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Coulomb excitation of the first excited state of 28Si
Volume
298.
number
10
COULOMB D. PELTE*.
PHYSICS
EXCITATION 0. HAUSSER. Chalk
River
OF
THE
LETTERS
FIRST
T. K. ALEXANDER,
Nuclear
Laboratories. Received
18 August 1969
EXCITED
STATE
OF
B. W. HOOTON** and H. C. EVANS***
Atomic
Energy
of Canada Limited
7 July 1969
A mean life 7m = 0.73 f 0.05 ps and a static quadropole moment Q = 0.22 f 0.09 b were measured first excited state of 28Si by studying the Coulomb excitation of 28Si with 60 MeV 32S ions.
The uadrupole moment of the first excited state of q24Mg has been measured recently by various groups [l-4]. The negative sign of the static moment may be interpreted as the experimental proof f r the predominantly prolate deformation of 29 Mg. However, calculations [ 5,6] for the next even-even. N = 2 nucleus 28Si, indicate the possibility of a change in the nuclear deformation between these two nuclei. A measurement of the quadrupole moment of the first excited state of 28Si is therefore of particular interest. In this letter we report on such a measurement, one of a series of experiments [7] carried out in order to study the electromagnetic properties of the 1.779 MeV state in 28Si. The quadrupole moment of the 1.78 MeV state was determined by means of the reorientation effect [8] in the Coulomb excitatiy with heav projectiles. A thick (16.9 mg&m6! natural 2&i target was bombarded with a S beam of 60 MeV and the y radiation from the 1.78 MeV state was observed with three Ge(Li) detectors, each with a volume of 40 cm3, positioned at O”, 90° and 125O with respect to the beam and at a distance of 7.5 cm from the target. If we use y. = 1.4 fm, the bombarding energy amounts to 75% of the relevant Coulomb barrier height for head-on collisions, which is considered a safe energy for measuring the reorientation effect [9]. The lifetime and quadrupole moment were deduced from the line shapes of the 1.78 MeV yray observed with the Ge(Li) detectors and from the absolute Coulomb excitation cross section. The cross section depends on the quadrupole moment Q and the E2 transition strength B(E2) and allows one of these parameters to be deter* N.R.C.
Fellow from the University of Heidelberg, Germany. ** On leave from A.E.R.E. Harwell, UK. *** Queen’s University, Kingston, Ontario, Canada.
660
28Si
for the
mined if the other one is known; B(E2) can be obtained from the analysis of the Doppler broadening of the 1.78 MeV y rays. Because of the high bombarding energy the Doppler broadening amounts to 7% in our case. The corresponding line shape depends also on the inelastic scattering cross section and is therefore sensitive to Q. This technique and the experimental procedures are explicitly described in ref. 3. As pointed out there, the method is best suited for the study of states at high excitation energy which have a short lifetime and small Coulomb excitation cross section. In the analysis of the experimental results, the multiple Coulomb excitation program of Winther and De Boer [lo] was used together with a line shape program written for the Chalk River CDC G20 + 3100 computer. Supplementary to the procedures outlined in ref. 3, all tensors of the scattered particle y-ray angular correlation [lo] were included in the line shape program. This inclusion mainly modified the calculated line shape at a detector angle 90°. However, the result of ref. 3 that the quadrupole moment does not influence the line shape observed at 90’ and the influence is largest at Oo is still valid. The 90° spectrum therefore allows the determination of the lifetime, whereas the quadrupole moment can be deduced from the O” spectrum. The energy loss of the projectiles and recoiling target nuclei were calculated as discussed in ref. 3. Because of the high bombarding energy and the short lifetime of the 1.78 MeV state, the results of this experiment depend on the accuracy of the determination of the energy loss at high velocities which is believed to be better than 5%. Fig. 1. shows the measured line shapes of the 1.78 MeV full-energy peak in the y-ray spectra at 90° and O”. The lower half of the figure illustrates the corresponding ~2 fits, from which a
Volume 29B.
number
PHYSICS
10
18 August 1969
LETTERS
-
Q= 0.3 BARNS Q = 0.0 BARNS
---90”
4000
0” 3000
II.-2
0
20
40
60
60
100
CHANNEL
NUMBER
LIFETIME
IN
120
140
0
20
40
60
6
0
IO
s 6
~75~o.l3--oio6!F’
F&e
PSEC
QUADRUFOLE MOMENT IN BARNS
Fig. 1. Line shapes of the 1.78 MeVy ray observed at 90° and Oo and corresponding x2 fits. Full curves calculated for a quadrupole moment Q = 0.3 b, dashed curves for Q = 0.0 b.
