDP, England

1974

The “%e(d,p) and 14’Nd(d, p) reactions have been studied at an incident deuteron energy of 19 MeV using the injector-tandem accelerator and the multichannel magnetic spectrograph of the University of Oxford. Deuteron optical-model parameters have been obtained from the analyses of elastic scattering experiments on enriched 140Ce and 142Nd targets. The parameters have been used to calculate theoretical (d, p) angular distributions on the basis of the DWBA. Orbital angular momentum transfers have been deduced and spectroscopic factors have been determined for almost all the levels observed up to an excitation energy of 3.5 MeV in 141Ce and 143Nd. The spectroscopic information is more complete than that derived from previous studies, and agrees satisfactorily with expected sum-rule limits. Unifiedmodel calculations have been made of odd-parity states and very good agreement with the experimental spectra of nuclei having N = 83 has been found.

Abstract:

E

NUCLEAR REACTIONS 14”Ce, deduced optical-model parameters.

14’Nd(d, d), E= 19 MeV; measured o(8); 140Ce, 142Nd(d, p), E = 19 MeV; measured

n(&,, 6). 141Ce, 143Nd deduced levels, 1, J, x,’ spectroscopic riched targets. Unified-model calculations.

factors,

Q, p.

En-

1. Introduction Most of the information currently available on the nuclei 141Ce and 143Nd, both of which have one neutron outside the N = 82 closed shell, has been obtained from high-resolution analyses of the (d, p) reaction lp3). However, previous investigators have used deuteron bombarding energies only slightly above the Coulomb barrier and although many states have been located in both nuclei, many of them, particularly in 141Ce, have not been assigned definite values of 1. Furthermore, previous estimates of summed spectroscopic factors for 1 = 1 and I = 3 transitions were well below the sum-rule limits while those for 1 = 5 transitions actually exceeded unity. This anomalous behaviour has recently been explained “) by the assignment of y’ to a lowlying state in each nucleus which had previously been assigned 8-, but the problem of generally low values of summed spectroscopic factors remains. Data on the nuclei 141Ce and 143Nd have also been obtained from a variety of other reactions. Indirect information is available from isobaric analogue resonances in elastic and inelastic proton scattering ‘, “). Polarized protons have been used in the latter method to make definite assignments of J” to a few low-lying states of both 301

302

W. BOOTH er

al.

nuclei 7-9). Data on hole states in i4’Ce and 133Nd have been obtained r”-i3) using pick-up reactions, and since it appears that the (d, p) reaction does not excite these hole states. the pick-up information supplements the (d, p) data. A number of levels in 143Nd which are not excited either by stripping or pick-up reactions have been reported by Christensen tt af. ‘) in their study of the 143Nd(d, d’) reaction. Additional information on the nuclear structure of 14’Ce has been obtained from studies of the p- decay 14) of 14iLa and the ““*Ce(n, y) reaction 15). It is noteworthy that the latter work has led Brown and Mlekodaj “) to assert that assignments based on a conventional DWBA analysis of the 14*Ce(d, p) reaction at 12 MeV are not consistent with those determined using the (11,y) reaction. There are a number of reasons why high-resoIution studies of the ‘“‘Ce and 142Nd(d, p) reactions at a high deuteron bombarding energy are desirable. A recent investigation of the 13’Ba(d, p) reaction 16) at Ed = 19 MeV has been successful in increasing the number of E-value assignments and in producing better agreement between summed spectroscopic factors and the sum-rule limits, compared with earlier measurements. This suggests that similar improvements in the spectroscopic information on the nucIei i4rCe and f43Nd might result from 14*Ce and i4’Nd(d, p) experiments carried out at 19 MeV. There is also the anomaly reported by Brown and Mlekodaj in the comparison of spin assignments determined from low-energy (d, p) experiments and the (n, r) reaction, which a high energy (d, p) experiment might help to resolve. It was therefore decided to make a study of the 14*Ce and ’ 42Nd(d, p) reactions at Ed = 19 MeV as part of a general study of the systematic features of nuclei having 83 neutrons. In a recent paper “) the even-parity states of N = 83 nuclei have been calculated using the unified model and rather good agreement was found for all the nuclei investigated. Although unified-model calculations of odd-parity states of these nuclei have been made by Vanden Berghe et al. “, ‘*), there is reason to believe that these calculations may be unreliable since the J$-’ single-particle state was either omitted, or included at too high an energy. In addition, experimental level schemes containing a few incorrect spin assignments were used to determine the values of the model parameters. For these reasons new unified-model calculations have been made for these nuclei and they are compared with the new experimental data on 14’Ce and 143Nd and with preliminary results of a low-resolution study of the ‘44Sm(d, p) reaction at 19 MeV in a later section of this paper.

2. Experimental

procedure

Since all the experiments reported in this paper were made with the help of the multichannel magnetic spectrograph at the University of Oxford and a detailed account of this instrument has appeared in an earlier publication r9), a brief description only will be presented here. Essentially it consists of 24 broad-range magnetic spectrographs of the Browne-Buechner type, arranged to have a common magnetic

“%e(d,

p)

