- Email: [email protected]
Specific energy-loss behaviour of fission fragments along their range in P-10 gas
Nuclear Instruments North-Holland
and Methods
in Physics
Research
B53 (1991) 251-254
251
Specific energy-loss behaviour of fission fragments along their range in P-10 gas D.C. Biswas a, M.N. Rao b and R.K. Choudhury 0 Nuclear Physics Division, B.A. R. C., Bombay-400085, India b Institute of Physics, Bhubaneswar-751005, Received
6 August
India
1990 and in revised form 8 October
1990
Energy loss of *‘*Cf fission fragments in P-10 gas (90% Ar+ 10% CH,) at different pressures has been measured using a hybrid AE- E, detector telescope. The data were fitted to a polynomial function and the differential or specific energy loss (d E/dx) along the range of the fission fragments was determined for different fragment kinetic energies. The experimentally measured energy-loss data for most probable light and heavy fragments are compared with calculations using different available energy-loss expressions based on the Bethe energy-loss formula.
1. Introduction Measurement of the energy loss of heavy ions and fission fragments in matter is important from the point of understanding the energy-loss mechanism and also for application in particle identification using detector telescopes. At sufficiently large velocities, the ions are completely stripped of their electrons and the main contribution to the energy loss is due to inelastic electronic collisions which is well described by the basic equation of Bethe [l]. However, at low velocities (< 1.5 MeV/amu), the ions are partially stripped, and the energy-loss mechanism becomes more complicated due to the dependence of effective ionic charge Z,,, on the heavy-ion velocity. Measurements of the specific energy loss of heavy ions in different media have been extensively carried out in the past and compared with various theoretical models [2-81. Nuclear fission provides a convenient source of heavy ions covering a wide range of Z, M and velocities (E/M < 1.3 MeV/amu) and attempts have been made to measure the specific energy loss and range of the fission fragments in different media [9-121. The dependence of Z,,, of fission fragments on their mass, charge and energy have also been studied in some detail. Rekha et al. [12] determined empirical expressions for the Z,,, of the light- and heavy-fragment mass groups by fitting the energy loss data in Ar + CH, (5%) gas mixtures. Ziegler [13] has empirically determined the dependence of Z,,, on the energy and mass of heavy ions by fitting the energy loss data over a large energy range. Recently we have also determined [14] the E,Z dependence of the fragment effective charge from measurements of energy loss of 0168-583X/91/$03.50
0 1991 - Elsevier
Science Publishers
charge-selected light fission fragments in a given thickness of Ar + CH, (10%) gas mixture. In order to examine further the specific energy-loss behaviour of lightand heavy-fragment groups, we carried out measurements of energy loss of fragments in the gas medium at different gas pressures for comparison with the various available forms of the energy-loss expression. The experiment was carried out using a hybrid detector telescope formed by a gas ionisation chamber (AE) and a solid state detector (ER) to measure the energy loss in P-10 gas at different pressures. The experimental energy-loss values for most porbable light and heavy fragments at different gas pressures were compared with calculations using the energy loss tables of Northcliffe and Schilling [8] and also using the energy loss expressions of Rekha et al., Ziegler and Rao et al. [12-141. From the present data we also obtained the specific energy loss of fission fragments along the range in P-10 gas for different fragment kinetic energies (70-115 MeV in 5 MeV steps) which are also compared with the various energy-loss expressions. The details of the experimental setup, data analysis and results are discussed in the following sections.
2. Experiment setup The schematic diagram of experimental setup is shown in fig. 1. The AE-E, detector telescope consists of a gas ionisation chamber (10.5 cm length) for measurement of energy loss in gas (AE) and a surface barrier detector for residual-energy ( ER) measurements. The details of the telescope and its performance are
B.V. (North-Holland)
252
D. C. Biswas et al. / Fissionfragment energy losses 80-
E =
70-115
MeV
in
61-
eL6> aJ
Fig. 1. Schematic diagram of the experimental setup.
