Neutron inelastic scattering from some odd-mass nuclei in the energy range 2.0 to 4.5 MeV

Nuclear Physics A315 (1979) 143- 156; ~ ) North-Hoiland Publishino Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

NEUTRON INELASTIC SCATTERING FROM SOME ODD-MASS NUCLEI IN THE ENERGY RANGE 2.0 TO 4.5 MeV E. RAMSTROM

The Studsvik Science Research Laboratory, Studsvik, Fack, S-611 01 Nyk6ping 1, Sweden t

Received 22 June 1978 (Revised 18 September 1978) Abstract: Fast neutron inelastic scattering from nine odd-mass nuclei, i.e. 27A1, sIV, SSMn, Sgco, 63Cu, 65Cu ' 89y, 2OTpb and 2°9Bi, has been measured with time-of-flight techniques for incident neutrons in the energy range 2.0 to 4.5 MeV. Excitation functions for the population of the individual levels in the nuclei have been derived. The experimental data have been used to investigate the usefulness of the Hauser-Feshbach statistical model modified according to Moldauer in describing the scattering process. It was found that the inelastic scattering cross sections calculated with the Hauser-FeshbachMoldauer model in most cases describe the experimental data welt within 20 per cent, with the exception of a few levels in the heavier nuclei with collective excited states.

NUCLEAR REACTION A1, V, Mn, Co, Cu, Y, 2°Tpb, Bi(n,n'), E = 2.0-4.5 MeV; measured a(E; E,,). Natural targets.

I

I

I

1. Introduction Fast neutrons have proved to be a suitable tool for the investigation of the properties and structure of atomic nuclei. Thus a great number of experiments have been performed in which the interaction of fast neutrons with various elements has been investigated. These measurements have included the study of both elastic and nonelastic interactions between atomic nuclei and neutrons. However, despite the number of measurements already performed there are still gaps in the knowledge of the different processesl Thus there is for instance still a lack of a more homogeneous set of experimental neutron inelastic scattering cross sections in the energy range 2.0 to 4.5 MeV for odd-mass nuclei. Such data can form a good background for the proper understanding of the l:eaction mechanism and of the usefulness of various nuclear models in describing the scattering process. In order to fill this gap the inelastic scattering cross sections for 9 odd-mass nuclei, i.e. 27A1, 5IV, SSMn, 59C0, 63Cu, 65Cu ' 89y, 207pb and 2°9Bi, have been measured and the usefulness of the HauserFeshbach statistical model in describing the experimental results has been investit Previous address: Neutron Physics Laboratory, Atomic Energy Company, Studsvik, S-611 01 Nyk6ping, Sweden. 143

144

E. RAMSTROM

gated. No attempt has been made to compare the experimental data with the results from calculations with other theories such as the coupled-channel theory.

2. Experimental arrangements The measurements were performed by using a time-of-flight spectrometer in conj u n c t i o n with a 6 MV Van de Graaff accelerator. This machine has a klystron bunching system giving pulses of 1 MHz repetition rate and a full width at half maximum of about 1.5 ns [ref. 1)]. The mean ion current on the target under these circumstances is at maximum about 8/~A. However, in the present work the nickel entrance window of the gas target used for the production of fast monoenergetic neutrons by the 3H(p, n)aHe reaction limits the maximum allowable mean ion current on the target to 3/~A. Most of the measurements in the present work were performed with a 10.2 cm diameter x 5.1 cm plastic scintillator t in optical contact with a photomultiplier *t In order to improve the signal-to-background ratio in the measurements the plastic scintillator was exchanged for a 12.7 crn diameter x 5.1 cm liquid scintillator with pulse shape discrimination properties t,t and on which a photomultiplier * was mounted via a light guide with reflector paint on the surface. The detector was positioned in a shielding consisting of iron, lead and paraffin mixed with lithium carbonate which has been described in ref. 2). The detector and the shielding arrangement were placed on an arm movable on a horizontal circular track with the scatterer positioned on the axis of rotation. Flight paths of between 300 and 350 cm were used. The scattering samples of the investigated elements consisted of hollow cylinders placed 10.5 cm in front of the target and having a height of 5.0 cm, an outer diameter of 2.5 cm and an inner diameter of 0.95 cm. However, the corresponding dimensions of the yttrium sample were 3.0, 1.8 and 0.95 cm. The 'relative neutron flux hitting the scatterer from the target was determined by using a direction-sensitive fast neutron monitor described in ref. 3). The monitor was positioned at an angle of 72° relative to the charged particle beam and at a distance of 300 cm from the target. Further details of the experimental arrangement can be found in ref. 4).

