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Observation of the [505]112− Nilsson state as an isomer in 159Dy
1.E.l:
/
l.E.4
Nuclear Not
to
Physics be
72 (1965)
reproduced
by
OBSERVATION
509-5514;
photoprint
or
@
H. J. FRAHM,
Institute
without
OF THE [SOS]:-
AS AN ISOMER J. BORGGREEN,
North-Holland
microfilm
Physics,
permission
NILSSON
Co., Amsterdam from
the
publisher
STATE
IN 159Dy
N. J. SIGURD
for Theoretical
Publishing
written
HANSEN
University
and S. BJBRNHOLM
of Copenhagen
Received 17 May 1965 The 115i 10 psec isomer in IboDy has been produced by bombardment of lssTb with pulsed beams of protons and deuterons. The delayed y-rays were recorded with a NaI scintillation spectrometer and the delayed conversion lines with a magnetic spectrometer. The results are interpreted in terms of an isomeric level at 356&3 keV with (K, In) equal to (9, +-), decaying by K-forbidden Ml and E2 transitions to the g- and g- members of the ground-state rotational band in lsaDy. These properties serve to identify the isomeric level as the [N, nE,/l]Qn = [505] J& neutron state predicted by Nilsson.
Abstract:
E
NUCLEAR REACTIONS rssTb(p, n), E = 8-12 MeV, lS8Tb(d, 2n) E = 12 MeV, Gd(a, xn), E = 18 MeV; measured o(E& py-delay. raeDy deduced Tt. RADIOACITIVITY rs9Dy measured EY, Z,, cc. lsODy deduced levels, .Z,n.
1. Introduction
Most of the predicted one-particle states of the Nilsson model have been found and identified in numerous experimental investigations l, “) and thus allow a closer definition of the parameters of the model. There is still an uncertainty with respect to the energy separation between the major shells, however, and it is therefore of special interest to complete the list of observed Nilsson levels with the strongly sloping states that move in from the next higher or next lower major shells. In the region of N = 90-100, no data are available for the [Nn,A]CY = [505]-Iz1_state, which plays an important role in defining the nuclear equilibrium shape. It has been pointed out that this state is not easily populated in /?-decay; on the other hand, it might be observed as a short-lived isomer following a nuclear reaction ‘). This report presents evidence for the existence of a K” = ye isomeric level in identified as the [505]J$- state. ;;9D~9,, 2. Experimental
Procedure
When a metallic 159Tb target was bombarded with a pulsed beam of 10 MeV protons from the Institute’s tandem van de Graaff accelerator, a delayed y-ray of 118 keV decaying with a half life of 115 + 10 ~LSwas observed between the beam bursts. The excitation function, measured between 8 and 12 MeV proton energy, exhibits a dependence of bombarding energy typical of a (p, n) reaction, with a peak cross 509
3000-
LOOO-
‘1
K I-
I I
1
LPY
.lOO
(keV)
150 Electron energy
200
250
220/220 Asec
Tbls9(p.n)Dy'igm,lOMeVp
300
Fig. 1. Conversion line spectrum from the decay of 16smDy. The spectrum was obtained with the irradiation period and the measuring period both equal to 220,~s. The arrows at the bottom of the figure show where direct half life measurements were done. In addition, the decay rate of the stronger lines in the spectrum was established through a comparison of the count rate in the early half of the measuring period with that in the latter half of the measuring neriod. Hatched reoinn~ inrlirate Inn*-lkrn~ ,-fi----_.ln
o-
1000-
lAJ zooom
4
m 6 h
L CY
;
u
5000.
