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Correlation technique with a new two-dimensional position sensitive detector
82
Nuclear Instruments and Methods in Physics Research A258 (1987) 82-86 North-Holland, Amsterdam
CORRELATION TECHNIQUE WITH A NEW TWO-DIMENSIONAL POSITION SENSITIVE DETECTOR W. MORAWEK, U. GOLLERTHAN and W. SCHWAB Institut für Kernphysik, Technische Hochschule Darmstadt, 6100 Darmstadt, FRG K .-H . SCHMIDT Gesellschaft für Schwerionenforschung mbH, 6100 Darmstadt, FRG
Received 16 February 1987 A new 2-dimensional position sensitive semiconductor detector was developed. With this detector the correlation between implanted fusion products and their subsequent a decays can be improved . The position resolution of the detector will be described as a function of the position . Measurements with a-particles and a model of the detector will be presented and the results for the correlation technique are demonstrated .
1. Introduction In semiconductor detectors the incident particles create free charges, electrons and holes, which are divided by the applied voltage and drift to the contacts of the detector. Semiconductor detectors which are position sensitive use time measurements between several contacts of the detector or a resistive layer on the surface of the detector, where the total charge is divided, to determine the position . In the second case two contacts are necessary to obtain a 1-dimensional position sensitive detector . For 2-dimensional position sensitive detectors three contacts are at least necessary and four are commonly used. They can be placed on one side of the detector - several forms of contacts have been used - or on both sides, each side bearing two contacts [1-4]. The technique of delayed coincidences was used to identify new isotopes which were produced at the velocity filter SHIP at GSI [5,6]. The fusion products were implanted in a semiconductor detector and the subsequent a decays were measured . This method is so powerful that single nuclei can be identified, e.g. in the observation of one nucleus of element 109 [7]. In this experiment a detector consisting of seven stripes, each one 1-dimensional position sensitive, was used [8]. The detector measures the position, time and energy of the incident particles and of their subsequent a decays . By the correlation between the unknown a decays and the consecutive known a decays it is possible to determine the decay chain and thus to identify the nuclei . The subdividision of the detector reduces the statistical 0168-9002/87/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
background and thus allows to determine correlations for a decays with longer lifetimes. With this 7-stripe detector the time limit could be expanded by a factor of about 30 compared to a detector which is not position sensitive. With a 2-dimensional position sensitive detector this factor can be increased once more . 2. Construction and technical data of the detector The detector was developed in a collaboration with ENERTEC Strasbourg, GSI and TH Darmstadt. The detector is of quadratic shape and has an active area of 24 X 24 mmz according to the beam spot behind SHIP . The total thickness amounts to 300 ym and the depletion depth of 100 ,um allows to stop the heavy ions in our experiments . The detector consists of n-type silicon with 1500 0 cm resistivity. The implantation of the detector is made with boron at the front and with arsenic at the rear side . The rear contact consists of an aluminum layer. Consideration of a model similar to the one described in sect . 3 showed that four contacts with a side length of 6 nun on the front of the detector fixed in the corners are well suited for our application (see fig. 1) . The charge which drifts to the front is divided by the resistive surface layer between the four contacts . The sum of the four front signals equals the signal from the rear, which represents the energy of the particle . The position information is stored in the four signals from the front side. From them the position must be extracted by reducing the four items of information to two
83
W. Morawek et al. / Correlation technique with a new position sensinue detector
B
A TT
3
IF
1-1
0
24
0 U)
a)
IV
C
D
0
2
4
6
8
10
Position from center to edge/mm
Fig. 1 . Shape and dimensions of the detector (in mm) parameters. This can be done by the following relations: XN -
2
( A+C ) 1000+1000, A+B+C+D
Fig. 3. Position resolution (fwhm) m the x direction for the line from the center to the edge of the detector . Symbols : experimental data . Full line : model calculation.