3. Experimental procedure Neutron inelastic scattering from the elements studied was mostly observed at one scattering angle, i.e. 125° and the total inelastic scattering cross sections for the t N E 104. *t 56 DVP/03. t*t NE 213. R C A 8850.

NEUTRON INELASTIC SCATTERING

145

separate levels were calculated by the formula = 4n dtr(125°) dO

.

(1)

However, at 3.0 MeV incident neutron energy the differential inelastic cross sections were observed at several angles. This will be further discussed in sect. 7. All cross sections were determined relative to those of neutron scattering from hydrogen. For this purpose scattering from polythene was measured at 30° at each primary neutron energy before and after the inelastic scattering experiments, thus giving an opportunity to check the reproducibility of the measurements at the same time. The total cross sections for the H(n, n)H reaction are, according to Horsley 5), known with an accuracy of I ~ and the scattering is isotropic in the c.m. system for energies less than about 9 MeV. The relative efficiency of the detector as a function of energy was determined by measuring neutron scattering from hydrogen at different angles and at different primary neutron energies using a polythene sample (height 3.0 cm, outer diameter 0.95 cm, inner diameter 0.62 cm). The detector energy bias was set at about 0.5 MeV. The low energy part of the efficiency curve has been measured by detecting the direct neutrons from the 3H(p, n)3He reaction at angles between 20° and 150° and at a proton energy of 3.0 MeV using the relative differential cross sections for this reaction given by Paulsen et al. 6). 4. Data analyses and corrections The resolution in the time-of-flight spectra was not sufficient to resolve neutrons scattered to individual levels in the residual nucleus for all elements and energies studied. However, a stripping procedure was used to permit the analysis of unresolved peaks. This procedure is based on the knowledge of the standard shape of a peak, which is a function of the corresponding neutron energy and also a weak function of the atomic mass number of the scattering element. Such a knowledge could be achieved from those spectra having well resolved peaks. However, in some cases even the stripping procedure failed to resolve the peaks so that cross sections for groups of levels have to be determined. The measurements have been performed with relatively large samples of the elements to be investigated. This is due to the comparatively low neutron flux obtainable in this type'of experiment and the small detection solid angle in combination with the relatively small inelastic neutron cross sections. The finite source-sample geometry makes it necessary to apply a number of corrections to the experimental data, viz. corrections for the anisotropic intensity distribution of the source neutrons as well as corrections for flux attenuation and neutron multiple scattering in the samples of the investigated elements and in the polythene sample. In order to show the approximate magnitudes of the various corrections those applied to the number of neutrons ob-

146

E. RAMSTROM TABLE 1

The sizes of the corrections applied to the observed number of neutrons scattered to thelfirst excited state in 5~V at an incident neutron energy of 3.0 MeV Correction for

Correction factor

the anisotropic intensity distribution of the source neutrons

1.02

flux attenuation in the vanadium sample

1.26

multiple scattering in the vanadium sample

0.93

flux attenuation and multiple scattering in the polythene sample

1.13

served as scattered to the first excited state in 5 ~V at a primary neutron energy of 3.0 MeV are given as an example in table 1. The corrections have been described in detail in ref. 4).