6OOOm
7000 -
-
OBSERVATION
OF
THE
[505]‘k-
NIUSON
511
STATE
section of about 3 mb. Irradiation of the target with 12 MeV deuterons produced the isomer with an eight times higher cross section, and also bombardments of natural gadolinium with 18 MeV z-particles produced the isomer. Furthermore, Krehbiel and Meyer-Berkhout 3, have observed the isomer in a (y, n) reaction with natural Dy. It can therefore safely be assigned to 15’Dy. The high ratio of the deuteron to proton cross sections indicates that the isomer has a rather high spin. In addition to the strong 118 keV y-ray several weaker y-rays together with K Xradiation were found (see table 1). The conversion electrons emitted between the beam bursts were recorded with a six-gap /?-spectrometer installed on the beam line. A spectrum is shown in fig. 1. TABLE
1
The y-rays. Energies, intensities and multipole orders
Transition &eV)
Assumed type
K/L theor.
(1)
(2)
(3)
-45 57kO.5 81 ho.7 10010.4 118hO.6 138ztl.O 181*1.0 218*1.5
K X-ray Ml
?
Ml Ml Ml E2 E2 E2
7.7 7.7 7.8 1.5 2.2 3.0
exp.
y-intensities % from from conversion y-spectrum lines
(4)
(5)
(6)
2.0 “)
192 15
183
6.811.2 6.5kl.O 1.9 10.7 2.410.4 2.5 ho.5
14 20 38 4.8 14 b) 5.6
12 17 48 <5 14 b) 5.0
mean value
Total intensity %
(7)
(8)
168&30 1515 14*3 18.5&3 43+8 4.8fl 14+3 5.6&l
168 *30 90 a)+30 75C)&l5 67 *lo 100 *20 8 +2 19 +4 7 il.5
8) The K conversion line intensity is obtained from cascade intensities instead of using the theoretical K/L intensity ratio. (The K electron binding energy of Dy is 53.8 keV. The extrapolation necessary for obtaining the theoretical value of the K conversion coefficient for the 57 keV transitions is therefore uncertain). b) This intensity is used as a normalization between the two spectra. “) K conversion line intensity obtained from K/L ratio and L line intensity.
The results, analysed in terms of energy, intensity and multipole orders, are presented in table 1. Columns 5 and 6 give a comparison between y-intensities deduced from the conversion line spectrum in fig. 1 and from scintillation y-spectra, respectively. Column 8 shows the total transition intensities in percentage of number of decays of the isomer. These values are obtained from the weighed mean values of the y-intensities in column 7 plus the intensities of the conversion lines. The resulting decay scheme, shown in fig. 2, is constructed from energy fits and a detailed intensity balance. It is consistent with the energy and intensity measurements within the limits of uncertainty.
J.
512
BORGGREEN
et al.
3. Discussion The four lower levels are interpreted Nilsson
state which forms the ground
as the rotational
band
built on the [521]3-
state ‘) of 159Dy. The energies,
and also the
E2/Ml intensity ratio for the decay of the f level, are closely similar to those of the analogous band 4, in 157Gd . The 356 keV level is regarded as the isomeric state. A calculation based on a best fit to the energies of the $, 3 and z levels indicates, however, that the y member of the rotational band lies at 362f 1 keV. It is suspiciously close to the measured energy of the isomeric level, and we cannot a priori exclude the
Fig.
2. Decay
scheme
of lssmDy. The total intensities in per cent are given addition to its energy and multipolarity.
for each
transition
in
possibility that the ylevel is a member of the rotational band. The isomeric level would then have to lie somewhat higher and decay by an unidentified transition. Such a possibility can, however, be ruled out through the following analysis of the E2/Ml branching ratios. Within a given rotational band the y-intensity ratio for the E2 cross-over transition and the Ml part of the cascade transition from a level (Z+2, K) to the levels (Z, K) and (I+ I, K), respectively, can be written Int,(E2; Int,(Ml;
Z+2 + I) Z+2 -+ Z+ 1)
’ (I+
1 +K)(Z+
K’(Z+
1 -K)
1)(21+3)
dE(E2)’ LLK(M~)~ ’
In the limit of adiabatic rotation, Qi/(gK-gR)2 is a constant; Q, is expressed in units of lo-24 cm2, (gK-gR) in nuclear magnetons and AE in keV, as in ref. ‘). The proportion of E2 y-radiation in the cascade transition can be calculated from the measured intensity of the pure E2 cross-over transition, using the formula “) for the branching ratios in the limit of adiabatic rotation. In this way the E2 component in the 81 keV y-ray is calculated to be only 3.2 ‘A of the total 81 keV y-intensity, in good agreement with the measurements by de Boer “) who finds a value of 3.8 % for the corresponding band in 15’Gd. From the formulae of ref. 6, one easily finds that the proportion of E2 radiation in the cascade transitions does not change more than
OBSERVATION
OF THE
[505]9-
10 % in going from Z+2 = s to Z+2 = y.