303

circuit. The 24 channels provide scattering angles at 7.5 o intervals either in the angular range 7.5” to 172.5” (A position) or 3.75” to 168.75” (B position). The beam optics were arranged to define the incident beam on the target as a rectangle 1.5 mm wide and 0.5 mm high. An energy resolution of one part in 1200 was thereby achieved and this corresponded to deuteron and proton groups having approximately 17 keV FWHM at the energies involved. The reaction products were detected by means of Ilford L4 nuclear emulsions 50 pm thick which were mounted in the focal plane of each of the 24 channels. The i4’Ce and 142Nd(d, p) reactions were investigated at an incident deuteron energy of 19 MeV, using targets approximately 150 ,ug - cmp2 thick. Each target was prepared by vacuum evaporation on to a thin carbon backing using isotopically enriched materials in oxide form which were obtained from Oak Ridge National Laboratory. The cerium and neodymium targets were enriched to 99.7 % 14’Ce and the beam current 98.3 % 142Nd, respectively. In order to prevent target deterioration was monitored on a Faraday cup and was not allowed to exceed 0.15 PA. Polythene absorbers 0.75 mm thick were placed in front of the emulsions to eliminate deuteron and triton tracks and to improve the quality of the proton tracks. The exposed zones of the plates were scanned in strips 0.24 mm wide, at intervals of 0.25 mm along the plate, by a group of scanners at the University of Bradford. Data from both the A and B sets of angles were obtained for the 14’Ce(d p) reaction but measurements were taken using the A set of angles only for the case of the ‘42Nd(d, p) reaction. Deuteron elastic scattering from 14’Ce and 14’Nd was studied at the same energy and under similar experimental conditions to the (d, p) reactions. The absorbers were removed from the high-energy half of the plates so that the elastic deuteron groups could be observed. Six separate exposures were taken for each nucleus with integrated beam currents ranging from 0.8 ,K to 2000 PC. The elastically scattered groups from these exposures were normalised to each other at several angles and full angular distributions with adequate statistics were thereby obtained for the angular range 15” 5 f3iab 5 172.5”. Absolute differential cross sections were determined by normalising the experimental results to the optical-model calculation which produced the best fit to the relative experimental cross sections. In the (d, d) experiments the absorbers were left over the low-energy half of the plates in order to record strongly excited proton groups from the (d, p) reactions, free from contaminaiion by deuteron tracks. The cross sections associated with these (d, p) transitions were calculated by comparing their intensities with those of the elastic groups. Further details of the technique used to obtain absolute differential cross sections may be found in sect. 3. 3. The results and analysis of the elastic scattering experiments The experimental angular distributions for the elastic scattering from 14’Ce and * 42Nd of 19 MeV deuterons are presented as the discrete points in fig. 1. The relative error on each point is a combination of scanning uncertainties (Z 4 %), errors arising

W. BOOTH

et al.

from Poisson statistics, and errors due to the normalization of data at the same scattering angle from different exposures. The results are presented as ratios to the Rutherford cross sections. For puvoses of comparison, deuteson elastic scattering distributions from 13%a and 144Sm at Ed = 19 MeV are also displayed in fig. 1, The former data are essentially those quoted in ref. I’)% except that the angular range of the measurements has recently been extended to include data at eIab = 15”, 22.5” and 30” in order to achieve consistency with the 14’Ce and 14Wd resulfs. The angular distributkn shown fur 144Sm represents the preliminary results nf an experiment identical to those outlined for 14*Ce and 14’Nde

‘+?e(d,

p)

305

Optical-model parameters were derived from each experimental elastic scattering distribution by determining the optical-model calculation which gave the best fit to the experimental data. The calculations were made using a version of the opticalmodel search program JIB 3 written for the ICL 1909 computer of the University of Bradford. A volume well of the Saxon-Woods form was used to describe the real nuclear potential and a derivative Saxon-Woods well was assumed for the imaginary potential. The Coulomb potential was taken to be that produced by a uniformly charged sphere of radius 1.3 A* fm and no spin-orbit potentials were included. The quantity x2/N, where N is the number of points in the experimental distribution, was used as a measure of the deviation between the experimental and calculated angular distributions. During each search, the depth I’, and diffuseness uR of the real well, and the depth V,, the radius r,A* and the diffuseness a, of the imaginary well were allowed to vary in order to achieve the minimum value of x2/N; the value of the radius r,A* of the real well was fixed throughout the search. Graphs displaying the variation as a function of rR of each minimised value of x2/N for deuterons elastically scattered by 13*Ba, 14’Ce, 142Nd and ‘44Sm targets are shown in fig. 2. Since the experimental arrangement could be used only for the measurement of relative cross sections, the experimental data were normalized to the theoretical cross sections predicted by the optical-model calculations, so that the search procedure in

REAL

Fig. 2. The variation

WELL

RADIUS(fm)

of x2/N and the normalization elastic deuteron scattering

factor with real well radius at Ed = 19 MeV.

parameter

ra for

306

W. BOOTH et ai.

fact determined a best fit to the shape of each experimental distribution. The normalization constants, which were used to convert the relative experimental cross sections into absoIute cross se&ions, were derived from the opting-modes calculations which corresponded to the lowest values of x2/N in fig, 2. A check on the accuracy of each of these normalization constants was obtained by comparing the theoretical and normalized experimental cross sections at f&, = 15” with the Rutherford cross section at this angle. since the Rutherford and opticalmode1 cross sections should be almost identical here. For the four N = 82 nuclei investigated the theoretical cross sections were indeed found to be within +2 % of the Rutherford values at Blab= 15”, but the normalized experimental cross sections were observed to be systematically 10 0/Ogreater than the Rutherford cross sections at this angle. It was therefore concluded that the uncertainties in the values of the normalization constants obtained were E 10 li’,.

Deuteran optical-model

parameters for N = 82 nuclei

Target

‘=Ba 140Ce 14*Nd 144Sm

6 (MeV) 94.04 102.75 102.98 101.31

I.20 1.10 1.10 1.10

0.564 0.845 0.817 0.886

If.24 13.736 12.440 14.676

1.339 1.345 1.367 1.343

0.819 0.778 0.813 0.782

2.0 1.6 1.2 0.8

The aptical-model parameter sets listed in tabk 1 correspond to values of r, close to the minima of x’/N in fig. 2. There are small differences in the values of the parameters of the imaginary well for 13*Ba compared with those quoted in ref. ’ “) and these are due to the inclusion of three extra data points in the present work. The opticalmodel distributions calculated with these parameters are shown as the full curves in fig. I, where the experimental data are normalized to them, The variation of the normalization constants as functions of rR are also shown in fig. 2 and it is evident that each varies slowly in the region near the radius at which x2/N minimises. Since a 10 % variation in each real-well radius on either side of the minimum causes an overall variation of less than 10% in the normalization constant, this supports the earlier estimate of 10 7: for the error in the absolute fd, d) cross sections. Some additional searches have been made in which optical-model calculations were fitted to experimental data restricted to the angular range 15” < Ojub< 100”. The theoretical parameters thus found did not differ significantly from those given by the full angular distribution and the normalisation constants remained the same within 5 %. From this observed lack of sensitivity to data from backward angles, it has been concluded that rhe omission of spin-orbit terms in the optimal-modes potential is justified and that the absolute cross sections are reliably estimated.