5. Experimental errors There are a number of different sources of errors contributing to the total uncertainty in the experimental inelastic cross sections. One of the main sources is the uncertainty in the determination of the areas of the peaks of the time-of-flight spectra. This uncertainty, which in most cases is less than 10 ~o, is dependent on the statistical errors in the number of counts, the insufficient resolution in the time-of-flight spectra as well as the continuous background obtained due to neutrons scattered in the room or from the materials of the gas cell as well as to the gammas produced by neutronreactions taking place anywhere in the room. Such a background is obtained even after the subtraction of the measured background especially when no (n, 7) discrimination was used. The relative efficiency of the neutron detector determined as described in sect. 3 is known within 3 ~ for energies above 1.0 MeV. Below this energy the increasing slope of the efficiency curve in combination with the experimental energy spread o f the source neutrons will introduce an increasing uncertainty in the determination of the detector efficiency. The uncertainties of the cross sections for neutron scattering from hydrogen, which are used as reference cross sections, are 1 ~o according to ref. 5). Furthermore the uncertainties in the total correction factors described in sect. 4 are less than 8 ~o. Thus taking into account all the different sources of errors a value between 10 and 15 ~ will be obtained for the total error in the inelastic cross section. 6. Theoretical calculations The interpretation o f the experimental data was made in terms of the Hauser and Feshbach statistical model 7) corrected according to Moldauer a). Thus the average

NEUTRON INELASTIC SCATTERING

147

compound nucleus cross section is given by

a.., = ~2 ..'Ey.K E T=,,'

(2)

where g. is a statistical weight factor and T~ and T., are the transmission coefficients of the initial and decay channels, respectively. The summation in the denominator is taken over all possible channels in which it is permitted for the compound nucleus to decay when the decay into channel m'can occur. K is a correction factor which takes into account the compound nucleus level width fluctuations and is given by

K = (~)/F"'F"~' (F,.}(F,~.}(F,) '

(3)

where F~ is the total width of the resonance/2. This correction factor has been calculated assuming the level widths, F, to be distributed according to a Z2 distribution with one degree of freedom (Porter-Thomas) 9). The correction factor K becomes unimportant for the calculated inelastic cross sections when the number of open channels is large. I

.

I

7

I

I

-+

112 +

?-.--+

o 0=-1.013 MeV 3/2

03 02 Ol o o

Q=-221

03

MeV 712

~ 02 o

(2=-2.73 MeV 5/2

@

01

=51 01 0

I 02

10

20

30 En MeV

40

50

Fig. 1. Excitation functions for inelastic scattering from AI. Data points indicate measured values referenced as follows: unfilled circles - this work, crosses - Towle et al. ' 3), filled circles - Chung e t al. t 4), filled triangles - Kinney et al. ~5) and unfilled triangles - Chien et al. t 6). The experimental data have been compared with those calculated with the Hauser-Feshbach (solid lines) and the Moldauer (dashed lines) formalisms.

148

E. R A M S T R O M

Using this theory the transmission coefficients have to be known. For the calculation of these a knowledge of the proper nuclear potential is necessary. In this work a local optical potential including a spin-orbit interaction term has been used. The sets of parameters used in the calculations are taken from an investigation at our laboratory on generalized optical model parameters based on experimental elastic scattering data ~0). The formulas given above are the results of Moldauer's more recent work s) where he shows that his original model picture x~' ~2) is inadequate as regards derivation. In this model ~'' ~2) he takes into account the level width fluctuations and the interference of the compound nucleus resonances by introducing the parameter Q,, which is allowed to vary between 0 and 1. In the more recent work a) Moldauer shows that apart from the resonance interference term there are terms which depend on resonance-resonance correlations of various kinds, terms which depend on channel-channel correlations and finally non-Hauser-Feshbach terms that remain important in the absence of all correlations. He also shows that all these different kinds of terms cancel to leave a remainder that is equal to the Hauser-Feshbach formula corrected only for level width fluctuations as described above. 7. Results and discussion

The experimental excitation functions representing the cross sections for fast neutron transitions to the individual levels of the investigated elements are shown in I

i

!