B+D-
YN - A+B- (C+D ) 1000+1000. A+B+C+D
(1)
XN and YN are approximations of the original position . Their values lie between 0 and 2000 . 3. Test experiments with a-particles In order to test the detector, an experiment with a-particles and a punched mask which was fixed in front of the detector was made. The mask consisted of 9 X 9 holes, each with 1 .6 mm diameter and a distance of 2.54 mm between the holes. The distribution of the signals XN and YN can be seen in fig. 2. The 9 X 9 holes 2000
1500
tn â)
C C N L 1000 U
fade away a little at the edges where the position resolution is worse. A regular distortion of the signals is clearly seen which shows that the signals XN and YN are not the original positions but approximations of them. The center rows, the horizontal and the vertical row, were projected onto the x axis and the y axis, respectively . From the resulting spectra the position resolution could be deduced by unfolding the shape of the holes, a projected circle. The resolution for the center cross of the detector in the direction along the cross is shown in fig. 3. As the resolution is symmetric with regard to the center of the detector, all points (2 X 9 from the two rows consisting of rune holes) are shown as a function of the distance from the center of the detector . The resolution varies from 0.6 mm in the center to 2.7 mm fwhm at the edges. Fig. 2 demonstrates that the resolution at point P, for example, is worse in the x direction (2 .7 mm) - the holes overlap while it is better in the y direction - the holes are clearly separated. The measured energy resolution of the detector was about 45 keV fwhm for 5.47 MeV a-particles. 4. A model for the detector
Z
In order to simulate the distortion of the signals X,,, and YN , a model (planar resistor) was developed by solving the Poisson equation numerically [9]:
500
3V(x, y) ~ -RI(x, y) . 0
0
500
1000
XN/channels
1500
2000
Fig. 2. XN, YN values for a-particles passing through a mask consisting of a regular grid of 9 X 9 holes. Point P refers to sect . 3.
is the delta operator, V is the potential at the position (x, y), R is the surface resistivity and I the current caused by the incident particle . For the numerical solution the detector is divided into (n + 1) X (n + 1) points . If the delta operator is replaced by the 5-point molecule, one gets the following discrete analog of the Pois-
84
W. Morawek et al / Correlation technique with a new position sensitive detector
son equation :
2000
V(1-1, J )+V(i+1, J )+17(1, j+1) +V(i, j-1)-417(1, j) = h 2 F(i, j),
1500
i, J E (I . . . n - 1),
N
h is step width, F= -RI .
This leads to a system of (n - 1) X (n - 1) linear equations which can be represented in matrix form : Here v is the potential as a vector of length (n - 1) X (n - 1) representing the V(i, J) in a line, M is the matrix of the equation system and b the right-hand-side vector . In order to solve this system the boundaries V(t, j) for 1 E (0 . . . n), j E (0, n) and i E (0, n), j G (0 . . . n) and the right-hand-side vector have to be fixed . The potential is set to zero when the points lie on a contact, whereas between the contacts the current density is set to zero by the following boundary condition which relates the three points nearest to the border (perpendicular to the boundary) [10] : V(bound) = 7 V(bound - 1) - V(bound - 2) .
(5)
The nght-hand-side vektor b of length (n - 1) X (n - 1) is set to zero except for one point (i, j), where the incident particle hits the detector . This point gets an arbitrary amount of 1. While the equations have to be solved for (n - 1) X (n - 1) different right-hand-side vectors the matrix was first factonzed. The LU factorization problem consists of finding two matrices L and U, lower and upper triangular, respectively, such that :
P-M=L-U,
(6)
where P is the permutation matrix. When the factorization is available, the solution can be found for different right-hand-side vectors by solving successively :
0 c c eu L 1000 U
Z r 500
0
0
500
1000
XN/channels
1500
2000
Fig. 4. XN , YN values for the 841 points of the model of the experiment with the a-particles (fig. 2) . By using searching and interpolating routines, the original X and Y positions can thus be determined from the measured XN and YN signals . In fig. 5 the original position distribution of the a-particles of fig. 2 is shown. The regular shape of the grid is well seen . The corners of the figure are cut off by the condition that the four signals must be higher than a certain threshold. With this model the position resolution can be calculated for all positions. Starting from eq . (1) and assuming a resolution of 133 keV for the four signals in the numerator and the energy resolution of 45 keV for
10
L-y=P-b and U-v=y.
