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Circular polarization and γ-γ angular correlation measurements in the 39K(n, γ)40K reaction
I
2J3
I
Nuclear Physics A222 (1974) 388-398; Not to be
CIRCULAR
@ North-Holland Publishing Co., Amsterdam
reproduced by photoprint or microfilm without written permission from the publisher
POLARIZATION
MEASUREMENTS
AND y-7 ANGULAR
CORRELATION
IN THE 3gK(n, Y)~‘K REACTION
A. M. F. OP DEN KAMP FOM-RCN Nuclear Structure Group, Reactor Centrum Nederland and Rijksuniuersiteit te Utrecht Received 25 October 1973
Abstract: Circular polarization
measurements of the y-radiation from polarized neutron capture combined with y-y angular correlation measurements in the 3gK(n,y)40K reaction lead to Jlr = 2- assignments to the E, = 0.80,2.05 and 2.42 MeV states of 40K, and to spin restrictions for the states at E, = 2.10, 3.44 and 4.25 MeV. Multipole mixing ratios for the y-rays which de-excite these levels have been determined.
’ E
NUCLEAR polarization
REACTIONS 39K(polarized n, y), E = thermal: measured circular P,(e), a&,, 0,). 40K deduced 1, TZ,6, fractions in the capture state. Natural target.
1. Introduction
The 40K nucleus has been investigated extensively in the last few years. From a study of the 3gK(n, y) reaction, precise values for the excitation energies, branching ratios and the reaction Q-value have been determined by Johnson and Kennett ‘) and Op den Kamp and Spits “). Spin assignments to a number of excited states in 40K, branching ratios and multipole mixing ratios for the y-decay of these states follow from the 40Ar(p, ny) reaction studied by Twin et al. “) and Wechsung et al. “). The latter also report the mean lives of thirteen excited states of 40K, which they determined from a study of the 37Cl(a, ny) reaction. Spins have been deduced 5*6) from circular polarization measurements of primary y-rays emitted after capture of polarized thermal neutrons. The coherent interference of the spin components in the capture state ‘) makes this method not very useful for other than doubly even target nuclei. Angular correlation measurements are not affected by this interference effect, but a correlation consists of an incoherent mixture of the two correlations corresponding to the two possible capture states. These measurements therefore generally do not lead either to unambiguous spins or y-ray mixing ratios. This article shows that a combination of these two types of (n, y) experiments can be applied for the determination of spins and y-ray mixing ratios. From these experiments also follows the population ratio of the two spin components in the capture state for primary y-ray transitions. 388
389
2. Theoretical
The circular polarization of y-rays emitted after capture of polarized thermal neutrons is given by P = RP,, cos 8, where P,, is the neutron polarization and 8 (chosen as 0” or lSO”) is the angle between the neutron polarization direction and the direction of the detected y-rays; R is a function of the spin of the target nucleus (Jt), the spin of the final state (Jr), the multipole mixing ratio (6) for the primary y-ray emitted and the coherent interference (q) between the two spin components J’ = Jt + f in the capture state. The quantity q is defined “) by the relation
where L is the y-ray multipolarity and s the spin of the incoming neutron. If CIis defined as the contribution of the capture state J: to the total intensity Z of a primary transition, the relation between a and q is given by a =
vt+w Jt+(Jt+
l)$’
The expression for R can then be written as R = (l-a)R(J,)+&x(l-cc)R(J:)fcrR(J,+),
where the functions R(J,), R(J,‘) and R(JT), wh’ICh can be expressed “) in terms of W and z, coefficients, still are functions of the mixing ratio 6. The coefficients can be found in existing tables 9, lo). The polarization P can be determined experimentally by measuring the ratio (If -I-)/(I+ +Z-), where I+ and I- are the intensities of the emitted y-rays corresponding to the two opposite neutron polarization directions. It is generally assumed I’) that primary transitions from an even-parity capture state to odd-parity levels are of pure El character. The El assumption has been tested in previous work “). Under this assumption, R is only a function of Mand Jr. An example of the theoretical dependence of R on CIfor different spins of the final state is given in fig. 4. As can be seen, the determination of R does not lead to unambiguous spin assignments. The angular correlation of y-rays emitted after capture of thermal neutrons is given by W(e) = aW(J,f, B)+(l-a)W(J,, e), where W(J,f ,0) and W(J;, 0) are the angular correlations of the y-rays emitted from the capture states Jc’ and J,, and 6 is the angle between the two cascading y-rays. The function W(J,, 0) is given by r2) W(J,, 0) = 1 +AzP2 (cos tI)+ A4P4 (cos 0). Here Pz and P4 are Legendre polynomials. The El assumption entails A4 = 0; A, is still a function of the multipole mixing ratio of the secondary y-ray involved. The F-coefficients, used in the expression for A,, can be found in existing tables 12,13).