I

0.6 0.4

I

2

0.10

Q=-0930 MeV 3/2-

0 0,06

02 0

.• #

0.2 0.1

~

1

I

I

I

Q=-2.41 MeV 312-

I

I Q=-2545 MeV 112+

~~ 0.020"04

-,"11~

~

I

X

0 ~- 0.10

" ' [ - 2 6 9 9 MeV 15/2-

0.2

0.05

0.1 I

o

2-

0

I

I

I

0=-2790 MeV 1/20.2

0.04

0.1

0.02

0 0.2

I 1.0

(} ¢ o

0 2.0

3.0 En MeV

4.0

5.0

0,2

I 1.0

I 2.0

~ 3,0

I .'.0

5.0

En MeV

Fig. 2. E x c i t a t i o n f u n c t i o n s for inelastic s c a t t e r i n g f r o m V. D a t a p o i n t s indicate m e a s u r e d values referenced as follows: unfilled circles - this w o r k , crosses - H o l m q v i s t et al. 17), unfilled t r i a n g l e s T o w l e Ls), filled circles - B a r r o w s et al. ~9), filled triangles - P e r e y et al. 2o), unfilled s q u a r e s - G u e n t h e r et al. 2 ,) a n d filled s q u a r e s - S m i t h et al. 22). T h e n o t a t i o n s for the curves are the s a m e as in fig. 1.

NEUTRON I

i

l

55Mn{n,n,)

08

-~

06

~

INELASTIC SCATTERING r

I

02

02

01

f-2197 MeV 7/2" /-2 251 MeV 912Q=,~-2266 MeV 11/2" |-2281 MeV 3/2I.-2311 MeV 5/;'I

0

I

1

0=-0983 MeV 9/2-

02

R

55Mnln.n'J

03

04

02

01

01

0

0

1112-

01

I

0 01

I

0 01

0 02

I 10

I

~ 1

~

~ I

II 20

I

I

01

i

~

~

£ (-2725 MeV 712-. J-2751 MeV 9/2U=l-2 823 MeV 1112L-2 87/, MeV 3/2" ¢-2.954 MeV 512/-2.975 MeV 712" |-2990 MeV 9121-3.004 MeV 11120='(-3037 MeV 312" 1-3045 HeY 512-' |-3 050 MeV 7/2" 1-3,081 MeV 912iL-3.129 MeV 1112"

0 01

v

1 30 En MeV

0

I

512-

0 ~

02

~

01 ] 40

0 50

20

30

I f-2355 MeV 7/20='1-2 396 MeV 9/2t-2 425 MeV 1112-

0 0 0 ° Q="L-2 1-2564 MeV 5/23/2582 MeV

312-

I

1

T

04

0=-0126 MeV 712"

0 03

149

40

50

En MeV

Fig. 3. E x c i t a t i o n f u n c t i o n s f o r inelastic scattering f r o m M n . D a t a p o i n t s indicate m e a s u r e d v a l u e s referenced as f o l l o w s : unfilled circles - this w o r k a n d filled circles - B a r r o w s ¢t al. 19). T h e n o t a t i o n s for the c u r v e s are the s a m e as in fig. 1.

figs 1-8 together with data previously reported from other laboratories 1 3 - 3 3 ) . The cross-section values refer in all cases to 100 ~ abundance of the isotopes. As mentioned in sect. 3 the differential inelastic cross sections have been measured at several angles at 3.0 MeV incident neutron energy for most of the elements studied in the present work in order to investigate the shape of the angular distributions. For AI, angular distributions for the different levels have also been measured at some incident neutron energies above 3.0 MeV. The results from these measurements show that all the distributions except those for the 2.73 MeV level in 27A1 are isotropic or slightly anisotropic but symmetric around 90 °. The curves have been fitted by the method of least squares using Legendre polynomial expansions of the form dtr(0)/dt2 = ~tBtPt(cos O). The highest term necessary in these expansions was the P2 term. Furthermore, in all cases the PI coefficients were so small that the excitation cross sections obtained by angle-integration of the Legendre expansions differed only slightly (less than 5 %) from those calculated on the basis of the differential cross sections at 125 ° according to eq. (1), ~vhich is valid if da(O)/df2 = ~,~ = o, 2BiPt( c ° s O) since at 0 = 125 ° the P2(cos 0) term is zero. The inelastic excitation functions shown in figs. 1-8 have been obtained by applying the latter procedure. The only exception is the experimental excitation function for

