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The energy levels of Mg24
1.E.I:
I
Nuclear Physics 37 (1962) 244--249; (~) North-Holland Publishing Co., Amsterdam
2.C
[
Not to be reproduced by photoprint or raicrofilm without written permission from the publisher
T H E E N E R G Y LEVELS OF M g 24 A. R. QUINTON t and G. P. LAWRENCE Research School o f Physical Sciences, Australian National University, Canberra Received 1 May 1962 Abstract: The reaction Al~7(p, (x)Mg24, induced by protons of energy 11 MeV, leads to levels of Mg ~4
at excitation energies of 1.368, 4.122, 4.232, 5.251, 6.010, 6.430, 7.344, 7.594, 7.797, 8.116, (8.36)
and (8.44) MeV.
1. Introduction A detailed study of the r e a c t i o n A127(p, 0 0 M g 24 with protons of energy between 3 and 11 MeV from a tandem Van de Graaff accelerator is in progress. During the investigation it has become clear that it is possible to establish the positions of a number of energy levels in M g 24 with precision and this paper describes these results.
2. Experimental Details The alpha particles were detected with a surface barrier counter of 300 ohm-cm resistivity. After linear amplification the pulses were stored in a multi-channel analyser, in some runs of 400-channel and in others 512-channel capacity. The detector was biassed in such a way that its active depth or depletion layer was roughly the range of a 2 MeV proton. In this fashion alpha particles of energy greater than 2 MeV could be cleanly separated from protons. No other type of heavily ionising particle could be present from reactions in the target. The aluminium target was made by evaporating aluminium from a tantalum boat on to a carbon backing. Energy loss measurements with an alpha particle source showed the target plus backing to be 130 pg/cm z thick. Energy loss measurements with the proton beam showed the backing to be 40/zg/cm z thick. The target was mounted on a rotatable support at the centre of a scattering chamber. The detector, also mounted inside the chamber, could be placed at any angle, with respect to the beam line, around the target. In fig. 1 we illustrate the resolution of the system for the alpha particles from Bi 212. The source was placed at the target position for this spectrum and the particles were not collimated on to the counter. A comparison with the absolute magnetic analysis National Science Foundation Postdoctoral Fellow. Permanent address: Sloane Physics Laboratory, Yale University, New Haven, Conn., U.S.A. 244
THE ENERGY LEVELS OF Mg 2
9,45
results reviewed by Briggs ~) for this source shows that the detector has a 0.5 ~FWHM resolution at 6 MeV. The beam protons falling on to the target were first subjected to magnetic analysis with their energies established to 10 keV by a slit system. Their energies E(MeV) were calculated from the relation E(1 + E / 2 M c 2) = K / M f 2, where M c 2 = 938.235 MeV is the proton rest mass energy, f is the proton magnetic resonance frequency
300-
i
i
~
~"
ii -~
o~
x$ 200-
cO
100-
150
200
I l
250
Channet
Fig. 1. The pulse-height spectrum of alpha particles from Bi~1~. in megahertz and K the constant of the analysing magnet. A value of K / M of 0.019900 established from (p, n) thresholds was used. The beam was collimated and focussed on to the target by a system of slits, quadrupole magnets and collimating holes. Its position and size were periodically monitored by viewing a disc of quartz placed at the target position. To determine an energy calibration curve for the detection system, advantage was taken of a previous study by Van Patter et al. 2 ) of the AIZT(p, ~)Mg 24 reaction.