5
described earlier [15]. A 252Cf source (strength - 4 X lo5 fission/min) deposited on a thick nickel backing was mounted inside the ionisation chamber. A collimator was placed in front of the surface barrier detector in order to minimise the dispersion in the path length of the fragments measured. The pulse height spectrum of the solid-state detector was first recorded in vacuum to determine the energy calibration. The chamber was then filled with P-10 gas (90% Ar + 10% CH, mixture) and the two-parameter data of AE and E, were collected for gas pressures varying from 10 Torr to 110 Torr in steps of 10 Torr, and recorded in LIST mode for further off-line analysis. The pulse height spectra for AE and E, at different gas pressures are shown in fig. 2. The solid state detec-
n 60
torr
1800
10 torr
70
%
-
3216 -
OOA
125
PRESSURE
(TORR)
Fig. 3. Most probable energy loss as a function of gas pressure for different fragment energies. Dashed lines are polynomial fits to the experimental data.
tor was energy calibrated from the measured pulse height spectrum in vacuum using the known most probable light- and heavy-fragment energies in 252Cf fission [16]. The energy calibration of the gas detector at each gas pressure was obtained by measuring the energy shifts of the light- and heavy-fragment peaks in the solid-state detector due to energy deposited in the gas medium. The fragment energy distributions obtained by adding the AE and E, values event by event at all the gas pressures agreed quite well with the vacuum data. The average energy loss of fragments of given initial kinetic energies were then determined at all the gas pressures, by fitting the energy loss data with Gaussian distributions.
l----L torr
1200 600 1800 1200
3. Results and discussion
600 1800 g-l 1200 5
600
g
1800 1200 600 1600 50 torr
1200 600
20
62
106 20
62
104
110
Fig. 3 shows the average AE values for each 1 MeV window of fragment energy in the range of 70-115 MeV, measured at various gas pressures. It is seen that at every gas pressure, the energy loss is more for higher fragment kinetic energy. These data were fitted by a polynomial function as shown by the dashed lines in the figure. The smooth polynomial values of the energy loss at successive gas pressures were used to determine the specific energy loss (dE/dX) in MeV/(mg/cm*) of fission fragments of different kinetic energies along their range in the gas medium as shown in fig. 4. It is seen that in the initial part of the range, the specific energy loss for heavy fragments is more than that for the light fragments, but afterwards heavy fragments lose much less energy than the light fragments. This behaviour is largely due to the dependence of the effective ionic charge on the kinetic energy or velocity of the fragments.
1 L&J! 30
55
torr
5
30
55
80
AE (MeV) E, (MeV) Fig. 2. Pulse height spectra of fission fragments observed in the surface barrier and gas detectors.
253
D.C. Biswaset al. / Fissionfragment energy losses where A = B + 0.0378 sin( nB/2), 33.6 F
B = 0.886( E/25M,)“2/Z:‘3, E is the ion energy in keV, MI is the ion mass in amu and Z, is the ion atomic number. A simple expression for y has been suggested by us recently [14] to explain the energy-loss data in a gas medium as given by
25.2
2 r % 3 fi
16.8 8.4
y=l-(aO+aa,/E)exp(-b,l/,+b,Vi),
W’c
TJ-CJ
I
1
0.42 Distance
1
0.84 along
I
I
I
I
1.26
I
1.68
range(mg
I cm2
2.10
)
Fig. 4. Specific energy loss (dE/dx) of fragments of different energies along their range.
The specific energy loss of an ion of velocity V and charge Z is given by the Bethe expression [l] -dE/dX[MeV/(mg/cm*)] = 3.072 x 10P4( Z&r/p2)(Z&AM)
ln(2m,V*/Z),
where p = V/c and Z = KZ, is the mean excitation energy of the atomic electrons of the medium of atomic number Z, and mass number A,. m, is the mass of the electron and u is the fragment velocity. The effective charge Z,,, is expressed as Z,,, = yZ, where y is the effective charge parameter which has a complicated dependence on the atomic number Z and energy of the fragment. A general form of y as suggested by Bohr can be written as [8]
where E is the fragment energy in MeV and the constants were obtained as a, = 1.005, a, = 1.296, b,, = 0.988, b, = 0.218. We used the above available forms of expressions for y to calculate the energy loss at different pressures for comparison with the present measured data. The energy loss at different pressures were calculated by integrating the specific energy loss over the gas length E = cL(dE/dX) /
dX,
where L is the gas length in mg/cm*. Calculations were done for the most probable lightand heavy-fragment energies for which the Z and A values are known from literature as Z, = 41.95, A, = 106 amu, Z, = 56.05 and A, = 142 amu, respectively.