150

E. R A M S T R O M I59Co(n n')

f/" ~f . .- _-

01

I I/

0 0,t

-

I ~

o:-11oo Mev 3/2-

T

I

~

I

Q=-1190 MeV 7/2-

03 02 01

I I

0

I

I

I 291 MeV 3/2-

01 b" J

0 06

/

I

,.~

1

l"

0,t

1

f-1434 NeV 1/2Q=4-1463 MeV 71282 NeV 512-

02 I

0

/

I

[

I

Q=-174,t MeV 7•2-

02 01 0 02

10

20

30

,tO

50

EF,MeV Fig. 4. E x c i t a t i o n f u n c t i o n s f o r inelastic scattering f r o m Co. Data p o i n t s indicate m e a s u r e d v a l u e s refere n c e d as f o l l o w s : unfilled circles - this w o r k a n d filled circles - G u e n t h e r et al. 23). T h e n o t a t i o n s f o r the c u r v e s are the s a m e as in fig. 1.

the 2.73 MeV level in A1, since as mentioned above the angular distributions for this level were found to be slightly anisotropic. The excitation functions show in general a smooth variation with the incident neutron energy except for the first two excited states in A1 for which some structure is observed at incident neutron energies of 2.77 and 3.78 M eV. For comparison the timeotLflight spectra for AI are plotted at three incident neutron energies, viz. 2.50, 2.77 and 3.01 MeV, in fig. 9. In figs. 1-8 the results of the neutron inelastic scattering measurements have been compared with those calculated with the Hauser-Feshbach (HF) formalism (solid lines) and the Moldauer (MHF) formalism (dashed lines). It is clear from the curves given in figs. 1-8 that the inelastic cross sections calculated with the MHF formalism are lower than those calculated with the HF formalism by at most 45 % at the lowest primary neutron energy. This figure decreases when the number of open decay channels for the compound nucleus increases with increasing primary neutron energy. Thus with for instance 17 open channels the cross sections calculated according to MHF are less than 20 % lower than those calculated with the HF formalism. In the present work the MHF calculations have been performed up to such an incident neutron energy that the MHF corrections are less than 10 %.

N E U T R O N INELASTIC S C A T T E R I N G

0.5

I

I

0.4. ~ 0.3 0.2 0.1 0 OJ.

I C u n l n . ) ' 6 =.

A~

a

0.3

151

I -

3C ",

0=-0.771 MeV 1/2-65(

0,2 ~ o.1

0.~0"6

~

6

3

(

0.2 0

0.8

0.6

0:-1.115 MeV 5/2- 65CL

OJ, 0.2 0 0.2

~ I 1.0

o 2.0

3.0 En MeV

,'..0

5.0

Fig. 5. Excitation functions for inelastic scattering f r o m Cu. D a t a points indicate measured values referenced as follows: unfilled c i r c l e s - this w o r k , unfilled squares - D a y 24), crosses - N i s h i m u r a et aL 25), unfilled triangles - S m i t h et al. 26), filled squares - G l a z k o v 27), filled circles - H o l m q v i s t et aL 2s) and filled triangles - Tucker et aL 29). The notations for the curves are the same as in fig. 1.

