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The radiative width of the 8+ member of the Kπ = 2+ band in 24Mg
Volume 69B, number 1
THE RADIATIVE
PHYSICS LETTERS
18 July 1977
W I D T H O F T H E 8 ÷ M E M B E R O F T H E K " = 2 ÷ B A N D I N 24 M g
L.K. FIFIELD, M.J. HURST, T.J.M. SYMONS, F. WATT and K.W. ALLEN Nuclear Physics Laboratory, Keble Road, Oxford, UK Received 2 May 1977 The radmtwe width of the 14.15 MeV, 8+, K ~r= 2+ level m 24Mg has been measured using the Z°Ne(a, ~.)24Mg reaction and a dffferentmlly cryopumped gas target. The result, F,r = 85 ± 23 meV, lmphes E2 strengths of 9.1 ± 2.4 and 0.8 +-0.2 W.u. for the transiUons to the 9.53 (6 ÷, K rr = 2+) and 8 11 (6 +, K ~r= 0÷) MeV levels, respectwely. These are in excellent agreement with the predictions of recent large basis shell model calculations. The extent to which rotational band structure persists in deformed hght nuclei as the nuclear spin Increases has been the subject o f considerable theoretical [ 1 - 3 ] and experimental [4, 5] interest in recent years. In 24Mg there are two well known positive parity bands which are believed to have the structure of eight particles in the 2 s - l d shell outside an 160 core, namely K ~r = 0 ÷ and 2 ÷ bands budt on the ground state and 4.24 MeV (2 +) state, respect:rely. Both bands have been identified only as far as the 8 + members, and m-band E2 v-ray transition strengths, which serve as an Indicator of band structure, have been measured [5] up to the 8 + member of the groundstate band and up to the 7 ÷ member of the K n = 2 + band. With the development of the Glasgow shell model code, it has become possible to calculate the excitation energies and electromagnetic transition rates within these bands using an untruncated (sd) 8 basis, and to extend the calculations to levels with J > 8 which have not yet been located experimentally. One would hope to determine from such calculations whether the band structure pers:sts up to the (sd) 8 spin 12 hmit, or only up to some critical lower spin value. The results, as reported recently by Watt, Kelvin and Whitehead [1 ], favour the latter possibility with the crit:cal spin value lying between J = 8 and J = 10. In b o t h bands, the in-band E2 v-ray transitions from the 8 + members are predicted to be substantially weaker than the strongly enhanced trans:tions between lower members of the bands, and above J = 9 the band structure effectwely disappears. In so far as the properties o f the bands have been determined experimentally, they are in reasonable agreement with the calculations. This applies to the
excitation energies, to the strongly enhanced in-band E2 v-ray transitions, and to the relatively weak crossband transitions. However, the crucial test of the calculations, and hence of their predictive power with respect to the states with J > 8, hes in the measurement of the in-band transltxon rates from the two 8 + states at 13.21 (K ~ = 0 +) and 14.15 (K ~r = 2 +) MeV. Although the lifetime of the 13.21 MeV level has been measured [5] by the Doppler shift attenuation method, the experimental uncertainty is large owing to the difficulties associated with measuring lifetimes of a few fs, and the result is not sufficiently accurate to verify the predicted fall-off in E2 transition strength. For the 14.15 MeV level, only a lower limit of 3 W.u. has been established [5] for the in-band E2 transition to the 9.53 MeV (6 +, K ~ --- 2 +) level using the same technique. However, whereas the 13 21 MeV level decays only by v-ray emission, the decay strength of the 14.15 MeV level is shared between v-ray emission and a-particle emission to the ground and 1.63 MeV states in 20Ne. This allows the possibihty o f measuring the radiative width of the 14.15 MeV level (but not of the 13.21 MeV level) by studying it as a resonance m the 20Ne(a, V)24Mg reaction. The purpose of this letter is to report the result of such a measurement which is sufficiently accurate to allow meaningful comparison with the theoretical calculations This measurement employed a differentially cryopumped gas target [6, 7], with beams o f a-particles obtained from the Oxford 10 MV Van de Graaff accelerator. The use of the gas target ensured that the level of background v-rays was low, and in particular that the yield of 6.13 MeV v-rays from the prolific 13C(a, n v ) 1 6 0 reaction was neghgible. This was an 45
Volume 69B, n u m b e r 1
PHYSICS LETTERS
I
8.7..
