- Email: [email protected]
Quadrupole moments of 81+ states in 92,94Mo
Volume 48B, number 3
PHYSICS LETTERS
QUADRUPOLE MOMENTS
4 February 1974
STATES IN 92'94Mo
OF 8~
C.V.K. BABA *1, D.B. FOSSAN .2,
Sektion Physik, Universita't Mfinchen, 8046, Garching, Germany T. FAESTERMANN, F. FEILITZSCH, K.E.G. LOBNER and C. SIGNORIN1.3
Physik-Department, Technische Universita't Mfinchen, 8046 Garching, Germany Received 11 January 1974 The ratio of the quadrupole moments of the 8~ states in 92'94Mo has been measured asQ(94Mo)/Q(92Mo) = 1.48 _+0.12 by means of the TD PAD method following the 9°,92Zr(ct, 2n)92,94Mo reactions on enriched Zr metal foils. This ratio is consistent wit.h the effective charge ratio for the 8 + ~ 6 + E2 transitions which demonstrates a prediction of the effective charge concept.
The present letter reports on a measurement of the ratio of two static quadrupole moments by means of the time-differential perturbed angular distribution (TD PAD) method following nuclear reactions. Such measurements have only been performed in a few cases until now [1, 2]. While the extraction of the quadrupole moment (QM) from such TD PAD experiments is not generally reliable, for lack o f knowledge o f the electric field gradient (EFG), the ratios o f excited-state QM values in isotopes of a given element can be reliably determined. In the present measurement, enriched metallic foils o f 90Zr and 92Zr ( ~ 2 mg/cm2), which have a hexagonal closed packed crystal structure, were used as b o t h target and stopping environment to study the quadrupole interaction o f the 8 + levels in 92Mo (E x = 2.76 MeV, T1/2 = 188-+4 ns) and 94Mo (E x = 2.95 MeV, T1/2 = 98-+2 ns) (see insets of fig. 1) populated by the 9°,92Zr(a, 2n)92,94Mo reactions. A pulsed 24 MeV a-particle beam (FWHM < 1 ns and repetition time 1.6/as) of ~ 10 nA from the Munich MP tandem accelerator was used. The beam was stopped in a thick Au foil immediately behind the Zr targets. The measurements were performed with two 5 cm X 5 cm ~ Na I(T1) detectors at 10 cm from the target. In the case of 94Mo, a broad energy window .1 Alexander yon Humboldt fellow; permanent address: Nuclear Physics Division, Bhabha Atomic Research Centre, Trombay, Bombay, India *2Present address: State University of New York at Stony Brook, N.Y. *3On leave from lstituto di Fisica and INFN Padova, Italy. 218
0.12-
'
~. ~L~o, 2;~
'
'
0.I00.080.06-
~"~0.04-
~k
0.020.00
94M°
t'~t~?'
'
I I' I
- 0.02-
I
I
I
I
¢
All°w"
0
,
I
I
I
I
1
4oo time
I
I
I
(
2oo
iI I
z761
/ /
I
I
600
I
800
(ns)
Fig. 1. Experimental results of A2(t) for the case of 94Mo (upper halo and the ratio W(0)/W(90 °) for the case of 92Mo (lower half). The solid lines represent least-squares fits to the data of a static quadrupole interaction.
Volume 48B, number 3
PHYSICS LETTERS
650 to 900 keV was selected to include the 6 + -+ 4 +, 4 + ~ 2 +, and 2 + ~ 0 + stretched E2 transitions, while the 773 keV 4 + ~ 2 + transition was selected in the case of 92Mo. The time spectra were obtained with counters at 0 °, -+45° and +90 ° with respect to the beam direction in the case of 94Mo and only at 0 ° and +90 ° in the case of 92Mo due to lower counting rates. The data were analysed to obtain the angular distribution coefficients A2(t) and A4(t) in the case of 94Mo and W(O°)/W(90 °) as a function of time in the case of 92Mo. The experimental results are presented in fig. 1. The angular distribution coefficients Ak(t ) expected for the case of a pure electric quadrupole interaction of a quadrupole moment Q of a state with spin I with an axially symmetric EFG (Vzz) are given by
Ak(t ) = Ak(O ) Gk(t ),
( 1a)
Gk(t) = ~ Skn cos (neOot),
(lb)
n
w ° = 3eQVzz/h4I(2I-
1).