NILSSON
513
STATE
We can therefore
correct for this contri-
bution and calculate Q$(gk-gR)* from the above equation by inserting the slightly corrected y-intensities from table 1, together with the energies. Table 2 gives the values of Q$/(gk - gR)* obtained in this way, assuming K = 3 for all levels. Within the limits of the uncertainties the two first values are equal, as expected within a rotational band. The last value deviates
by almost
an order of magnitude,
indicating
that the
Z = q- level does not belong to the K = 3 band. It can therefore be concluded that it is the isomeric level. The long lifetime assures that it has Z = K (since Z = t is excluded). The decay by Ml and E2 transitions is compatible with K = 3,% or I$. The former two possibilities would, however, require that the 218 keV transition be predominantly Ml, in contrast to our observations, and also require the occurrence of a strong 299 keV E2/Ml transition which is not seen at all. Hence, the Kn = -'_:-assignment remains the only possible one. TABLE
2
Reduced E2/Ml branching ratios Branching
The partial
half lives of the isomeric
transitions
are for the y-part
218 keV E2: 2200 Z.LLS or 1 x lo5 s.p.u. 118 keV Ml: where s.p.u. E2 transition
285 ps or 2 x 10’ s.p.u.,
refers to the Weisskopf single-particle unit ‘). The twice K-forbidden is thus hindered 310 times and the Ml transition 270 times for each de-
gree of K-forbiddenness. These values are typical of the retardation caused by the K-selection rule. (It is worth noting that the possible mixing with the close-lying ‘-:_ level of the ground-state rotational band does not seem to cause any special enhancement of the transition rate). At an excitation energy of 356 keV, three-particle configurations are excluded for energetic reasons. The isomer must therefore represent a single-particle excitation. Examination of the Nilsson diagram then reveals the [505]?state as the only, and actually very straightforward, choice. Unfortunately, the measurements cannot tell whether the 356 keV level is a particle- or a hole-excitation; i.e. whether the [505]%state is located above or below the [521]$- state in the Nilsson diagram. A distinction between these alternatives would be possible if the K = J$ level could be identified in a number of other nuclei in the vicinity of ‘59Dy.
514
1.
BORGGREEN
et
01.