ENHANCEMENT
IN W.U.
1
1
/J\\
1
0=0.20+0.14
BARNS
I i __-
1.0
0.6
09
LIF:&4E
IN0.6SEC
Fig. 2. Relation between the E2 transition strength and the quadrupole moment of the 1.78 MeV state deduced from the measured absolute Coulomb excitation cross section. 7m = 0.73 f 0.05 ps and a quadrupole Q = 0.23 * 0.12 b were deduced. The effect of the finite solid angle of the Ge(Li) detector on the value of Q was estimated by analyzing meanlife moment
are
the O” spectrum with line shapes calculated for detector angles 5O and 10’. The uncertainty in Q resulting from solid-angle effects is included in the quoted error. The relationship between the quadrupole moment and the E2 transition strength obtained from the measured Coulomb excitation cross section is illustrated in fig. 2. From the lifetime Jrn = 0.73 f 0.05 ps determined above a quadrupole moment Q = 0.20 f 0.14 b was deduced. The averaged quadrupole moment Q = = 0.22 * 0.09 b and the mean lifetime Tm = = 0.73 f 0.05 ps corresponding to an E2 enhancement of 12.4 * 0.9 WLIare in agreement with the values Q = 0.16 & 0.05 b and 7, = 0.720 k 0.042~s obtained in this laboratory by a separate experiment [7] using a completely different technique to observe the reorientation effect. The lifetime reported here agrees with the results (Jm = = 0.708 * 0.045 ps) of Skorka et al. [ll] but disagrees with a recent measurement (TV = 0.878 * rt 0.068 ps ) of Robinson and Bent [12], The positive sign of the static moment allows the interpretation that the first excited state of 28Si has negative deformation. It is direct experimental evidence for the sign change of the quadrupole 661
Volume 29B. number 10
PHYSICS
moment between 24Mg and 28Si. The value of Q is, within the errors, in agreement with the quadrupole moment Q = 0. 16 f 0.05 b obtained from the simple rotational model and the measured E2 transition strength. It should be noted however, that the E2 transition strengths for the 4+- 2+ and the 6+ -+ 4+ transitions in 28Si do not follow the rotational model predictions [ 131.
LETTERS
6. R. Y. Cusson, to be published. 7. T. K. Alexander et al. Bull. Amer. Phys. Sot. 14
8. 9.
10. References 1. A. Bamberger, 2. 3. 4. 5.
P. G. Bisseti and B. Povh, Phys.
Rev. Letters 21 (1968) 1599. O.Hausser et al. Phys. Rev. Letters 22 (1969) 359. D. Pelte, 0. Hausser, T. K. Alexander and H. C. Evans, Can. J. Phys., to be published. R. C. Haight, J. X. Saladin and D. Vitoux, Bull. Amer. Phys. Sot. 14 (1.969) 554. G. Ripka, in: Adv. Nucl. Phys. I, eds. M. Baranger and E. Vogt (Plenum Press, New York, 1968).
*****
662
18 August 1969
11.
12. 13.
(1969) 555; O.Hausser. T.K. Alexander. D.Pelte. B W. Hooton and H. C. Evans, to be published. J. De Boer and J. Eichler, in: Adv. Nucl. Phys. I, eds. M. Baranger and E. Vogt (Plenum Press, New York, 1968). D. Cline et al., University of Rochester preprint UR-NSRL-15. A. Winther and J. De Boer, in: Coulomb excitation, perspectives in physics, eds. K. Alder and A.Winther (Academic Press, New York, London, 1966). S. J. Skorka and T. W. Retz-Schmidt, Nucl. Phys. 46 (1963) 225; S. J. Skorka et al., Nucl. Phys. 81 (1966) 370. S. W. Robinson and R. D. Bent, Phys. Rev. 168 (1968) 1266. A. E. Litherland. P. J. M. Smulders and T. K. Alexander, Can: J. Phys.47 (1969) 639: S. T. Lam. A. E. Litherland and T. K. Alexander Can. J. Phys.,to be published.
