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High energy gamma ray energy measurements
NUCLLAR INSYRUMLNT9 AND METI-IO~.)S 54 (1967) 317--320 ; ( NORTH-HOLLAND PUBLISHING CO .
é°IIGI-I ENERGY GAMMA RAY ENERGY MEASUREMENTS* D. K. McDANlht_S, K, W . DOLAN and C. .1 . PILUSO Dtfmr1mc1N
oJ
1"hyJFGd,
â.tFÜt ~ F.~il,y
uf
t1rc-Ko ", L"Kc11c, orcgun, U.S.A .
Reewive;i, 0 June 1967 An easy method to memure gamma ray energies to about 0.(X)3 MeV in suggested which utilizes the reaction Q-value, and, de-
energies between two levels and the energy of the direct transition . This procedure is applied to the 0.9363-MeV resonance in the 27 Al(p,y) 28Si reaction .
There are a number of possible techniques for measuring gamma-ray enerl4ies to an accuracy of 0.101 or better'). For energies between 0.100- and 3.000-MeV the most satisfactory method consists of running a known reference spectrum simultaneously with the unknown spectrum') . For higher energy transitions, this method fails due to a lack of gamma ray energy standards which can be run simultaneously with the desired spectrum . Methods involving a precision pulser are usually adequate, but we prefer to avoid the large amount of care and work which they require. Instead we have found a variation of the Q-value method') to be quite accurate and much simpler with an accuracy of about ±0.003 MeV. In this note we will outline our procedure, apply it to the determination of the gammaray energies in the 0.9363-MeV resonance spectrum of the " AI(p,y) 2" Si reaction and point out a possible weakness in the routine application of pulser calibration methods. We illustrate our calibration procedure with the Al( p,y) 2 'Si reaction . First it is necessary to establish two reference points in each spectrum . The ground state Q-value for this reaction is 11 .5828±0.003 McV3). This, combined with the known resonance capture energy (usually known to about ± 0.001 MeV) gives the energy of the resonance capturing state in the "Si compound nucleus within the quoted errors . One calibration point is established by measuring a low energy gamma ray simultaneously with a number of well-known standards . For "Si this has usually been chosen to be the 1 .779-MeV transition between the 2 + first-excited state and the ground state. The energy of the gamma ray going directly from the capturing state to the first excited state is then computed, and it provides a calibration point at the high energy end of the spectrum . A linear fit is then made between these two points, and the remaining gamma-ray energies are calculated in this linear approximation. We can then make use of the fact that if non-linearities are present ' Work supported in part by the U.S . Atomic Energy Com-
due to the electronics and the detector, the energy of the direct transition will be different from the value obtained from the sum of the cascade gamma rays between the same two levels . In order to bring the cross-over and cascade sum energies into agreement, a small quadratic correction term is added to the linear calibration curve. This procedure will be clarified by determining the gamma-ray energies in the spectrum obtained at the 0.9363-MeV resonance. Fig. 1 shows the spectrum obtained at 90° to the incident beam with a 30 cm' Ge(Li) detector . The electronics consisted of a Tennelec TCI30 FET pre-amplifier, TC-200 main-amplifier, TC-250 post-amplifier and a Nuclear Data ND-161 analog-todigital converter. The experimental arrangement utilized with the University of Oregon 4-MeV Van de Graaff will be described in another publication') . The decay scheme for this resonance is rattier well established and as slightly modified is shown in fig. 1 . In addition to the direct transition from the capturing state to the first excited state, there are three different cascades between the two reference levels as shown by lieav,, lines. We characterize the amount of quadratic correction by a, the fractional deviation from linearity at the midpoint between the upper calibration point at 10.706-MeV and the lower calibration point at 1 .779MeV, and calculate the energies of the cascade transitions for a series of values of a to determine the quadratic correction which just makes the average cascade sum equal to the cross-over energy . The deviation between the cascade sum and the crass-aver energy plotted as a function of a is shown for E. = 0.9363MeV on fig. 2. 'The resultant value of a = -0 .0012 can then be used to calculate the energies of the individual gamma rays . To estimate the error associated with the uncertainty ii, the energy of the resonance capturing level we have repeated this procedure after varying the upper reference state energy by ± CX4 MeV . This results in a maximum change in the gamma ray energies of about 0.003 MeV. Using a = -0.0012 and ER = 0.936 3-MeNf, the
mands comistency between the gum of the cascade gamma ray
27
mission.
