- Email: [email protected]
On the spin assignment of neutron resonances in 149Sm using (n, α) reaction
I
2.G
I
Nuclear Physics A97 (1967) 187--192; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
O N T H E SPIN A S S I G N M E N T OF N E U T R O N R E S O N A N C E S IN 149Sm U S I N G (n, ~) R E A C T I O N M. D A K O W S K I , T. K R O G U L S K I , E. P I A S E C K I , H. P I E K A R Z a n d M. S O W I ~ S K I
Institute of Nuclear Research, Warsaw Received 13 J a n u a r y 1967 Abstract: M e a s u r e m e n t s o f t h e r m a l - n e u t r o n cross sections for the 149Sin(n, ~)t46Nd reaction have
been done using a 99 % enriched 149Sm target. Results are c o m p a r e d with theoretical values o f cross sections calculated on the basis o f the c o m p o u n d nucleus a n d statistical model. Experim e n t a l a n d calculated values are consistent only when a s s u m i n g that the spins o f the b o u n d state a n d the 0.0967 eV resonance in 149Sm+n are 3 a n d 4 , respectively. F o r such a spin sequence the 2200 m/see experimental n e u t r o n cross sections are: 4 6 . 0 ± 5 m b for l~gSm(n, ~) 14~Nd2+ a n d 8 . 5 ± 1 . 5 m b for 149Sm(n, ~)146Nd0+.
E
NUCLEAR
R E A C T I O N S x4SSm(n, c0, E = thermal; m e a s u r e d a(E~). 15°Sm resonances, deduced ~, J. Enriched target.
1. Introduction The (n, ~) reaction induced by thermal neutrons in 149Sm has been studied in several experiments ~-4). There are, however, big discrepancies between the results. It was our aim to measure the cross section for this reaction with a higher accuracy *. Comparison of the experimental data with theoretical predictions gave us spin values for low-energy 1 4 9 S m r e s o n a n c e s . The question of spin assignment of those resonances was recently discussed by several authors 5-s).
2. Experimental arrangement and results The samples of 1 4 9 S m enriched to 99 ~ were irradiated with a slow neutron beam from the E W A reactor. The energy spectra of the alpha particles from 1 4 9 S m ( n , y ) 146Nd reaction were obtained using a semiconductor spectrometer. A typical energy spectrum obtained from irradiation of a 149Sm target with slow and epi-cadmium neutrons is shown in fig. 1. The energy of the most energetic ~-line is 9154 keV. The experimental values of the "2200" m/sec cross section for ~49Sm (n, ~)t46Nd0÷ and 149Sm(n, c0146Nd2 + reactions were obtained by the use of the g-factor 9) for a Maxwellian-like neutron flux spectrum with a temperature lo) of 350 °. The spin and parity of the capture states are 3- or 4 - as the 1 4 9 S m ground state t T h e experimental part o f our work was already p e r f o r m e d when Beg and M a c F a r l a n e ' s 4) results b e c a m e available for us. 187
M. DAKOWSKI et al.
188
spin is ~. Both
11) the
b o u n d state of 1 4 9 S m + n a n d the positive resonance at 0.0967
eV c o n t r i b u t e to the cross section for the 149Sin(n, ~) reaction. C o n t r i b u t i o n s from the 0.87 eV and higher resonances are negligible. The observed alpha decay to the 0 + g r o u n d state of 146Nd proves that at least one
300
250
3
200
%..
15o
E Ioo
5~
tJsv~l"r"'6"'
v
,,,
~
8
g
.......
Energ~l (MeV) Fig. 1. Energy spectrum from the irradiation of a 1498m target with thermal neutrons. It was obtained by subtraction the spectrum with epi-cadmium neutrons from the spectrum with slow neutrons. TABLE 1 Experimental values of "2000" m/see cross sections for 149Sm(n,~)146Nd0+ and ]agSm(n, ~)146Nd2+ Spin combination (3,4)
]46Nd spin
Macfarlane
Cheifetz
Andreev
Macfarlane
et al. ])
et al. 2)
et al. 3)
et aL 4)
0+
22±10
5±1.5
7-5=3
2+
121±15
37±10
48±10
(3,3)
0~
or (4, 3)
2+
Present work 8.5~-1.5.
43.6_+0.6
46 ±5 4.3±0.7 46 ~5
of the resonances has spin 3 - . Thus we have examined three possible c o m b i n a t i o n s of spins - (3, 4), (3, 3) a n d (4, 3) of the negative a n d positive resonances, correspondingly. Calculated cross sections were o b t a i n e d in an analogous way to that used in paper l).