C24~
A. R. Q U I N T O N
AND
G. P.
LAWRENCE
These magnetic analysis measurements have established both ground state and first excited state Q-values to an accuracy of 0.5 ~ . Then the well-known Q-value equation establishes the energies of two alpha groups ao and al for a particular incident proton energy. In practice the proton energy was varied from 4 to 11 MeV in 0.5 MeV steps with the surface barrier detector at 90 ° with respect to the beam to generate the energy versus pulse-height scale. This calibration was checked at a single energy with the Bi 212 source of alpha particles. The measured value agreed with the accepted value of 6.047 MeV to within 20 keV. This error was treated as a systematic error and a correction to the calibration curve applied accordingly. 200 3.2.1,0 .°
.m t_)
98j 6
0
lbo
260
300
Channet Fig. 2(a). The spectrum of pulse-heights of alpha particles from the reaction AP~(p, c¢)Mg2~observed at 45° (Ep= 11 MeV). The method of setting the angle of observation of the counter was such that, although changes in angles were known accurately, the absolute angle was not known well. To establish an absolute scale of angles, pulse-heights for an alpha group (Co) were observed at nominally 135 ° to the beam of 4 MeV protons on both sides of zero angle. A further observation at 130 ° allowed the rate of change of pulse-height with angle be to determined. These three observations served to establish the absolute setting for zero degrees. Care was taken that the beam intercepted the target through the axis of rotation of the counter and that the beam was in the plane of rotation of the counter. Then with the accelerator energy set at 11.000 MeV observations were made at 45 °, 90 ° and 135 °. The resulting pulse-height spectra are displayed in figs. 2(a), (b) and (c). Runs were also made with a carbon target o f approximately the same thickness as that used as a backing for the aluminium.
THE ENERGY LEVELS OF Mg 24
247
200-
~E
gloo-
IJ
8
o
7
26o
100
3oo
Channel. Fig. 2(b). The spectrum of pulse-heights of alpha particles from the reaction AW(p, ~)Mg 24 observed at 90 ° (Ep = 11 MeV).
200-
3 ."7 C.) 0
100
o
100
Channel.
~o
300
Fig. 2(c). The spectrum of pulse-heights of alpha particles from the reaction AW(p, c~)Mg~4 observed at 135°(Ep = 11 MeV).
~4:8
A. R. QUINTON AND G. P. LAWRENCE
To improve the reliability of the data, observations of a similar kind were made with different detectors and multi-channel analysers. Also by using other detector biasses and amplifier gains the low energy portions of the spectra were examined to expose as much detail of the level structure as possible. 3. Results When analysed to determine the Q-values of groups of alpha particles it was found that the data from the different angles for a particular group agreed in all cases to better than 40 keV. Because the spectrometer was set for measuring alpha particles in the range 3 to 8 MeV some groups did not show at all angles and their Q-values are correspondingly less reliable.
/
8.359 .............. 8.116--
7.797~ 7.594/// 7.3/,/_,/'//
12.203
6.010~/~ -
5.25~-// /`.232/
Ate7+p_ o¢ 1.596
/,. 1 2 2 - -
Mg2~
Fig. 3. An energy level diagram illustrating the results of this experiment, t One group appears only at 45 ° and is identified as the ground state group for the reaction O16(p, c~)N13 (Q -- - 5 . 2 1 8 MeV). Such a peak appears at the same energy when a carbon target is bombarded with 11 MeV protons presumably because of oxygen contaminant picked up in the thin film preparation. It should be pointed out that the general background level of alphas from the carbon is very low and coupled with the high negative Q-values for the reactions C12(p, a)B 9 and C13(p, a) B 1o makes these thin carbon backings ideal for this class of experiment. TABLE l
Sources of error Source Ground state Q-value Alpha energies (location of peaks and energy calibration) Beam proton energy Counter angle Non-relativistic kinematics
Probable error (keV) 5 20 10 10 3
t It has come to our attention that the region of excitation of Mg24, discussed in this paper, has previously been examined 4) through the reaction NaZ3(HeS, d)Mg24.
THE ENERGY LEVELS OF Mg 24
249
A n overall check on the m e t h o d is p r o v i d e d b y the m e a s u r e d value for the g r o u p labelled 2. W e o b t a i n a n excitation energy o f 4.122 M e V in excellent agreement with the value given in the review b y E n d t a n d B r a a m s 3). F o r the levels c~2 . . . e~o we assign a p r o b a b l e error for the excitation energies o f + 25 keV. The sources o f this error is s h o w n in table 1. W e w o u l d like to t h a n k Professor E. W. T i t t e r t o n for his e n c o u r a g e m e n t a n d generous a l l o c a t i o n o f l a b o r a t o r y facilities to us. O n e o f us ( A R Q ) w o u l d like to t h a n k the N a t i o n a l Science F o u n d a t i o n for its support.