317
D. K. McDAN I ELS et al.
-50 : w 1 .0
t ^ 2 .0
ENERGY IN MeV 3.0 N r
N
ô
O
I
w.
`= in o
N r
A
aO
ab
wi
s
w
rO
A Ô
S
X 11,
AI"(py)Si to 0.936 MeV RESONANCE SPECTRUM,30 CC DETECTOR
8.0
9.0
ENERGY IN MeV
t .
.
10 .0
Fig. ! , Ge(Li) spectrum for the 0.9363-MeV 27 AI(p,y)28Si resonance obtained with a 30 cm3 detector . The level scheme is based on singles measurements only and is essentially consistent with the results of other workers.
energies of the second, third, and ninth e; ited states of "Si were found to be 4.619-, 6.274 and 6.878-MeV respectively, in agreement to within 2 keV of the values found by Azuma et A') and by Hinds and Middleton'7). The rest of the decay scheme at this resonance is found to be in essential agreement with the results of Nordhagens). The uncertainty about the 4.075-MeV transition is removed as this gamma ray definitely populates the 8.410-MeV level .
apply this technique too the mEP.~çatrement of the We ~e v apply this energy of the 6.127-MeV transition in the "F(p,ay)160 reaction which occurs weakly at the 0 .9363-MeV resonance in 27 Al(p,y)28Si due to the presence of fluorine as a contaminant on the target . We obtain a value of 6.128-MeV for this transition after correcting for the recoil loss . A similar measurement of the single escape peak yielded 6.127-MeV, so that our best estimate is 6.127 ± 0 .004MeV . This measurement is of some
HIGH ENERGY GAMMA RAY ENERGY MEASUREMENTS
319
al2 ac W
W IO
Ep-2 .203 MeV EFFECT OF DETECTOR CONTRIBUTION ALONE.
d CC
2
W
Q
Fig. 2. Plot of the difference between the average of the cascade sums and the cross-over transitions for the 0.9363- and the 2.203-MeV 27Al(p,V) 28 Si resonances. Alpha is a measure of the non-linearity involved and is the fractionai deviation from linearity at the midl point between the resonance level and the 1 .779-MeV state. It refers to the fractional deviation from linearity as a function of channenumbers for the 0.9363-MeV resonance and as a function of potentiometer reading for the 2.203-MeV resonance.
importance in establishing the linearity of Ge(Li) detectors, which would be expected to be extremely linea.. -. The processes which would prevent the total charg..e from being collected, such as recombination and trapping should not ordinarily be dependent on the number of hole-electron pairs produced by the secondary electrons resulting from photoelectric or pair formation processes. Very few experimental tests of the linearity ofGe(Li) detectors have been made") . Above 2 MeV the only precise measurement is that of Berg and Kashy 9) which involved a capacitor multiplying technique for the determination of the 6.127-MeV 160 gamma-ray energy by calibrating against well known, standards of lower energy . They obtained a result of 6.129 ± 0.001-MeV . Our result would lower their limit on Ge(Li) non-linearity to be less than 6 parts in 10000. As a final note we would like to express a word of caution about the use of pulser calibration techniques . We have made a study of the possible non-linearity of ....r In ,,,3 (~pt%ill riptPrrç~, which hi , a 1_arYe dead area and a fairly poor resolution (~ 50 keV at 10-MeV). To check on the non-linearity of this detector we have established the behavior of the electronics between the two reference points using a Hg pulses and a precision potentiometer which allowed us to measure the voltage at the pulser to about one part in 20000 quite easily and reliably. We then assumed that the gamma ray energies were directly proportional to the Y"
VNl
rV
4"
`
~~
V