(lc)
From a least-squares fit of the A2(t ) data for 94Mo to eq..(1) the parametersA2(0 ) = 0.125 +- 0.010 and w o = 0.93 + 0.05 MHz were obtained. The Skn values for I = 8 were taken from a tabulation by Raghavan [3]. The frequency w o obtained from the A4(t ) data is less accurate but is consistent with the value obtained from the A2(t ) data. In the case of 92Mo, only the anisotropy W(O°)/W(90 °) was measured as a function of time; it was fit withA2(0) and w o as parameters keeping the ratio A 4(0)/A 2(0) fixed to the value obtained for 94Mo. The results are: A2(0 ) = 0.082 + 0.015 and ~ o = 0.63 -+ 0.04 MHz. The uncertainties account for the fact that up to 15% of the recoiling nuclei may stop in the cubic Au backing. The A 2(0) coefficients in these two cases are approximately the same, as expected, but they are significantly lower than the calculated values for complete alignment of the 8 + states. The least-squares fits are presented in fig. 1 by the solid lines. From the ratio o f the two interaction frequencies one obtains Q(8 + 94Mo)/Q(8 + 92Mo) = 1.48 +- 0.12. The lowest-lying positive parity levels in 92Mo have been interpreted as largely seniority-two states arising
4 February 1974
from a (Tr.g9/2) 2 configuration. The effective charges for the 8 + -+ 6 + and 6 + -~ 4 + transitions have been found to be equal [4] with eeff = 1.45 + 0.05 e. In 94Mo, there are two 6 + states (see fig. 1) to which the 8 + level decays by E2 transitions. The 7ray decay data [5] and the measured magnetic moment [6] point to the (7rg9/2) 2 nature of the 8 + level in 94Mo. From the known data [5, 6] one can deduce the B(E2) values for the two 8 + ~ 6 + E2 transitions of 84 and 532 keV to be 97 +- 18 e2fm 4 and 0.1 e 2 fm 4, respectively. It is reasonable on the basis o f these drastically different B(E2) values to conclude that the 2.87 MeV 6 + level originates from the (n g9/2) 2 configuration while the 2.42 MeV level most likely results from neutron excitation. The 7rg9/2 effective charge obtained from the 84 keV B(E2) in 94Mo is 2.54 -+ 0.22 e which is 1.75 + 0.18 times that in 92Mo. This ratio of the effective charges from the 8 + 6 + B(E2) values of 92,94Mo is in reasonable agreement with the ratio of the measured quadrupole moments of the 8 + levels in those isotopes. Those two ratios are expected to be the same according to the concept of the effective charge, provided that the wave functions are pure, in our case seniority-two (Trg9/2) 2, configurations. According to this concept the following relations are valid for the quadrupole moment Q of state I (//-)2 and B(E2) values between levels I (lj)2 and I ' (//')2:
IQ{ I(lj)2) I =
2(2I+1)
x / . ~ ( I I I 2)(I I ~} F IOjj
and
x/N{E2;i(lj)2_.l,(lj)2}__2 ~
{,,} 1
2 F
JJJ with
F = (ljtlM(E2)
lllj)(eeff/e).