This was done with IBM PL/1-maths procedures for
n = 30 [11] . From the potential distribution of the dif-
5
ferent hit points the currents of the four contacts could be evaluated by the following equation :
1 rad V J = Rg with j the current per unit length . In the discrete case one has to sum over all potentials of adjacent points to one contact. This is the amount of current of this contact. The sum of the current over the four contacts gives the arbitrary amount which was chosen for the right-hand-side vector (charge conservation) . From the four signals the XN and YN can be calculated with eq . (1). For results see fig. 4, which shows the calculated XN , Yv for the 841 (29 X 29) points . A distortion can be seen which is similar to that
-5
X/mm Fig. 5 . Two-dimensional position spectrum of the a-particles from fig. 2, determined by a searching and interpolating program based on the model.
W. Morawek et al. / Correlation technique with a new position sensitive detector
85
90 Zr + 90 Zr
9
117'H
800
E E
N 600 1
4
C
175pt
Û 400 200
5700 5800 5900 6000 6100 6200 6300 6400
Energy/keV
Fig. 7 . Measured a spectrum of evaporation residues obtained m the reaction 9° Zr+ 9° Zr (4 .02 MeV/u). Fig. 6. Position resolution in the x direction in mm fwhm as a function of the position for the hole detector area, evaluated with the model Cuts : 0.42 to 0.7 by 0 .04, 0 .7 to 1 .0 by 0.1, 1 .0 to 1 .8 by 0 .2 .
the sum in the denominator, the mean error of the XN , YN can be calculated with the formulae for the propagation of errors . The value of 133 keV was chosen to fit the experimental position resolution in the center of the detector. By using the searching and interpolating programm, this error could be expressed in the original position. For the middle line of the detector, the results are presented in fig. 3. In fig. 6 the calculated resolution in mm fwhm in the x direction is plotted as a function of the position for the hole detector . To see the resolution in the y direction the picture has to be turned by 90 0 .
179H
n5pt
800
(n c
70 U
600
t,=3 7s
400 200
1
10 -2
1
10 1
1
T/s
10 2
Fig. 8 . Spectrum of time distances between a decays of 179 Hg and 175 pt, taking the position resolution into account.
5. Correlation For testing the correlation technique with this detector, an experiment where 90 Zr projectiles with an energy of 4.02 MeV/u impinge on a target of 90 Zr was made . Evaporation residues are separated from the primary beam and directed to the detector position by the velocity filter SHIP [12] . Different kinds of unstable nuclei are implanted near the surface of the detector and decay mostly by a radioactivity . The measured a spectrum is shown in fig. 7 . The correlation in time and position of the detected particles and the subsequent a decay has been widely 10 used for their identification. In figs . 8 and 9 the spectra of the time differences between the occurrence of the 179Hg a decay and the subsequent 175 Pt a decay are shown, using the position information and without using
_>
9
179H
4 ~--
800
c ô
U
9
_> 1t
175pt
=p 5s
600 400 200
10
-4
-2
6
T/s
2
4
6
Fig. 9. Spectrum of time distances between a decays of n9Hg and 175 Pt, without taking the position resolution into account.