References 1) 2) 3) 4)
G. H. Briggs, Rev. Mod. Phys. 26 (1954) 1 Van Patter, Porter and Rothman, Phys. Rev. 106 (1957) 1016 P. M. Endt and C. M. Braams, Rev. Mod. Phys. 29 (1957) 683 S. Hinds and R. Middletom Proc" Phys. Soc. 76 (1960) 553
I
Nuclear Physics 37 (1962) 244--249; (~) North-Holland Publishing Co., Amsterdam
2.C
[
Not to be reproduced by photoprint or raicrofilm without written permission from the publisher
T H E E N E R G Y LEVELS OF M g 24 A. R. QUINTON t and G. P. LAWRENCE Research School o f Physical Sciences, Australian National University, Canberra Received 1 May 1962 Abstract: The reaction Al~7(p, (x)Mg24, induced by protons of energy 11 MeV, leads to levels of Mg ~4
at excitation energies of 1.368, 4.122, 4.232, 5.251, 6.010, 6.430, 7.344, 7.594, 7.797, 8.116, (8.36)
and (8.44) MeV.
1. Introduction A detailed study of the r e a c t i o n A127(p, 0 0 M g 24 with protons of energy between 3 and 11 MeV from a tandem Van de Graaff accelerator is in progress. During the investigation it has become clear that it is possible to establish the positions of a number of energy levels in M g 24 with precision and this paper describes these results.
2. Experimental Details The alpha particles were detected with a surface barrier counter of 300 ohm-cm resistivity. After linear amplification the pulses were stored in a multi-channel analyser, in some runs of 400-channel and in others 512-channel capacity. The detector was biassed in such a way that its active depth or depletion layer was roughly the range of a 2 MeV proton. In this fashion alpha particles of energy greater than 2 MeV could be cleanly separated from protons. No other type of heavily ionising particle could be present from reactions in the target. The aluminium target was made by evaporating aluminium from a tantalum boat on to a carbon backing. Energy loss measurements with an alpha particle source showed the target plus backing to be 130 pg/cm z thick. Energy loss measurements with the proton beam showed the backing to be 40/zg/cm z thick. The target was mounted on a rotatable support at the centre of a scattering chamber. The detector, also mounted inside the chamber, could be placed at any angle, with respect to the beam line, around the target. In fig. 1 we illustrate the resolution of the system for the alpha particles from Bi 212. The source was placed at the target position for this spectrum and the particles were not collimated on to the counter. A comparison with the absolute magnetic analysis National Science Foundation Postdoctoral Fellow. Permanent address: Sloane Physics Laboratory, Yale University, New Haven, Conn., U.S.A. 244
THE ENERGY LEVELS OF Mg 2
9,45
results reviewed by Briggs ~) for this source shows that the detector has a 0.5 ~FWHM resolution at 6 MeV. The beam protons falling on to the target were first subjected to magnetic analysis with their energies established to 10 keV by a slit system. Their energies E(MeV) were calculated from the relation E(1 + E / 2 M c 2) = K / M f 2, where M c 2 = 938.235 MeV is the proton rest mass energy, f is the proton magnetic resonance frequency
300-
i
i
~
~"
ii -~
o~
x$ 200-
cO
100-
150
200
I l
250
Channet
Fig. 1. The pulse-height spectrum of alpha particles from Bi~1~. in megahertz and K the constant of the analysing magnet. A value of K / M of 0.019900 established from (p, n) thresholds was used. The beam was collimated and focussed on to the target by a system of slits, quadrupole magnets and collimating holes. Its position and size were periodically monitored by viewing a disc of quartz placed at the target position. To determine an energy calibration curve for the detection system, advantage was taken of a previous study by Van Patter et al. 2 ) of the AIZT(p, ~)Mg 24 reaction.
C24~
A. R. Q U I N T O N
AND
G. P.
LAWRENCE
These magnetic analysis measurements have established both ground state and first excited state Q-values to an accuracy of 0.5 ~ . Then the well-known Q-value equation establishes the energies of two alpha groups ao and al for a particular incident proton energy. In practice the proton energy was varied from 4 to 11 MeV in 0.5 MeV steps with the surface barrier detector at 90 ° with respect to the beam to generate the energy versus pulse-height scale. This calibration was checked at a single energy with the Bi 212 source of alpha particles. The measured value agreed with the accepted value of 6.047 MeV to within 20 keV. This error was treated as a systematic error and a correction to the calibration curve applied accordingly. 200 3.2.1,0 .°
.m t_)
98j 6
0
lbo
260
300
Channet Fig. 2(a). The spectrum of pulse-heights of alpha particles from the reaction AP~(p, c¢)Mg2~observed at 45° (Ep= 11 MeV). The method of setting the angle of observation of the counter was such that, although changes in angles were known accurately, the absolute angle was not known well. To establish an absolute scale of angles, pulse-heights for an alpha group (Co) were observed at nominally 135 ° to the beam of 4 MeV protons on both sides of zero angle. A further observation at 130 ° allowed the rate of change of pulse-height with angle be to determined. These three observations served to establish the absolute setting for zero degrees. Care was taken that the beam intercepted the target through the axis of rotation of the counter and that the beam was in the plane of rotation of the counter. Then with the accelerator energy set at 11.000 MeV observations were made at 45 °, 90 ° and 135 °. The resulting pulse-height spectra are displayed in figs. 2(a), (b) and (c). Runs were also made with a carbon target o f approximately the same thickness as that used as a backing for the aluminium.