90
I
72 -
y=l--Aexp(-BVR),
Gas
thicknesst
,662 8
I
HEAVY
,
I
mg lCm2) 1.386 I
I
1
FRAGMENT 0’
I
2.310
,-:
5L-
where V, is defined as the ratio of the ion velocity to the Thomas-Fermi electron velocity (V, = V/V0Z2/3), V, being the orbital velocity of the electron in the first Bohr orbit. Rekha et al. [12] have obtained two separate functional forms of y for the light- and heavy-fragment groups by fitting the energy-loss data in the Ar + CH, (5%) gas mixture as given by yL = 1 - 0.95 exp( - 0.72Va)
>
P
LIGHT
FRAGMENT
72
: 36
and yu = 1 - 0.99 exp( - 0.82Vn).
This shows that the coefficients in the expression for y are a function of mass and energy of the fragments. Using the heavy-ion stopping-power data, Ziegler [13] has derived an empirical expression for y of heavy ions relative to protons of the following form y = 1 - exp( -A)[1.034
- 0.1777 exp( -0.081142,)],
18 0 0
110
Gi: Pr&ure66c tom? Fig. 5. Comparison of measured energy-loss values at various gas pressures, with calculations using available energy-loss expressions (- - - Northcliffe and Schilling, 1970; . . . . . Ziegler, 1980; Rekha et al, 1984; -+Rao et al., 1990).
254
D. C. Biswas et al. / Fission jragment
energy losses
4. Summary .
L1.6 “.‘....> T
312
“E
20.6
. ’
“.\,
HEAVY 1O.L
.
“+.a
: 7
.
v
In the present work we have measured the energy loss of fission fragments of different kinetic energies at various gas pressures in a detector telescope. These data were used to determine the specific energy loss along the range of the fragments. The energy-loss data for the most probable light and heavy fragments were compared with the calculations using the energy-loss expressions available in literature. It is found that the data are well reproduced by the expressions given in refs. [12-141, whereas the calculations using the expressions of Northcliffe and Schilling overpredict the energy loss to a large extent.
‘._ ..*
FRAGMENT
.N._ ‘\..! ‘%$....,.,, *
i-------I
206
LIGHT
0
0 L2
FRAGMENT
0.6L
1.26
1.68
2 10
Distance along range (mg/cm2) Fig. 6. Comparison of the measured specific energy loss along the range of the most probable light and heavy fragments with calculations using available energy loss expressions. Symbols are as in fig. 4.
These results are compared
in fig. 5 with the experimentally obtained energy-loss values at different gas pressures. The calculations using the simple expressions of Northcliffe and Schilling [8] for y are also shown in the same figure. It is seen that the calculations using the y expression of Northcliffe and Schilling grossly overprediet the energy-loss values, whereas the other three forms [12-141 give a good description of the energy-loss behaviour of the fission fragments. Fig. 6 shows the specific energy loss of the most probable light and heavy fragments along the range as compared with the calculated values from different energy-loss expressions. It is again seen that the values of Northcliffe and Schilling clearly overestimate the energy-loss data, whereas other three expressions are in agreement with the data within a few MeV. The calculations tend to differ from each other more towards the end of the fragment range, corresponding to very small E/M values. Further energy-loss data measured closer to the end of the range for both heavy- and light-fragment groups are needed to learn about the energy-loss behaviour of the fission fragments. Moreover measurements of energy loss of Z,A-selected fragments at different gas pressures over the entire range will be very useful to look for any finer variations and for detailed comparison with the available energy-loss expressions.