Comparisons between calculated and experimental excitation functions make it possible to determine spins and parities of the levels. Thus for levels for which these quantities are unknown or uncertain and for which experimental cross sections have been determined in the present work, calculations have been performed with several spin and parity assignments to these levels. The spin and parity values recommended in this work will then be the ones which give the best theoretical description of the experimental excitation functions, This procedure has been applied to the 1.19 MeV level.in Co and the 2.22 MeV level in Y. For the 1.190 MeV level in 59Co, calculations with three alternative values of I ~, i.e. ~-, ~- and ~-, have been performed, since all these spin assignments to this level are possible according to ref. 34). The change of the spin of this level will not affect the cross sections of the other levels to any extent. As seen in the figure, good agreement is obtained with I" = 2z - . The cross sections calculated with the MHF formalism for this level as well as those for the other levels calculated with the HF and the MHF formalisms and shown in the figure, are those obtained with this spin assignment to the 1.190 MeV level. For the 2.22 MeV level in sgy two values of/" have been suggested, viz. t + and ~+

152

E. R A M S T R O M 04 1MeV9/2" "

03 02 01

~

0 06 04 02

E

MeV312-

o%

MeV 5 / 2 "

04 02 J

0 03

~ I

I

1

Q=- 2.22 NeV 712 +

02 01 I

0 03

J

~v

712:

0=4- 2.57 MeV11/2 t-

262

MeV 9/2"

02 01 0 02

10

20

30

0

40

En MeV

Fig. 6. E x c i t a t i o n functions for inelastic s c a t t e r i n g from Y. D a t a p o i n t s i n d i c a t e m e a s u r e d values referenced as follows: unfilled circles - this w o r k , crosses S h a f r o t h et al. 30) a n d unfilled triangles T o w l e 31). The n o t a t i o n s for the c u r v e s are the s a m e as in fig. 1.

15

i

i

i

i

207pb(n.n') 0=-0570 MeV 5121.0

~

o5

N o 0:-089,4 MeV 3/2~

06 04 02 0

02

II 10

I

2.0

I

30 En MeV

I

40

50

Fig. 7. E x c i t a t i o n functions for inelastic s c a t t e r i n g f r o m 2°vpb. D a t a p o i n t s indicate m e a s u r e d values referenced as follows: unfilled circles this w o r k w i t h a Pb scatterer, unfilled triangles - this w o r k with a Pb r scatterer a n d crosses - C r a n b e r g et al. 32), The n o t a t i o n s for the c u r v e s are the s a m e as in fig. 1.

[ref. 35)]. As shown in the figure the best agreement between calculations and experiments is obtained with I ~ = ~+. Accordingly, this will be the spin assignment to this level suggested in the present work and the calculated cross section values given in the figure for the other levels are obtained with this spin and parity assignment.

NEUTRON 08 -~

060402 ~

0

I

M

II

06 04

INELASTIC SCATTERING _ 1

e

I ~

I

153

I

V

~

I

I I O=- 1509 MeV1312~

712-'

o

02 • -~ 1.0 08

f-2492 MeV 3/2" /-2.563 MeV 9/~'" J-2,562 MeV 7/2" ~=]-2.699 MeV 11/2"J-2.601 MeV 13/2"

0 03

I

I

"-2 741 eV 15/2~ 0=4;21822 eV 5/2I.-2 827 MeV 712--

~0

02 01

0

I

10

I 20

I I 30 Ep MeV

I 4.0

I 50

Fig. 8. Excitation functions for inelastic scattering f r o m Bi. D a t a points indicate measured values referenced as follows: unfilled circles - this work, crosses - Cranberg et al. 32) _ and unfilled triangles T a n a k a et al. 33). The notations for the curves are the same as in fig. 1.