390
A. M. F. OP DEN KAMP
The fact that A4 = 0 means that it is only necessary to measure at two angles (0” and 907. On the other hand, with a measurement at more than two angles, one can test the El assumption. This procedure has been followed in the experiments described below. 3. Experimental The experiments have been performed at the Dutch High Flux Reactor at Petten, the Netherlands. 3.1. THE y-RAY
CIRCULAR
POLARIZATION
EXPERIMENT
The neutrons were polarized with a magnetic mirror system. This set-up has been described by Stecher-Rasmussen et a2. “1. The neutron flux density at the target position was about 3 x 10’ cm-’ * s- I. The degree of polarization was (90 + 5)0/,; the polarization direction was reversed every 10 s. It was necessary to use a densily packed’ target because (i> the thermal-neutron capture cross section is not high (2.1 b), (ii) the intensities of the primary y-rays studied are less than 10 0/0(see fig. I), (iii) the polarization detection efficiency is not more than 3 % [ref. “)I and (iv) the dintensions of the target are limited by the experimental set-up. Therefore, 24 g of compressed potassium fluoride was chosen as target material. The density of the KF wab 85 % of the theoretically possible value. To avoid depolarization of the neutron beam by scattering on II atoms, the hygroscopic KF target was placed in a thin (0.6 mm) quartz ~holder which was filled with dry argon gas. Two detection units, each consisting of a circular y-ray polarimeter, a 40 cm3 Ge(Li) detector and a 4096 channel pulse-height analyser were placed opposite to each other in a direction perpendicular to that of the incoming neutron beam. Asymmetries in the experimental set-up should lead to, difl’erent values for the y-ray polarization measured with the two detection units. It was found, however, that the error introduced by these asymmetries is negligible compared to the statistical error in the experimental R-values. The memory of each analyser was divided into two groups corresponding to the two neutron polarization directions, Each 12 h the collected data were read out on paper tape. The spectra thus obtained were corrected for possible gain shifts and zero shifts by comparison with a reference spectrum. After this transforma~on the spectra were summed for each detection unit and for each neutron polarization direction. The total measuring time was 3’7 days. The measurements were calibrated with the intense primary 5.42 MeV (capture state + 3.22 MeV) transition in sulphur. This transition has pure El character “). The calibration measurements were performed at the beginning, half-way and at the end of the experiment. 3.2. THE y-y ANGULAR
CORRELATION
EXPERIMENT
A filtering system, consisting of one bismuth and four quartz single crystals was used to attenuate the fast-neutron component in the beam. The experimental set-up
39K(n,y)40K
391
of this filtering system has been described by Van Middelkoop and Spilling 14). The thermal-neutron flux at the target position was lo7 cm-’ * s-l. As a target 4 g &CO, was used. The target was encapsulated in a thin-walled cylindrical teflon tube with an inner diameter of 1 cm centered on the neutron beam. The detection unit consisted of a 12 cm x 12 cm NaI crystal and a 60 cm3 Ge(Li) detector. The overall resolution of the Ge(Li) detector was 7 keV at E7 = 1.24 MeV over the whole measuring time of 25 days. The NaI detector could rotate in a plane perpendicular to the neutron beam. The solid angles for the two detectors were 1 % and 0.7 % for the Ge(Li) and NaI detector, respectively. A fast timing system of two constant-fraction timers and a time-to-amplitude converter was used. The FWHM of the time spectrum was 25 ns for the full range of O-8 MeV. The contribution of accidental coincidences in the time spectrum was 25 %. Gates were placed on the Ge(Li) and NaI spectra which covered energy regions of 1.0-2.2 MeV and 4-7 MeV, respectively. With a digital discriminator ’ “) following one of the ADC units, three windows were placed (in the 4-7 MeV region) on the NaI pulse-height spectrum. Gate 1 (see insert of fig. 3) could be used for (i) background correction and (ii) correction for accidental coincidences. The contribution of the accidental coincidences after the discriminator was less than 5 %; the counting rate in the memory was 10 s-l. The coincidence spectra were measured at five angles, 0”, 30”, 45”, 60” and 90”. The measuring time at each angle was 2 h corrected for dead time in the ADC. All spectra were recorded on magnetic tape, while additional information such as the neutron flux, the number of coincidences and the counting rate in each detector, was recorded separately on a typewriter. The measuring cycle of five angles was repeated many times. 4. Results Fig. 1 shows a partial decay scheme of 40K, Only transitions which have been studied in the present investigation are given. For a complete decay scheme, see e.g. ref. “). The branching ratios for the states at 2.05, 2.07 and 2.10 MeV are from the present investigation. They are given, with their error, in table 1. Branching ratios for the other states and the relative intensities of the primary y-ray transitions are from ref. ‘), because not all decay y-rays have been observed in the present investigation. The measured polarization spectrum with the best resolution is given in fig. 2. From the two spectra, corresponding to the two neutron polarization directions, the sum and difference spectra are given here. The background has not been subtracted. The measured effects appear clearly in the difference spectrum. The spectrum obtained from the other detection unit is essentially the same. The relative polarization detection efficiency of the polarimeter as a function of energy is given in ref. 5), while from the sulphur calibration measurements the
392
A. M. F. OP DEN KAMP
7.80
=K+n
J= l,,
Fig. 1. Partial y-ray decay scheme of 40K. Only those transitions have been given which are also studied in the present investigation. The intensities of the primary y-rays (per 100 neutron captures) are taken from ref. *). The branching ratios (in %) of the bound levels at E, = 2.05, 2.07 and 2.10 MeV are from the present investigation; those of the other levels are taken from ref. *). The 1. values are from ref. I’).
absolute efficiency at Ey = 5.42 MeV was determined as 0.0242f0.0008. Peak areas in the two spectra, which correspond to the two neutron polarization directions, were calculated with the same peak and background regions. The experimental Rvalues for the primary transitions in 40K, given in table 1, are the weighted means of the values obtained from the two polarimeters. The coincidence spectra measured at 90” for gates 2 and 3 are given in fig. 3. The insert shows the gate setting on the NaI pulse-height spectrum. The spectra are corrected for background and accidental coincidences. The coincidence spectrum obtained from gate 1, which covers an energy region from 6.2-6.7 MeV, could be used for these corrections, because the reaction Q-value is 7.80 MeV [ref. “)I and the primary transitions in this gate thus will feed the levels at 0.03 and 0.80 MeV (the ground state and the Ex = 0.89and 1.64 MeV levels are not excited). Gates 2 and 3 cover the energy range from 5.2 to 6.1 MeV. The energies of the primary y-rays in these gates correspond to levels below 2.6 MeV. The spectra of both gates can be added because other than primary transitions, which also feed the
difference spectrum
*
Fig. 2. Polarization spectrum (sum and difference spectra) of y-rays emitted after capture of polarized thermal neutrons in 3gK. In background regions in the sum spectrum, the mean of each four consecutive points is plotted; in the difference spectrum all points are plotted. Pull-energy peaks are labelled with they-ray energy in keV; single- and double-escape peaks with the primed and double primedy-ray energy, respectively.