The presently measured QM ratio 1.48 +- 0.12 for the 8 + levels and the ratio of the B(E2; 8 + ~ 6 +) values in 92,94Mo 1.75 -+ 0.18 are equal within the error limits showing that the effective charge concept is correct in this respect. Assuming thus that the effective g9/2 proton charge is the same for the transition rates and the quadrupole moments, the QM values o f the 8 + levels in 92Mo and 94Mo can be calculated to be IQ(8 + 92Mo)1 219
Volume 48B, number 3
PHYSICS LETTERS
= 0.35 -+ 0.02 b and IQ(8 + 94Mo)1 = 0.52 -+ 0.07 b. Further the calculated QM of the ground state of 93Nb is: IQI = 0.36 -+ 0.03 b for eeff(Trg9/2) = 1.46 +--0.05 e and eeff(Pds/2) --- 2.1 -+ 0.2 e using the ground state wave function for 93Nb as given by Sweet et al. [7]. This value is in reasonable agreement with the experimental results o f - 0 . 2 5 -+ 0.15 b and - 0 . 2 0 b [8]. From the deduced QM value of the 92Mo 8 + state and tile observed quadrupole interaction frequency, one obtains Vzz ~ 1.9 X 1017 V c m - 2 for the EFG at the Mo site in a Zr lattice. It is a pleasure to acknowledge Dipl. Phys. R.P. Rudolph for continuous assistance with the pulsing system. Two of the authors (C.V.K.B. and D.B.F.) wish to thank Sektion Physik der Universit~t Mtinchen and Professor J. de Boer for hospitality during their stay in Munich.
220
4 February 1974
References [1] J.M. McDonald, P.M.S. Lesser and D.B. Fossan, Phys. Rev. Lett. 28 (1972) 1057. [2] H. Haas et al., Suppl. J. Phys. Soc. Japan 34 (1973) 221. [3] P. Raghavan, private communication (1971). [4] S. Cochavi, J.M. McDonald and D.B. Fossan, Phys. Rev. C3 (1971) 1352; there is a numerical error of a factor in this reference for the effective charge of the 8+ ~ 6+ and 6+ ~ 4÷ transitions. The correct values are 1.46 and 1.44, respectively. [5 ] C.M. Lederer, J.M. Jaklevic and J.M. Hollander, Nucl. Phys. A169 (1971) 449. [6] T. Faestermann et al., Suppl. J. Phys. Soc. Japan 34 (1973) 261. [7] R.F. Sweet, K.H. Bhatt and J.B. Ball, Phys. Lett. 8 (1964) 131. [8] G.H. Fuller and V.W. Cohen, Nucl. Data Tables A5 (1969) 433.
PHYSICS LETTERS
QUADRUPOLE MOMENTS
4 February 1974
STATES IN 92'94Mo
OF 8~
C.V.K. BABA *1, D.B. FOSSAN .2,
Sektion Physik, Universita't Mfinchen, 8046, Garching, Germany T. FAESTERMANN, F. FEILITZSCH, K.E.G. LOBNER and C. SIGNORIN1.3
Physik-Department, Technische Universita't Mfinchen, 8046 Garching, Germany Received 11 January 1974 The ratio of the quadrupole moments of the 8~ states in 92'94Mo has been measured asQ(94Mo)/Q(92Mo) = 1.48 _+0.12 by means of the TD PAD method following the 9°,92Zr(ct, 2n)92,94Mo reactions on enriched Zr metal foils. This ratio is consistent wit.h the effective charge ratio for the 8 + ~ 6 + E2 transitions which demonstrates a prediction of the effective charge concept.
The present letter reports on a measurement of the ratio of two static quadrupole moments by means of the time-differential perturbed angular distribution (TD PAD) method following nuclear reactions. Such measurements have only been performed in a few cases until now [1, 2]. While the extraction of the quadrupole moment (QM) from such TD PAD experiments is not generally reliable, for lack o f knowledge o f the electric field gradient (EFG), the ratios o f excited-state QM values in isotopes of a given element can be reliably determined. In the present measurement, enriched metallic foils o f 90Zr and 92Zr ( ~ 2 mg/cm2), which have a hexagonal closed packed crystal structure, were used as b o t h target and stopping environment to study the quadrupole interaction o f the 8 + levels in 92Mo (E x = 2.76 MeV, T1/2 = 188-+4 ns) and 94Mo (E x = 2.95 MeV, T1/2 = 98-+2 ns) (see insets of fig. 1) populated by the 9°,92Zr(a, 2n)92,94Mo reactions. A pulsed 24 MeV a-particle beam (FWHM < 1 ns and repetition time 1.6/as) of ~ 10 nA from the Munich MP tandem accelerator was used. The beam was stopped in a thick Au foil immediately behind the Zr targets. The measurements were performed with two 5 cm X 5 cm ~ Na I(T1) detectors at 10 cm from the target. In the case of 94Mo, a broad energy window .1 Alexander yon Humboldt fellow; permanent address: Nuclear Physics Division, Bhabha Atomic Research Centre, Trombay, Bombay, India *2Present address: State University of New York at Stony Brook, N.Y. *3On leave from lstituto di Fisica and INFN Padova, Italy. 218
0.12-
'
~. ~L~o, 2;~
'
'
0.I00.080.06-
~"~0.04-
~k
0.020.00
94M°
t'~t~?'