298.
number
10
COULOMB D. PELTE*.
PHYSICS
EXCITATION 0. HAUSSER. Chalk
River
OF
THE
LETTERS
FIRST
T. K. ALEXANDER,
Nuclear
Laboratories. Received
18 August 1969
EXCITED
STATE
OF
B. W. HOOTON** and H. C. EVANS***
Atomic
Energy
of Canada Limited
7 July 1969
A mean life 7m = 0.73 f 0.05 ps and a static quadropole moment Q = 0.22 f 0.09 b were measured first excited state of 28Si by studying the Coulomb excitation of 28Si with 60 MeV 32S ions.
The uadrupole moment of the first excited state of q24Mg has been measured recently by various groups [l-4]. The negative sign of the static moment may be interpreted as the experimental proof f r the predominantly prolate deformation of 29 Mg. However, calculations [ 5,6] for the next even-even. N = 2 nucleus 28Si, indicate the possibility of a change in the nuclear deformation between these two nuclei. A measurement of the quadrupole moment of the first excited state of 28Si is therefore of particular interest. In this letter we report on such a measurement, one of a series of experiments [7] carried out in order to study the electromagnetic properties of the 1.779 MeV state in 28Si. The quadrupole moment of the 1.78 MeV state was determined by means of the reorientation effect [8] in the Coulomb excitatiy with heav projectiles. A thick (16.9 mg&m6! natural 2&i target was bombarded with a S beam of 60 MeV and the y radiation from the 1.78 MeV state was observed with three Ge(Li) detectors, each with a volume of 40 cm3, positioned at O”, 90° and 125O with respect to the beam and at a distance of 7.5 cm from the target. If we use y. = 1.4 fm, the bombarding energy amounts to 75% of the relevant Coulomb barrier height for head-on collisions, which is considered a safe energy for measuring the reorientation effect [9]. The lifetime and quadrupole moment were deduced from the line shapes of the 1.78 MeV yray observed with the Ge(Li) detectors and from the absolute Coulomb excitation cross section. The cross section depends on the quadrupole moment Q and the E2 transition strength B(E2) and allows one of these parameters to be deter* N.R.C.
Fellow from the University of Heidelberg, Germany. ** On leave from A.E.R.E. Harwell, UK. *** Queen’s University, Kingston, Ontario, Canada.
660
28Si
for the
mined if the other one is known; B(E2) can be obtained from the analysis of the Doppler broadening of the 1.78 MeV y rays. Because of the high bombarding energy the Doppler broadening amounts to 7% in our case. The corresponding line shape depends also on the inelastic scattering cross section and is therefore sensitive to Q. This technique and the experimental procedures are explicitly described in ref. 3. As pointed out there, the method is best suited for the study of states at high excitation energy which have a short lifetime and small Coulomb excitation cross section. In the analysis of the experimental results, the multiple Coulomb excitation program of Winther and De Boer [lo] was used together with a line shape program written for the Chalk River CDC G20 + 3100 computer. Supplementary to the procedures outlined in ref. 3, all tensors of the scattered particle y-ray angular correlation [lo] were included in the line shape program. This inclusion mainly modified the calculated line shape at a detector angle 90°. However, the result of ref. 3 that the quadrupole moment does not influence the line shape observed at 90’ and the influence is largest at Oo is still valid. The 90° spectrum therefore allows the determination of the lifetime, whereas the quadrupole moment can be deduced from the O” spectrum. The energy loss of the projectiles and recoiling target nuclei were calculated as discussed in ref. 3. Because of the high bombarding energy and the short lifetime of the 1.78 MeV state, the results of this experiment depend on the accuracy of the determination of the energy loss at high velocities which is believed to be better than 5%. Fig. 1. shows the measured line shapes of the 1.78 MeV full-energy peak in the y-ray spectra at 90° and O”. The lower half of the figure illustrates the corresponding ~2 fits, from which a
Volume 29B.
number
PHYSICS
10
18 August 1969
LETTERS
-
Q= 0.3 BARNS Q = 0.0 BARNS
---90”
4000
0” 3000
II.-2
0
20
40
60
60
100
CHANNEL
NUMBER
LIFETIME
IN
120
140
0
20
40
60
6
0
IO
s 6
~75~o.l3--oio6!F’
F&e
PSEC
QUADRUFOLE MOMENT IN BARNS
Fig. 1. Line shapes of the 1.78 MeVy ray observed at 90° and Oo and corresponding x2 fits. Full curves calculated for a quadrupole moment Q = 0.3 b, dashed curves for Q = 0.0 b.