References [l] M.S. Livingston and H.A. Bethe, Rev. Mod. Phys. 9 (1937) 261. [2] T.E. Pierce and M. Blan, Phys. Rev. 173 (1968) 390. (31 H.L. Heckman, B.L. Parkins, W.G. Simons, F.M. Smith and W.H. Barkas, Phys. Rev. 117 (1960) 544. (41 C.D. Moak and M.D. Brown, Phys. Rev. 149 (1966) 244. [5] J.S. Forster, W. Ward H.R. Andrews, G.C. Ball, G.J. Costa, W.G. Davies and I.V. Mitchell, Nucl. Instr. and Meth. 136 (1976) 349. [6] H. Pape, H.G. Clerc and K.H. Schmidt, Z. Phys. 286 (1978) 159. [7] H.D. Betz and L. Grodzins, Phys. Rev. Lett. 25 (1970) 211. [8] L.C. Northcliffe and R.F. Schilling, Nucl. Data Tables A7 (1970) 233. [91 M. Hakim and N.H. Shafrir, Can. J. Phys. 49 (1971) 3024. WI M. Pickering and J.M. Alexander, Phys. Rev. C6 (1972) 343. illI Y. Laichter, H. Geissel and N.H. Shafrir, Nucl. Instr. and Meth. 194 (1982) 45. WI Rekha Govil, S.S. Kapoor, D.M. Nadkarni, S.R.S. Murthy and P.N. Rama Rao, Nucl. Instr. and Meth. B4 (1984) 13. 1131 J.F. Ziegler, Handbook of Stopping Cross-sections of Energetic Ions in all Elements, vol. 5 (Pergamon, 1980); J.F. Ziegler, Appl. Phys. Lett. 31 (1977) 544. 1141 M.N. Rao, D.C. Biswas and R.K. Choudhury, Nucl. Instr. and Meth. B51 (1990) 102. 1151 D.C. Biswas, P.N. Rama Rao, Aruna N and R.K. Choudhury, Proc. Nucl. Phys. Symp, Jaipur, 1985 DAE, vol. 28B (1985) p. 136. WI J.P. Unik, J.E. Gindler, L.E. Glendenin, K.F. Flynn, A. Gorski and R.K. Sjoblom, Proc. Phys. and Chem. of Fission, Rochester, NY, 1973, Vol. II (IAEA, 1973) p. 19.
and Methods
in Physics
Research
B53 (1991) 251-254
251
Specific energy-loss behaviour of fission fragments along their range in P-10 gas D.C. Biswas a, M.N. Rao b and R.K. Choudhury 0 Nuclear Physics Division, B.A. R. C., Bombay-400085, India b Institute of Physics, Bhubaneswar-751005, Received
6 August
India
1990 and in revised form 8 October
1990
Energy loss of *‘*Cf fission fragments in P-10 gas (90% Ar+ 10% CH,) at different pressures has been measured using a hybrid AE- E, detector telescope. The data were fitted to a polynomial function and the differential or specific energy loss (d E/dx) along the range of the fission fragments was determined for different fragment kinetic energies. The experimentally measured energy-loss data for most probable light and heavy fragments are compared with calculations using different available energy-loss expressions based on the Bethe energy-loss formula.