11. 11.5 800
R "-'~ 6 12
60(] 1.00 200
4.0,.< E y ¢ 4 7 R .--~ 9 . 5 3
300
20C
~
100
I
I
3 4~
30C
9.53 ~
i
6 01
200 100
I
I
5 80
5 81 E~ (MeV)
Fig 1. Gamma-ray yield curves for the 2°Ne(~, -r)24Mg reaction m the viciruty o f E a = 5.8 MeV. The three curves shown were obtained with gates set about the m & c a t e d regions o f the y-ray energy spectrum, and the resonances are labelled by the corresponding excitation energy m 24Mg. All energies are m MeV. The 8 + resonance would be expected to appear only in the lower two gates.
essential requirement in the present work since the 14.15 MeV level 7 decays by a cascade of "),-rays all with energies substantially less than 6.1 MeV. In order to locate the 14.15 MeV (8 +) level as a resonance, T-ray yield curves were measured in the vicinity o f E ~ = 5.8 MeV using a 7.6 X 7.6 cm NaI(T1) crystal and an automatic beam energy modulation technique. A target gas pressure of 0.2 torr, corresponding to a target thickness of 1.2 keV, was used in order both to emphasize sharp resonances and to reduce the counting rate from the extremely prohfic 2°Ne(a, a'T)20Ne reaction. The result, m the form of three yield curves with gates set about the indicated regions of the T-ray spectrum, ]s shown m fig. 1. A 46
18 July 1977
prominent sharp resonance at E a = 5.797 MeV ]s evident in the hzgh-energy gate, and corresponds to a resonance observed previously by H]ghland and Thwaites [8]. In the present work it was found to decay predominantly through the 4.12 MeV (4 +) level, which rules it out as a can&date for the 8 + level. However, the 14.15 MeV (8 +) level is clearly visible m the two lower-energy gates as a weak resonance at an aparticle energy 8 keV above the 5.797 MeV resonance. Having located the 8 + resonance, its T-ray decay scheme was measured by taking spectra on and off resonance with an 85 cm 3 Ge(Li) detector at 135 ° to the beam direction and 13 cm from the centre of the target. For these measurements, the target gas pressure was increased to 1 torr to ensure an effective ttuck target yield. The 8 + resonance was located centrally in the target chamber by first locating the much stronger 5.797 MeV resonance using a yield curve taken at a pressure of 1 torr, and then Increasing the beam energy by 8 keV. The resulting on-resonance spectrum clearly exhibited the T-rays corresponding to decays through the 9.53 and 8.11 MeV 6 + levels, whereas the offresonance spectrum taken at a beam energy 18 keV above the resonance did not. Furthermore, the T-ray branch to the 9.53 MeV (6 +, K ~r = 2 +) level carried (71 + 5)% of the T-ray decay strength, and the excitation energy was determined to be 14153 + 4 keV, both in good agreement with previous measurements
[5]. The resonance strength, cot = ( 2 J + 1)(F,rFa0/F), was determined by comparison of the yield of T-rays from the R --> 9.53 MeV and 9.53 --> 6.01 MeV transitions with the yield of 8.64 MeV T-rays from the 6.93 MeV resonance in the 160(o~, T)20Ne reaction. Care was taken to measure the yield from the reference resonance with as nearly as possible the same target thickness and resonance position as in the 2°Ne(a, T)24Mg measurement. Relative stopping powers were taken from ref. [9], and small corrections were applied for differences in the angular distributions of T-rays from the two resonances and for the extended nature of the ")'-ray emitting region along the beam direction [7]. Using a value of 19.7 -+ 1.6 eV for of the reference resonance [10], co'), of the R 9.53 MeV transition was determined to be 0.24 -+ 0.04 eV. Before F.t can be derived from coT, a knowledge of F~o/F is required.-This latter quantity has been meas-
Volume 69B, number 1
PHYSICS LETTERS
18 July 1977
Table 1 E2 transition rates for members of the K n = 2 + band in 24Mg.
In band K 1 = 2, Kf --- 2
Cross band K 1 = 2, Kf = 0
El (MeV)
j~r
Ef (MeV)
j~r
B(E2)exp a (W.u.)