The authors wish to thank Civilingenirar Mogens Olesen and Civilingeni0r Per Hay-Christensen for their support in providing the experimental facilities at the tandem Van de Graaff accelerator and Professor Ben Mottelson for stimulating discussions References 1) B. Mottelson and S. G. Nilsson, Mat. Fys. Skr. Dan. Vid. Selsk. 1, No. 8 (1959) 2) 0. Nathan and S. G. Nilsson, in Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1965); A. Johansen, private communication (1963) 3) H. Krehbiel and U. Meyer-Berkhout, Z. Phys. 165 (1961) 99 4) J. de Boer, Helv. Phys. Acta 5 (1959) 377 5) P. Alexander, F. Boehm and E. Kankeleit, Phys. Rev. 133 (1964) B284 6) A. Bohr and B. Mottelson, Mat. Fys. Medd. Dan. Vid. Selsk. 27, No. 16 (1953) 7) A. H. Wapstra, G. 5. Nijgh and R. van Lieshout, Nuclear Spectroscopy Tables (North-Holland Publ. Co., Amsterdam, 1959)
/
l.E.4
Nuclear Not
to
Physics be
72 (1965)
reproduced
by
OBSERVATION
509-5514;
photoprint
or
@
H. J. FRAHM,
Institute
without
OF THE [SOS]:-
AS AN ISOMER J. BORGGREEN,
North-Holland
microfilm
Physics,
permission
NILSSON
Co., Amsterdam from
the
publisher
STATE
IN 159Dy
N. J. SIGURD
for Theoretical
Publishing
written
HANSEN
University
and S. BJBRNHOLM
of Copenhagen
Received 17 May 1965 The 115i 10 psec isomer in IboDy has been produced by bombardment of lssTb with pulsed beams of protons and deuterons. The delayed y-rays were recorded with a NaI scintillation spectrometer and the delayed conversion lines with a magnetic spectrometer. The results are interpreted in terms of an isomeric level at 356&3 keV with (K, In) equal to (9, +-), decaying by K-forbidden Ml and E2 transitions to the g- and g- members of the ground-state rotational band in lsaDy. These properties serve to identify the isomeric level as the [N, nE,/l]Qn = [505] J& neutron state predicted by Nilsson.
Abstract:
E
NUCLEAR REACTIONS rssTb(p, n), E = 8-12 MeV, lS8Tb(d, 2n) E = 12 MeV, Gd(a, xn), E = 18 MeV; measured o(E& py-delay. raeDy deduced Tt. RADIOACITIVITY rs9Dy measured EY, Z,, cc. lsODy deduced levels, .Z,n.
1. Introduction
Most of the predicted one-particle states of the Nilsson model have been found and identified in numerous experimental investigations l, “) and thus allow a closer definition of the parameters of the model. There is still an uncertainty with respect to the energy separation between the major shells, however, and it is therefore of special interest to complete the list of observed Nilsson levels with the strongly sloping states that move in from the next higher or next lower major shells. In the region of N = 90-100, no data are available for the [Nn,A]CY = [505]-Iz1_state, which plays an important role in defining the nuclear equilibrium shape. It has been pointed out that this state is not easily populated in /?-decay; on the other hand, it might be observed as a short-lived isomer following a nuclear reaction ‘). This report presents evidence for the existence of a K” = ye isomeric level in identified as the [505]J$- state. ;;9D~9,, 2. Experimental
Procedure
When a metallic 159Tb target was bombarded with a pulsed beam of 10 MeV protons from the Institute’s tandem van de Graaff accelerator, a delayed y-ray of 118 keV decaying with a half life of 115 + 10 ~LSwas observed between the beam bursts. The excitation function, measured between 8 and 12 MeV proton energy, exhibits a dependence of bombarding energy typical of a (p, n) reaction, with a peak cross 509
3000-
LOOO-
‘1
K I-
I I
1
LPY
.lOO
(keV)
150 Electron energy
200
250
220/220 Asec
Tbls9(p.n)Dy'igm,lOMeVp
300
Fig. 1. Conversion line spectrum from the decay of 16smDy. The spectrum was obtained with the irradiation period and the measuring period both equal to 220,~s. The arrows at the bottom of the figure show where direct half life measurements were done. In addition, the decay rate of the stronger lines in the spectrum was established through a comparison of the count rate in the early half of the measuring period with that in the latter half of the measuring neriod. Hatched reoinn~ inrlirate Inn*-lkrn~ ,-fi----_.ln
o-
1000-
lAJ zooom
4
m 6 h
L CY
;
u
5000.