- $04
0
w z
ii
;:
0
1
2
3
4
5
2f x1036
Fig. 3. Coincidence
r------~---r-
spectra at 30” for gates 2 and 3. The insert shows the gate setting.
1.62
-----T-
I
J
-I
395
3eK(n, +*K TABLE 1
Results from the present investigation C -+ Ei -+ Ef
R(C-+Eg)
(MeV)
c + 0.03 3 0 C + 0.80 -+ 0.03
-0.50*0.03 i-0.63&0.06
c -+ 2.05
+0.0810.03
0
4
-+ 0.03 + 0.80 c -+ 2.07 -?- 0 -+ 0.03 -+ 0.80 c -+ 2.10 -+ 0.03 -+ 0.80 C -+ 2.29 C + 2.42 + 0.80 c-+3.44 C + 4.25
-0.46&0.05
-0.41&0.04
Branching (%I (Ei -+ G)
2952 32&2 3912 3712 55&2 8&l 72&l 28&l
-j-0.70&0.06 0.00f0.03 +0.98&0.09 +0*49~0.10
a7
AZ “)
-0.09&0.02 +0.08&0.02 -0.21&0.01 +0.07&0.06 -0.20&0.02
Interference “)
1 0.09*0.04 0.9110.04 0.02+0.01
C D
1
D
-+-0.05&0.02 -0.13~0.02 -i_O.19&0.02
D
0.9610.02
“) Corrected for solid-angle attenuation. b, The fraction of the 2+ component in the capture state. “) The interference in the capture state: D and C denote destructive and constructive interference, respectively.
TABLE2 Deduced spins for levels in “OK and the multipole mixing ratio for theiry-ray C -+ El -+ Ef (MeV)
C -+ 0.80 C -+ 2.05 -+ 0 -+ 0.03 --f C -+ 2.07 -+ -+ c -+ 2.10 -+
0.80 0 0.03 0.03
C 2.29 -+ 0.80 c --f -+ 2.42 c -+ 3.44 C + 4.25
Wi + Ed “1
Jn W
Sb)
J= b,
decay
SC) -.-
E2 -0.07~0.04 9 &2 -0.10&0.04 -0.01 io.10 -0.2 10.2
22-
(3k
E2 -0.01~0.02 -0.13f0.09 +0.07&0.10 -0.27&0.10
2-
3(1-3)-
(l-3)-0.06~0.06 -1.9 10.3
2-
-0.0510.10 -2.0 fO.6
(132) (1,2)_
“) High values for 8 which were not given in refs. 3*4) are omitted. b, Ref. 3). ‘) Ref. “).
(A-
E2 -0.05~0.03 9.0 k2.0 -0.ld~O.05 +0.07~0.10 -0.25~0.15
396
A. M. F. OP DEN KAMP
levels below 2.6 MeV, cannot enter in these gates. Nevertheless, two gates were used as a check, because the Ey = 1.62 MeV transition (2.42 --P0.80 MeV) may be observed in the coincidence spectrum of gate 3 only. As can be seen from fig. 3, the peak at 1.62 MeV completely disappears in the spectrum of gate 2 after the corrections mentioned above. The peaks were analysed by a least-squares fitting of a slightly asymmetric response function. This was necessary in, order to resolve the three doublets in the 2.01-2.08 MeV region (see fig. 3). The asymmetry and the FWHM as a function of energy were obtained from the peaks at E,, = 1.25, 1.30 and 1.62 MeV. The calculated A, coefficients for the measured angular correlations are given in table 1. For all correlations the A4 coefficient was smaller than the error in Ah.
Fig. 4. The theoretical R-values for different spins of the finai state as a function of the 2+ fraction in the capture state. The measured (R, a) vaIues for the E, = 0.80,2.05 and 2.42 MeV levels are given as rectangles.
A least-squares program was used to calculate the population ratio of the two capture states and the m~tipole mixing ratios 6 for all secondary y-rays involved; the sign convention is that of Rose and Brink 16). The results from these c~cuIations are given in table 2 together with the deduced spins for the intermediate states. All results are compared with those of Twin et al. “) and Wechsung et al. “). In fig. 4 the theoretical R-values as a function of CC for different intermediate state spins are compared with the R(E) values obtained from the present investigation.