86
W Morawek et al. / Correlation technique with a new position sensitive detector
it, respectively . By choosing a logarithmic time scale an ideal radioactive decay curve becomes a peak with a universal shape independent of the lifetime . True correlations are characterized by the occurrence of time distances between the mother and daughter decay shorter than expected for the random distribution . In fig . 9 the time distances between an event with the energy of the mother decay and the subsequent event with the energy of the daughter decay were plotted. No true correlations can be seen . The random peak with a peak position of tP = 0.5 s does not allow to detect true correlations with a mean lifetime of 3.64 s for 175 Pt . In fig. 8 the position information was taken into account. Events with the energy of the mother decay were stored in an array with their position and time of occurrence . Then the time difference of a daughter decay not to the last mother decay but to the last mother decay which was inside a certain area around the daughter decay, was plotted. The area was determined by the position resolution . Then the true coincidences with tP = 3.6 s are clearly separated from the random distribution with tP = 237 s. By taking the position information into account it is possible to detect correlations for nuclei with 450 times longer lifetimes . The theoretical factor is about 700, which is the ratio of the total detector area and the area in which the correlations are searched for. In the experiment this factor can only be realized when the detector is irradiated in such a way that areas with the same position resolution get the same counts . Thus with this detector and the mentioned proce-
dures the correlation technique can be extended to appreciably longer time distances. References [1] S. Kalbitzer, R. Bader, W. Melzer and W. Stumpfi, Nucl. Instr. and Meth. 54 (1967) 323. [2] R.B . Owen and M.L . Awcock, IEEE Trans. Nucl . Sci. NS-15 (1968) 290. [3] J.T. Walton, G.S. Hubbard, E.E. Haller and H.A . Sommer, IEEE Trans. Nucl . Sci. NS-26 (1979) 334. [4] K. Yamamoto, S. Yamaguchi and Y. Terada, IEEE Trans. Nucl . Sci. NS-32 (1985) 438. [5] K.-H. Schmidt, W. Faust, G. Münzenberg, H -G . Clerc, W. Lang, K. Pielenz, D. Vermeulen, H. Wohlfarth, H. Edwald and K. Güttner, Nucl . Phys. A318 (1979) 253. [6] K.-H. Schmidt, C.-C. Sahm, K. Pielenz and H.-G. Clerc, Z. Phys . A316 (1984) 19 . G. Münzenberg, P. Armbruster, F.P . Hessberger, S. Hofmann, K. Poppensieker, W. Reisdorf, J.R .H . Schneider, K.H . Schmidt, C.C. Sahm and D. Vermeulen, Z. Phys . A309 (1982) 89. [8] S. Hofmann, G. Münzenberg, F.P . Hessberger and H.-J. Schbtt, Nucl . Instr. and Meth . 223 (1984) 312. [9] M. Lampton and C.W . Carlson, Rev . Sci . Instr. 50 (1979) 1093 . [10] E. Stiefel, Einführung in die numerische Mathematik, (Teubner, Stuttgart, 1963) p. 182. [11] IBM Technical Newsletter No. SN20-0985-0 (1971) p. 23 . [12] G. Münzenberg, W. Faust, S. Hofmann, P. Armbruster, K. Güttner and H. Ewald, Nucl . Instr. and Meth . 161 (1979) 65 .
Nuclear Instruments and Methods in Physics Research A258 (1987) 82-86 North-Holland, Amsterdam
CORRELATION TECHNIQUE WITH A NEW TWO-DIMENSIONAL POSITION SENSITIVE DETECTOR W. MORAWEK, U. GOLLERTHAN and W. SCHWAB Institut für Kernphysik, Technische Hochschule Darmstadt, 6100 Darmstadt, FRG K .-H . SCHMIDT Gesellschaft für Schwerionenforschung mbH, 6100 Darmstadt, FRG
Received 16 February 1987 A new 2-dimensional position sensitive semiconductor detector was developed. With this detector the correlation between implanted fusion products and their subsequent a decays can be improved . The position resolution of the detector will be described as a function of the position . Measurements with a-particles and a model of the detector will be presented and the results for the correlation technique are demonstrated .
