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α-Particle stopping power for titanium and vanadium
Nuclear instruments and Methods in Physics Research Bl (1984) 9-12 North-Holland, Amsterdam
a-PARTICLE
STOPPING
R.C. HAIGHT
POWER
FOR
TITANIUM
AND
VANADIUM
*
and H.K. VONACH
Lawrence Livermore National Luhoraror_v,Livermore. CA 94550, USA Received
25 January
1983 and in revised form 13 July 1983
A method for accurate measurement of the specific energy loss dE/dx of o-particles is described and results are given for titanium in the a-energy range 5.25-13 MeV and for vanadium in the range 5.25-12 MeV with uncertainties of about 3%. The results are in excellent agreement with the stopping power predictions of Ziegler and earlier precision measurements of the stopping power of protons and deuterons in Ti and V.
1. Introduction Accurate information on the specific energy loss dE/d.x of charged particles in matter is needed for many purposes in both basic and applied nuclear physics. For this reason all existing experimental data on stopping powers have recently been evaluated in the framework of the existing theory of atomic and nuclear energy loss of charged particles [l-4] resulting in predictions of dE/dx values for all elements. These stopping power predictions certainly represent our best estimate of the energy loss of charged particles in matter. They do not contain, however, quantitative information on the accuracy of the predicted stopping powers. Furthermore the experimental data bases for proton and o-particle stoppping powers are of different quality: Whereas measurements of proton stopping powers accurate to better than 1% have been made for many elements [5-71, measurements of a-particle stopping powers have been rather sparse and mostly in the accuracy range of about 5% [1,3]. Stopping powers for low energy o-particles, however, are of great practical importance because of the increasing use of so-called a-gauges for determining the thickness of foils. At present the accuracy of such measurements is limited by the accuracy of the tabulated stopping power values. Thus it is quite important to test the accuracy of these values for a-particles in the energy region of the natural o-emitters by some precise measurements. Therefore, in connection with precision measurements of ((Y, n) activation cross-sections where accurate
* Work performed
under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract no. W-7405-ENG-48.
0168-583X/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
energy loss measurements were needed, we have measured the specific energy loss of 5-13 MeV a-particles in titanium and S-12 MeV cY-particles in vanadium with an uncertainty of about 3%. In section 2 we describe the experimental procedure. In section 3 the results are presented and compared both with the stopping power calculations and with the experimentally determined stopping powers for hydrogen in these elements.
2. Experimental procedure Because of the high specific energy loss of low energy or-particles rather thin foils ( < 1 mg/cm*) have to be used in stopping power measurements and thus the determination of the foil thickness has been the largest source of error in most previous measurements. In order to reduce this error we have combined the energy loss measurements with a simultaneous measurement of the thickness of the very part of the foil used in the energy loss measurement as shown in fig. 1. The foils of titanium and vanadium were rolled [8] to - 1 mg/cm” and were uniform in thickness over a 1 cm* circular area to 5% or better as determined by the energy loss of 5.41 MeV alpha particles from a 241Am source. The LLNL Cyclograaff was used to irradiate the foils with 6-13 MeV cr-particles over an area of approximately 5 mm2. Both intensity and energy of the a-particles scattered at some forward angle within the range of pure Rutherford scattering were observed in two silicon detectors positioned at angles 0 and - 8 with respect to the incident beam. The energy loss in these foils was determined by calibrating the energy scale of the %-detectors with n-particles elastically scattered by a thin (250 pg/cm*) gold foil. From results of these measurements the stopping
R.C. Haight, H.K. Vonach / a- Particle stopping power As2
= solid angle of the detector apertures. charge (PC), A = atomic weight of Ti or V, da/dQa[(E, - $d. dE/dx),B] = Rutherford scattering cross section for a-particles of energy corresponding to foil center and angle t9 for Ti or V. The quantities n,, and AE were always determined for both detectors and the average inserted in eqs. (2) and (3). Thus the accuracy of the measurement is essentially determined by the accuracy with which the scattering angle, the solid angles of the detectors, the integrated charge, and the various contributions to the energy loss AE’ can be determined. With the use of two detectors placed symmetrically with respect to the incident beam, the effects of deviations of the direction of the incident beam from the nominal beam direction cancel to first order and the uncertainty in the scattering angle is determined by the accuracy of the relative angular positioning of the two detectors. With the mechanical setup used the uncertainty in this angle 20 was approximately 0.25”. The uncertainty in the detector solid angle was 1% due to the uncertainty in the radius of the counter apertures (1.014 + 0.004 and 1.030 f 0.005 mm). The integrated charge was measured by means of a digital charge integrator which had been calibrated before the experiment by means of a standard current source to better 1%. The pulses from the charge integrator were fed into the same ADCs as the Si-detector pulses. In this way the n,,/Q ratio was automatically corrected for dead-time which amounted to at most 10%. The energy difference A E between the Au peak and the Ti or V peak was measured with an error of about +4 keV. The average energy loss A EAu was calculated to an accuracy of f 2 keV from the dE/dx values of ref. 3 and the thickness as determined by Rutherford scattering. The uncertainties of the kinematic energy losses are negligible. Using the described procedure the energy loss was measured for incident a-energies ranging from 6-13 MeV for titanium and 6.5-12 MeV for vanadium using scattering angles in the range 12”-37”. In addition a low energy point at 5.25 MeV was determined for both elements by measuring the average energy loss of 241Am a-particles in several of the foils, the thickness of which had been determined by Rutherford scattering as described before.