B(E2)T h b (W.u.)
5.24 6.01 7.81 7.81 9 53 12 35 14.15
3+ 4+ 5+ 5+ 6+ 7+ 8+
4.24 4.24 5 24 6.01 6.01 7 81 9.53
2+ 2+ 3+ 4+ 4+ 5+ 6+
34 +- 6 16 +- 3 28 -+ 5 (14 -+ 6) c +23 23 ~ 4 20 - 6 9 1 -+2.4
34 9.5 14.4 18.3 11.6 15.0 7.6
4.24 4.24 5.24 6 01 6.01 7.81 9.53 14.15
2+ 2+ 3+ 4+ 4+ 5+ 6+ 8+
0.0 1.37 1.37 1.37 4.12 4.12 4.12 8.11
0+ 2+ 2+ 2+ 4+ 4+ 4+ 6+
1.4 2.7 2.1 1.0 1.0 39 0.8 0.8
-+ 0.3 +- 0.4 +- 0.3 +- 0.2 -+ 1.0 +- 0.8 +0.8 -0.a -+ 0.2
17 4 8 2.7 0.2 4.3 1.1 0.2 0.9
a All values taken from Branford et al. [5 ] with the exception of the 8+ -~ 6 + transitions. b Ref. [12]. EffecUve charges 0.5 e. c Assumes a pure E2 transition.
ured [11] using t h e 1 6 0 ( 1 2 C , aa)20Ne and 160(12C, orf)24Mg reactions, but the accuracy was limited by the presence of other states in 24Mg whach also a-decay to the 20Ne ground state and which were not resolved from the 14.15 MeV (8 +) level. We estimate that the uncertainty in determining the relative contributions of these unresolved levels to the ct-a angular correlation contributes an uncertainty of 20% to the value of F~o/P, which we take to be 0.22 + 0.04. Taken together with the measured value of 6o% this implies a value of 64 + 17 meV for the radiative width P~, of the in-band 14.15 (8 +) -+ 9.53 (6 +) MeV transition, which corresponds to an E2 transition strength of 9.1 + 2.4 W.u. The available information on electromagnetic E2 transition rates for m-band and cross-band trans:tions revolving the K 7r = 2 + band in 24Mg is collected in table 1 and compared with (sd) 8 shell model predictions [1,12] using the interaction of Preedom and Wildenthal. It is immediately evident that the predicted fall-off in the in-band transition strength at the 8 + member is borne out by the present work, and further, that very good quantitative agreement between
theory and experiment is obtained for both the inband and cross-band transitions from the 8 + level. We conclude that the full basis ( 2 s - l d ) 8 shell model calculations give a good account of the K ~r = 2 + band in 24Mg, and of the properhes of the 8 + state in particular. Consequently, these calculations can be used with some confidence to indicate both the whereabouts and the properties of the higher spin states in 24Mg, and should be of considerable ass:stance in the continuing search for these levels. We w:sh to thank Dr. A. Watt and Dr. D. Kelvin for communicating some of their results prior to publication.
References [1] A Watt, D. Kelvin and R R. Wtutehead, Phys Lett. 63B (1976) 385 [2] S. Plttel, Phys Lett. 34B (1971) 555. [3} M. Harvey, m. Advances in nuclear physics, vol 1, eds. M. Baranger and E. Vogt (Plenum Press, New York, 1968).
47
Volume 69B, number 1
PHYSICS LETTERS
[4] T.K. Alexander et al., Nucl. Phys. A179 (1972) 477. [5 ] D. Branford, A.C. McGough and I.F. Wright, Nucl. Phys. A241 (1975) 349. [6] K.W. Allen et al., Nucl. Instr 134 (1976) 1. [7] F Watt et al., to be published. [8] G.J. Highland and T.T. Thwaltes, Nucl. Phys. A109 (1968) 163.
48
18 July 1977
[9] L.C. Northcliffe and R.F Schdhng, Nucl. Data A7 (1970) 233. [10] P.D. Ingalls, Nucl. Phys A265 (1976) 93. [11] L.K. Fifield, R.W. Zurmuhle and D.P. Balamuth, Phys. Rev. C8 (1973) 2217. [12] D. Kelvin, A. Watt and R.R. Whitehead, to be published.