'
I I' I
- 0.02-
I
I
I
I
¢
All°w"
0
,
I
I
I
I
1
4oo time
I
I
I
(
2oo
iI I
z761
/ /
I
I
600
I
800
(ns)
Fig. 1. Experimental results of A2(t) for the case of 94Mo (upper halo and the ratio W(0)/W(90 °) for the case of 92Mo (lower half). The solid lines represent least-squares fits to the data of a static quadrupole interaction.
Volume 48B, number 3
PHYSICS LETTERS
650 to 900 keV was selected to include the 6 + -+ 4 +, 4 + ~ 2 +, and 2 + ~ 0 + stretched E2 transitions, while the 773 keV 4 + ~ 2 + transition was selected in the case of 92Mo. The time spectra were obtained with counters at 0 °, -+45° and +90 ° with respect to the beam direction in the case of 94Mo and only at 0 ° and +90 ° in the case of 92Mo due to lower counting rates. The data were analysed to obtain the angular distribution coefficients A2(t) and A4(t) in the case of 94Mo and W(O°)/W(90 °) as a function of time in the case of 92Mo. The experimental results are presented in fig. 1. The angular distribution coefficients Ak(t ) expected for the case of a pure electric quadrupole interaction of a quadrupole moment Q of a state with spin I with an axially symmetric EFG (Vzz) are given by
Ak(t ) = Ak(O ) Gk(t ),
( 1a)
Gk(t) = ~ Skn cos (neOot),
(lb)
n
w ° = 3eQVzz/h4I(2I-
1).
(lc)
From a least-squares fit of the A2(t ) data for 94Mo to eq..(1) the parametersA2(0 ) = 0.125 +- 0.010 and w o = 0.93 + 0.05 MHz were obtained. The Skn values for I = 8 were taken from a tabulation by Raghavan [3]. The frequency w o obtained from the A4(t ) data is less accurate but is consistent with the value obtained from the A2(t ) data. In the case of 92Mo, only the anisotropy W(O°)/W(90 °) was measured as a function of time; it was fit withA2(0) and w o as parameters keeping the ratio A 4(0)/A 2(0) fixed to the value obtained for 94Mo. The results are: A2(0 ) = 0.082 + 0.015 and ~ o = 0.63 -+ 0.04 MHz. The uncertainties account for the fact that up to 15% of the recoiling nuclei may stop in the cubic Au backing. The A 2(0) coefficients in these two cases are approximately the same, as expected, but they are significantly lower than the calculated values for complete alignment of the 8 + states. The least-squares fits are presented in fig. 1 by the solid lines. From the ratio o f the two interaction frequencies one obtains Q(8 + 94Mo)/Q(8 + 92Mo) = 1.48 +- 0.12. The lowest-lying positive parity levels in 92Mo have been interpreted as largely seniority-two states arising
4 February 1974
from a (Tr.g9/2) 2 configuration. The effective charges for the 8 + -+ 6 + and 6 + -~ 4 + transitions have been found to be equal [4] with eeff = 1.45 + 0.05 e. In 94Mo, there are two 6 + states (see fig. 1) to which the 8 + level decays by E2 transitions. The 7ray decay data [5] and the measured magnetic moment [6] point to the (7rg9/2) 2 nature of the 8 + level in 94Mo. From the known data [5, 6] one can deduce the B(E2) values for the two 8 + ~ 6 + E2 transitions of 84 and 532 keV to be 97 +- 18 e2fm 4 and 0.1 e 2 fm 4, respectively. It is reasonable on the basis o f these drastically