189
14OSm(n, :x)146Nd REACTION
The cross section for an e-transition to a definite level in the final nucleus is a/J(n, e) = os(CN) Z, F~s,l F~ where we can put o ' J ( C N ) = O'J,n ~ with a good accuracy. Here J is the spin of the capturing state, I is the spin of 146Nd. Besides, it was assumed, that F~ is the same for both resonances and is equal to F as F,,/F. l ~ 8" 10 . 3 and F~/F
~
10 -6.
We assume, that cross sections for ~ de-excitation of the compound nucleus is a product of two factors: one is the structural factor, which is responsible for the creation and appearing of the c~-particle on the surface of the nucleus and the second is the barrier transmission coefficient. As for the structural factor in an excited nucleus we do not know anything, and we assume, in accordance with the statistical model, that the structural factor is proportional to the average level spacing for the states near the capturing states of the same spin and parity. This assumption is justified provided that at this excitation energy the shell structure is destroyed. Thus, for the c~-particle emitted with definite orbital momentum DJ
-
r,,
where D is the average level spacing and T the transmission coefficients. For D, ~rn,7' and F.~ we used the values 6.0 eV, 40800+3000 b and 6 3 + 1 2 MeV, respectively
(refs. 9, i2,13)). The negative resonance component of the (n, 7) cross section for natural Sm has the magnitude 48/,rE eV ~ b according to H6hne's i l) measurements. Transmission coefficients were calculated in tile JWKB approximation assuming that the z-cluster does not decay in the barrier region, i.e. taking into account only the real part of the optical potential. The first calculations were performed with the Igo potential
{
U=--l100exp~--
r-- 1.17A~'t /"
O.57;
Thus we have examined three possible combinations of spins of the negative and positive resonances: (3-, 4-),
(3-, 3 - ) ,
(4-, 3 - ) .
As one can see from fig. 2 only the first sequence of spins gives good agreement between the calculated and the experimental results. To verify this conclusion, we have investigated the influence of the assumed nuclear potential on the transmission coefficient and estimated the upper limit of error caused by applying the J W K B method.
~,t DAKO\VSKI el
190
al.
Our calculations were performed with the Igo potential varying the depth of this potential, and with the Saxon-Woods potential U = Uo
¢4e.
"
1 + exp
,
F---
Nd ~6
T
I "£ranstftons
to- T
Expemmental
2
,, ~--_,U;N,
0
A ] e |
% 6rob2
3----
-7-'3-
~3
Neufron ~
4
J
2"!_1
_
3epQi'Gt1071
~nergf]
l
2+.t..~ *~4J
.SmrSO
~Od ~6
5m ~50
200[
Nd¢~s 501450 0
i tO0
50
20 fO
~a m
5
2
4
Fig. 2. C o m p a r i s o n of calculated a n d experimental cross sections for three possible c o m b i n a t i o n s o f spins. Calculations have been m a d e by using the lgo potential.
l¢SSln(n, ~)l~6Nd REACTION
191
varying the parameters U o and ro. The results of the latter calculation are displayed in fig. 3. It is clear that for (3-, 3 - ) and (4-, 3 - ) sequences there is no such pair of parameters (Uo, ro) for which the calculated and experimental cross-section ratios ~7(2+)/a(0 +) are in qualitative agreement. Such pairs of parameters exist only for the
~ nc( E~.'b ]
(3-¢)
transt#ons
-
t r o n s J h o n s to 8 "
-
H; s)
(3~ ~-)
ro
¢000:
to
~
_ (535
500
/ / / - ~./~. .,,5
ro
f00,
// .,-"
~ (5
/ / / ~ 4,,535
. ,,535
i .. i-
/
/"
'~5
///i//// ///z
i//
/"
ro (535
/..,"~t5
//...~
2"
.....
¢4
~~¢4
50 ~.i~,..~c.. ""' " .-. . ."_: ~ ::i w. :.. -'L'£"X . . .JJ.ZL~'~ ... - ~ ~ ,.535+~i'~i+!"-!-i!~f4
1,4~Mo2,
~op - - / / v ' ....................... ..// ........... L
_
5(
50
~
_
4
75
t00
5o
7-'5- ,bo 5'o
75
,oo
uo(MeV) Fig. 3, The dependence of the calculated cross section on the parameters U0 and r 0 of the SaxonW o o d s potential for three possible combinations of spins.
(3-, 4 - ) sequence and in this case we observe the ambiguity in the parameters of the optical potential, known already from fitting data from scattering experiments to the predictions of the optical model. This ambiguity makes only the absolute cross section undetermined, but it does not influence the relative cross sections.