THE RADIATIVE
PHYSICS LETTERS
18 July 1977
W I D T H O F T H E 8 ÷ M E M B E R O F T H E K " = 2 ÷ B A N D I N 24 M g
L.K. FIFIELD, M.J. HURST, T.J.M. SYMONS, F. WATT and K.W. ALLEN Nuclear Physics Laboratory, Keble Road, Oxford, UK Received 2 May 1977 The radmtwe width of the 14.15 MeV, 8+, K ~r= 2+ level m 24Mg has been measured using the Z°Ne(a, ~.)24Mg reaction and a dffferentmlly cryopumped gas target. The result, F,r = 85 ± 23 meV, lmphes E2 strengths of 9.1 ± 2.4 and 0.8 +-0.2 W.u. for the transiUons to the 9.53 (6 ÷, K rr = 2+) and 8 11 (6 +, K ~r= 0÷) MeV levels, respectwely. These are in excellent agreement with the predictions of recent large basis shell model calculations. The extent to which rotational band structure persists in deformed hght nuclei as the nuclear spin Increases has been the subject o f considerable theoretical [ 1 - 3 ] and experimental [4, 5] interest in recent years. In 24Mg there are two well known positive parity bands which are believed to have the structure of eight particles in the 2 s - l d shell outside an 160 core, namely K ~r = 0 ÷ and 2 ÷ bands budt on the ground state and 4.24 MeV (2 +) state, respect:rely. Both bands have been identified only as far as the 8 + members, and m-band E2 v-ray transition strengths, which serve as an Indicator of band structure, have been measured [5] up to the 8 + member of the groundstate band and up to the 7 ÷ member of the K n = 2 + band. With the development of the Glasgow shell model code, it has become possible to calculate the excitation energies and electromagnetic transition rates within these bands using an untruncated (sd) 8 basis, and to extend the calculations to levels with J > 8 which have not yet been located experimentally. One would hope to determine from such calculations whether the band structure pers:sts up to the (sd) 8 spin 12 hmit, or only up to some critical lower spin value. The results, as reported recently by Watt, Kelvin and Whitehead [1 ], favour the latter possibility with the crit:cal spin value lying between J = 8 and J = 10. In b o t h bands, the in-band E2 v-ray transitions from the 8 + members are predicted to be substantially weaker than the strongly enhanced trans:tions between lower members of the bands, and above J = 9 the band structure effectwely disappears. In so far as the properties o f the bands have been determined experimentally, they are in reasonable agreement with the calculations. This applies to the
excitation energies, to the strongly enhanced in-band E2 v-ray transitions, and to the relatively weak crossband transitions. However, the crucial test of the calculations, and hence of their predictive power with respect to the states with J > 8, hes in the measurement of the in-band transltxon rates from the two 8 + states at 13.21 (K ~ = 0 +) and 14.15 (K ~r = 2 +) MeV. Although the lifetime of the 13.21 MeV level has been measured [5] by the Doppler shift attenuation method, the experimental uncertainty is large owing to the difficulties associated with measuring lifetimes of a few fs, and the result is not sufficiently accurate to verify the predicted fall-off in E2 transition strength. For the 14.15 MeV level, only a lower limit of 3 W.u. has been established [5] for the in-band E2 transition to the 9.53 MeV (6 +, K ~ --- 2 +) level using the same technique. However, whereas the 13 21 MeV level decays only by v-ray emission, the decay strength of the 14.15 MeV level is shared between v-ray emission and a-particle emission to the ground and 1.63 MeV states in 20Ne. This allows the possibihty o f measuring the radiative width of the 14.15 MeV level (but not of the 13.21 MeV level) by studying it as a resonance m the 20Ne(a, V)24Mg reaction. The purpose of this letter is to report the result of such a measurement which is sufficiently accurate to allow meaningful comparison with the theoretical calculations This measurement employed a differentially cryopumped gas target [6, 7], with beams o f a-particles obtained from the Oxford 10 MV Van de Graaff accelerator. The use of the gas target ensured that the level of background v-rays was low, and in particular that the yield of 6.13 MeV v-rays from the prolific 13C(a, n v ) 1 6 0 reaction was neghgible. This was an 45
Volume 69B, n u m b e r 1
PHYSICS LETTERS
I
8.7..