potentiometer readings using the same two reference points as above to determine the energy scale. This was done for the gamma-ray spectrum obtained at the 2.203-MeV resonance which has 4 cascade series between the resonance capture level and the 1 .779-MeV state2). Ifthe detector were strictly linear the sum of the cascades should be exactly equal to the cross-over energy . We find that a definite detector non-linearity is indicated as shown by the graph labelled 2.203-MeV in fig. 2. Here a is now the fractional deviation at the midpoint of the spectrum from the linear formula t. E= A + BV, where E is the gamma ray energy and is the potentiometer reading. The first conclusion is that our detector is non-linear . This is highly possible since it has such a poor geometry and poor resolution and had to be operated with a very short integration time constant (0.8 jlsec) to maintain even this resolution . However, there can be a number of other explanations. The simplest would be that the pulse shape at the pre-amplifier input of the pulser is somehow amplitude dependent so that the amount of charge deposited at the input to the pre-amplifier is not accurately proportional to the %,oltage applied across the pulses . This possibility has b"n pointed out b Emery and Rabson' °). Our aim here is not zo claim that we have found a non-linear Ge(Li) detector . but rather to point out that direct calibration by means of a precision pulser should be used with caution and extreme care . In our case errors of as much as 0 .020-
D. K. MCDANIELS et al,
MeV could easily have been made if we had simply followed the pulser results. kef~nae~ 1) Tl. J. K'aatiect, Physics
'oday 14 (1966) 86; also private +cammunic~ttion . s) K, W. Dolan, D. K. Mcpaniels and D. 0 . Wells, Phys. Rev . 14 (1966) 1131 . 3) J. R. E. Mattau ch, . Thide and A. H. Wapstra, Nucl . . .32 Physim 67,(1%S)
s) C. J. Piluse, K. W. Dolan and D. K. McDaniels, to be published. s) R. Nordhagen, Nucl. Physics 44 (1963) 130. e) R. E. Azuma, L. E. Carlson, A. M. Charlesworth, K. P. Jackson, N. Anyas-Weiss and B. Lalovic, Can. J. Phys. 44 (1966) 3075. 7) S. Hinds and R. Middleton, Prec. Phys . Soc. 76 (1960) 50.
a) G. T. lEwan and A. J. Tavendale, Can. J. Phys. 42(1964) 2286. 9) R. E Berg and E. Kashy, Nucl . Instr. and Moth . 39 (t966) 169. 10) F. E. Emery and T. A. Rabson, Nud Instr. and Meth. . 34 (1963) 171.
é°IIGI-I ENERGY GAMMA RAY ENERGY MEASUREMENTS* D. K. McDANlht_S, K, W . DOLAN and C. .1 . PILUSO Dtfmr1mc1N
oJ
1"hyJFGd,
â.tFÜt ~ F.~il,y
uf
t1rc-Ko ", L"Kc11c, orcgun, U.S.A .
Reewive;i, 0 June 1967 An easy method to memure gamma ray energies to about 0.(X)3 MeV in suggested which utilizes the reaction Q-value, and, de-
energies between two levels and the energy of the direct transition . This procedure is applied to the 0.9363-MeV resonance in the 27 Al(p,y) 28Si reaction .
There are a number of possible techniques for measuring gamma-ray enerl4ies to an accuracy of 0.101 or better'). For energies between 0.100- and 3.000-MeV the most satisfactory method consists of running a known reference spectrum simultaneously with the unknown spectrum') . For higher energy transitions, this method fails due to a lack of gamma ray energy standards which can be run simultaneously with the desired spectrum . Methods involving a precision pulser are usually adequate, but we prefer to avoid the large amount of care and work which they require. Instead we have found a variation of the Q-value method') to be quite accurate and much simpler with an accuracy of about ±0.003 MeV. In this note we will outline our procedure, apply it to the determination of the gammaray energies in the 0.9363-MeV resonance spectrum of the " AI(p,y) 2" Si reaction and point out a possible weakness in the routine application of pulser calibration methods. We illustrate our calibration procedure with the Al( p,y) 2 'Si reaction . First it is necessary to establish two reference points in each spectrum . The ground state Q-value for this reaction is 11 .5828±0.003 McV3). This, combined with the known resonance capture energy (usually known to about ± 0.001 MeV) gives the energy of the resonance capturing state in the "Si compound nucleus within the quoted errors . One calibration point is established by measuring a low energy gamma ray simultaneously with a number of well-known standards . For "Si this has usually been chosen to be the 1 .779-MeV transition between the 2 + first-excited state and the ground state. The energy of the gamma ray going directly from the capturing state to the first excited state is then computed, and it provides a calibration point at the high energy end of the spectrum . A linear fit is then made between these two points, and the remaining gamma-ray energies are calculated in this linear approximation. We can then make use of the fact that if non-linearities are present ' Work supported in part by the U.S . Atomic Energy Com-