192
M. DAKOWSKIet al.
We have examined the accuracy of JWKB method in our case according to the method presented in ref. 14), and estimated that the transmission coefficients are at least three times bigger than the exact values and that the error does not depend strongly on the height of the centrifugal barrier. In contradistinction to ~-decay, in cases similar to ours when the ~-particle energy is more than one half of the potential barrier height, we cannot apply the JWKB method to more accurate calculations of absolute cross sections. 3. Conclusion All known sources of errors in calculated cross sections: ambiguity of parameters in optical potential, error involved by JWKB approximation, error connected with applying the average level spacing, have little influence on the relative cross sections. Other quantities, which we know with limited accuracy, give a total error not exceeding 20 %. Consequently the comparison of the calculated and experimental relative cross sections is sufficient for unique spin assignment. We are grateful to Dr. K. Grotowski and Dr. A. Budzanowski for helpful discussions about the optical model aspects of the presented work. We want to thank Dr. J. Chwaszczewska for preparing the semiconductor detectors, and Miss l. Jarstorff and Dr. R. Brandt for kindly performing the chemical analysis. References 1) 2) 3l 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
R. D. Macfarlane and J. Almodovar, Phys. Rev. 127 (1962) 1665 E. Cheifetz et al., Phys. Lett. 1 (1962) 289 W. N. Andreev and S. M. Sirotkin, Yadern. Fiz. 1 (1965) 252 K. Beg and R. D. Macfarlane, Bull. Am. Phys. Soc. 10/6 (1965) 724 H. Marshak e t al., Phys. Rev. 128 (1962) 1287 H. Ceulemans et al., .I. Phys. 24 (1963) 1003 F. Poortmans et al., Compt. Rend. Congr. Int. Phys. Nucl., Paris (1964) 554 F. Poortmans e t al., Nuclear Physics 82 (1966) 331 J. W. Gordeev et al., Yaderno-fizicheskye constanty (Moscm~, 1963) A. D. O'Connor, J. Sosnowski, Institute of Nuclear Research Report 98 (1958) P. H6hne, Ann. der Phys. 7 (1961) 50 A. Stolovy, J. A. Harvey, Phys. Rev. 108 (1957) 353 Nuclear Data Sheets, 1964 N. FrOman and P. C. Fr/3man, J W K B approximation (North-Holland Publ. Company, Amsterdam, 1965)
2.G
I
Nuclear Physics A97 (1967) 187--192; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
O N T H E SPIN A S S I G N M E N T OF N E U T R O N R E S O N A N C E S IN 149Sm U S I N G (n, ~) R E A C T I O N M. D A K O W S K I , T. K R O G U L S K I , E. P I A S E C K I , H. P I E K A R Z a n d M. S O W I ~ S K I
Institute of Nuclear Research, Warsaw Received 13 J a n u a r y 1967 Abstract: M e a s u r e m e n t s o f t h e r m a l - n e u t r o n cross sections for the 149Sin(n, ~)t46Nd reaction have
been done using a 99 % enriched 149Sm target. Results are c o m p a r e d with theoretical values o f cross sections calculated on the basis o f the c o m p o u n d nucleus a n d statistical model. Experim e n t a l a n d calculated values are consistent only when a s s u m i n g that the spins o f the b o u n d state a n d the 0.0967 eV resonance in 149Sm+n are 3 a n d 4 , respectively. F o r such a spin sequence the 2200 m/see experimental n e u t r o n cross sections are: 4 6 . 0 ± 5 m b for l~gSm(n, ~) 14~Nd2+ a n d 8 . 5 ± 1 . 5 m b for 149Sm(n, ~)146Nd0+.
E
NUCLEAR
R E A C T I O N S x4SSm(n, c0, E = thermal; m e a s u r e d a(E~). 15°Sm resonances, deduced ~, J. Enriched target.
1. Introduction The (n, ~) reaction induced by thermal neutrons in 149Sm has been studied in several experiments ~-4). There are, however, big discrepancies between the results. It was our aim to measure the cross section for this reaction with a higher accuracy *. Comparison of the experimental data with theoretical predictions gave us spin values for low-energy 1 4 9 S m r e s o n a n c e s . The question of spin assignment of those resonances was recently discussed by several authors 5-s).