ENHANCEMENT
IN W.U.
1
1
/J\\
1
0=0.20+0.14
BARNS
I i __-
1.0
0.6
09
LIF:&4E
IN0.6SEC
Fig. 2. Relation between the E2 transition strength and the quadrupole moment of the 1.78 MeV state deduced from the measured absolute Coulomb excitation cross section. 7m = 0.73 f 0.05 ps and a quadrupole Q = 0.23 * 0.12 b were deduced. The effect of the finite solid angle of the Ge(Li) detector on the value of Q was estimated by analyzing meanlife moment
are
the O” spectrum with line shapes calculated for detector angles 5O and 10’. The uncertainty in Q resulting from solid-angle effects is included in the quoted error. The relationship between the quadrupole moment and the E2 transition strength obtained from the measured Coulomb excitation cross section is illustrated in fig. 2. From the lifetime Jrn = 0.73 f 0.05 ps determined above a quadrupole moment Q = 0.20 f 0.14 b was deduced. The averaged quadrupole moment Q = = 0.22 * 0.09 b and the mean lifetime Tm = = 0.73 f 0.05 ps corresponding to an E2 enhancement of 12.4 * 0.9 WLIare in agreement with the values Q = 0.16 & 0.05 b and 7, = 0.720 k 0.042~s obtained in this laboratory by a separate experiment [7] using a completely different technique to observe the reorientation effect. The lifetime reported here agrees with the results (Jm = = 0.708 * 0.045 ps) of Skorka et al. [ll] but disagrees with a recent measurement (TV = 0.878 * rt 0.068 ps ) of Robinson and Bent [12], The positive sign of the static moment allows the interpretation that the first excited state of 28Si has negative deformation. It is direct experimental evidence for the sign change of the quadrupole 661
Volume 29B. number 10
PHYSICS
moment between 24Mg and 28Si. The value of Q is, within the errors, in agreement with the quadrupole moment Q = 0. 16 f 0.05 b obtained from the simple rotational model and the measured E2 transition strength. It should be noted however, that the E2 transition strengths for the 4+- 2+ and the 6+ -+ 4+ transitions in 28Si do not follow the rotational model predictions [ 131.
LETTERS
6. R. Y. Cusson, to be published. 7. T. K. Alexander et al. Bull. Amer. Phys. Sot. 14
8. 9.
10. References 1. A. Bamberger, 2. 3. 4. 5.
P. G. Bisseti and B. Povh, Phys.
Rev. Letters 21 (1968) 1599. O.Hausser et al. Phys. Rev. Letters 22 (1969) 359. D. Pelte, 0. Hausser, T. K. Alexander and H. C. Evans, Can. J. Phys., to be published. R. C. Haight, J. X. Saladin and D. Vitoux, Bull. Amer. Phys. Sot. 14 (1.969) 554. G. Ripka, in: Adv. Nucl. Phys. I, eds. M. Baranger and E. Vogt (Plenum Press, New York, 1968).
*****
662
18 August 1969
11.
12. 13.
(1969) 555; O.Hausser. T.K. Alexander. D.Pelte. B W. Hooton and H. C. Evans, to be published. J. De Boer and J. Eichler, in: Adv. Nucl. Phys. I, eds. M. Baranger and E. Vogt (Plenum Press, New York, 1968). D. Cline et al., University of Rochester preprint UR-NSRL-15. A. Winther and J. De Boer, in: Coulomb excitation, perspectives in physics, eds. K. Alder and A.Winther (Academic Press, New York, London, 1966). S. J. Skorka and T. W. Retz-Schmidt, Nucl. Phys. 46 (1963) 225; S. J. Skorka et al., Nucl. Phys. 81 (1966) 370. S. W. Robinson and R. D. Bent, Phys. Rev. 168 (1968) 1266. A. E. Litherland. P. J. M. Smulders and T. K. Alexander, Can: J. Phys.47 (1969) 639: S. T. Lam. A. E. Litherland and T. K. Alexander Can. J. Phys.,to be published.