The proper application of the HF formalism demands a knowledge of the energies, spins and parities of all levels in the nuclei excited at a certain incident neutron energy. However, for some elements only the energies and not the spins and parities are known for levels with higher excitation energies, and no excitation functions have been determined for these levels. Thus, to enable the performance of the theoretical calculations the spins and parities for these levels have to be estimated. This has been done by calculating the distribution of the values of spins and parities among the levels using a method derived by Eriksson 36). This method, which primarily was derived for the calculation of level densities, is based on the counting of excited shell model states. As a rule the calculated inelastic cross sections describe the experimental data well within 20 % for the lighter odd-mass nuclei investigated, i.e. 27A1, 5IV, 55Mn, 59Co and 63, 6 5 C u " Exceptions are the results of some groups of levels with unknown spins and parities. Since in these cases the numbers~of excited states with unknown spins and parities are relatively high and the excitation functions are only determined for groups of levels, the spins and parities of the individual levels cannot be determined unambigously in the present work. Thus no good descriptions of the experimental data can be expected since, as discussed above, the application of the HF formalism demands a knowledge of these quantities. It is further obvious that in those cases

154

E. R A M S T R O M !

i

i

i

!

i

i

Ai

1200

,o,

En=2.50 MeV~

~

0

~

~

9~

0:125 ° 1000

800

,y,4

600

400

200

0 1200

1000

At

>

g

En =2.77 MeV

I

I

0 =125°

~

800

II

II

O

o

o

I;,,4 t

G00

400

200

0

W

o

1200

AI

I

I

En :3.01MeV

~

oo

0:12S °

~u o

u O

1000

o

x 114

/

800

-

600

--o~j.

4OO2oo .~,

~'

)

0

~

540

L1

" ~ ' ~ °'°

560

580

600

620

640

66O CHANNEL NUMBER

680

70O

720

740

I

Fig. 9, Time-of-flight spectra of Al at incident neutron energies of 2.50, 2.77 and 3.01 MeV.

NEUTRON INELASTIC SCATTERING

155

where there are few open competing decay channels for the compound nucleus, the cross sections calculated with the MHF formalism give the best description of the experimental data as a rule. The calculated inelastic scattering cross sections for some of the levels in the heavier elements investigated with either the number of protons or the number of neutrons equal to a magic number, i.e. s9y, 207pb and 2°9Bi, differ by up to as much as a factor of 2 from the experimental results. In order to explain these discrepancies the nuclear structure of the different isotopes will be discussed. In general odd-mass nuclei can be looked upon as a single nucleon outside the even-even core. de-Shalit 37) has pointed out the possibility of describing some of the excited states of such nuclei in terms of the excitation of the even-even core. Then, if the excited states of the eveneven core are collective in nature, the corresponding excited states in the odd-even nuclei will be collective to the same extent. This type of collective excited states can be found in all the odd-mass nuclei mentioned above, for which there are disagreements between experimental and calculated inelastic cross sections. Thus certain features s9 of the structure of 39Y5o might according to ref. 30) result from coupling of the 39th p½ proton to excited states of the ss 3sSrso core, which have been shown to be collective in nature to some extent. For 209u: 83Ln1126 it has been proposed 3s) that the seven levels 2.492 MeV ~ +, 2.563 MeV ~ +, 2.582 MeV ~ +, 2.599 MeV ~ + , 2.601 MeV 13+ q, 2.626 MeV ~+ and 2.741 MeV ~ + can be considered to form an excited core multiplet resulting from the coupling of an h a proton to the 3- octupole excited state in 2°8pb, Finally, the 2.625 MeV ~2+ and 2.664 MeV 7+ levels in 2°Tpb are according to ref. 38) the results of the weak coupling of a 3p~ neutron to the 2.649 MeV 3vibrational state in 2 ° 6 p b . In both the Hauser-Feshbach and the Moldauer formalisms wave functions for single-particle nuclear states are used. However, it is clear that all the odd-mass isotopes discussed above have collective states in the investigated excitation energy region. Therefore, this could be a possible explanation of the discrepancies between calculated and experimental cross sections for some of the levels in these isotopes. References 1) P. Tykesson and T. Wiedling, Nucl. Instr. 77 (1970) 277 2) B. Holmqvist, Ark. Fys. 38 (1969) 403 3) B. Antolkovic, B. Holmqvist and T. Wiedling, Atomic Energy Company, Sweden, Report AE-144 (1964) 4) E. Alm~n-Ramstr6m, Atomic Energy Company, Sweden, Report AE-503 (1975) (Dissertation, University of Lurid) 5) A. Horsley, Nucl. Data 2A (1966) 243 6) A. Paulsen and H. Liskien, Nuclear data f6r reactors, Proc. conf. Paris, 17-21 Oct. 1966, 1AEA, Vienna, 1967, vol. 1, p. 217 7) W. Hauser and H. Feshbach, Phys. Rev. 87 (1952) 366 8) P. A. Moldauer, Phys. Rev. Cll (1975) 426 9) C. E. Porter and R. G. Thomas, Phys. Rev. 104 (1956) 483 10) B. Holmqvist and T. Wiedling, J. Nucl. Energy 27 (1973) 543