391
5. Discussion The El assumption limits the spins to be discussed for-the odd-parity Ievzls excited by a primary y-ray transition to J = (O-3). The Ex = 0.03 MeV level. This level is strongly excited in the (d, p) reaction via
an 1, = 3 transfer ” ), which limits the possible J” values to J” = (2-5)-. The El assumption for primary capture radiation then gives a further limitation to J” = (2, 3)-. The measured lifetime Is) excludes quadrupole character for the 0.03 -+ 0 MeV transition, which leads to J” = 3-. Conclusion: the measured R-value (table 1) for the transition C -+ 0.03 MeV is in agreement with the calculated value of -0.50 for J” = J-. The E;, = 0.80 MeV level, Again, the value I,(d, p) 5 3 [ref. “)I, combined with the El assumption, limits the possibilities to J” = (2,3)-. The measured Rvalue of +0.63+0.06 excludes J” = 3-. Conclusion: J” = 2-. The E, = 2.05 MeV level. This level is excited by Z,,(d,p) = 1 transfer 17) and hence has J” = (O-3)-. The decay of this level (fig. 1) in combination with the measured lifetime “) limits the possibilities to J” = (2, 3)-. The measured R-value for the C -+ 2.05 MeV tsansition excludes J” = 3-, such that the conclusion is J” = 2- (with either M = 0.02~0.0~ or 0.98rtO.01). The large value for a is excluded by the result of the C -+ 2.05 -+ 0 MeV angular correlation measurement (both transitions unmixed). The angular correlation measurement further yields the mixing ratios of the 2.05 -+ 0.03 and 2.05 --f 0.80 MeV transitions, in agreement with previous results 3, “). The Ex = 2.07 Mefi Eeael. The (d, p) work I’) has yielded I,, = 1 and thus J” = (O-3)-. The decay of this level (fig. 2) combined with the measured life&e “), gives a further restriction to J z = (2, 3)-. The results from the 40Ar(p, ny) reaction, studied by Twin et al. 3), lead to J” = 3-. The mixing ratios of the secondary y-ray transitions to the ground state and 0.03 MeV state follow from the present angular correlation experiment. The results are in agreement with those reported by Twin et al. “) and Wechsung et al. “)_ TIze E, = 2.70 MeY level. An 1, = 1 value for this fevel follows from the (d, p) work 17). Th e ar gument for a J’ = l- assignment given by Twin et al. 3)2 is model dependent; it is based on the assumption that this level belongs to the p+d, ’ quadruplet. From the present experiment, only J” = 0 could be excluded, because the C -+ 2.10 + 0.80 MeV angular correlation is anisotropic. conclusion: J” = (l-3)-. The E, = 2290 keV level. From the two levels at E, = 2290 and 2291 keV, only the lowest one is excited by a primary y-ray transition “). The present experiment confirms this interpretation because in coincidence with the primary transition only the 1.49 MeV y-ray (2290 -+ 800 keV) has been observed (fig. 3), whereas the 1.40 MeV y-ray, which must be interpreted as the 2291 --, 892 keV transition 2*“) has not been observed. A J = 1 assignment to the 2290 keV Ievel is made by Twin et ai. “).
398
A. M. F. OP DEN KAMP
The E, = 2.42 MeV level. From the branching ratios 2), the E, = 1 value I’) and the measured lifetime “) for the 2.42 MeV level, follows a restriction to J’ = (2, 3)-. The measured R-value of O.OOJrO.03clearly excludes J” = 3-. The multipole mixing ratio for the 1.62 MeV y-ray transition to the 0.80 MeV level follows from the angular correlation experiment. The two possible values (table 2) are in agreement with those reported by Twin et al. “). Independent of the branching ratios and the measured lifetime, the present experiment also excludes J” = (0, 1,3)-. Conclusion: Jn = 2-. The 15, = 3.44 and 4.25 MeV levels. No angular correlations have beeg measured for these levels. The parity of the 3.44 MeV level is unknown. However, a spin restriction to J = (1,2) can be made because independently of the parity of this level and the mixing of the two spin components in the capture state, the upper limits for the R-values for mixed primary transitions are 0.5 and 0.18 for J(3.44) = 0 and 3, respectively. Conclusion: J = (1,Z). The circular polarization result leads to 5’ = (1, 2)-(En = 1 [ref. 1‘)I) for the 4.25 MeV state.
The author wishes to thank Professor P. M. Endt and Dr. H. Gruppelaar for their interest in this work and their criticism of the manuscript. The assistance of P. Koonen in analysing the polarization data was appreciated. This investigation was performed as a joint research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Stichting Reactor Centrum N~derland (RCNI. References 1) L. V. Johnson and T. J. Kennet, Can. J. Phys. 48 (1970) 1109 2) A. M. F. Op den Kamp and A. M. J. Spits, Nucl. Phys. A180 (1972) 569 3) P. J. Twin, W. C. Olsen and D. M. Sheppard, Nucl. Phys. Al43 (1970) 481 4) R. Wechsnng, W. Strassheim and R. Bass, Nucl. Phys. Al79 (1971) 557 5) I?. Stecher-Rasmussen, K. Abrahams and J. Kopeckf, Nucl. Phys. A181 (1972) 225 6) J. Kopeckjr, K. Abrahams and F. Stecher-Rasmussen, Nucl. Phys. A188 (1972) 535 7) A. M. F. Op den Kamp et aZ., Phys. Lett. 39B (1972) 204 8) J. Honz&tko and J. Kajfosz, Phys. Lett. 38B (1972) 499 9) A. 3. Ferguson, Angular correlation methods in gamma-ray spectroscopy (North”~olland~ Amsterdam, 1965) 10) W. T. J. Sharp, J. M. Kennedy, B. 3. Sears and M. G. Hoyle, Tables of coefficients for angular ~s~ibution analysis, Chalk River report AECL-97 11) G. A. Bartholomew, Ann. Rev. of Nucl. Sci. 11 (1961) 259; H. T. Motz, Ann. Rev. &cl. Sci. 20 (1970) 1 12) K. Siegbahn, Alpha-, beta- and gamma-ray spectroscopy, vol. 2 (North-Holland, Amsterdam, 1965) 13) A. H. Wapstra, G. J. Nijgh and R. van Lieshout, Nuclear spectroscopy tables (North-Holland, Amsterdam, 1959) 14) G. van Middelkoop and P. Spilling, Nucl. Phys. 72 (1969) 1 15) P. Spilling, H. Gruppelaar and P. C. van den Berg, Int. Symp. on nuclear electronics, Versailles, 1968, part II, Contr. 140 16) H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 17) H. A. Enge, E. J. Irvin and D. H. Weaner, Phys. Rev. 115 (1959) 949 18) J. F. Boultier, W. V. Prestwich and B. Arad, Can. J. Phys. 47 (1969) 591
2J3
I
Nuclear Physics A222 (1974) 388-398; Not to be
CIRCULAR
@ North-Holland Publishing Co., Amsterdam
reproduced by photoprint or microfilm without written permission from the publisher
POLARIZATION
MEASUREMENTS
AND y-7 ANGULAR
CORRELATION
IN THE 3gK(n, Y)~‘K REACTION
A. M. F. OP DEN KAMP FOM-RCN Nuclear Structure Group, Reactor Centrum Nederland and Rijksuniuersiteit te Utrecht Received 25 October 1973
Abstract: Circular polarization
measurements of the y-radiation from polarized neutron capture combined with y-y angular correlation measurements in the 3gK(n,y)40K reaction lead to Jlr = 2- assignments to the E, = 0.80,2.05 and 2.42 MeV states of 40K, and to spin restrictions for the states at E, = 2.10, 3.44 and 4.25 MeV. Multipole mixing ratios for the y-rays which de-excite these levels have been determined.