1. Introduction Measurement of the energy loss of heavy ions and fission fragments in matter is important from the point of understanding the energy-loss mechanism and also for application in particle identification using detector telescopes. At sufficiently large velocities, the ions are completely stripped of their electrons and the main contribution to the energy loss is due to inelastic electronic collisions which is well described by the basic equation of Bethe [l]. However, at low velocities (< 1.5 MeV/amu), the ions are partially stripped, and the energy-loss mechanism becomes more complicated due to the dependence of effective ionic charge Z,,, on the heavy-ion velocity. Measurements of the specific energy loss of heavy ions in different media have been extensively carried out in the past and compared with various theoretical models [2-81. Nuclear fission provides a convenient source of heavy ions covering a wide range of Z, M and velocities (E/M < 1.3 MeV/amu) and attempts have been made to measure the specific energy loss and range of the fission fragments in different media [9-121. The dependence of Z,,, of fission fragments on their mass, charge and energy have also been studied in some detail. Rekha et al. [12] determined empirical expressions for the Z,,, of the light- and heavy-fragment mass groups by fitting the energy loss data in Ar + CH, (5%) gas mixtures. Ziegler [13] has empirically determined the dependence of Z,,, on the energy and mass of heavy ions by fitting the energy loss data over a large energy range. Recently we have also determined [14] the E,Z dependence of the fragment effective charge from measurements of energy loss of 0168-583X/91/$03.50
0 1991 - Elsevier
Science Publishers
charge-selected light fission fragments in a given thickness of Ar + CH, (10%) gas mixture. In order to examine further the specific energy-loss behaviour of lightand heavy-fragment groups, we carried out measurements of energy loss of fragments in the gas medium at different gas pressures for comparison with the various available forms of the energy-loss expression. The experiment was carried out using a hybrid detector telescope formed by a gas ionisation chamber (AE) and a solid state detector (ER) to measure the energy loss in P-10 gas at different pressures. The experimental energy-loss values for most porbable light and heavy fragments at different gas pressures were compared with calculations using the energy loss tables of Northcliffe and Schilling [8] and also using the energy loss expressions of Rekha et al., Ziegler and Rao et al. [12-141. From the present data we also obtained the specific energy loss of fission fragments along the range in P-10 gas for different fragment kinetic energies (70-115 MeV in 5 MeV steps) which are also compared with the various energy-loss expressions. The details of the experimental setup, data analysis and results are discussed in the following sections.
2. Experiment setup The schematic diagram of experimental setup is shown in fig. 1. The AE-E, detector telescope consists of a gas ionisation chamber (10.5 cm length) for measurement of energy loss in gas (AE) and a surface barrier detector for residual-energy ( ER) measurements. The details of the telescope and its performance are
B.V. (North-Holland)
252
D. C. Biswas et al. / Fissionfragment energy losses 80-
E =
70-115
MeV
in
61-
eL6> aJ
Fig. 1. Schematic diagram of the experimental setup.
5
described earlier [15]. A 252Cf source (strength - 4 X lo5 fission/min) deposited on a thick nickel backing was mounted inside the ionisation chamber. A collimator was placed in front of the surface barrier detector in order to minimise the dispersion in the path length of the fragments measured. The pulse height spectrum of the solid-state detector was first recorded in vacuum to determine the energy calibration. The chamber was then filled with P-10 gas (90% Ar + 10% CH, mixture) and the two-parameter data of AE and E, were collected for gas pressures varying from 10 Torr to 110 Torr in steps of 10 Torr, and recorded in LIST mode for further off-line analysis. The pulse height spectra for AE and E, at different gas pressures are shown in fig. 2. The solid state detec-
n 60
torr
1800
10 torr
70
%
-
3216 -
OOA
125
PRESSURE
(TORR)
Fig. 3. Most probable energy loss as a function of gas pressure for different fragment energies. Dashed lines are polynomial fits to the experimental data.
tor was energy calibrated from the measured pulse height spectrum in vacuum using the known most probable light- and heavy-fragment energies in 252Cf fission [16]. The energy calibration of the gas detector at each gas pressure was obtained by measuring the energy shifts of the light- and heavy-fragment peaks in the solid-state detector due to energy deposited in the gas medium. The fragment energy distributions obtained by adding the AE and E, values event by event at all the gas pressures agreed quite well with the vacuum data. The average energy loss of fragments of given initial kinetic energies were then determined at all the gas pressures, by fitting the energy loss data with Gaussian distributions.
l----L torr
1200 600 1800 1200
3. Results and discussion
600 1800 g-l 1200 5
600
g
1800 1200 600 1600 50 torr
1200 600
20
62
106 20
62
104
110
Fig. 3 shows the average AE values for each 1 MeV window of fragment energy in the range of 70-115 MeV, measured at various gas pressures. It is seen that at every gas pressure, the energy loss is more for higher fragment kinetic energy. These data were fitted by a polynomial function as shown by the dashed lines in the figure. The smooth polynomial values of the energy loss at successive gas pressures were used to determine the specific energy loss (dE/dX) in MeV/(mg/cm*) of fission fragments of different kinetic energies along their range in the gas medium as shown in fig. 4. It is seen that in the initial part of the range, the specific energy loss for heavy fragments is more than that for the light fragments, but afterwards heavy fragments lose much less energy than the light fragments. This behaviour is largely due to the dependence of the effective ionic charge on the kinetic energy or velocity of the fragments.