140CeCd,

p)

307

4. Results of the 14’Ce and 14*Nd(d, p) experiments The spectrum shown in fig. 3 may be regarded as typical of the spectra generally obtained. Major impurity groups resulting from the presence in the target of carbon and oxygen and minor groups resulting from the presence of small amounts of sodium. silicon and sulphur were easily identified and differentiated from ‘“‘Ce and 143Nd groups by their larger kinematic shift in energy with varying angle. In general the energy resolution observed in the 141Ce(d, p) and 14’Nd(d, p) reactions were 18 keV and 17 keV respectively, although slightly better resolution was found on certain channels of the spectrograph, in particular the one corresponding to elab = 37.5”. The experimetal data for the reactions 14’Ce(d, p) and ld3Nd(d, p) are summarised in tables 2 and 3 respectively. Detailed analyses have been carried out for all the observed levels below an excitation energy of 2.43 MeV in 141Ce and 2.81 MeV in 143Nd, but above these energies only the strongly excited levels have been reported. Excitation energies were derived using the calibration of the Oxford multichannel spectrograph determined by Jones ‘O) and the values quoted in tables 2 and 3 are expected to be accurate to within _t 10 keV. Apart from a notable discrepancy concerning the doublet at E,, z 1.36 MeV, which has already been discussed in detail in ref. 4), the excitation energies are in excellent agreement with those derived from previous studies. The experimental angular distribution of each level is displayed by the discrete points in figs. 4 and 5, and for purposes of illustration each distribution has been normalized to eight units on the vertical scale. The errors shown have been compounded from statistical errors, scanning errors (T 4 y{) and uncertainties arising from background subtraction. In some cases the errors have been increased because of difficulties in separating closely spaced groups. The peak cross section and the angle at which it was observed are listed for each level in columns 5 and 6 of tables 2 and 3. The absolute cross sections quoted in tables 2 and 3 are subject to four sources of error. Two of these are systematic error,,9’ the first is the 10 % uncertainty in the determination of the normalization constant from elastic deuteron scattering; the other is an error z 2 % in the comparison of the intensities of the strong proton groups from levels 0 and 1 observed in the 14’Ce and 142Nd (d, d) experiments, with the corresponding intensities observed in the (d, p) experiments. The latter error is comparatively small because measurements were made at several angles for each level. The remaining two are random errors representing the statistical error, which was never greater than 6 % for any peak count, apart from level 10 in table 2, and the 4 yi uncertainty in the scanning. When the four sources of error are compounded, it is seen that the errors on the peak cross sections generally range from 11 % to 13 o’,. Also shown in figs. 4 and 5 are DWBA curves calculated according to the prescription outlined in sect. 5 and these have been used to assign values of the angular momentum I transferred by the captured neutron to all but two of the observed transitions. Values of I are listed in column 3 of tables 2 and 3 and column 4 lists the spin and parity J”

1.353s) 1.363’)

3 4

0

0 0.662 1.137

__”

5 6

3 1 1

#9’

H$;-

1.02

5.49 4.48 2.76

30

22.5 15 7.5

Results of the present experiment & = 19MeV _........-_--~ J” 0 I ~,a, (mb * sr-‘) (d:;)

1 2

Level number

5.26 5.39

6.14 1.84 0.78

(2J+l)S

0 0.665 1.142

^- E,, (MeV)

1

f

3

2

7.12 1.68 0.76

(2J+l)S

Wiedner et al. *) Ed = 12MeV

Data on the structure of ‘41Ce

TABLE 2

Fig. 3, Typical spectrum for the 14*Ndcd, p> reaction.

I

Brown and M~ekodaj 3 Ed = 12 MeV

0 0.66205 1.1370 1.2431 1.35452 1.36868 “)

Auble z2)

:-. t-

-5-

J”

3.450

3.352

3.272

2.906 3.074

2.429

f? :I I,1 I

i: I

6 1 3 I

3’ *-, B.5- 7z 11 I- 8z ,‘i Iz ,%nf-, $&-, ;.-

not assigned *- p2 >‘2 i: +-,p$-, +I1 1 3

3 I

1.5

1.59

1.11

0.73 7.5

7.5

7.5

7.5

0.34 1.16

30

0.32

7.5

22.5

1.12

1.24

I5

7.5

0.26

1.51

22.5

7.5

7.5

30 15

22.5

3.15 0.05 10.12 0.32 0.08 I 0.26 0.26

0.27 ( 0.19 0.49 0.18 ( 0.52

0.40 I 0.29

0.61

(0.09)

0.71 0.38

2.17 0.98

1.42 3

1.80

2.170 2.190

1.995

1.807

not assigned not assigned

not assigned

not assigned

not observed 1.736 3 2.28

1.501

4, t

1,$

4, $

(W

F, H-

Q-9 f-

due to masking by impurity

2.440 2.5229 2.519 ‘)

2.406 2.423

2.1711 2.1740 2.1896 2.2074 2.2269 (2.3289)

(1.910) 1.9438 1.9940 2.03019 2.0492

1.8087

1.49702 1.6261 1.69331 1.73901 1.780

2.3363 2.4108 2.4256

2.331

2.188

1.993

1.811

“) These levels were incompletely resolved in most channels of the spectrograph. “) A level at 1.383 MeV appears in Nucl. Data Sheets but has been omitted for the reasons explained in ref. 4). “) This level was very weakly excited in the present experiment but its angular distribution could not be determined groups in the forward channels of the spectrograph.