2. Experimental arrangement and results The samples of 1 4 9 S m enriched to 99 ~ were irradiated with a slow neutron beam from the E W A reactor. The energy spectra of the alpha particles from 1 4 9 S m ( n , y ) 146Nd reaction were obtained using a semiconductor spectrometer. A typical energy spectrum obtained from irradiation of a 149Sm target with slow and epi-cadmium neutrons is shown in fig. 1. The energy of the most energetic ~-line is 9154 keV. The experimental values of the "2200" m/sec cross section for ~49Sm (n, ~)t46Nd0÷ and 149Sm(n, c0146Nd2 + reactions were obtained by the use of the g-factor 9) for a Maxwellian-like neutron flux spectrum with a temperature lo) of 350 °. The spin and parity of the capture states are 3- or 4 - as the 1 4 9 S m ground state t T h e experimental part o f our work was already p e r f o r m e d when Beg and M a c F a r l a n e ' s 4) results b e c a m e available for us. 187
M. DAKOWSKI et al.
188
spin is ~. Both
11) the
b o u n d state of 1 4 9 S m + n a n d the positive resonance at 0.0967
eV c o n t r i b u t e to the cross section for the 149Sin(n, ~) reaction. C o n t r i b u t i o n s from the 0.87 eV and higher resonances are negligible. The observed alpha decay to the 0 + g r o u n d state of 146Nd proves that at least one
300
250
3
200
%..
15o
E Ioo
5~
tJsv~l"r"'6"'
v
,,,
~
8
g
.......
Energ~l (MeV) Fig. 1. Energy spectrum from the irradiation of a 1498m target with thermal neutrons. It was obtained by subtraction the spectrum with epi-cadmium neutrons from the spectrum with slow neutrons. TABLE 1 Experimental values of "2000" m/see cross sections for 149Sm(n,~)146Nd0+ and ]agSm(n, ~)146Nd2+ Spin combination (3,4)
]46Nd spin
Macfarlane
Cheifetz
Andreev
Macfarlane
et al. ])
et al. 2)
et al. 3)
et aL 4)
0+
22±10
5±1.5
7-5=3
2+
121±15
37±10
48±10
(3,3)
0~
or (4, 3)
2+
Present work 8.5~-1.5.
43.6_+0.6
46 ±5 4.3±0.7 46 ~5
of the resonances has spin 3 - . Thus we have examined three possible c o m b i n a t i o n s of spins - (3, 4), (3, 3) a n d (4, 3) of the negative a n d positive resonances, correspondingly. Calculated cross sections were o b t a i n e d in an analogous way to that used in paper l).
189
14OSm(n, :x)146Nd REACTION
The cross section for an e-transition to a definite level in the final nucleus is a/J(n, e) = os(CN) Z, F~s,l F~ where we can put o ' J ( C N ) = O'J,n ~ with a good accuracy. Here J is the spin of the capturing state, I is the spin of 146Nd. Besides, it was assumed, that F~ is the same for both resonances and is equal to F as F,,/F. l ~ 8" 10 . 3 and F~/F
~
10 -6.
We assume, that cross sections for ~ de-excitation of the compound nucleus is a product of two factors: one is the structural factor, which is responsible for the creation and appearing of the c~-particle on the surface of the nucleus and the second is the barrier transmission coefficient. As for the structural factor in an excited nucleus we do not know anything, and we assume, in accordance with the statistical model, that the structural factor is proportional to the average level spacing for the states near the capturing states of the same spin and parity. This assumption is justified provided that at this excitation energy the shell structure is destroyed. Thus, for the c~-particle emitted with definite orbital momentum DJ
-
r,,
where D is the average level spacing and T the transmission coefficients. For D, ~rn,7' and F.~ we used the values 6.0 eV, 40800+3000 b and 6 3 + 1 2 MeV, respectively
(refs. 9, i2,13)). The negative resonance component of the (n, 7) cross section for natural Sm has the magnitude 48/,rE eV ~ b according to H6hne's i l) measurements. Transmission coefficients were calculated in tile JWKB approximation assuming that the z-cluster does not decay in the barrier region, i.e. taking into account only the real part of the optical potential. The first calculations were performed with the Igo potential
{
U=--l100exp~--
r-- 1.17A~'t /"
O.57;
Thus we have examined three possible combinations of spins of the negative and positive resonances: (3-, 4-),
(3-, 3 - ) ,
(4-, 3 - ) .
As one can see from fig. 2 only the first sequence of spins gives good agreement between the calculated and the experimental results. To verify this conclusion, we have investigated the influence of the assumed nuclear potential on the transmission coefficient and estimated the upper limit of error caused by applying the J W K B method.
~,t DAKO\VSKI el
190
al.
Our calculations were performed with the Igo potential varying the depth of this potential, and with the Saxon-Woods potential U = Uo
¢4e.