1. Introduction In semiconductor detectors the incident particles create free charges, electrons and holes, which are divided by the applied voltage and drift to the contacts of the detector. Semiconductor detectors which are position sensitive use time measurements between several contacts of the detector or a resistive layer on the surface of the detector, where the total charge is divided, to determine the position . In the second case two contacts are necessary to obtain a 1-dimensional position sensitive detector . For 2-dimensional position sensitive detectors three contacts are at least necessary and four are commonly used. They can be placed on one side of the detector - several forms of contacts have been used - or on both sides, each side bearing two contacts [1-4]. The technique of delayed coincidences was used to identify new isotopes which were produced at the velocity filter SHIP at GSI [5,6]. The fusion products were implanted in a semiconductor detector and the subsequent a decays were measured . This method is so powerful that single nuclei can be identified, e.g. in the observation of one nucleus of element 109 [7]. In this experiment a detector consisting of seven stripes, each one 1-dimensional position sensitive, was used [8]. The detector measures the position, time and energy of the incident particles and of their subsequent a decays . By the correlation between the unknown a decays and the consecutive known a decays it is possible to determine the decay chain and thus to identify the nuclei . The subdividision of the detector reduces the statistical 0168-9002/87/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
background and thus allows to determine correlations for a decays with longer lifetimes. With this 7-stripe detector the time limit could be expanded by a factor of about 30 compared to a detector which is not position sensitive. With a 2-dimensional position sensitive detector this factor can be increased once more . 2. Construction and technical data of the detector The detector was developed in a collaboration with ENERTEC Strasbourg, GSI and TH Darmstadt. The detector is of quadratic shape and has an active area of 24 X 24 mmz according to the beam spot behind SHIP . The total thickness amounts to 300 ym and the depletion depth of 100 ,um allows to stop the heavy ions in our experiments . The detector consists of n-type silicon with 1500 0 cm resistivity. The implantation of the detector is made with boron at the front and with arsenic at the rear side . The rear contact consists of an aluminum layer. Consideration of a model similar to the one described in sect . 3 showed that four contacts with a side length of 6 nun on the front of the detector fixed in the corners are well suited for our application (see fig. 1) . The charge which drifts to the front is divided by the resistive surface layer between the four contacts . The sum of the four front signals equals the signal from the rear, which represents the energy of the particle . The position information is stored in the four signals from the front side. From them the position must be extracted by reducing the four items of information to two
83
W. Morawek et al. / Correlation technique with a new position sensinue detector
B
A TT
3
IF
1-1
0
24
0 U)
a)
IV
C
D
0
2
4
6
8
10
Position from center to edge/mm
Fig. 1 . Shape and dimensions of the detector (in mm) parameters. This can be done by the following relations: XN -
2
( A+C ) 1000+1000, A+B+C+D
Fig. 3. Position resolution (fwhm) m the x direction for the line from the center to the edge of the detector . Symbols : experimental data . Full line : model calculation.
B+D-
YN - A+B- (C+D ) 1000+1000. A+B+C+D
(1)
XN and YN are approximations of the original position . Their values lie between 0 and 2000 . 3. Test experiments with a-particles In order to test the detector, an experiment with a-particles and a punched mask which was fixed in front of the detector was made. The mask consisted of 9 X 9 holes, each with 1 .6 mm diameter and a distance of 2.54 mm between the holes. The distribution of the signals XN and YN can be seen in fig. 2. The 9 X 9 holes 2000
1500
tn â)
C C N L 1000 U
fade away a little at the edges where the position resolution is worse. A regular distortion of the signals is clearly seen which shows that the signals XN and YN are not the original positions but approximations of them. The center rows, the horizontal and the vertical row, were projected onto the x axis and the y axis, respectively . From the resulting spectra the position resolution could be deduced by unfolding the shape of the holes, a projected circle. The resolution for the center cross of the detector in the direction along the cross is shown in fig. 3. As the resolution is symmetric with regard to the center of the detector, all points (2 X 9 from the two rows consisting of rune holes) are shown as a function of the distance from the center of the detector . The resolution varies from 0.6 mm in the center to 2.7 mm fwhm at the edges. Fig. 2 demonstrates that the resolution at point P, for example, is worse in the x direction (2 .7 mm) - the holes overlap while it is better in the y direction - the holes are clearly separated. The measured energy resolution of the detector was about 45 keV fwhm for 5.47 MeV a-particles. 4. A model for the detector
Z
In order to simulate the distortion of the signals X,,, and YN , a model (planar resistor) was developed by solving the Poisson equation numerically [9]:
500
3V(x, y) ~ -RI(x, y) . 0
0
500
1000
XN/channels
1500
2000
Fig. 2. XN, YN values for a-particles passing through a mask consisting of a regular grid of 9 X 9 holes. Point P refers to sect . 3.
is the delta operator, V is the potential at the position (x, y), R is the surface resistivity and I the current caused by the incident particle . For the numerical solution the detector is divided into (n + 1) X (n + 1) points . If the delta operator is replaced by the 5-point molecule, one gets the following discrete analog of the Pois-
84
W. Morawek et al / Correlation technique with a new position sensitive detector
son equation :
2000
V(1-1, J )+V(i+1, J )+17(1, j+1) +V(i, j-1)-417(1, j) = h 2 F(i, j),
1500
i, J E (I . . . n - 1),
N
h is step width, F= -RI .
