Fission fragment velocity distribution measurement using time of flight technique

Accepted Manuscript Fission fragment velocity distribution measurement using time of flight technique D.C. Biswas, R.P. Vind, Nishant Kumar, Y.K. Gupta, R.V. Jangale, A.L. Inkar, L.A. Kinage, B.N. Joshi, S. Mukhopadhyay, G.K. Prajapati, Shradha Dubey

PII: DOI: Reference:

S0168-9002(18)30658-2 https://doi.org/10.1016/j.nima.2018.05.043 NIMA 60827

To appear in:

Nuclear Inst. and Methods in Physics Research, A

Received date : 25 October 2017 Revised date : 15 May 2018 Accepted date : 20 May 2018 Please cite this article as: D.C. Biswas, R.P. Vind, N. Kumar, Y.K. Gupta, R.V. Jangale, A.L. Inkar, L.A. Kinage, B.N. Joshi, S. Mukhopadhyay, G.K. Prajapati, S. Dubey, Fission fragment velocity distribution measurement using time of flight technique, Nuclear Inst. and Methods in Physics Research, A (2018), https://doi.org/10.1016/j.nima.2018.05.043 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Fission fragment velocity distribution measurement using time of flight technique

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D.C. Biswas1,2 , R.P. Vind1 , Nishant Kumar1,2 , Y.K. Gupta1 , R.V. Jangale1 , A.L. Inkar1 , L.A. Kinage1 , B.N. Joshi1 , S. Mukhopadhyay1 , G.K. Prajapati1,2 , Shradha Dubey 1,3 1

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Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India 2

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3

Homi Bhabha National Institute, Mumbai 400094, India

Physics Department, Faculty of Science, M.S.University of Baroda, Vadodara-390002, India

10

Abstract

11

Two large area position sensitive Multi Wire Proportional Counters (MW-

12

PCs) have been developed for the detection of Fission Fragments (FFs). The

13

detectors were characterized using FFs from

14

information by employing delay-line read out method and the resolution is

15

about 1 mm in both X and Y directions. Velocity distribution of the FFs

16

produced from spontaneous fission of

17

time-of-flight (TOF) technique, using a barium fluoride (BaF2 ) detector and

18

a MWPC. The most probable velocities obtained for the heavy and light

19

fragment groups are 1.035 ± 0.003 and 1.378 ± 0.004 cm/ns, respectively.

20

The energy dependence of fragment velocity distribution was also studied af-

21

ter degrading the energy of the fragments by using Mylar foils. It is observed

22

that the width of the distribution for the heavy fission fragments decreases

23

with the reduction in the energies, but for light fragments it does not show

24

any significant dependence on the energy.

252

252

Cf source to obtain position

Cf has been measured employing a

Email address: [email protected] (D.C. Biswas1,2) Preprint submitted to Nuclear Inst. and Methods in Physics Research, A

May 15, 2018

25 26

Keywords: Position sensitive multi-wire proportional counter, Fission

27

fragment velocity, Delay-line read out method

28

1. Introduction

29

Nuclear fission is a complex process and fission fragment mass distribu-

30

tion provides valuable information in the understanding of fission dynamics.

31

There are several methods for studying the fission fragment mass distribution;

32

from the coincident measurement of kinetic energies of both the fragments

33

(2E ) [1, 2], simultaneous measurement of fragment energy and velocity (E -v )

34

or correlated velocity of both the fission fragments (2v ) [3–6]. The silicon

35

detector and gas ionization chambers offer very good energy resolution. In

36

the past, these detectors have been used for fission fragment energy and mass

37

distribution measurements by employing 2E method. For fission fragments,

38

the specific energy loss is large in the beginning of the range and hence

39

the energy signals are affected due to the dead layer of the silicon detector.

40

Moreover, for these detectors the pulse height defect becomes significantly

41

important due to the high rate of electron-hole recombination in the dense

42

plasma created along the ion track, particularly near the end of the range.

43

Thus in case of semiconductor detectors, the correction for the pulse height

44

defect is required for the energy measurement [7]. Although gas ionization

45

chambers provide stable operation, the corrections due to the energy loss in

46

the entrance window, causes uncertainty in mass measurements [8, 9]. The

47

timing signals from ionization chamber are slow, having rise time ∼ 100-200

48

ns and these detectors are rarely used for TOF measurements using E -v or

2

49

2v methods. In addition, these detectors cannot handle high count rates at

50

forward angles in nuclear physics experiments.

51

In comparison to the gas ionization chambers, the proportional counters

52

provide fast timing signals and are found to be suitable in the high counting

53

experiments. Since the invention of the MWPC by Charpak et al ., these de-

54

tectors are extensively used in high energy physics experiments for particle

55

localization [10, 11]. The MWPC detector has very good timing character-

56

istics and is commonly used for particle tracking and velocity measurement.