different B(E2) values to conclude that the 2.87 MeV 6 + level originates from the (n g9/2) 2 configuration while the 2.42 MeV level most likely results from neutron excitation. The 7rg9/2 effective charge obtained from the 84 keV B(E2) in 94Mo is 2.54 -+ 0.22 e which is 1.75 + 0.18 times that in 92Mo. This ratio of the effective charges from the 8 + 6 + B(E2) values of 92,94Mo is in reasonable agreement with the ratio of the measured quadrupole moments of the 8 + levels in those isotopes. Those two ratios are expected to be the same according to the concept of the effective charge, provided that the wave functions are pure, in our case seniority-two (Trg9/2) 2, configurations. According to this concept the following relations are valid for the quadrupole moment Q of state I (//-)2 and B(E2) values between levels I (lj)2 and I ' (//')2:
IQ{ I(lj)2) I =
2(2I+1)
x / . ~ ( I I I 2)(I I ~} F IOjj
and
x/N{E2;i(lj)2_.l,(lj)2}__2 ~
{,,} 1
2 F
JJJ with
F = (ljtlM(E2)
lllj)(eeff/e).
The presently measured QM ratio 1.48 +- 0.12 for the 8 + levels and the ratio of the B(E2; 8 + ~ 6 +) values in 92,94Mo 1.75 -+ 0.18 are equal within the error limits showing that the effective charge concept is correct in this respect. Assuming thus that the effective g9/2 proton charge is the same for the transition rates and the quadrupole moments, the QM values o f the 8 + levels in 92Mo and 94Mo can be calculated to be IQ(8 + 92Mo)1 219
Volume 48B, number 3
PHYSICS LETTERS
= 0.35 -+ 0.02 b and IQ(8 + 94Mo)1 = 0.52 -+ 0.07 b. Further the calculated QM of the ground state of 93Nb is: IQI = 0.36 -+ 0.03 b for eeff(Trg9/2) = 1.46 +--0.05 e and eeff(Pds/2) --- 2.1 -+ 0.2 e using the ground state wave function for 93Nb as given by Sweet et al. [7]. This value is in reasonable agreement with the experimental results o f - 0 . 2 5 -+ 0.15 b and - 0 . 2 0 b [8]. From the deduced QM value of the 92Mo 8 + state and tile observed quadrupole interaction frequency, one obtains Vzz ~ 1.9 X 1017 V c m - 2 for the EFG at the Mo site in a Zr lattice. It is a pleasure to acknowledge Dipl. Phys. R.P. Rudolph for continuous assistance with the pulsing system. Two of the authors (C.V.K.B. and D.B.F.) wish to thank Sektion Physik der Universit~t Mtinchen and Professor J. de Boer for hospitality during their stay in Munich.
220
4 February 1974
References [1] J.M. McDonald, P.M.S. Lesser and D.B. Fossan, Phys. Rev. Lett. 28 (1972) 1057. [2] H. Haas et al., Suppl. J. Phys. Soc. Japan 34 (1973) 221. [3] P. Raghavan, private communication (1971). [4] S. Cochavi, J.M. McDonald and D.B. Fossan, Phys. Rev. C3 (1971) 1352; there is a numerical error of a factor in this reference for the effective charge of the 8+ ~ 6+ and 6+ ~ 4÷ transitions. The correct values are 1.46 and 1.44, respectively. [5 ] C.M. Lederer, J.M. Jaklevic and J.M. Hollander, Nucl. Phys. A169 (1971) 449. [6] T. Faestermann et al., Suppl. J. Phys. Soc. Japan 34 (1973) 261. [7] R.F. Sweet, K.H. Bhatt and J.B. Ball, Phys. Lett. 8 (1964) 131. [8] G.H. Fuller and V.W. Cohen, Nucl. Data Tables A5 (1969) 433.