This leads to a system of (n - 1) X (n - 1) linear equations which can be represented in matrix form : Here v is the potential as a vector of length (n - 1) X (n - 1) representing the V(i, J) in a line, M is the matrix of the equation system and b the right-hand-side vector . In order to solve this system the boundaries V(t, j) for 1 E (0 . . . n), j E (0, n) and i E (0, n), j G (0 . . . n) and the right-hand-side vector have to be fixed . The potential is set to zero when the points lie on a contact, whereas between the contacts the current density is set to zero by the following boundary condition which relates the three points nearest to the border (perpendicular to the boundary) [10] : V(bound) = 7 V(bound - 1) - V(bound - 2) .
(5)
The nght-hand-side vektor b of length (n - 1) X (n - 1) is set to zero except for one point (i, j), where the incident particle hits the detector . This point gets an arbitrary amount of 1. While the equations have to be solved for (n - 1) X (n - 1) different right-hand-side vectors the matrix was first factonzed. The LU factorization problem consists of finding two matrices L and U, lower and upper triangular, respectively, such that :
P-M=L-U,
(6)
where P is the permutation matrix. When the factorization is available, the solution can be found for different right-hand-side vectors by solving successively :
0 c c eu L 1000 U
Z r 500
0
0
500
1000
XN/channels
1500
2000
Fig. 4. XN , YN values for the 841 points of the model of the experiment with the a-particles (fig. 2) . By using searching and interpolating routines, the original X and Y positions can thus be determined from the measured XN and YN signals . In fig. 5 the original position distribution of the a-particles of fig. 2 is shown. The regular shape of the grid is well seen . The corners of the figure are cut off by the condition that the four signals must be higher than a certain threshold. With this model the position resolution can be calculated for all positions. Starting from eq . (1) and assuming a resolution of 133 keV for the four signals in the numerator and the energy resolution of 45 keV for
10
L-y=P-b and U-v=y.
This was done with IBM PL/1-maths procedures for
n = 30 [11] . From the potential distribution of the dif-
5
ferent hit points the currents of the four contacts could be evaluated by the following equation :
1 rad V J = Rg with j the current per unit length . In the discrete case one has to sum over all potentials of adjacent points to one contact. This is the amount of current of this contact. The sum of the current over the four contacts gives the arbitrary amount which was chosen for the right-hand-side vector (charge conservation) . From the four signals the XN and YN can be calculated with eq . (1). For results see fig. 4, which shows the calculated XN , Yv for the 841 (29 X 29) points . A distortion can be seen which is similar to that
-5
X/mm Fig. 5 . Two-dimensional position spectrum of the a-particles from fig. 2, determined by a searching and interpolating program based on the model.
W. Morawek et al. / Correlation technique with a new position sensitive detector
85
90 Zr + 90 Zr
9
117'H
800
E E
N 600 1
4
C
175pt
Û 400 200
5700 5800 5900 6000 6100 6200 6300 6400
Energy/keV
Fig. 7 . Measured a spectrum of evaporation residues obtained m the reaction 9° Zr+ 9° Zr (4 .02 MeV/u). Fig. 6. Position resolution in the x direction in mm fwhm as a function of the position for the hole detector area, evaluated with the model Cuts : 0.42 to 0.7 by 0 .04, 0 .7 to 1 .0 by 0.1, 1 .0 to 1 .8 by 0 .2 .
the sum in the denominator, the mean error of the XN , YN can be calculated with the formulae for the propagation of errors . The value of 133 keV was chosen to fit the experimental position resolution in the center of the detector. By using the searching and interpolating programm, this error could be expressed in the original position. For the middle line of the detector, the results are presented in fig. 3. In fig. 6 the calculated resolution in mm fwhm in the x direction is plotted as a function of the position for the hole detector . To see the resolution in the y direction the picture has to be turned by 90 0 .
179H
n5pt
800
(n c
70 U
600
t,=3 7s
400 200
1
10 -2
1
10 1
1
T/s
10 2
Fig. 8 . Spectrum of time distances between a decays of 179 Hg and 175 pt, taking the position resolution into account.