THE ENERGY LEVELS OF Mg 24
247
200-
~E
gloo-
IJ
8
o
7
26o
100
3oo
Channel. Fig. 2(b). The spectrum of pulse-heights of alpha particles from the reaction AW(p, ~)Mg 24 observed at 90 ° (Ep = 11 MeV).
200-
3 ."7 C.) 0
100
o
100
Channel.
~o
300
Fig. 2(c). The spectrum of pulse-heights of alpha particles from the reaction AW(p, c~)Mg~4 observed at 135°(Ep = 11 MeV).
~4:8
A. R. QUINTON AND G. P. LAWRENCE
To improve the reliability of the data, observations of a similar kind were made with different detectors and multi-channel analysers. Also by using other detector biasses and amplifier gains the low energy portions of the spectra were examined to expose as much detail of the level structure as possible. 3. Results When analysed to determine the Q-values of groups of alpha particles it was found that the data from the different angles for a particular group agreed in all cases to better than 40 keV. Because the spectrometer was set for measuring alpha particles in the range 3 to 8 MeV some groups did not show at all angles and their Q-values are correspondingly less reliable.
/
8.359 .............. 8.116--
7.797~ 7.594/// 7.3/,/_,/'//
12.203
6.010~/~ -
5.25~-// /`.232/
Ate7+p_ o¢ 1.596
/,. 1 2 2 - -
Mg2~
Fig. 3. An energy level diagram illustrating the results of this experiment, t One group appears only at 45 ° and is identified as the ground state group for the reaction O16(p, c~)N13 (Q -- - 5 . 2 1 8 MeV). Such a peak appears at the same energy when a carbon target is bombarded with 11 MeV protons presumably because of oxygen contaminant picked up in the thin film preparation. It should be pointed out that the general background level of alphas from the carbon is very low and coupled with the high negative Q-values for the reactions C12(p, a)B 9 and C13(p, a) B 1o makes these thin carbon backings ideal for this class of experiment. TABLE l
Sources of error Source Ground state Q-value Alpha energies (location of peaks and energy calibration) Beam proton energy Counter angle Non-relativistic kinematics
Probable error (keV) 5 20 10 10 3
t It has come to our attention that the region of excitation of Mg24, discussed in this paper, has previously been examined 4) through the reaction NaZ3(HeS, d)Mg24.
THE ENERGY LEVELS OF Mg 24
249
A n overall check on the m e t h o d is p r o v i d e d b y the m e a s u r e d value for the g r o u p labelled 2. W e o b t a i n a n excitation energy o f 4.122 M e V in excellent agreement with the value given in the review b y E n d t a n d B r a a m s 3). F o r the levels c~2 . . . e~o we assign a p r o b a b l e error for the excitation energies o f + 25 keV. The sources o f this error is s h o w n in table 1. W e w o u l d like to t h a n k Professor E. W. T i t t e r t o n for his e n c o u r a g e m e n t a n d generous a l l o c a t i o n o f l a b o r a t o r y facilities to us. O n e o f us ( A R Q ) w o u l d like to t h a n k the N a t i o n a l Science F o u n d a t i o n for its support.
References 1) 2) 3) 4)
G. H. Briggs, Rev. Mod. Phys. 26 (1954) 1 Van Patter, Porter and Rothman, Phys. Rev. 106 (1957) 1016 P. M. Endt and C. M. Braams, Rev. Mod. Phys. 29 (1957) 683 S. Hinds and R. Middletom Proc" Phys. Soc. 76 (1960) 553