20 21 22 23 24 25 26

2.271 2.335

14 I.5 16 17 18 19

2.416

2.177a) 2.193 “)

0.85

12 13

Q-, s-

2.123

11

3

(0.32)

(&-, t-)

1.989

(1)

0.29 1.30

#-, H-

s-

10

5 3

1.57

+I-

2.20

1.692 1.740

6 7

3

8 9

1.496

5

w

f 2 a s

W. BOOTH ef nl.

310

TABL Data on th Christense

Results of the present experiment Ed = 19 MeV

Level number

Ed =

(4 P)

(4 P) I

P

Gax (mb

. sr- I)

8mar (deg)

QJ+ 1)s

22.5 7.5 37.5 7.5 37.5

7.67 2.26 6.12 1.03 6.24

0 0.740 1.226 1.305 1.405

3 1 5 1 5

5.28 1.60 4.80 0.74 7.10

I

QJ+l)J

0

3

;E-

0.741 1.223 1.298 1.401

1

$-

6 1 5

$’ $I-

5.67 6.70 0.41 3.16 0.55

5

1.549

3

a-

1.39

22.5

1.60

1.555

3

1.02

6

1.737

5

f-

0.26

30

2.52

1.740

5

2.70

1.851

(3)

(1.24)

1.911

3

1.02

0 1 2 3 4

7 8 9

1.845

15

1.902

15

0.28 10.85 1.52

10

2.008

15

0.45

2.016

3

0.27

11 12

2.126 2.185

0.19 (0.65)

2.127 2.183

1 3

0.13 0.40

2.250

1

0.24

2.319 2.363

1 1

0.12 0.21

2.416

not assigned

13 14 15 16 11 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

3

%-,H-

0.44

0.44 0.64

15 22.5

0.93

7.5

0.57 0.88

7.5 15

I 0.27 0.18 1.03

0.72

7.5

0.22

2.462

0.27

7.5

2.496 2.530

0.33

7.5 7.5 15 15 15 37.5 22.5 15 7.5 7.5 7.5 7.5

1 4-9 $(3) (Q, P-)

2.252 2.326

1

&-,S-

2.363 “)) 2.428 2.419 B

: 1

:“:’

2.558 2.624 2.696

1-I 8-l

1.09 3 %-,;znot assigned 1 3-,Q-

2.807 3.112

61

t”‘s-

3.368 3.405 3.419

3 1 1

%--,S&-,S_ 4-9 %-

“) These levels were incompletely

0.65 0.13 0.24 0.28 0.16 0.35 0.73 1.05 0.63 0.49

0.23

0.08

10.07 0.11 0.35 0.59

2.459

not assigned

2.496 2.529 2.552

not assigned not assigned not assigned

0.08 3.31 0.09 0.45 0.26 0.27 0.20 0.19

resolved in most channels of the spectrograph.

140Ce(d, p)

31

3 structure OF 14%d ci a[. 1) 12 MeV

-.-

Wiedner et at. 2, Ed = 12 MeV (d, P)

(d, d’) J*

I

,*__ f2J"Sf~S

Gales et ai. 13) Ed = 12.6MeV Cd*t) __(__.P

Gelletly 23) -CLY) J”

__.0 0.740 1.226 1.305 1.405 1.432 1.506 I.555 1.607 1.740

J-, $?+ t-

1.801

g--q-

0 0.742 1.234 1.309 1.424

3 1 5 1 5

6.64 1.60 6.50 0.50 8.00

1.559

3

1.44

1.748

5

2.50

1.851

&-, t-

1.860

(f)

(0.40)

1.911 1.995 2.016 2.074 2.090 2.127 2.183

%-, s-

1.91s

3

I.50

I-. 5?+ ?+ it--YF-

2.018

2.250

$-. z-

0 0.737

;I

0 0.7420

;’

1.297

(Q-

1.3055

t-

1,545

g*

1.596

_2’

1.6086

1.761

&f

1.I744 1.7994 1.8528 1.9010

1.975

2.136

(g*)

(0.36)

2.0042

not assigned

2.1257

;p-. a-

2.3181

$-, +-

2.5345

if-, +I-

(3)

2.200

(p-)

Q-, $-

W. BOOTH et a[.

312

t -I’ 0

P‘t

5496 t-:3

‘1,

30

60

9c 10

30

60

90 0

30

60

SO

eCM Fig. 4. Angular distributions for the “%e(d, p)14’Ce reaction at Ed = 19 MeV. The solid lines are DWBA curves fitted to the experimental data.

of the states of 141Ce and 143Nd where they are known from previous work or where it is possible to make reasonable conjectures from shell-model considerations. In general spin assignments have not been attempted for 1 = 1 transitions. Since the ground states of both nuclei are known to have spin I- and their spectroscopic factors are close to unity, strong I = 3 transitions to excited states have been assumed to populate $- states but no definite assignments have been made for weak 1% 3 transitions. Shell-model arguments have been used to assign all the I = 5 transitions as transfers of h, neutrons. Likewise, al1 the I = 6 transitions have been regarded a transfers of i, neutrons. 5. The DWBA analysis The experimental data shown in figs. 4 and 5 were fitted by DWBA calculations made using the program DWWCK available on the IBM 360,095 computer of the

“Tk(d,

5

30

60

905

30

60

900

30 0

p)

63

9t

GM

Fig. 5. Angular distributions for the 14*Nd(d, p)‘43Nd reaction at Ed = 19 MeV. The solid lines am DWBA curves fitted to the experimental data.

Rutherford Laburatory. Essentially the calculations were very similar to those reported in ref. ‘“1 in that the parameters used to describe the bound-state neutron weli were r,, = 1.25 fm, a, = 0.65 fm and a depth twelve times greater than the Thomas value in the spin-orbit part of the potential. Non-lacal potentials, specified by the usual values of Brr = 0.85 fm and 0.54 fm for protons and deuterons respectively, were employed in the calculations. The deuteron parameters defining the opticalmodel potential were those listed in table I. There were two basic differences between the DWBA calculations reported here

314

W. BOOTH

et al.