11. 11.5 800
R "-'~ 6 12
60(] 1.00 200
4.0,.< E y ¢ 4 7 R .--~ 9 . 5 3
300
20C
~
100
I
I
3 4~
30C
9.53 ~
i
6 01
200 100
I
I
5 80
5 81 E~ (MeV)
Fig 1. Gamma-ray yield curves for the 2°Ne(~, -r)24Mg reaction m the viciruty o f E a = 5.8 MeV. The three curves shown were obtained with gates set about the m & c a t e d regions o f the y-ray energy spectrum, and the resonances are labelled by the corresponding excitation energy m 24Mg. All energies are m MeV. The 8 + resonance would be expected to appear only in the lower two gates.
essential requirement in the present work since the 14.15 MeV level 7 decays by a cascade of "),-rays all with energies substantially less than 6.1 MeV. In order to locate the 14.15 MeV (8 +) level as a resonance, T-ray yield curves were measured in the vicinity o f E ~ = 5.8 MeV using a 7.6 X 7.6 cm NaI(T1) crystal and an automatic beam energy modulation technique. A target gas pressure of 0.2 torr, corresponding to a target thickness of 1.2 keV, was used in order both to emphasize sharp resonances and to reduce the counting rate from the extremely prohfic 2°Ne(a, a'T)20Ne reaction. The result, m the form of three yield curves with gates set about the indicated regions of the T-ray spectrum, ]s shown m fig. 1. A 46
18 July 1977
prominent sharp resonance at E a = 5.797 MeV ]s evident in the hzgh-energy gate, and corresponds to a resonance observed previously by H]ghland and Thwaites [8]. In the present work it was found to decay predominantly through the 4.12 MeV (4 +) level, which rules it out as a can&date for the 8 + level. However, the 14.15 MeV (8 +) level is clearly visible m the two lower-energy gates as a weak resonance at an aparticle energy 8 keV above the 5.797 MeV resonance. Having located the 8 + resonance, its T-ray decay scheme was measured by taking spectra on and off resonance with an 85 cm 3 Ge(Li) detector at 135 ° to the beam direction and 13 cm from the centre of the target. For these measurements, the target gas pressure was increased to 1 torr to ensure an effective ttuck target yield. The 8 + resonance was located centrally in the target chamber by first locating the much stronger 5.797 MeV resonance using a yield curve taken at a pressure of 1 torr, and then Increasing the beam energy by 8 keV. The resulting on-resonance spectrum clearly exhibited the T-rays corresponding to decays through the 9.53 and 8.11 MeV 6 + levels, whereas the offresonance spectrum taken at a beam energy 18 keV above the resonance did not. Furthermore, the T-ray branch to the 9.53 MeV (6 +, K ~r = 2 +) level carried (71 + 5)% of the T-ray decay strength, and the excitation energy was determined to be 14153 + 4 keV, both in good agreement with previous measurements
[5]. The resonance strength, cot = ( 2 J + 1)(F,rFa0/F), was determined by comparison of the yield of T-rays from the R --> 9.53 MeV and 9.53 --> 6.01 MeV transitions with the yield of 8.64 MeV T-rays from the 6.93 MeV resonance in the 160(o~, T)20Ne reaction. Care was taken to measure the yield from the reference resonance with as nearly as possible the same target thickness and resonance position as in the 2°Ne(a, T)24Mg measurement. Relative stopping powers were taken from ref. [9], and small corrections were applied for differences in the angular distributions of T-rays from the two resonances and for the extended nature of the ")'-ray emitting region along the beam direction [7]. Using a value of 19.7 -+ 1.6 eV for of the reference resonance [10], co'), of the R 9.53 MeV transition was determined to be 0.24 -+ 0.04 eV. Before F.t can be derived from coT, a knowledge of F~o/F is required.-This latter quantity has been meas-
Volume 69B, number 1
PHYSICS LETTERS
18 July 1977
Table 1 E2 transition rates for members of the K n = 2 + band in 24Mg.
In band K 1 = 2, Kf --- 2
Cross band K 1 = 2, Kf = 0
El (MeV)
j~r
Ef (MeV)
j~r
B(E2)exp a (W.u.)