6OOOm
7000 -
-
OBSERVATION
OF
THE
[505]‘k-
NIUSON
511
STATE
section of about 3 mb. Irradiation of the target with 12 MeV deuterons produced the isomer with an eight times higher cross section, and also bombardments of natural gadolinium with 18 MeV z-particles produced the isomer. Furthermore, Krehbiel and Meyer-Berkhout 3, have observed the isomer in a (y, n) reaction with natural Dy. It can therefore safely be assigned to 15’Dy. The high ratio of the deuteron to proton cross sections indicates that the isomer has a rather high spin. In addition to the strong 118 keV y-ray several weaker y-rays together with K Xradiation were found (see table 1). The conversion electrons emitted between the beam bursts were recorded with a six-gap /?-spectrometer installed on the beam line. A spectrum is shown in fig. 1. TABLE
1
The y-rays. Energies, intensities and multipole orders
Transition &eV)
Assumed type
K/L theor.
(1)
(2)
(3)
-45 57kO.5 81 ho.7 10010.4 118hO.6 138ztl.O 181*1.0 218*1.5
K X-ray Ml
?
Ml Ml Ml E2 E2 E2
7.7 7.7 7.8 1.5 2.2 3.0
exp.
y-intensities % from from conversion y-spectrum lines
(4)
(5)
(6)
2.0 “)
192 15
183
6.811.2 6.5kl.O 1.9 10.7 2.410.4 2.5 ho.5
14 20 38 4.8 14 b) 5.6
12 17 48 <5 14 b) 5.0
mean value
Total intensity %
(7)
(8)
168&30 1515 14*3 18.5&3 43+8 4.8fl 14+3 5.6&l
168 *30 90 a)+30 75C)&l5 67 *lo 100 *20 8 +2 19 +4 7 il.5
8) The K conversion line intensity is obtained from cascade intensities instead of using the theoretical K/L intensity ratio. (The K electron binding energy of Dy is 53.8 keV. The extrapolation necessary for obtaining the theoretical value of the K conversion coefficient for the 57 keV transitions is therefore uncertain). b) This intensity is used as a normalization between the two spectra. “) K conversion line intensity obtained from K/L ratio and L line intensity.
The results, analysed in terms of energy, intensity and multipole orders, are presented in table 1. Columns 5 and 6 give a comparison between y-intensities deduced from the conversion line spectrum in fig. 1 and from scintillation y-spectra, respectively. Column 8 shows the total transition intensities in percentage of number of decays of the isomer. These values are obtained from the weighed mean values of the y-intensities in column 7 plus the intensities of the conversion lines. The resulting decay scheme, shown in fig. 2, is constructed from energy fits and a detailed intensity balance. It is consistent with the energy and intensity measurements within the limits of uncertainty.
J.
512
BORGGREEN
et al.
3. Discussion The four lower levels are interpreted Nilsson
state which forms the ground
as the rotational
band
built on the [521]3-
state ‘) of 159Dy. The energies,
and also the
E2/Ml intensity ratio for the decay of the f level, are closely similar to those of the analogous band 4, in 157Gd . The 356 keV level is regarded as the isomeric state. A calculation based on a best fit to the energies of the $, 3 and z levels indicates, however, that the y member of the rotational band lies at 362f 1 keV. It is suspiciously close to the measured energy of the isomeric level, and we cannot a priori exclude the
Fig.
2. Decay
scheme
of lssmDy. The total intensities in per cent are given addition to its energy and multipolarity.
for each
transition
in
possibility that the ylevel is a member of the rotational band. The isomeric level would then have to lie somewhat higher and decay by an unidentified transition. Such a possibility can, however, be ruled out through the following analysis of the E2/Ml branching ratios. Within a given rotational band the y-intensity ratio for the E2 cross-over transition and the Ml part of the cascade transition from a level (Z+2, K) to the levels (Z, K) and (I+ I, K), respectively, can be written Int,(E2; Int,(Ml;
Z+2 + I) Z+2 -+ Z+ 1)
’ (I+
1 +K)(Z+
K’(Z+
1 -K)
1)(21+3)
dE(E2)’ LLK(M~)~ ’
In the limit of adiabatic rotation, Qi/(gK-gR)2 is a constant; Q, is expressed in units of lo-24 cm2, (gK-gR) in nuclear magnetons and AE in keV, as in ref. ‘). The proportion of E2 y-radiation in the cascade transition can be calculated from the measured intensity of the pure E2 cross-over transition, using the formula “) for the branching ratios in the limit of adiabatic rotation. In this way the E2 component in the 81 keV y-ray is calculated to be only 3.2 ‘A of the total 81 keV y-intensity, in good agreement with the measurements by de Boer “) who finds a value of 3.8 % for the corresponding band in 15’Gd. From the formulae of ref. 6, one easily finds that the proportion of E2 radiation in the cascade transitions does not change more than
OBSERVATION
OF THE
[505]9-
10 % in going from Z+2 = s to Z+2 = y.