and those described in detail in ref. i6 ). In the present work a local rather than a nonlocal potential has been preferred for the transferred neutron. Jeans et al. 19) have discussed the effect of including non-localities in the neutron potential and concluded that this is equivalent to using a local potential with an increased value of r,. The other difference concerned the values of the optical-model parameters in the proton channel. The parameters quoted in ref. 16), which were derived from a 13*Ba(p, p) experiment at E,, = 17 MeV, were employed except that the depth of the real well was reduced to account for the energy dependence found by Perey ‘l). The actual values used for the modified proton well depths were 48.5 MeV and 48.2 MeV for 14’Ce and 143Nd respectively. The solid curves in figs. 4 and 5 show the results of the DWBA calculations, and the spectroscopic strengths (2J+ 1)s obtained by comparing the experimental cross sections with the DWBA calculations are listed in column 7 in table 2 and table 3. The usual method of obtaining spectroscopic factors is to compare the peak experimental and theoretical cross sections. However, the theoretical fits to the experimental shapes of the lowest I = 1 distributions were of rather poor quality and it was therefore decided to normalize theory and experiment by making an unweighted leastsquares fit to the points in the angular range 7.5” 5 &, s 60”. This procedure was consistently adopted for all levels. For I = 1 and I = 3 transitions to levels of unknown final spin, the spectroscopic strengths listed in tables 2 and 3 are the average of those forj = Z&t. In order to account for the finite range of the internal deuteron potential calculated using the HulthCn wave function, the cross sections given by the program DWUCK were multiplied by a factor of 1.5 before comparing them with the experimental data. 6. Discussion of the results of the (d, p) experiments Considering first the nucleus 141Ce earlier high-resolution studies of the 14’Ce(d,p) reaction at Ed = 12 MeV have been made by Wiedner et al., and by Brown and Mlekodaj and the relevant experimental data from these sources are summarized in table 2. The level structure of 141Ce has recently been surveyed by Auble ‘“) and his adopted levels presented in Nuclear Data Sheets are included in table 2. This compilation comprises the (n, y) data of Gelletley et al., the y-decay scheme proposed by Talbert et al. from their study of the /I- decay of 141La, a summary of the pick-up information derived frcm the ‘42Ce(d, t) and 141Ce(p, d) reactions and the (d, p) reaction data of Wiedner et al. and Brown and Mlekodaj. On comparing the results of the present (d, p) experiment with the data of Wiedner et al. it can be seen that a number of important discrepancies exist. The disagreement concerning the energies and the spin assignments of the members of the 14 keV doublet at E,, x 1.36 MeV has been discussed in an earlier paper “). It is also surprising that Wiedner et al. did not observe the levels at E,, = 1.692 and 2.123 MeV and yet reported the existence of the level at E_ = 1.989 MeV which was very weakly

‘@‘Ce(d,

p)

315

excited in the present (d, p) experiment at 19 MeV. Finally, the spectroscopic factor quoted in ref. “) for the I = 3 transition to level 7 exceeds the value determined in the present study by a factor of 2.3, which contrasts with the reasonably good agreement observed for the other spectroscopic factors which Wiedner et al. have measured. Although Brown and Mlekodaj have not yet reported the complete analysis of their study of the 14’Ce(d 9p) reaction at Ed = 12 MeV and have not determined spectroscopic factors, their published data have been included in table 2 because of their assertion that serious anomalies are present when the DWBA is used to analyse this reaction. Their evidence is based on the fact that the six levels shown in table 2, which they observed through I = 3 (d, p) transitions and hence assigned J” = $- or 3-, were the same states that Gelletly et al. had assigned +- and $- from their observation of strongly excited primary y-ray transitions in the 14’Ce(n, y) reaction. Inspection of fig. 4 reveals that three of these transitions of interest (1.810, 2.335 and 2.429 MeV) could not be fitted by a single I-value in the present work and this suggests that doublets populated by I = 1 +I = 3 transitions exist. This explains the failure of Brown and Mlekodaj to obtain an adequate fit to the polarization data of Veeser et al. ‘) for the isobaric analogue state corresponding to the 1.811 MeV level. Furthermore, the angular distributions shown in fig. 4 for levels 13 and 17 are clearly seen to be fitted well by 1 = 1 transitions in the 14’Ce(d, p) reaction at Ed = 19 MeV and although no definite evidence is available on the Z-value of the transition to the 2.52 MeV level, which was partly obscured by impurities in the present experiment on the most forward channels of the spectrograph, there would appear to be few grounds for questioning the validity of the DWBA in this mass region. It is felt that most of the difficulties experienced in making Z-value assignments in the analysis of (d, p) reaction data at Ed = 12 MeV are caused by the bombarding energy being only slightly in excess of the Coulomb barrier. A comparison between the present results and the level scheme adopted by Auble generally shows good agreement. However, it appears from the present (d, p) data that the reaction does not excite the hole states observed using the (d, t) and (p, d) reactions and this is evidence in favour of closure of the N = 82 shell. It is interesting that the level adopted by Auble at Eex = 1.2431 MeV has only been observed by Talbert et cd in their study of the /?- decay of 141La; it is certainly not excited by the (n, y) reaction, by stripping reactions or by pick-up reactions. The evidence for the existence of this level is not entirely conclusive, since it consists of a tentative p- decay transition followed by a single weak y-ray transition. If it does exist it would be difficult to account for it on any simple model of 141Ce. Levels 6, 14 and 15 which have been excited in the present experiment but were not excited in previous (d, p) experiments appear to correspond to levels adopted by Auble. The level rather strongly excited in the present (d, p) experiment at E,, = 2.123 MeV and several states with E,, > 3 MeV have not been previously reported. Turning now to the level structure of the nucleus 143Nd, earlier high-resolution studies of the 143Nd(d, p) reaction at E,, = 12 MeV have been made by Wiedner et

316

W. BOOTH

et al.