due to the electronics and the detector, the energy of the direct transition will be different from the value obtained from the sum of the cascade gamma rays between the same two levels . In order to bring the cross-over and cascade sum energies into agreement, a small quadratic correction term is added to the linear calibration curve. This procedure will be clarified by determining the gamma-ray energies in the spectrum obtained at the 0.9363-MeV resonance. Fig. 1 shows the spectrum obtained at 90° to the incident beam with a 30 cm' Ge(Li) detector . The electronics consisted of a Tennelec TCI30 FET pre-amplifier, TC-200 main-amplifier, TC-250 post-amplifier and a Nuclear Data ND-161 analog-todigital converter. The experimental arrangement utilized with the University of Oregon 4-MeV Van de Graaff will be described in another publication') . The decay scheme for this resonance is rattier well established and as slightly modified is shown in fig. 1 . In addition to the direct transition from the capturing state to the first excited state, there are three different cascades between the two reference levels as shown by lieav,, lines. We characterize the amount of quadratic correction by a, the fractional deviation from linearity at the midpoint between the upper calibration point at 10.706-MeV and the lower calibration point at 1 .779MeV, and calculate the energies of the cascade transitions for a series of values of a to determine the quadratic correction which just makes the average cascade sum equal to the cross-over energy . The deviation between the cascade sum and the crass-aver energy plotted as a function of a is shown for E. = 0.9363MeV on fig. 2. 'The resultant value of a = -0 .0012 can then be used to calculate the energies of the individual gamma rays . To estimate the error associated with the uncertainty ii, the energy of the resonance capturing level we have repeated this procedure after varying the upper reference state energy by ± CX4 MeV . This results in a maximum change in the gamma ray energies of about 0.003 MeV. Using a = -0.0012 and ER = 0.936 3-MeNf, the
mands comistency between the gum of the cascade gamma ray
27
mission.
317
D. K. McDAN I ELS et al.
-50 : w 1 .0
t ^ 2 .0
ENERGY IN MeV 3.0 N r
N
ô
O
I
w.
`= in o
N r
A
aO
ab
wi
s
w
rO
A Ô
S
X 11,
AI"(py)Si to 0.936 MeV RESONANCE SPECTRUM,30 CC DETECTOR
8.0
9.0
ENERGY IN MeV
t .
.
10 .0
Fig. ! , Ge(Li) spectrum for the 0.9363-MeV 27 AI(p,y)28Si resonance obtained with a 30 cm3 detector . The level scheme is based on singles measurements only and is essentially consistent with the results of other workers.
energies of the second, third, and ninth e; ited states of "Si were found to be 4.619-, 6.274 and 6.878-MeV respectively, in agreement to within 2 keV of the values found by Azuma et A') and by Hinds and Middleton'7). The rest of the decay scheme at this resonance is found to be in essential agreement with the results of Nordhagens). The uncertainty about the 4.075-MeV transition is removed as this gamma ray definitely populates the 8.410-MeV level .
apply this technique too the mEP.~çatrement of the We ~e v apply this energy of the 6.127-MeV transition in the "F(p,ay)160 reaction which occurs weakly at the 0 .9363-MeV resonance in 27 Al(p,y)28Si due to the presence of fluorine as a contaminant on the target . We obtain a value of 6.128-MeV for this transition after correcting for the recoil loss . A similar measurement of the single escape peak yielded 6.127-MeV, so that our best estimate is 6.127 ± 0 .004MeV . This measurement is of some
HIGH ENERGY GAMMA RAY ENERGY MEASUREMENTS
319
al2 ac W
W IO
Ep-2 .203 MeV EFFECT OF DETECTOR CONTRIBUTION ALONE.