’ E
NUCLEAR polarization
REACTIONS 39K(polarized n, y), E = thermal: measured circular P,(e), a&,, 0,). 40K deduced 1, TZ,6, fractions in the capture state. Natural target.
1. Introduction
The 40K nucleus has been investigated extensively in the last few years. From a study of the 3gK(n, y) reaction, precise values for the excitation energies, branching ratios and the reaction Q-value have been determined by Johnson and Kennett ‘) and Op den Kamp and Spits “). Spin assignments to a number of excited states in 40K, branching ratios and multipole mixing ratios for the y-decay of these states follow from the 40Ar(p, ny) reaction studied by Twin et al. “) and Wechsung et al. “). The latter also report the mean lives of thirteen excited states of 40K, which they determined from a study of the 37Cl(a, ny) reaction. Spins have been deduced 5*6) from circular polarization measurements of primary y-rays emitted after capture of polarized thermal neutrons. The coherent interference of the spin components in the capture state ‘) makes this method not very useful for other than doubly even target nuclei. Angular correlation measurements are not affected by this interference effect, but a correlation consists of an incoherent mixture of the two correlations corresponding to the two possible capture states. These measurements therefore generally do not lead either to unambiguous spins or y-ray mixing ratios. This article shows that a combination of these two types of (n, y) experiments can be applied for the determination of spins and y-ray mixing ratios. From these experiments also follows the population ratio of the two spin components in the capture state for primary y-ray transitions. 388
389
2. Theoretical
The circular polarization of y-rays emitted after capture of polarized thermal neutrons is given by P = RP,, cos 8, where P,, is the neutron polarization and 8 (chosen as 0” or lSO”) is the angle between the neutron polarization direction and the direction of the detected y-rays; R is a function of the spin of the target nucleus (Jt), the spin of the final state (Jr), the multipole mixing ratio (6) for the primary y-ray emitted and the coherent interference (q) between the two spin components J’ = Jt + f in the capture state. The quantity q is defined “) by the relation
where L is the y-ray multipolarity and s the spin of the incoming neutron. If CIis defined as the contribution of the capture state J: to the total intensity Z of a primary transition, the relation between a and q is given by a =
vt+w Jt+(Jt+
l)$’
The expression for R can then be written as R = (l-a)R(J,)+&x(l-cc)R(J:)fcrR(J,+),
where the functions R(J,), R(J,‘) and R(JT), wh’ICh can be expressed “) in terms of W and z, coefficients, still are functions of the mixing ratio 6. The coefficients can be found in existing tables 9, lo). The polarization P can be determined experimentally by measuring the ratio (If -I-)/(I+ +Z-), where I+ and I- are the intensities of the emitted y-rays corresponding to the two opposite neutron polarization directions. It is generally assumed I’) that primary transitions from an even-parity capture state to odd-parity levels are of pure El character. The El assumption has been tested in previous work “). Under this assumption, R is only a function of Mand Jr. An example of the theoretical dependence of R on CIfor different spins of the final state is given in fig. 4. As can be seen, the determination of R does not lead to unambiguous spin assignments. The angular correlation of y-rays emitted after capture of thermal neutrons is given by W(e) = aW(J,f, B)+(l-a)W(J,, e), where W(J,f ,0) and W(J;, 0) are the angular correlations of the y-rays emitted from the capture states Jc’ and J,, and 6 is the angle between the two cascading y-rays. The function W(J,, 0) is given by r2) W(J,, 0) = 1 +AzP2 (cos tI)+ A4P4 (cos 0). Here Pz and P4 are Legendre polynomials. The El assumption entails A4 = 0; A, is still a function of the multipole mixing ratio of the secondary y-ray involved. The F-coefficients, used in the expression for A,, can be found in existing tables 12,13).