5. Correlation For testing the correlation technique with this detector, an experiment where 90 Zr projectiles with an energy of 4.02 MeV/u impinge on a target of 90 Zr was made . Evaporation residues are separated from the primary beam and directed to the detector position by the velocity filter SHIP [12] . Different kinds of unstable nuclei are implanted near the surface of the detector and decay mostly by a radioactivity . The measured a spectrum is shown in fig. 7 . The correlation in time and position of the detected particles and the subsequent a decay has been widely 10 used for their identification. In figs . 8 and 9 the spectra of the time differences between the occurrence of the 179Hg a decay and the subsequent 175 Pt a decay are shown, using the position information and without using
_>
9
179H
4 ~--
800
c ô
U
9
_> 1t
175pt
=p 5s
600 400 200
10
-4
-2
6
T/s
2
4
6
Fig. 9. Spectrum of time distances between a decays of n9Hg and 175 Pt, without taking the position resolution into account.
86
W Morawek et al. / Correlation technique with a new position sensitive detector
it, respectively . By choosing a logarithmic time scale an ideal radioactive decay curve becomes a peak with a universal shape independent of the lifetime . True correlations are characterized by the occurrence of time distances between the mother and daughter decay shorter than expected for the random distribution . In fig . 9 the time distances between an event with the energy of the mother decay and the subsequent event with the energy of the daughter decay were plotted. No true correlations can be seen . The random peak with a peak position of tP = 0.5 s does not allow to detect true correlations with a mean lifetime of 3.64 s for 175 Pt . In fig. 8 the position information was taken into account. Events with the energy of the mother decay were stored in an array with their position and time of occurrence . Then the time difference of a daughter decay not to the last mother decay but to the last mother decay which was inside a certain area around the daughter decay, was plotted. The area was determined by the position resolution . Then the true coincidences with tP = 3.6 s are clearly separated from the random distribution with tP = 237 s. By taking the position information into account it is possible to detect correlations for nuclei with 450 times longer lifetimes . The theoretical factor is about 700, which is the ratio of the total detector area and the area in which the correlations are searched for. In the experiment this factor can only be realized when the detector is irradiated in such a way that areas with the same position resolution get the same counts . Thus with this detector and the mentioned proce-
dures the correlation technique can be extended to appreciably longer time distances. References [1] S. Kalbitzer, R. Bader, W. Melzer and W. Stumpfi, Nucl. Instr. and Meth. 54 (1967) 323. [2] R.B . Owen and M.L . Awcock, IEEE Trans. Nucl . Sci. NS-15 (1968) 290. [3] J.T. Walton, G.S. Hubbard, E.E. Haller and H.A . Sommer, IEEE Trans. Nucl . Sci. NS-26 (1979) 334. [4] K. Yamamoto, S. Yamaguchi and Y. Terada, IEEE Trans. Nucl . Sci. NS-32 (1985) 438. [5] K.-H. Schmidt, W. Faust, G. Münzenberg, H -G . Clerc, W. Lang, K. Pielenz, D. Vermeulen, H. Wohlfarth, H. Edwald and K. Güttner, Nucl . Phys. A318 (1979) 253. [6] K.-H. Schmidt, C.-C. Sahm, K. Pielenz and H.-G. Clerc, Z. Phys . A316 (1984) 19 . G. Münzenberg, P. Armbruster, F.P . Hessberger, S. Hofmann, K. Poppensieker, W. Reisdorf, J.R .H . Schneider, K.H . Schmidt, C.C. Sahm and D. Vermeulen, Z. Phys . A309 (1982) 89. [8] S. Hofmann, G. Münzenberg, F.P . Hessberger and H.-J. Schbtt, Nucl . Instr. and Meth . 223 (1984) 312. [9] M. Lampton and C.W . Carlson, Rev . Sci . Instr. 50 (1979) 1093 . [10] E. Stiefel, Einführung in die numerische Mathematik, (Teubner, Stuttgart, 1963) p. 182. [11] IBM Technical Newsletter No. SN20-0985-0 (1971) p. 23 . [12] G. Münzenberg, W. Faust, S. Hofmann, P. Armbruster, K. Güttner and H. Ewald, Nucl . Instr. and Meth . 161 (1979) 65 .