"
1 + exp
,
F---
Nd ~6
T
I "£ranstftons
to- T
Expemmental
2
,, ~--_,U;N,
0
A ] e |
% 6rob2
3----
-7-'3-
~3
Neufron ~
4
J
2"!_1
_
3epQi'Gt1071
~nergf]
l
2+.t..~ *~4J
.SmrSO
~Od ~6
5m ~50
200[
Nd¢~s 501450 0
i tO0
50
20 fO
~a m
5
2
4
Fig. 2. C o m p a r i s o n of calculated a n d experimental cross sections for three possible c o m b i n a t i o n s o f spins. Calculations have been m a d e by using the lgo potential.
l¢SSln(n, ~)l~6Nd REACTION
191
varying the parameters U o and ro. The results of the latter calculation are displayed in fig. 3. It is clear that for (3-, 3 - ) and (4-, 3 - ) sequences there is no such pair of parameters (Uo, ro) for which the calculated and experimental cross-section ratios ~7(2+)/a(0 +) are in qualitative agreement. Such pairs of parameters exist only for the
~ nc( E~.'b ]
(3-¢)
transt#ons
-
t r o n s J h o n s to 8 "
-
H; s)
(3~ ~-)
ro
¢000:
to
~
_ (535
500
/ / / - ~./~. .,,5
ro
f00,
// .,-"
~ (5
/ / / ~ 4,,535
. ,,535
i .. i-
/
/"
'~5
///i//// ///z
i//
/"
ro (535
/..,"~t5
//...~
2"
.....
¢4
~~¢4
50 ~.i~,..~c.. ""' " .-. . ."_: ~ ::i w. :.. -'L'£"X . . .JJ.ZL~'~ ... - ~ ~ ,.535+~i'~i+!"-!-i!~f4
1,4~Mo2,
~op - - / / v ' ....................... ..// ........... L
_
5(
50
~
_
4
75
t00
5o
7-'5- ,bo 5'o
75
,oo
uo(MeV) Fig. 3, The dependence of the calculated cross section on the parameters U0 and r 0 of the SaxonW o o d s potential for three possible combinations of spins.
(3-, 4 - ) sequence and in this case we observe the ambiguity in the parameters of the optical potential, known already from fitting data from scattering experiments to the predictions of the optical model. This ambiguity makes only the absolute cross section undetermined, but it does not influence the relative cross sections.
192
M. DAKOWSKIet al.
We have examined the accuracy of JWKB method in our case according to the method presented in ref. 14), and estimated that the transmission coefficients are at least three times bigger than the exact values and that the error does not depend strongly on the height of the centrifugal barrier. In contradistinction to ~-decay, in cases similar to ours when the ~-particle energy is more than one half of the potential barrier height, we cannot apply the JWKB method to more accurate calculations of absolute cross sections. 3. Conclusion All known sources of errors in calculated cross sections: ambiguity of parameters in optical potential, error involved by JWKB approximation, error connected with applying the average level spacing, have little influence on the relative cross sections. Other quantities, which we know with limited accuracy, give a total error not exceeding 20 %. Consequently the comparison of the calculated and experimental relative cross sections is sufficient for unique spin assignment. We are grateful to Dr. K. Grotowski and Dr. A. Budzanowski for helpful discussions about the optical model aspects of the presented work. We want to thank Dr. J. Chwaszczewska for preparing the semiconductor detectors, and Miss l. Jarstorff and Dr. R. Brandt for kindly performing the chemical analysis. References 1) 2) 3l 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
R. D. Macfarlane and J. Almodovar, Phys. Rev. 127 (1962) 1665 E. Cheifetz et al., Phys. Lett. 1 (1962) 289 W. N. Andreev and S. M. Sirotkin, Yadern. Fiz. 1 (1965) 252 K. Beg and R. D. Macfarlane, Bull. Am. Phys. Soc. 10/6 (1965) 724 H. Marshak e t al., Phys. Rev. 128 (1962) 1287 H. Ceulemans et al., .I. Phys. 24 (1963) 1003 F. Poortmans et al., Compt. Rend. Congr. Int. Phys. Nucl., Paris (1964) 554 F. Poortmans e t al., Nuclear Physics 82 (1966) 331 J. W. Gordeev et al., Yaderno-fizicheskye constanty (Moscm~, 1963) A. D. O'Connor, J. Sosnowski, Institute of Nuclear Research Report 98 (1958) P. H6hne, Ann. der Phys. 7 (1961) 50 A. Stolovy, J. A. Harvey, Phys. Rev. 108 (1957) 353 Nuclear Data Sheets, 1964 N. FrOman and P. C. Fr/3man, J W K B approximation (North-Holland Publ. Company, Amsterdam, 1965)