156 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38)

E. RAMSTROM P. A. Moldauer, Phys. Rev. 135 (1964) B642 P. A. Moldauer, Rev. Mod. Phys. 36 (1964) 1079 J. H. Towle and W. B. Gilboy, Nucl. Phys. 39 (1962) 300 K. C. Chung, D. E. Velkley, J. D. Brandenberger and M. T. McEllistrem, Nucl. Phys. A l l 5 (1968) 476 W. E. Kinney and F. G. Perey, Oak Ridge National Laboratory, Report ORNL-4516 (1970) J. P. Chien and A. B. Smith, Nucl. Sci. Eng. 26 (1966) 500 B. Holmqvist, S. G. Johansson, G. Lodin and T. Wiedling, Nucl. Phys. A146 (1970) 321 J. H. Towle, Nucl. Phys. All7 (1968) 657 A. W. Barrows, R. C. Lamb, D. Velkley and M. T. McEllistrem, Nucl. Phys. A107 (1968) 153 F. G. Perey and W. E. Kinney, Oak Ridge National Laboratory Report ORNL-4551 (1970) P. Guenther, D. Havel, R. Howerton, F. Mann, D. Smith, A. Smith and J. Whalen, Argonne National Laboratory Report AN L/N DM-24 (1977) A. B. Smith, J. F. Whalen and K. Takeuchi, Phys. Rev. CI (1970) 581 P. T. Guenther, P. A. Moldauer, A. B. Smith, D. L. Smith and J. F. Whalen, Argonne National Laboratory Report ANL/NDM-1 (1973) R. B. Day, Phys. Rev. 102 (1956) 767 K. Nishimura, K. Okano and S. Kikuchi, Nucl. Phys. 70 (1965) 421 A. B. Smith, C. A. Engelbrecht and D. Reitmann, Phys. Rev. 135 (1964) B76 N. P. Glazkov, Soviet Atomic Energy 15 (1964) 1173 B. Holmqvist and T. Wiedling, Ark,. Fys. 35 (1967) 71 A. B. Tucker, J. T. Wells and W. E. Meyerhof, Phys. Rev. 137 (1965) BI181 S. M. Shafroth, P. N. Trehan and D. M. Van Patter, Phys. Rev. 129 (1963) 704 J. H. Towle, Nucl. Phys. AI31 (1969) 561 L. Cranberg, T. A. Oliphant, J. Levin and C. D. Zafiratos, Phys. Rev. 159 (1967) 969 S. Tanaka, YI Tomita, K. ldeno and S. Kikuchi, Nucl. Phys. A!79 (1972) 513 Nucl. Data Sheets, B2 (1968) 5 P. S. Buchanan, S. C. Mathur, W. E. Tucker and 1. L. Morgan, Phys. Rev. 158 (1967) 1041 J. Eriksson, Private communication A. de-Shalit, Phys. Rev. 122 (1961) 1530 J. C. Hafele and R. Woods, Phys. Lett. 23 (1966) 579