Q
Fig. 1. Experimental loss of a-particles.
setup
for measuring
the specific
power could be derived in the following dE
energy
way:
AE’ 1 =d 0.5 + O.S/cos 0 ’ E,
t-1 dx
with AE’=AE-AE,,+AE,K:“-AEKin, d(mg/cm’)
=
(2) nsc
da/dQ,[(E,-fd.dE/dx)J]AJZ X2”
*
(3)
Q 6.02 x 10” ’
and
)I’ =1.2953
_ da doa
E-‘ddE = * ‘dx
(j
(2Z12
(E,-$d.dE/dx)2
1 (4) sin4(e/2)’
where the symbols have the following meaning: = incident a-particle energy, E_a = average a-energy on path through foil E, to detectors, = average energy loss of the a-particles AE’ scattered by the Ti or V foil into the detectors on their path through the foils, = energy difference between the peak AE positions (centroids) from Au and from the Ti or V scattering as observed in the detectors, = average energy loss of the a-particles A E.+u scattered by the 250 pg/cm Au foil, AEAy,AE’” = average kinematic energy loss for aparticles of incident energy E, in the gold and in the Ti or V foils, = thickness of the Ti or V foils d nsc
(mg/cm* ), = number of a-particles scattered by angle 0 from the Ti or V foils and recorded by the Si-detectors,
= integrated
3. Result and discussion The results of the measurements are given in tables 1 and 2. The listed errors are standard deviations obtained by quadratic addition of all recognized error
R.C. Huight, H.K. Table 1 Specific energy loss of a-particles dE/dx
12.79 11.80 10.80 9.75 8.75 7.73 6.73 5.68 5.25
266+ 8 2g1* 9 295* 9 316*10 343*11 368 * 12 402+12 457 + 14 475*15
i?* (MeV)
dE/dx
11.80 10.79 9.76 8.75 7.74 6.73 6.21 5.25
277+ 8 294* 9 313i 9 331510 3542 11 403112 413+13 463i15
11
in titanium.
% (MeV)
Table 2 Specific energy loss of a-particles
Vonach / a- Portrcle stopping power
(keV.mg-‘.cm*)
E, (MeVI
in vanadium. (keV.mg-‘.cm*)
Fig. 3. Specific energy loss of a-particles
in vanadium: Ziegler’s calculation [3] (solid line), calculation from measured hydrogen stopping powers of ref. 5 (triangles), calculation from measured hydrogen stopping powers of ref. 6 (open circles), and present results (closed circles).
The mean energy values E, are believed to be accurate to better than +0.02 MeV. In figs. 2 and 3 we compare our values with the calculated values of ref. 3 and stopping power values derived from proton and deuteron measurements by means of the relation
contributions.
(E,
Fig. 2. Specific energy loss of a-particies in titanium: Ziegler’s calculation [3] (solid fine), calculation of Northcliffe and Shilling [lo] (dusked line), calculation from measured hydrogen stopping powers of ref. 5 (rriangles), calculation from measured hydrogen stopping powers of ref. ‘I (open circles), and present results (closed circles).