d CC
2
W
Q
Fig. 2. Plot of the difference between the average of the cascade sums and the cross-over transitions for the 0.9363- and the 2.203-MeV 27Al(p,V) 28 Si resonances. Alpha is a measure of the non-linearity involved and is the fractionai deviation from linearity at the midl point between the resonance level and the 1 .779-MeV state. It refers to the fractional deviation from linearity as a function of channenumbers for the 0.9363-MeV resonance and as a function of potentiometer reading for the 2.203-MeV resonance.
importance in establishing the linearity of Ge(Li) detectors, which would be expected to be extremely linea.. -. The processes which would prevent the total charg..e from being collected, such as recombination and trapping should not ordinarily be dependent on the number of hole-electron pairs produced by the secondary electrons resulting from photoelectric or pair formation processes. Very few experimental tests of the linearity ofGe(Li) detectors have been made") . Above 2 MeV the only precise measurement is that of Berg and Kashy 9) which involved a capacitor multiplying technique for the determination of the 6.127-MeV 160 gamma-ray energy by calibrating against well known, standards of lower energy . They obtained a result of 6.129 ± 0.001-MeV . Our result would lower their limit on Ge(Li) non-linearity to be less than 6 parts in 10000. As a final note we would like to express a word of caution about the use of pulser calibration techniques . We have made a study of the possible non-linearity of ....r In ,,,3 (~pt%ill riptPrrç~, which hi , a 1_arYe dead area and a fairly poor resolution (~ 50 keV at 10-MeV). To check on the non-linearity of this detector we have established the behavior of the electronics between the two reference points using a Hg pulses and a precision potentiometer which allowed us to measure the voltage at the pulser to about one part in 20000 quite easily and reliably. We then assumed that the gamma ray energies were directly proportional to the Y"
VNl
rV
4"
`
~~
V
potentiometer readings using the same two reference points as above to determine the energy scale. This was done for the gamma-ray spectrum obtained at the 2.203-MeV resonance which has 4 cascade series between the resonance capture level and the 1 .779-MeV state2). Ifthe detector were strictly linear the sum of the cascades should be exactly equal to the cross-over energy . We find that a definite detector non-linearity is indicated as shown by the graph labelled 2.203-MeV in fig. 2. Here a is now the fractional deviation at the midpoint of the spectrum from the linear formula t. E= A + BV, where E is the gamma ray energy and is the potentiometer reading. The first conclusion is that our detector is non-linear . This is highly possible since it has such a poor geometry and poor resolution and had to be operated with a very short integration time constant (0.8 jlsec) to maintain even this resolution . However, there can be a number of other explanations. The simplest would be that the pulse shape at the pre-amplifier input of the pulser is somehow amplitude dependent so that the amount of charge deposited at the input to the pre-amplifier is not accurately proportional to the %,oltage applied across the pulses . This possibility has b"n pointed out b Emery and Rabson' °). Our aim here is not zo claim that we have found a non-linear Ge(Li) detector . but rather to point out that direct calibration by means of a precision pulser should be used with caution and extreme care . In our case errors of as much as 0 .020-
D. K. MCDANIELS et al,
MeV could easily have been made if we had simply followed the pulser results. kef~nae~ 1) Tl. J. K'aatiect, Physics
'oday 14 (1966) 86; also private +cammunic~ttion . s) K, W. Dolan, D. K. Mcpaniels and D. 0 . Wells, Phys. Rev . 14 (1966) 1131 . 3) J. R. E. Mattau ch, . Thide and A. H. Wapstra, Nucl . . .32 Physim 67,(1%S)
s) C. J. Piluse, K. W. Dolan and D. K. McDaniels, to be published. s) R. Nordhagen, Nucl. Physics 44 (1963) 130. e) R. E. Azuma, L. E. Carlson, A. M. Charlesworth, K. P. Jackson, N. Anyas-Weiss and B. Lalovic, Can. J. Phys. 44 (1966) 3075. 7) S. Hinds and R. Middleton, Prec. Phys . Soc. 76 (1960) 50.
a) G. T. lEwan and A. J. Tavendale, Can. J. Phys. 42(1964) 2286. 9) R. E Berg and E. Kashy, Nucl . Instr. and Moth . 39 (t966) 169. 10) F. E. Emery and T. A. Rabson, Nud Instr. and Meth. . 34 (1963) 171.