1 L&J! 30
55
torr
5
30
55
80
AE (MeV) E, (MeV) Fig. 2. Pulse height spectra of fission fragments observed in the surface barrier and gas detectors.
253
D.C. Biswaset al. / Fissionfragment energy losses where A = B + 0.0378 sin( nB/2), 33.6 F
B = 0.886( E/25M,)“2/Z:‘3, E is the ion energy in keV, MI is the ion mass in amu and Z, is the ion atomic number. A simple expression for y has been suggested by us recently [14] to explain the energy-loss data in a gas medium as given by
25.2
2 r % 3 fi
16.8 8.4
y=l-(aO+aa,/E)exp(-b,l/,+b,Vi),
W’c
TJ-CJ
I
1
0.42 Distance
1
0.84 along
I
I
I
I
1.26
I
1.68
range(mg
I cm2
2.10
)
Fig. 4. Specific energy loss (dE/dx) of fragments of different energies along their range.
The specific energy loss of an ion of velocity V and charge Z is given by the Bethe expression [l] -dE/dX[MeV/(mg/cm*)] = 3.072 x 10P4( Z&r/p2)(Z&AM)
ln(2m,V*/Z),
where p = V/c and Z = KZ, is the mean excitation energy of the atomic electrons of the medium of atomic number Z, and mass number A,. m, is the mass of the electron and u is the fragment velocity. The effective charge Z,,, is expressed as Z,,, = yZ, where y is the effective charge parameter which has a complicated dependence on the atomic number Z and energy of the fragment. A general form of y as suggested by Bohr can be written as [8]
where E is the fragment energy in MeV and the constants were obtained as a, = 1.005, a, = 1.296, b,, = 0.988, b, = 0.218. We used the above available forms of expressions for y to calculate the energy loss at different pressures for comparison with the present measured data. The energy loss at different pressures were calculated by integrating the specific energy loss over the gas length E = cL(dE/dX) /
dX,
where L is the gas length in mg/cm*. Calculations were done for the most probable lightand heavy-fragment energies for which the Z and A values are known from literature as Z, = 41.95, A, = 106 amu, Z, = 56.05 and A, = 142 amu, respectively.
90
I
72 -
y=l--Aexp(-BVR),
Gas
thicknesst
,662 8
I
HEAVY
,
I
mg lCm2) 1.386 I
I
1
FRAGMENT 0’
I
2.310
,-:
5L-
where V, is defined as the ratio of the ion velocity to the Thomas-Fermi electron velocity (V, = V/V0Z2/3), V, being the orbital velocity of the electron in the first Bohr orbit. Rekha et al. [12] have obtained two separate functional forms of y for the light- and heavy-fragment groups by fitting the energy-loss data in the Ar + CH, (5%) gas mixture as given by yL = 1 - 0.95 exp( - 0.72Va)
>
P
LIGHT
FRAGMENT
72
: 36
and yu = 1 - 0.99 exp( - 0.82Vn).
This shows that the coefficients in the expression for y are a function of mass and energy of the fragments. Using the heavy-ion stopping-power data, Ziegler [13] has derived an empirical expression for y of heavy ions relative to protons of the following form y = 1 - exp( -A)[1.034
- 0.1777 exp( -0.081142,)],
18 0 0
110
Gi: Pr&ure66c tom? Fig. 5. Comparison of measured energy-loss values at various gas pressures, with calculations using available energy-loss expressions (- - - Northcliffe and Schilling, 1970; . . . . . Ziegler, 1980; Rekha et al, 1984; -+Rao et al., 1990).
254
D. C. Biswas et al. / Fission jragment
energy losses
4. Summary .
L1.6 “.‘....> T
312
“E
20.6
. ’
“.\,
HEAVY 1O.L
.