= E,. M,/M~,,)
.(l + correction
terms),
where the correction terms are higher powers of the projectile charge f9]. For titanium the stopping power predictions of Northcliffe and Schilling [lo] are also indicated. As the figures show our results agree within experimental error very well both with the calculated stopping powers of refs. 3 and 10 and the value derived from the precision stopping power measurements for hydrogen of ref. 5. Our accuracy, however, is not sufficient to decide between the two calculations which yield only slightly different results. Thus our results confirm that the calculated stopping powers of ref. 3 are accurate to better than +3% also for a-particles in the energy region of the natural OLemitters used in the thickness measurements of foils. Finally it should be emphasized that these experimental results were obtained as a by-product of an effort primarily devoted to another purpose (precise total a-reaction cross sections) and thus the setup was not completely optimized for the d E,/dx measurements. Using some obvious improvements, however, the described method should allow d E/dx measurements for a-particles in the l-28 region without much difficulty.
12
R. C. Height,
H. K. Vonach / LX-Particle stopping power
References [I] H.H. Andersen, Bibliography and index of experimental range and stopping power data (Pergamon, New York, 1977). [2] H.H. Andersen and J.F. Ziegler, Hydrogen stopping powers and ranges in all elements (Pergamon, New York, 1977). [3] J.F. Ziegler, Helium stopping powers and ranges in all elements (Pergamon, New York, 1977). [4] J.F. Ziegler, Stopping cross-sections for energetic ions in all elements (Pergamon, New York, 1980).
[5] H.H.
[6] [7] [8] [9] [lo]
Andersen, C.C. Hanke, H. Simonsen, H. Smensen and P. Vajda, Phys. Rev. 175 (1968) 389. D. Powers, W.K. Chu and P.D. Bourland, Phys. Rev. 165 (1967) 376. E. Leminen, Ann. Acad. Sci. Fenn., Series A, VI. Phys. Nr. 386 (1972). Micromatter Co., Rt. 1, Box 72-B, Eastsound, WA, USA, 98245. H.H. Anderson, J.F. Bak, H. Knudsen and B.R. Nielsen, Phys. Rev. A 16 (1977) 1929. L.C. Northcliffe and R.F. Schilling, Nucl. Data Tables A7 (1970) 233.
a-PARTICLE
STOPPING
R.C. HAIGHT
POWER
FOR
TITANIUM
AND
VANADIUM
*
and H.K. VONACH
Lawrence Livermore National Luhoraror_v,Livermore. CA 94550, USA Received
25 January
1983 and in revised form 13 July 1983
A method for accurate measurement of the specific energy loss dE/dx of o-particles is described and results are given for titanium in the a-energy range 5.25-13 MeV and for vanadium in the range 5.25-12 MeV with uncertainties of about 3%. The results are in excellent agreement with the stopping power predictions of Ziegler and earlier precision measurements of the stopping power of protons and deuterons in Ti and V.
1. Introduction Accurate information on the specific energy loss dE/d.x of charged particles in matter is needed for many purposes in both basic and applied nuclear physics. For this reason all existing experimental data on stopping powers have recently been evaluated in the framework of the existing theory of atomic and nuclear energy loss of charged particles [l-4] resulting in predictions of dE/dx values for all elements. These stopping power predictions certainly represent our best estimate of the energy loss of charged particles in matter. They do not contain, however, quantitative information on the accuracy of the predicted stopping powers. Furthermore the experimental data bases for proton and o-particle stoppping powers are of different quality: Whereas measurements of proton stopping powers accurate to better than 1% have been made for many elements [5-71, measurements of a-particle stopping powers have been rather sparse and mostly in the accuracy range of about 5% [1,3]. Stopping powers for low energy o-particles, however, are of great practical importance because of the increasing use of so-called a-gauges for determining the thickness of foils. At present the accuracy of such measurements is limited by the accuracy of the tabulated stopping power values. Thus it is quite important to test the accuracy of these values for a-particles in the energy region of the natural o-emitters by some precise measurements. Therefore, in connection with precision measurements of ((Y, n) activation cross-sections where accurate
* Work performed
under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract no. W-7405-ENG-48.