390
A. M. F. OP DEN KAMP
The fact that A4 = 0 means that it is only necessary to measure at two angles (0” and 907. On the other hand, with a measurement at more than two angles, one can test the El assumption. This procedure has been followed in the experiments described below. 3. Experimental The experiments have been performed at the Dutch High Flux Reactor at Petten, the Netherlands. 3.1. THE y-RAY
CIRCULAR
POLARIZATION
EXPERIMENT
The neutrons were polarized with a magnetic mirror system. This set-up has been described by Stecher-Rasmussen et a2. “1. The neutron flux density at the target position was about 3 x 10’ cm-’ * s- I. The degree of polarization was (90 + 5)0/,; the polarization direction was reversed every 10 s. It was necessary to use a densily packed’ target because (i> the thermal-neutron capture cross section is not high (2.1 b), (ii) the intensities of the primary y-rays studied are less than 10 0/0(see fig. I), (iii) the polarization detection efficiency is not more than 3 % [ref. “)I and (iv) the dintensions of the target are limited by the experimental set-up. Therefore, 24 g of compressed potassium fluoride was chosen as target material. The density of the KF wab 85 % of the theoretically possible value. To avoid depolarization of the neutron beam by scattering on II atoms, the hygroscopic KF target was placed in a thin (0.6 mm) quartz ~holder which was filled with dry argon gas. Two detection units, each consisting of a circular y-ray polarimeter, a 40 cm3 Ge(Li) detector and a 4096 channel pulse-height analyser were placed opposite to each other in a direction perpendicular to that of the incoming neutron beam. Asymmetries in the experimental set-up should lead to, difl’erent values for the y-ray polarization measured with the two detection units. It was found, however, that the error introduced by these asymmetries is negligible compared to the statistical error in the experimental R-values. The memory of each analyser was divided into two groups corresponding to the two neutron polarization directions, Each 12 h the collected data were read out on paper tape. The spectra thus obtained were corrected for possible gain shifts and zero shifts by comparison with a reference spectrum. After this transforma~on the spectra were summed for each detection unit and for each neutron polarization direction. The total measuring time was 3’7 days. The measurements were calibrated with the intense primary 5.42 MeV (capture state + 3.22 MeV) transition in sulphur. This transition has pure El character “). The calibration measurements were performed at the beginning, half-way and at the end of the experiment. 3.2. THE y-y ANGULAR
CORRELATION
EXPERIMENT
A filtering system, consisting of one bismuth and four quartz single crystals was used to attenuate the fast-neutron component in the beam. The experimental set-up
39K(n,y)40K
391
of this filtering system has been described by Van Middelkoop and Spilling 14). The thermal-neutron flux at the target position was lo7 cm-’ * s-l. As a target 4 g &CO, was used. The target was encapsulated in a thin-walled cylindrical teflon tube with an inner diameter of 1 cm centered on the neutron beam. The detection unit consisted of a 12 cm x 12 cm NaI crystal and a 60 cm3 Ge(Li) detector. The overall resolution of the Ge(Li) detector was 7 keV at E7 = 1.24 MeV over the whole measuring time of 25 days. The NaI detector could rotate in a plane perpendicular to the neutron beam. The solid angles for the two detectors were 1 % and 0.7 % for the Ge(Li) and NaI detector, respectively. A fast timing system of two constant-fraction timers and a time-to-amplitude converter was used. The FWHM of the time spectrum was 25 ns for the full range of O-8 MeV. The contribution of accidental coincidences in the time spectrum was 25 %. Gates were placed on the Ge(Li) and NaI spectra which covered energy regions of 1.0-2.2 MeV and 4-7 MeV, respectively. With a digital discriminator ’ “) following one of the ADC units, three windows were placed (in the 4-7 MeV region) on the NaI pulse-height spectrum. Gate 1 (see insert of fig. 3) could be used for (i) background correction and (ii) correction for accidental coincidences. The contribution of the accidental coincidences after the discriminator was less than 5 %; the counting rate in the memory was 10 s-l. The coincidence spectra were measured at five angles, 0”, 30”, 45”, 60” and 90”. The measuring time at each angle was 2 h corrected for dead time in the ADC. All spectra were recorded on magnetic tape, while additional information such as the neutron flux, the number of coincidences and the counting rate in each detector, was recorded separately on a typewriter. The measuring cycle of five angles was repeated many times. 4. Results Fig. 1 shows a partial decay scheme of 40K, Only transitions which have been studied in the present investigation are given. For a complete decay scheme, see e.g. ref. “). The branching ratios for the states at 2.05, 2.07 and 2.10 MeV are from the present investigation. They are given, with their error, in table 1. Branching ratios for the other states and the relative intensities of the primary y-ray transitions are from ref. ‘), because not all decay y-rays have been observed in the present investigation. The measured polarization spectrum with the best resolution is given in fig. 2. From the two spectra, corresponding to the two neutron polarization directions, the sum and difference spectra are given here. The background has not been subtracted. The measured effects appear clearly in the difference spectrum. The spectrum obtained from the other detection unit is essentially the same. The relative polarization detection efficiency of the polarimeter as a function of energy is given in ref. 5), while from the sulphur calibration measurements the
392
A. M. F. OP DEN KAMP
7.80
=K+n
J= l,,
Fig. 1. Partial y-ray decay scheme of 40K. Only those transitions have been given which are also studied in the present investigation. The intensities of the primary y-rays (per 100 neutron captures) are taken from ref. *). The branching ratios (in %) of the bound levels at E, = 2.05, 2.07 and 2.10 MeV are from the present investigation; those of the other levels are taken from ref. *). The 1. values are from ref. I’).
absolute efficiency at Ey = 5.42 MeV was determined as 0.0242f0.0008. Peak areas in the two spectra, which correspond to the two neutron polarization directions, were calculated with the same peak and background regions. The experimental Rvalues for the primary transitions in 40K, given in table 1, are the weighted means of the values obtained from the two polarimeters. The coincidence spectra measured at 90” for gates 2 and 3 are given in fig. 3. The insert shows the gate setting on the NaI pulse-height spectrum. The spectra are corrected for background and accidental coincidences. The coincidence spectrum obtained from gate 1, which covers an energy region from 6.2-6.7 MeV, could be used for these corrections, because the reaction Q-value is 7.80 MeV [ref. “)I and the primary transitions in this gate thus will feed the levels at 0.03 and 0.80 MeV (the ground state and the Ex = 0.89and 1.64 MeV levels are not excited). Gates 2 and 3 cover the energy range from 5.2 to 6.1 MeV. The energies of the primary y-rays in these gates correspond to levels below 2.6 MeV. The spectra of both gates can be added because other than primary transitions, which also feed the
difference spectrum
*
Fig. 2. Polarization spectrum (sum and difference spectra) of y-rays emitted after capture of polarized thermal neutrons in 3gK. In background regions in the sum spectrum, the mean of each four consecutive points is plotted; in the difference spectrum all points are plotted. Pull-energy peaks are labelled with they-ray energy in keV; single- and double-escape peaks with the primed and double primedy-ray energy, respectively.