B(E2)T h b (W.u.)
5.24 6.01 7.81 7.81 9 53 12 35 14.15
3+ 4+ 5+ 5+ 6+ 7+ 8+
4.24 4.24 5 24 6.01 6.01 7 81 9.53
2+ 2+ 3+ 4+ 4+ 5+ 6+
34 +- 6 16 +- 3 28 -+ 5 (14 -+ 6) c +23 23 ~ 4 20 - 6 9 1 -+2.4
34 9.5 14.4 18.3 11.6 15.0 7.6
4.24 4.24 5.24 6 01 6.01 7.81 9.53 14.15
2+ 2+ 3+ 4+ 4+ 5+ 6+ 8+
0.0 1.37 1.37 1.37 4.12 4.12 4.12 8.11
0+ 2+ 2+ 2+ 4+ 4+ 4+ 6+
1.4 2.7 2.1 1.0 1.0 39 0.8 0.8
-+ 0.3 +- 0.4 +- 0.3 +- 0.2 -+ 1.0 +- 0.8 +0.8 -0.a -+ 0.2
17 4 8 2.7 0.2 4.3 1.1 0.2 0.9
a All values taken from Branford et al. [5 ] with the exception of the 8+ -~ 6 + transitions. b Ref. [12]. EffecUve charges 0.5 e. c Assumes a pure E2 transition.
ured [11] using t h e 1 6 0 ( 1 2 C , aa)20Ne and 160(12C, orf)24Mg reactions, but the accuracy was limited by the presence of other states in 24Mg whach also a-decay to the 20Ne ground state and which were not resolved from the 14.15 MeV (8 +) level. We estimate that the uncertainty in determining the relative contributions of these unresolved levels to the ct-a angular correlation contributes an uncertainty of 20% to the value of F~o/P, which we take to be 0.22 + 0.04. Taken together with the measured value of 6o% this implies a value of 64 + 17 meV for the radiative width P~, of the in-band 14.15 (8 +) -+ 9.53 (6 +) MeV transition, which corresponds to an E2 transition strength of 9.1 + 2.4 W.u. The available information on electromagnetic E2 transition rates for m-band and cross-band trans:tions revolving the K 7r = 2 + band in 24Mg is collected in table 1 and compared with (sd) 8 shell model predictions [1,12] using the interaction of Preedom and Wildenthal. It is immediately evident that the predicted fall-off in the in-band transition strength at the 8 + member is borne out by the present work, and further, that very good quantitative agreement between
theory and experiment is obtained for both the inband and cross-band transitions from the 8 + level. We conclude that the full basis ( 2 s - l d ) 8 shell model calculations give a good account of the K ~r = 2 + band in 24Mg, and of the properhes of the 8 + state in particular. Consequently, these calculations can be used with some confidence to indicate both the whereabouts and the properties of the higher spin states in 24Mg, and should be of considerable ass:stance in the continuing search for these levels. We w:sh to thank Dr. A. Watt and Dr. D. Kelvin for communicating some of their results prior to publication.
References [1] A Watt, D. Kelvin and R R. Wtutehead, Phys Lett. 63B (1976) 385 [2] S. Plttel, Phys Lett. 34B (1971) 555. [3} M. Harvey, m. Advances in nuclear physics, vol 1, eds. M. Baranger and E. Vogt (Plenum Press, New York, 1968).
47
Volume 69B, number 1
PHYSICS LETTERS
[4] T.K. Alexander et al., Nucl. Phys. A179 (1972) 477. [5 ] D. Branford, A.C. McGough and I.F. Wright, Nucl. Phys. A241 (1975) 349. [6] K.W. Allen et al., Nucl. Instr 134 (1976) 1. [7] F Watt et al., to be published. [8] G.J. Highland and T.T. Thwaltes, Nucl. Phys. A109 (1968) 163.
48
18 July 1977
[9] L.C. Northcliffe and R.F Schdhng, Nucl. Data A7 (1970) 233. [10] P.D. Ingalls, Nucl. Phys A265 (1976) 93. [11] L.K. Fifield, R.W. Zurmuhle and D.P. Balamuth, Phys. Rev. C8 (1973) 2217. [12] D. Kelvin, A. Watt and R.R. Whitehead, to be published.