al. and by Christensen et al. and their results are summarized in table 3. In general there is very good agreement between these results and the present work for the lowlying levels, apart from the reassignment of J$’ to the state with E,, = 1.223 MeV, which has already been reported and discussed. However, the results of the present work suggests that an unresolved doublet exists at 1.845 MeV and this would explain previous differences in the I-value assignments made to this level. Other unresolved doublets are suggested by the present work at E,, = 2.252 and 2.462 MeV where Christensen et al. report single levels. The only other disagreement between the 19 MeV data and earlier results concerns the assignment of 1 = 3 in the present work to the level at E,, = 2.363 MeV, compared with the assignment of 1 = 1 by Christensen et al. As in the case of 141Ce, the hole states in 143Nd which have baen observed in the 144Nd(d, t) reaction are not excited in the present (d, p) experiment. In his study of the ‘42Nd(n, 7) reaction, Gelletly has observed strong y-ray transitions from the neutron capture state to some of these hole states and this contrasts sharply with the absence of corresponding transitions in the 14’Ce(n, 7) reaction. This and many other interesting differences between the (n, 7) data for 14’Ce and 143Nd have been discussed in some detail by Gelletly 23). In summary it appears that independent investigations of the structure of 143Nd using a wide variety of reactions are generally consistent with each other, and hence that the level scheme of this nucleus is well established below E,, = 2 MeV. 7. Systematics of N = 83 nuclei observed through (d, p) reactions One of the primary aims at the outset of the present study of N = 83 nuclei using the (d, p) reaction at Ed = 19 MeV was the investigation of the systematic features of the levels which are excited by this reaction. Previous authors ““) have extrapolated the level schemes of 13’Ba, 14’Ce, 143Nd and 145Sm to predict excitation energies and other properties of low-lying levels in ’ 3‘Xe and 14 ‘Gd, about which very little is currently known. Although this procedure will not be carried out here it is of some interest to tabulate the chief features of the levels excited by the (d, p) reaction in the light of the new information on ’ 41Ce and ’ 43Nd reported in sect. 6 and this has been done in table 4. The data on 13’Ba and ‘45Sm included in table 4 have also been obtained from (d, p) experiments carried out by the present authors. The results for 145Sm are preliminary values derived from a low-resolution experiment on a target containing 144Sm enriched to 85.6 %. A high-resolution (d, p) experiment using a “44Sm target with a much higher enrichment is planned and it is hoped that a detailed account of the results will be published later. The information on 13’Ba is essentially that reported in ref. 16) but it should be noted that the spectroscopic factors listed here differ by approximately 15 % from the values previously quoted. This is due partly to the additional measurements which have been made on the 13*Ba(d, d) reaction (see sect. 3) and partly to the use of a local potential for the bound neutron in the present work (see sect. 5).

140Ce(d, p)

317

TABLE 4 Systematic features of the low-lying states of N = 83 nuclei ‘j9Ba

0

0

0

0

6.24

6.14

7.67

6.82

f

E. WeV) GJ+ 1W

0.634 I .63

0.662 1.84

0.741 2.26

0.894 2.13

i

EC, fMW t2Jfll.S

I.088 0.10

1.137 0.78

1.298 1.03

1.620 1.26

1

E, (MeV) (2Jfl)S

1.284 5.19

1.353 5.26

1.401 6.24

1.430 6.41

&. (MeV)

1.540 6.46

1.363 5.39

1.223 6.12

I.099 6.44

E.,

(MeV) w+1>s

1.420 1.50

1.496 1.42

1.549 1.60

1.676 1.25

E,, WeW

1.626 1.81

1.692 2.17

1.737 2.52

1.796 3.19

EC. WW

1.684 0.72

1.740 0.98

1.845 0.85

1.875 0.71

E,, (MeW

1.699 0.88

1.810 0.7 I

I.902 1.52

2.006 1.56

3-

(2J+ 1)s

i

I

s- “1 “1

“?Sm

-5, (MeV) (2Jfl)S z

b-

lQ3Nd

(2J41)S (~+l)S

I

t2J+lP

“) These assignments were based on the predictions of the unified-model calculations.

The most striking feature of this table is the smooth change in the properties of the low-lying levels from nucleus to nucleus. In generai, the excitation energies of the odd-parity states increase with increasing mass while the energy of the 9’ state decreases. This behaviour is clearly connected with the variation in the excitation energies of the lowest-lying 2+ and 3- levels of the respective N = 82 nuclei. The observed reguIarity in the properties of the levels in table suggests that the excitation energies and spectroscopic factors of the corresponding levels of 13’xe and 14’Gd could be estimated with a fair degree of certainty by extrapolation of the data in this table. The level schemes predicted by this procedure would differ substantially from those quoted by Newman et al. In fact, the present data suggest that the first excited state of 14’Gd may well have 1” = 9’. Summed spectroscopic strengths for 141Ce and 143Nd have been calculated from the data shown in tables 2 and 3. The values thus obtained are listed in table 5. In view of the fact that cross sections calculated using the DWBA are usually assumed to be uncertain by 420 % it can be seen that excellent agreement with theoretical sum-rule limits exists for 1 = 1, 3 and 5 transitions in the 14’Nd(d, p) reaction. For i41Ce , however 3the experimental values are systematicahy lower by about 20 % than the sum-rule limits, which is a little surprising since both (d, p) experiments were carried out under practically identical conditions. Experimental (d, p) cross sections

318

W. BOOTH et al. TABLE5 strengths for 141Ce and ‘43Nd

Summed spectroscopic I

3

1

(ZJ+l)S for 141Ce (2J+ 1)s for 143Nd Theoretical sum-rule limit

5.03 6.02 6

6

5

11.35 15.15 14

1.43 8.76 10

8.54 9.43 14

are expected to decrease as the atomic number of the target increases for constant deuteron bombarding energy but inspection of the absolute cross sections listed in tables 2 and 3 shows that those for 143Nd are generally comparable with those for 14’Ce. This suggests that the experimental cross sections for 14rCe may have been underestimated while those for 143Nd may have been overestimated. Since the errors on the cross sections have been estimated to be + 10 % for both nuclei the discrepancy in summed spectroscopic factors is not serious. It does however imply that cross sections cannot be measured to an accuracy much better than 10 % by normalizing relative elastic cross sections to the cross sections calculated using the optical model. Centroid energies have also been calculated for the valence neutron orbits in ’ 41Ce and ’ 43Nd but since these are important parameters in the unified-model calculations described in the next section, their values are tabulated in that section. 8. Description, results and discussion of the unifi~-model calculations In the present work, odd-parity states of the nuclei 13g13a,141Ce, 143Nd and 14%rn have been computed using the unified model. As in the earlier calculations “) of evenparity states of these nuclei made by the present authors the chief objective has been to make a realistic test of the application of the unified model to N = 83 nuclei. TO this end, the values of all the parameters of the model except one have been taken from experimental data, in contrast to the calculations made by Vanden Berghe et al. I’* ‘*), in which the values of all the parameters were varied to obtain a best fit to the low lying levels in these nuclei. TABLE Values of the parameters used i kuz

3%

(MeV)

13sBa “‘Ce lh3Nd ‘45Sm

0.061 0.076 0.068 0.062

1.43 1.59 1.57 1.65

ho

(MeV) 0.084 0.107 0.104 0.102

2.88 2.46 2.08 1.81

Ef+

(Me\ 0 0 0 0

14”Ce(d, p)