- $04
0
w z
ii
;:
0
1
2
3
4
5
2f x1036
Fig. 3. Coincidence
r------~---r-
spectra at 30” for gates 2 and 3. The insert shows the gate setting.
1.62
-----T-
I
J
-I
395
3eK(n, +*K TABLE 1
Results from the present investigation C -+ Ei -+ Ef
R(C-+Eg)
(MeV)
c + 0.03 3 0 C + 0.80 -+ 0.03
-0.50*0.03 i-0.63&0.06
c -+ 2.05
+0.0810.03
0
4
-+ 0.03 + 0.80 c -+ 2.07 -?- 0 -+ 0.03 -+ 0.80 c -+ 2.10 -+ 0.03 -+ 0.80 C -+ 2.29 C + 2.42 + 0.80 c-+3.44 C + 4.25
-0.46&0.05
-0.41&0.04
Branching (%I (Ei -+ G)
2952 32&2 3912 3712 55&2 8&l 72&l 28&l
-j-0.70&0.06 0.00f0.03 +0.98&0.09 +0*49~0.10
a7
AZ “)
-0.09&0.02 +0.08&0.02 -0.21&0.01 +0.07&0.06 -0.20&0.02
Interference “)
1 0.09*0.04 0.9110.04 0.02+0.01
C D
1
D
-+-0.05&0.02 -0.13~0.02 -i_O.19&0.02
D
0.9610.02
“) Corrected for solid-angle attenuation. b, The fraction of the 2+ component in the capture state. “) The interference in the capture state: D and C denote destructive and constructive interference, respectively.
TABLE2 Deduced spins for levels in “OK and the multipole mixing ratio for theiry-ray C -+ El -+ Ef (MeV)
C -+ 0.80 C -+ 2.05 -+ 0 -+ 0.03 --f C -+ 2.07 -+ -+ c -+ 2.10 -+
0.80 0 0.03 0.03
C 2.29 -+ 0.80 c --f -+ 2.42 c -+ 3.44 C + 4.25
Wi + Ed “1
Jn W
Sb)
J= b,
decay
SC) -.-
E2 -0.07~0.04 9 &2 -0.10&0.04 -0.01 io.10 -0.2 10.2
22-
(3k
E2 -0.01~0.02 -0.13f0.09 +0.07&0.10 -0.27&0.10
2-
3(1-3)-
(l-3)-0.06~0.06 -1.9 10.3
2-
-0.0510.10 -2.0 fO.6
(132) (1,2)_
“) High values for 8 which were not given in refs. 3*4) are omitted. b, Ref. 3). ‘) Ref. “).
(A-
E2 -0.05~0.03 9.0 k2.0 -0.ld~O.05 +0.07~0.10 -0.25~0.15
396
A. M. F. OP DEN KAMP
levels below 2.6 MeV, cannot enter in these gates. Nevertheless, two gates were used as a check, because the Ey = 1.62 MeV transition (2.42 --P0.80 MeV) may be observed in the coincidence spectrum of gate 3 only. As can be seen from fig. 3, the peak at 1.62 MeV completely disappears in the spectrum of gate 2 after the corrections mentioned above. The peaks were analysed by a least-squares fitting of a slightly asymmetric response function. This was necessary in, order to resolve the three doublets in the 2.01-2.08 MeV region (see fig. 3). The asymmetry and the FWHM as a function of energy were obtained from the peaks at E,, = 1.25, 1.30 and 1.62 MeV. The calculated A, coefficients for the measured angular correlations are given in table 1. For all correlations the A4 coefficient was smaller than the error in Ah.
Fig. 4. The theoretical R-values for different spins of the finai state as a function of the 2+ fraction in the capture state. The measured (R, a) vaIues for the E, = 0.80,2.05 and 2.42 MeV levels are given as rectangles.
A least-squares program was used to calculate the population ratio of the two capture states and the m~tipole mixing ratios 6 for all secondary y-rays involved; the sign convention is that of Rose and Brink 16). The results from these c~cuIations are given in table 2 together with the deduced spins for the intermediate states. All results are compared with those of Twin et al. “) and Wechsung et al. “). In fig. 4 the theoretical R-values as a function of CC for different intermediate state spins are compared with the R(E) values obtained from the present investigation.