0168-583X/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
energy loss measurements were needed, we have measured the specific energy loss of 5-13 MeV a-particles in titanium and S-12 MeV cY-particles in vanadium with an uncertainty of about 3%. In section 2 we describe the experimental procedure. In section 3 the results are presented and compared both with the stopping power calculations and with the experimentally determined stopping powers for hydrogen in these elements.
2. Experimental procedure Because of the high specific energy loss of low energy or-particles rather thin foils ( < 1 mg/cm*) have to be used in stopping power measurements and thus the determination of the foil thickness has been the largest source of error in most previous measurements. In order to reduce this error we have combined the energy loss measurements with a simultaneous measurement of the thickness of the very part of the foil used in the energy loss measurement as shown in fig. 1. The foils of titanium and vanadium were rolled [8] to - 1 mg/cm” and were uniform in thickness over a 1 cm* circular area to 5% or better as determined by the energy loss of 5.41 MeV alpha particles from a 241Am source. The LLNL Cyclograaff was used to irradiate the foils with 6-13 MeV cr-particles over an area of approximately 5 mm2. Both intensity and energy of the a-particles scattered at some forward angle within the range of pure Rutherford scattering were observed in two silicon detectors positioned at angles 0 and - 8 with respect to the incident beam. The energy loss in these foils was determined by calibrating the energy scale of the %-detectors with n-particles elastically scattered by a thin (250 pg/cm*) gold foil. From results of these measurements the stopping
R.C. Haight, H.K. Vonach / a- Particle stopping power As2
= solid angle of the detector apertures. charge (PC), A = atomic weight of Ti or V, da/dQa[(E, - $d. dE/dx),B] = Rutherford scattering cross section for a-particles of energy corresponding to foil center and angle t9 for Ti or V. The quantities n,, and AE were always determined for both detectors and the average inserted in eqs. (2) and (3). Thus the accuracy of the measurement is essentially determined by the accuracy with which the scattering angle, the solid angles of the detectors, the integrated charge, and the various contributions to the energy loss AE’ can be determined. With the use of two detectors placed symmetrically with respect to the incident beam, the effects of deviations of the direction of the incident beam from the nominal beam direction cancel to first order and the uncertainty in the scattering angle is determined by the accuracy of the relative angular positioning of the two detectors. With the mechanical setup used the uncertainty in this angle 20 was approximately 0.25”. The uncertainty in the detector solid angle was 1% due to the uncertainty in the radius of the counter apertures (1.014 + 0.004 and 1.030 f 0.005 mm). The integrated charge was measured by means of a digital charge integrator which had been calibrated before the experiment by means of a standard current source to better 1%. The pulses from the charge integrator were fed into the same ADCs as the Si-detector pulses. In this way the n,,/Q ratio was automatically corrected for dead-time which amounted to at most 10%. The energy difference A E between the Au peak and the Ti or V peak was measured with an error of about +4 keV. The average energy loss A EAu was calculated to an accuracy of f 2 keV from the dE/dx values of ref. 3 and the thickness as determined by Rutherford scattering. The uncertainties of the kinematic energy losses are negligible. Using the described procedure the energy loss was measured for incident a-energies ranging from 6-13 MeV for titanium and 6.5-12 MeV for vanadium using scattering angles in the range 12”-37”. In addition a low energy point at 5.25 MeV was determined for both elements by measuring the average energy loss of 241Am a-particles in several of the foils, the thickness of which had been determined by Rutherford scattering as described before.
Q
Fig. 1. Experimental loss of a-particles.