319

The essential formulae of the unified model have been described in many previous publications * 5-“‘) and so a brief account only of the theoretical prescription will be given here. The first-order approximation for the interaction between the odd neutron and the vibrational core has been used and both quadrupole and octupole vibrations have been included. In order to limit the dimensions of the matrices diagonalized during the computations, only core states up to and including three quadrupole phonons and up to and including two octupole phonons have been employed. This core space includes all states below an excitation energy of at least 5 MeV for all four nuclei. In the calculations the values of the quadrupole and octupole phonon energies ho2 and hw, , respectively, were taken from the experimental spectra of the relevant N = 82 nuclei and are listed in table 6. The core states were allowed to interact with a neutron in the 3p+, 3p+, 2fi, 2f%, Ih,, li, or 2g, orbit. The unperturbed energies EIj of these states relative to the 2ft orbit are listed in table 6. The values of _E,%were chosen to fit the y’ states of the N = 83 nuclei as previously reported. The 2g, orbit was included in the present calculations to ensure consistency with the calculations of the even-parity states, but its inclusion had little effect on the calculated spectra. For the neutron orbits having odd parity, the values of Eli were chosen to be the experimental centroid energies derived from the (d, p) experiments at Ed = 19 MeV. Unfortunately the majority of the experimental levels in the N = 83 nuclei of interest have not been assigned a unique spin and so the following prescription was employed to determine the centroid energies. The centre-of-gravity energies for I = 1, 3 and 5 (d, p) transitions in 143Nd were first calculated in the normal manner using the experimental values of (2J+ 1)s. In order to obtain from these values the centroid energies of states with i = I+$ and j = Z-4 an estimate of the strength VS.,. of the spin-orbit interaction VS.,. 1. s was required. It was decided to calculate a value for VS.,. by considering the +- and 3states, since the ground state has J” = 3- and is known to exhaust most of the fS spectroscopic strength. Preliminary calculations suggested that the majority of the remaining fS strength was contained in the level having Eex = 1.845 MeV and so all the other I = 3 (d, p) transitions were assumed to populate $- states. In this way a value of V,,,, was deduced and this was then used to calculate the centroid energies

the unified-model calculations

Ehs

(MW 1.17 1.21 1.31 1.37

E

(MZ) 1.00 1.12 1.28 1.16

E (M3) 1.80 1.94 2.10 1.97

Ef+

(M-W 1.69 1.78 1.90 1.86

E. (Mi:) 1.6 1.6 1.6 1.5

E (&) 5.0 5.0 5.0 5.0

W. BOOTH et al.

320

of the +- and $- states in 143Nd . The single-particle energy of the h, orbit was taken to be the centroid energy of the observed 1 = 5 (d, p) transitions. The energies of the valence neutron orbits in the nuclei 13’Ba, r4rCe and ‘45Sm were obtained using the same procedure. Also shown in table 6 are the values used in the calculations of the deformation parameters J5/3, and J?fl, which were derived from (a, a’) reaction data 28-30). In the absence of experimental data, values of pz and p3 for 142Nd were obtained by Me’ V2.t3-

1.c I-

%--163....

--.~;-226.-

q--1.84----__%;_2.12_

%---2.20

14”CE

13gBA c)-

7;-_6.2& exp

a)

&--6&~~ theoryb)

. . . . -&---2~0~

_&_-7.04

-

theory?

?;---6.14

. . . . “;-6.55..

__.?;___7.04

theoryb)

exP)

theory?

Me 2.

1.

%-

133ND 7;--7.67 . .._?-;___.6.67m~ exP)

theoryb)

2.13.

“‘%;-2.34

----

-3l-

1.16

?;_

7.20

‘45SM T;-7.04

theory?

_

?z--6.62 expa)

. . . . _&.--

6.77. .

theoryb)

theory@)

Fig. 6. Comparison of experimental data with results of unified-model calculations for low-lying states of N = 83 nuclei; “) present experimental work at Ed = 19 MeV; b, present unified-model calculations; ‘) ref. I’); d, ref. I*).

140Ce(d,

p)

321

interpolation from the 14’Ce and ‘44Sm values. The only other parameter k appearing in the unified-model formalism was fixed at 50 MeV. These values of j2, p3 and k are exactly the same as those used in the earlier calculations of even-parity states described in ref. “). The results of the unified-model calculations are compared with the (d, p) data at 19 MeV and with the results of the calculations made by Vanden Berghe et al. in fig. 6. The experimental and theoretical level schemes have been reproduced up to an excitation energy of about 2.1 MeV only, because above this energy many more states have been observed than the calculations predict. This discrepancy is due to the presence of Of, 4+ and 6+ states at an excitation energy of about 2 MeV in the experimental spectra of the relevant N = 82 cores which are not properly accounted for by the unified model. Inspection of fig. 6 reveals that the present calculations predict possible theoretical counterparts for almost all the experimentally observed levels below E,* = 2 MeV in all four nuclei. In fact, the only state in this energy range which is not reproduced is a level observed through an I = 1 (d, p) transition with (25+ 1) Sz 0.2 and E,, z 1.8 MeV in all four nuclei. This discrepancy is not serious since it occurs at an excitation energy near which the calculations are expected to start to fail. The experimental level which the calculations are least successful in reproducing is the lowest-lying +level in each nucleus. Although the spectroscopic strength of this level is accurately predicted in each case, the excitation energy is consistently calculated to be too high by approximately 300 keV. The remaining eight states which have been excited by the (d, p) reaction below an excitation energy of 2 MeV in all four nuclei are extremely well reproduced, with energy discrepancies usually less than 150 keV and with many of the spectroscopic factors reproduced within the experimental errors. The calculaby the configuration tions also predict a low-lying A;-- state essentially dominated formed by coupling the f+ neutron to the quadrupole state of the core in all four nuclei. The (d, p) reaction does not appear to populate this state but a likely experimental candidate exists in 143Nd in that a negative-parity state strongly excited in the ‘43Nd(d, d’) reaction has been reported by Christensen et al. ‘) at an excitation energy of 1.432 MeV. Although the agreement between the experimental and calculated level schemes is satisfactory for all four nuclei it is noticeable that the agreement improves with increasing atomic number and is exceptionally good for the nucleus ‘45Sm. Considering the fact that no attempt has been made to vary the values of the model parameters to fit the individual experimental levels, the general level of agreement is remarkable. In the unified-model calculations of Vanden Berghe et al. shown in fig. 6 all the model parameters were varied to achieve a best fit to the level schemes which existed before the present experimental data became available. For the nuclei ‘39Ba and ’ 41Ce the two theoretical level schemes are not markedly different, although Vanden Berghe et al. have reproduced the energy of the lowest-lying +- states better than in the present work but at the expense of poorer agreement concerning the spectroscopic