57

Because of the good position resolution and detector efficiency, multi-wire

58

proportional detectors have also been used for nuclear physics experiments

59

in different sizes and geometries [12–15], in particular for studying heavy-

60

ion induced fission reactions. In these experiments, the velocity of the fis-

61

sion fragment is determined by combining accurate measurement of the path

62

length and the TOF measured by using two MWPC detectors [16, 17].

63

The precise measurement of the fragment velocity is very crucial for ob-

64

taining the fission fragment mass distribution. The fragment velocity distri-

65

bution for

66

using a pair of detectors having fast timing response [18]. The accuracy of

67

the time intervals of the signals of the detectors separated by a flight distance

68

is important for the velocity measurement and the uncertainty in the time

69

measurement can be minimized by using two detectors having fast timing re-

70

sponse. The mass distribution is broadened significantly due to the emission

71

of prompt neutrons in case of the double energy measurements, whereas it

72

is less influenced for double velocity measurements. The measured velocities

73

are, on the average, equal to the initial velocities of the fragments before

252

Cf fission, has been measured earlier from the coincident TOF

3

74

neutron emission and the data analysis is much simpler for mass distribution

75

studies using TOF method [19]. Thus no correction due to neutron emission

76

is required in 2v method and the mass measurement by employing the TOF

77

technique using MWPC is more accurate in contrast to the 2E measurement

78

[20].

79

In nuclear fission, various fragment nuclei are produced with different

80

masses and charges, having varying velocities/energies. In contrast to light-

81

ions, the enegy loss mechanism for FFs is a complex process. There is a strong

82

variation of the specific energy loss with the fragment energy or velocity [21].

83

So far there is no measurement on the energy dependence of the fragment

84

velocity distribution and detail investigations are required to understand the

85

energy loss mechanism of fission fragments. In the present work, the energy

86

dependence of the width of velocity distribution has been studied for the

87

first time by degrading the fragment’s energy using Mylar foils of different

88

thickness. Here, we have used a novel technique for measuring the velocity

89

distribution of fission fragments produced from the spontaneous fission of

90

252

Cf, by employing TOF method. A BaF2 scintillator was used for the

91

detection of prompt gamma rays emitted from the fragment nuclei, that was

92

used as the “Start Signal” in the TOF setup. The fast anode signal from

93

MWPC due to the fission fragments was used as “Stop Signal”. The timing

94

characteristics of MWPC have been investigated in detail to use this detector

95

for the measurement of the velocity of the fission fragments produced in

96

spontaneous fission and heavy-ion induced reactions. Present results will be

97

very useful for the calculation of energy loss in the target material and window

98

foils of the gas detectors that are regularly used in heavy-ion experiments.

4

Detector Platform

Figure 1: Schematic diagram of the experimental TOF setup using a BaF2 detector and MWPC mounted inside a vacuum chamber. 99

2. Experimental details

100

The TOF measurements were carried out using a BaF2 scintillator and

101

a MWPC detector. The schematic diagram of the experimental set up is

102

shown in Fig. 1. A

103

chamber, which was evacuated to a vacuum of ≤ 10−3 Torr. For the detection

104

of FFs, the MWPC detector was mounted on a platform inside the vacuum

105

chamber at two distances 54.5 cm and 85.5 cm from the source in two different

106

measurements. The BaF2 detector was mounted outside the flange of the

107

vacuum chamber at a distance of 1.0 cm from the source. In spontaneous

108

fission of 252 Cf about 10 prompt γ-rays are also emitted along with the fission

109

fragments [22]. The gamma rays are detected by the BaF2 detector, which

110

gives a fast signal and was used as “Start Signal” for the TOF experiment.

111

After traveling the flight path in vacuum, the fission fragments reach the

112

MWPC and lose energy in the gaseous medium. It gives a fast timing signal

113

from the anode that was used as “Stop Signal” in the experiment.

252

Cf source was mounted on a flange inside a scattering

5

114

3. Timing characteristics of the signals from MWPC

115

For the detection of fission fragments (FFs), we have developed two-

116

dimensional position sensitive MWPC detectors, having an active area of

117

17.5 cm × 7.0 cm for heavy ion induced fission reaction studies at Pelletron-

118

LINAC facility, Mumbai. The MWPC consists of one anode (A) wire plane,

119

two sense wire planes (X and Y) for position information and two cathode (C)

120

wire planes. The schematic sketch of the cathode, anode, X and Y sense wire

121

planes and their geometric separations are shown in Fig. 2. Appropriate PCB

122

spacers were introduced between the wire planes for maintaining constant

123

distance between the planes and hence providing uniformity in the applied

124

electric field inside the detector region. The separation between the anode

125

wire plane and X (or Y) planes are 2 mm, while the separation between X

126

(or Y) and the cathode plane is 4.8 mm. The wires were fixed on PCB board

127

of thickness 1.6 mm. The main body of the MWPC is made of aluminum to

128

mount all the wire planes inside it. The mounting arrangement of the wire

129

planes and the electronic connectors inside the detector main body is shown

130

in Fig. 3. The anode wire plane is placed between the two cathode planes.