“+.a
: 7
.
v
In the present work we have measured the energy loss of fission fragments of different kinetic energies at various gas pressures in a detector telescope. These data were used to determine the specific energy loss along the range of the fragments. The energy-loss data for the most probable light and heavy fragments were compared with the calculations using the energy-loss expressions available in literature. It is found that the data are well reproduced by the expressions given in refs. [12-141, whereas the calculations using the expressions of Northcliffe and Schilling overpredict the energy loss to a large extent.
‘._ ..*
FRAGMENT
.N._ ‘\..! ‘%$....,.,, *
i-------I
206
LIGHT
0
0 L2
FRAGMENT
0.6L
1.26
1.68
2 10
Distance along range (mg/cm2) Fig. 6. Comparison of the measured specific energy loss along the range of the most probable light and heavy fragments with calculations using available energy loss expressions. Symbols are as in fig. 4.
These results are compared
in fig. 5 with the experimentally obtained energy-loss values at different gas pressures. The calculations using the simple expressions of Northcliffe and Schilling [8] for y are also shown in the same figure. It is seen that the calculations using the y expression of Northcliffe and Schilling grossly overprediet the energy-loss values, whereas the other three forms [12-141 give a good description of the energy-loss behaviour of the fission fragments. Fig. 6 shows the specific energy loss of the most probable light and heavy fragments along the range as compared with the calculated values from different energy-loss expressions. It is again seen that the values of Northcliffe and Schilling clearly overestimate the energy-loss data, whereas other three expressions are in agreement with the data within a few MeV. The calculations tend to differ from each other more towards the end of the fragment range, corresponding to very small E/M values. Further energy-loss data measured closer to the end of the range for both heavy- and light-fragment groups are needed to learn about the energy-loss behaviour of the fission fragments. Moreover measurements of energy loss of Z,A-selected fragments at different gas pressures over the entire range will be very useful to look for any finer variations and for detailed comparison with the available energy-loss expressions.
References [l] M.S. Livingston and H.A. Bethe, Rev. Mod. Phys. 9 (1937) 261. [2] T.E. Pierce and M. Blan, Phys. Rev. 173 (1968) 390. (31 H.L. Heckman, B.L. Parkins, W.G. Simons, F.M. Smith and W.H. Barkas, Phys. Rev. 117 (1960) 544. (41 C.D. Moak and M.D. Brown, Phys. Rev. 149 (1966) 244. [5] J.S. Forster, W. Ward H.R. Andrews, G.C. Ball, G.J. Costa, W.G. Davies and I.V. Mitchell, Nucl. Instr. and Meth. 136 (1976) 349. [6] H. Pape, H.G. Clerc and K.H. Schmidt, Z. Phys. 286 (1978) 159. [7] H.D. Betz and L. Grodzins, Phys. Rev. Lett. 25 (1970) 211. [8] L.C. Northcliffe and R.F. Schilling, Nucl. Data Tables A7 (1970) 233. [91 M. Hakim and N.H. Shafrir, Can. J. Phys. 49 (1971) 3024. WI M. Pickering and J.M. Alexander, Phys. Rev. C6 (1972) 343. illI Y. Laichter, H. Geissel and N.H. Shafrir, Nucl. Instr. and Meth. 194 (1982) 45. WI Rekha Govil, S.S. Kapoor, D.M. Nadkarni, S.R.S. Murthy and P.N. Rama Rao, Nucl. Instr. and Meth. B4 (1984) 13. 1131 J.F. Ziegler, Handbook of Stopping Cross-sections of Energetic Ions in all Elements, vol. 5 (Pergamon, 1980); J.F. Ziegler, Appl. Phys. Lett. 31 (1977) 544. 1141 M.N. Rao, D.C. Biswas and R.K. Choudhury, Nucl. Instr. and Meth. B51 (1990) 102. 1151 D.C. Biswas, P.N. Rama Rao, Aruna N and R.K. Choudhury, Proc. Nucl. Phys. Symp, Jaipur, 1985 DAE, vol. 28B (1985) p. 136. WI J.P. Unik, J.E. Gindler, L.E. Glendenin, K.F. Flynn, A. Gorski and R.K. Sjoblom, Proc. Phys. and Chem. of Fission, Rochester, NY, 1973, Vol. II (IAEA, 1973) p. 19.