W. BOOTH et a[.

322

factors. The assignment of -li”_’ rather than 4- to the second excited states of the nuclei 143Nd and r4’Srn by the present authors has resulted in significant differences between the results of the two sets of calculations. Since the -$$’ state is very low in excitation energy in these nuclei it is not surprising that the calculations of Vanden Berghe et al. result in a poorer agreement with experiment than the present calculations. Since some experimental data exist on the static moments of the ground states of 14iCe and 143Nd values of Q, the electric qua~upole moment and p, the magnetic dipole moment have been computed for the ground state of each N = 83 nucleus using the previously calculated wave functions. In these computations the same formulae as those quoted in ref. “‘) have been used except that the second-order term and the correction to the orbital angular momentum have been omitted. The values of the gyromagnetic ratios employed in calculating p were gr = 0, gs = - 1.91 and gR = Z/A and an effective neutron charge e,, = e was assumed in order to calculate Q. The nuclear radius was taken to be 1.2 A* fm. These values are identical to those used by Vanden Berghe et al. “) in their calculations of electromagnetic properties of r3 ‘Xe, 139Ba, 14’Ce and 143Nd. The results of our calculations are compared with the corresponding experimental data in table 7. Calculated and experimental

TASLE 7 values of Q and p for ground states of hi = 83 nuclei hheo

(mm.) 139Ba 141Ce 143Nd 14%rn

-0.37 -0.43 -0.41 -0.38

-0.52 “)

“) This value is the average of the measurements b, Ref. 31).

-0.92 -0.92 -0.94 -0.96

PCXP

(n.m.)

10.9 b> -1.08 b,

reported in refs. 3**32).

It is evident that good agreement between theory and experiment has been obtained for the magnetic dipole moments but that the calculated value of Q for 143Nd is about 20 % lower than the experimental value. However, the values of & used in the present work were extracted from inelastic scattering data and they are approximately 30 % smaller than the corresponding values deduced from y-decay data. Therefore this discrepancy could be removed by using the larger values of & but in order to preserve the agreement between the calculated and experimental level schemes this would then necessitate reducing the value of k used in the calculations from 50 to 33 MeV. Alternatively, the calculated values of Q in table 7 could be increased by increasing the effective charge parameter. Insufficient information is currently available on the electromagnetic properties of N = 83 nuclei to fix unambiguously the values of the parameters used in the unified-model calculations.

“We(d,

p)

323

9. Conclusions Many of the original

aims of this study have been achieved.

Compared

with earlier

work on the 140Ce(d, p) reaction, a few new states have been found and many new I-value assignments have been made to a number of levels below E,, = 2.2 MeV. The 140Ce(d, p) experiment carried out at Ed = 19 MeV has also resolved the anomaly which previously existed regarding assignments of J” made using the (d, p) and (n, y) reactions and no discrepancies now remain. The results of the i4’Nd(d, p) experiment show excellent agreement with data obtained by previous workers using lower deuteron bombarding energies. In both reactions a number of new levels have been detected and assigned values of I above an excitation energy of 2.5 MeV. The summed spectroscopic strengths for 1 = I,3 and 5 (d, p) t ransitions which have been calculated in the present work are significantly larger than those obtained in earlier (d, p) reaction studies and now agree well with theoretical sum-rule limits. From the similarity which is known to exist between the experimental spectra of 14’Ce and 14’Nd it is expected that there should be a close correspondence between the number of low-lying levels found in 14iCe and 143Nd. This has indeed been found to be the case in the present work, due to the detection of several new levels, some of them members of closely spaced doublets, in the nucleus 141Ce. Smooth variations in the properties of the low-lying levels of the N = 83 nuclei investigated through the (d, p) reaction are evident in the experimental data at Ed = 19 MeV. In view of this regular behaviour there is a strong possibility that the level schemes of the neighbouring isotones i3 7Xe and 14’Gd could be predicted with a fair degree of certainty. Unified-model calculations have been made of the odd-parity states of 139Ba, i41Ce, 143Nd and r4%m and they have been very successful in reproducing the (d, p) data at Ed = 19 MeV. In the calculations the most recent experimental values of the deformation parameters and the strength of the particle-core interaction were used and the only parameter adjusted to optimize the agreement with experiment was the i, single-particle energy. The fact that the agreement between the theoretical and experimental level schemes improves with increasing 2 suggests that the lowest-lying 2+ states of i4’Nd and 144Sm are closer approximations to the pure quadrupole states than the corresponding states in 13*Ba and 14’Ce. Whilst good agreement has also been observed between the calculated and experimental static moments of the 141Ce and 143Nd ground states it is clear that a complete test of the unified-model wave functions cannot be made until accurately measured lifetimes become available for a number of the excited states of N = 83 nuclei. Finally, it would be extremely interesting to make shell-model calculations of the N = 83 nuclei to see if a level of agreement with experiment comparable to that already produced by the unified-model calculations could be obtained. The authors would like to thank Mrs. A. Long, Mrs. J. Lees and Mrs. N. Wade for their careful scanning of the nuclear emulsions and also Mr. T. L. Morgan for preparing the targets used in the experimental work. The cooperation of the accelerator

324

W. BOOTH er al.

staff at the Nuclear Physics Laboratory of the University of Oxford is gratefully acknowledged and the authors would also like to express their thanks to Prof. K. Allen for the provision of experimental facilities at Oxford. It is a pleasure to record our appreciation to Dr. W. Gelletly of the University of Manchester for permission to include the results of his study of the 14’Nd(n, 7) reaction prior to publication. Finally we would like to express our gratitude to the Science Research Council for its financial support for the work and for the use of the computer facilities at the Rutherford Laboratory. 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) 32)

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