391
5. Discussion The El assumption limits the spins to be discussed for-the odd-parity Ievzls excited by a primary y-ray transition to J = (O-3). The Ex = 0.03 MeV level. This level is strongly excited in the (d, p) reaction via
an 1, = 3 transfer ” ), which limits the possible J” values to J” = (2-5)-. The El assumption for primary capture radiation then gives a further limitation to J” = (2, 3)-. The measured lifetime Is) excludes quadrupole character for the 0.03 -+ 0 MeV transition, which leads to J” = 3-. Conclusion: the measured R-value (table 1) for the transition C -+ 0.03 MeV is in agreement with the calculated value of -0.50 for J” = J-. The E;, = 0.80 MeV level, Again, the value I,(d, p) 5 3 [ref. “)I, combined with the El assumption, limits the possibilities to J” = (2,3)-. The measured Rvalue of +0.63+0.06 excludes J” = 3-. Conclusion: J” = 2-. The E, = 2.05 MeV level. This level is excited by Z,,(d,p) = 1 transfer 17) and hence has J” = (O-3)-. The decay of this level (fig. 1) in combination with the measured lifetime “) limits the possibilities to J” = (2, 3)-. The measured R-value for the C -+ 2.05 MeV tsansition excludes J” = 3-, such that the conclusion is J” = 2- (with either M = 0.02~0.0~ or 0.98rtO.01). The large value for a is excluded by the result of the C -+ 2.05 -+ 0 MeV angular correlation measurement (both transitions unmixed). The angular correlation measurement further yields the mixing ratios of the 2.05 -+ 0.03 and 2.05 --f 0.80 MeV transitions, in agreement with previous results 3, “). The Ex = 2.07 Mefi Eeael. The (d, p) work I’) has yielded I,, = 1 and thus J” = (O-3)-. The decay of this level (fig. 2) combined with the measured life&e “), gives a further restriction to J z = (2, 3)-. The results from the 40Ar(p, ny) reaction, studied by Twin et al. 3), lead to J” = 3-. The mixing ratios of the secondary y-ray transitions to the ground state and 0.03 MeV state follow from the present angular correlation experiment. The results are in agreement with those reported by Twin et al. “) and Wechsung et al. “)_ TIze E, = 2.70 MeY level. An 1, = 1 value for this fevel follows from the (d, p) work 17). Th e ar gument for a J’ = l- assignment given by Twin et al. 3)2 is model dependent; it is based on the assumption that this level belongs to the p+d, ’ quadruplet. From the present experiment, only J” = 0 could be excluded, because the C -+ 2.10 + 0.80 MeV angular correlation is anisotropic. conclusion: J” = (l-3)-. The E, = 2290 keV level. From the two levels at E, = 2290 and 2291 keV, only the lowest one is excited by a primary y-ray transition “). The present experiment confirms this interpretation because in coincidence with the primary transition only the 1.49 MeV y-ray (2290 -+ 800 keV) has been observed (fig. 3), whereas the 1.40 MeV y-ray, which must be interpreted as the 2291 --, 892 keV transition 2*“) has not been observed. A J = 1 assignment to the 2290 keV Ievel is made by Twin et ai. “).
398
A. M. F. OP DEN KAMP
The E, = 2.42 MeV level. From the branching ratios 2), the E, = 1 value I’) and the measured lifetime “) for the 2.42 MeV level, follows a restriction to J’ = (2, 3)-. The measured R-value of O.OOJrO.03clearly excludes J” = 3-. The multipole mixing ratio for the 1.62 MeV y-ray transition to the 0.80 MeV level follows from the angular correlation experiment. The two possible values (table 2) are in agreement with those reported by Twin et al. “). Independent of the branching ratios and the measured lifetime, the present experiment also excludes J” = (0, 1,3)-. Conclusion: Jn = 2-. The 15, = 3.44 and 4.25 MeV levels. No angular correlations have beeg measured for these levels. The parity of the 3.44 MeV level is unknown. However, a spin restriction to J = (1,2) can be made because independently of the parity of this level and the mixing of the two spin components in the capture state, the upper limits for the R-values for mixed primary transitions are 0.5 and 0.18 for J(3.44) = 0 and 3, respectively. Conclusion: J = (1,Z). The circular polarization result leads to 5’ = (1, 2)-(En = 1 [ref. 1‘)I) for the 4.25 MeV state.
The author wishes to thank Professor P. M. Endt and Dr. H. Gruppelaar for their interest in this work and their criticism of the manuscript. The assistance of P. Koonen in analysing the polarization data was appreciated. This investigation was performed as a joint research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Stichting Reactor Centrum N~derland (RCNI. References 1) L. V. Johnson and T. J. Kennet, Can. J. Phys. 48 (1970) 1109 2) A. M. F. Op den Kamp and A. M. J. Spits, Nucl. Phys. A180 (1972) 569 3) P. J. Twin, W. C. Olsen and D. M. Sheppard, Nucl. Phys. Al43 (1970) 481 4) R. Wechsnng, W. Strassheim and R. Bass, Nucl. Phys. Al79 (1971) 557 5) I?. Stecher-Rasmussen, K. Abrahams and J. Kopeckf, Nucl. Phys. A181 (1972) 225 6) J. Kopeckjr, K. Abrahams and F. Stecher-Rasmussen, Nucl. Phys. A188 (1972) 535 7) A. M. F. Op den Kamp et aZ., Phys. Lett. 39B (1972) 204 8) J. Honz&tko and J. Kajfosz, Phys. Lett. 38B (1972) 499 9) A. 3. Ferguson, Angular correlation methods in gamma-ray spectroscopy (North”~olland~ Amsterdam, 1965) 10) W. T. J. Sharp, J. M. Kennedy, B. 3. Sears and M. G. Hoyle, Tables of coefficients for angular ~s~ibution analysis, Chalk River report AECL-97 11) G. A. Bartholomew, Ann. Rev. of Nucl. Sci. 11 (1961) 259; H. T. Motz, Ann. Rev. &cl. Sci. 20 (1970) 1 12) K. Siegbahn, Alpha-, beta- and gamma-ray spectroscopy, vol. 2 (North-Holland, Amsterdam, 1965) 13) A. H. Wapstra, G. J. Nijgh and R. van Lieshout, Nuclear spectroscopy tables (North-Holland, Amsterdam, 1959) 14) G. van Middelkoop and P. Spilling, Nucl. Phys. 72 (1969) 1 15) P. Spilling, H. Gruppelaar and P. C. van den Berg, Int. Symp. on nuclear electronics, Versailles, 1968, part II, Contr. 140 16) H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 17) H. A. Enge, E. J. Irvin and D. H. Weaner, Phys. Rev. 115 (1959) 949 18) J. F. Boultier, W. V. Prestwich and B. Arad, Can. J. Phys. 47 (1969) 591