setup
for measuring
the specific
power could be derived in the following dE
energy
way:
AE’ 1 =d 0.5 + O.S/cos 0 ’ E,
t-1 dx
with AE’=AE-AE,,+AE,K:“-AEKin, d(mg/cm’)
=
(2) nsc
da/dQ,[(E,-fd.dE/dx)J]AJZ X2”
*
(3)
Q 6.02 x 10” ’
and
)I’ =1.2953
_ da doa
E-‘ddE = * ‘dx
(j
(2Z12
(E,-$d.dE/dx)2
1 (4) sin4(e/2)’
where the symbols have the following meaning: = incident a-particle energy, E_a = average a-energy on path through foil E, to detectors, = average energy loss of the a-particles AE’ scattered by the Ti or V foil into the detectors on their path through the foils, = energy difference between the peak AE positions (centroids) from Au and from the Ti or V scattering as observed in the detectors, = average energy loss of the a-particles A E.+u scattered by the 250 pg/cm Au foil, AEAy,AE’” = average kinematic energy loss for aparticles of incident energy E, in the gold and in the Ti or V foils, = thickness of the Ti or V foils d nsc
(mg/cm* ), = number of a-particles scattered by angle 0 from the Ti or V foils and recorded by the Si-detectors,
= integrated
3. Result and discussion The results of the measurements are given in tables 1 and 2. The listed errors are standard deviations obtained by quadratic addition of all recognized error
R.C. Huight, H.K. Table 1 Specific energy loss of a-particles dE/dx
12.79 11.80 10.80 9.75 8.75 7.73 6.73 5.68 5.25
266+ 8 2g1* 9 295* 9 316*10 343*11 368 * 12 402+12 457 + 14 475*15
i?* (MeV)
dE/dx
11.80 10.79 9.76 8.75 7.74 6.73 6.21 5.25
277+ 8 294* 9 313i 9 331510 3542 11 403112 413+13 463i15
11
in titanium.
% (MeV)
Table 2 Specific energy loss of a-particles
Vonach / a- Portrcle stopping power
(keV.mg-‘.cm*)
E, (MeVI
in vanadium. (keV.mg-‘.cm*)
Fig. 3. Specific energy loss of a-particles
in vanadium: Ziegler’s calculation [3] (solid line), calculation from measured hydrogen stopping powers of ref. 5 (triangles), calculation from measured hydrogen stopping powers of ref. 6 (open circles), and present results (closed circles).
The mean energy values E, are believed to be accurate to better than +0.02 MeV. In figs. 2 and 3 we compare our values with the calculated values of ref. 3 and stopping power values derived from proton and deuteron measurements by means of the relation
contributions.
(E,
Fig. 2. Specific energy loss of a-particies in titanium: Ziegler’s calculation [3] (solid fine), calculation of Northcliffe and Shilling [lo] (dusked line), calculation from measured hydrogen stopping powers of ref. 5 (rriangles), calculation from measured hydrogen stopping powers of ref. ‘I (open circles), and present results (closed circles).
= E,. M,/M~,,)
.(l + correction
terms),
where the correction terms are higher powers of the projectile charge f9]. For titanium the stopping power predictions of Northcliffe and Schilling [lo] are also indicated. As the figures show our results agree within experimental error very well both with the calculated stopping powers of refs. 3 and 10 and the value derived from the precision stopping power measurements for hydrogen of ref. 5. Our accuracy, however, is not sufficient to decide between the two calculations which yield only slightly different results. Thus our results confirm that the calculated stopping powers of ref. 3 are accurate to better than +3% also for a-particles in the energy region of the natural OLemitters used in the thickness measurements of foils. Finally it should be emphasized that these experimental results were obtained as a by-product of an effort primarily devoted to another purpose (precise total a-reaction cross sections) and thus the setup was not completely optimized for the d E,/dx measurements. Using some obvious improvements, however, the described method should allow d E/dx measurements for a-particles in the l-28 region without much difficulty.
12
R. C. Height,
H. K. Vonach / LX-Particle stopping power
References [I] H.H. Andersen, Bibliography and index of experimental range and stopping power data (Pergamon, New York, 1977). [2] H.H. Andersen and J.F. Ziegler, Hydrogen stopping powers and ranges in all elements (Pergamon, New York, 1977). [3] J.F. Ziegler, Helium stopping powers and ranges in all elements (Pergamon, New York, 1977). [4] J.F. Ziegler, Stopping cross-sections for energetic ions in all elements (Pergamon, New York, 1980).
[5] H.H.
[6] [7] [8] [9] [lo]
Andersen, C.C. Hanke, H. Simonsen, H. Smensen and P. Vajda, Phys. Rev. 175 (1968) 389. D. Powers, W.K. Chu and P.D. Bourland, Phys. Rev. 165 (1967) 376. E. Leminen, Ann. Acad. Sci. Fenn., Series A, VI. Phys. Nr. 386 (1972). Micromatter Co., Rt. 1, Box 72-B, Eastsound, WA, USA, 98245. H.H. Anderson, J.F. Bak, H. Knudsen and B.R. Nielsen, Phys. Rev. A 16 (1977) 1929. L.C. Northcliffe and R.F. Schilling, Nucl. Data Tables A7 (1970) 233.