NILSSON
513
STATE
We can therefore
correct for this contri-
bution and calculate Q$(gk-gR)* from the above equation by inserting the slightly corrected y-intensities from table 1, together with the energies. Table 2 gives the values of Q$/(gk - gR)* obtained in this way, assuming K = 3 for all levels. Within the limits of the uncertainties the two first values are equal, as expected within a rotational band. The last value deviates
by almost
an order of magnitude,
indicating
that the
Z = q- level does not belong to the K = 3 band. It can therefore be concluded that it is the isomeric level. The long lifetime assures that it has Z = K (since Z = t is excluded). The decay by Ml and E2 transitions is compatible with K = 3,% or I$. The former two possibilities would, however, require that the 218 keV transition be predominantly Ml, in contrast to our observations, and also require the occurrence of a strong 299 keV E2/Ml transition which is not seen at all. Hence, the Kn = -'_:-assignment remains the only possible one. TABLE
2
Reduced E2/Ml branching ratios Branching
The partial
half lives of the isomeric
transitions
are for the y-part
218 keV E2: 2200 Z.LLS or 1 x lo5 s.p.u. 118 keV Ml: where s.p.u. E2 transition
285 ps or 2 x 10’ s.p.u.,
refers to the Weisskopf single-particle unit ‘). The twice K-forbidden is thus hindered 310 times and the Ml transition 270 times for each de-
gree of K-forbiddenness. These values are typical of the retardation caused by the K-selection rule. (It is worth noting that the possible mixing with the close-lying ‘-:_ level of the ground-state rotational band does not seem to cause any special enhancement of the transition rate). At an excitation energy of 356 keV, three-particle configurations are excluded for energetic reasons. The isomer must therefore represent a single-particle excitation. Examination of the Nilsson diagram then reveals the [505]?state as the only, and actually very straightforward, choice. Unfortunately, the measurements cannot tell whether the 356 keV level is a particle- or a hole-excitation; i.e. whether the [505]%state is located above or below the [521]$- state in the Nilsson diagram. A distinction between these alternatives would be possible if the K = J$ level could be identified in a number of other nuclei in the vicinity of ‘59Dy.
514
1.
BORGGREEN
et
01.
The authors wish to thank Civilingenirar Mogens Olesen and Civilingeni0r Per Hay-Christensen for their support in providing the experimental facilities at the tandem Van de Graaff accelerator and Professor Ben Mottelson for stimulating discussions References 1) B. Mottelson and S. G. Nilsson, Mat. Fys. Skr. Dan. Vid. Selsk. 1, No. 8 (1959) 2) 0. Nathan and S. G. Nilsson, in Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1965); A. Johansen, private communication (1963) 3) H. Krehbiel and U. Meyer-Berkhout, Z. Phys. 165 (1961) 99 4) J. de Boer, Helv. Phys. Acta 5 (1959) 377 5) P. Alexander, F. Boehm and E. Kankeleit, Phys. Rev. 133 (1964) B284 6) A. Bohr and B. Mottelson, Mat. Fys. Medd. Dan. Vid. Selsk. 27, No. 16 (1953) 7) A. H. Wapstra, G. 5. Nijgh and R. van Lieshout, Nuclear Spectroscopy Tables (North-Holland Publ. Co., Amsterdam, 1959)