131

Each wire is essentially independent and behaves like a proportional counter.

132

The anode plane consists of gold plated tungsten (Au-W) wires having 10

133

µm diameter and the separation between two adjacent wires is 2 mm. Both

134

the cathode, X and Y sense wire planes were also made of Au-W wires having

135

50 µm diameter and fixed at a separation of 2 mm. The orientation of the

136

X and Y sense wire planes is orthogonal to each other.

137

Stretched Mylar foil of thickness ∼ 1 µm and of size 17.5 cm × 7.0 cm

138

was used as entrance window of the detector. The window foil was supported 6

Gas inlet

Gas outlet

Cathode 2 -260 V 4.8 mm

Y Anode

2.0 mm 2.0 mm

350 V X

4.8 mm

Cathode 1 -260 V

1 micron thin Mylar window

Figure 2: Schematic drawing of the vertical cross-sectional view of MWPC showing 5 wire planes. The separation and typical voltages applied to the cathodes and anode are also shown in the figure.

139

by stainless steel wires of diameter 0.5 mm by fixing on a PCB frame at a

140

separation of 10 mm in both X as well as Y directions. Two gas feed-through

141

were connected to the detector for operating the MWPC in gas-flow mode.

142

The flow of the gas was maintained at a constant low pressure (2-3 Torr)

143

by using an automatically controlled gas-flow system supplied by M/s Alpha

144

Pneumatics, Thane, India.

145

The X-sense wire plane has 100 wires with a pitch of 2 mm, while 40 wires

146

of 2 mm pitch are used for Y-sense wires. We have employed the delay-line

147

read out method for deriving X and Y position information of the detector.

148

The delay between the successive X-sense wires is 2 ns, while that between

149

the Y-sense wire is 5 ns. Using the anode signal as a “Start” and X-signal as

150

“Stop”, the time difference between these two signals gives the X-position of

151

the detector. Similarly, the time difference between the anode and Y-signal

152

defines the Y-position.

153

The detector was tested in the laboratory with 7

252

Cf source for the uni-

154

formity of the position readouts, and also for checking correlation between

155

the timing of anode pulse and position (X,Y) delay-line signals. Fig. 4 shows

156

the schematic block diagram of the electronic setup along with the data ac-

157

quisition system. The anode and the cathode wire planes were biased at

158

+350 V and -260 V respectively, whereas the X and Y sense wire planes were

159

not given any bias voltage and grounded through delay-lines. The MWPC

160

detector has been operated with isobutene gas at a pressure of 3 Torr. The

161

E/p ratio, where E is the electric field between the cathode and anode wire

162

planes, and p is the gas pressure, was high enough (∼ 300 V cm−1 Torr−1 ) to

163

produce secondary multiplication of the primary electrons produced in the

164

region between the cathodes and the sense wires. The secondary electrons

165

enter the region between the sense wires and the anode. Due to the large elec-

166

tric field near the anode wires, it causes a localized avalanche of electrons and

167

ions in the vicinity of the anode, which produces a fast rising negative pulse

168

at the anode and positive signals at the sense wires. A wide band ORTEC

169

VT120A type fast timing pre-amplifier (Fast PA) was used to amplify the

170

negative anode pulses. The X and Y sense wire signals have positive polarity

171

and were amplified by two ORTEC VT120B type fast timing pre-amplifiers.

172

We have measured the rise time of the signals with and without the timing

173

filter amplifiers (TFA) as shown in Fig.5(a) and (b) respectively. The rise

174

time of the anode, X and Y signals were ∼ 6 ns immediately after the fast

175

amplifier and it is about ∼ 9 ns after the TFA, using suitable integration and

176

differentiation time of about 10-20 ns.

177

178

Typical anode pulses from VT120A pre-amplifier with

252

Cf source were

500 mV for FFs and less than 5 mV for alpha particles. Since the anode signal

8

Wire Delay-line Aluminum Gas outlet Gas inlet Planes Chips chamber

Figure 3: (Color online) Photograph showing mounting arrangement of the anode, 2 cathodes, X and Y sense wire planes of the MWPC inside an aluminum chamber. The delay-line chips (10 in X and 4 in Y) are also shown in the figure.

X-position delay line

BaF2 Detector

X Y

Fast PA

TFA

CFD delay

TAC

Y-position delay line

P1 TAC

252Cf

C

Fast PA

P2 P3

delay A

P5 P4

TFA CFD

Fast PA

C

PC based data Acquisition system

CFD GDG

Pre Amp

Shaping Amp

TFA

CFD

delay

TAC

Shaping Amp

Figure 4: (Color online) Electronic block diagram of the setup used for the TOF measurement.

9

179

is primarily used for the timing measurement of fission fragments, its output

180

from fast pre-amplifier is directly fed to Constant Fraction Discriminator

181

(CFD) for further processing. The timing outputs of the sense wire signals

182

(X and Y) were about 150 mV, which were filtered through timing filter

183

amplifiers (TFAs) and fed to CFD. After the TFA, the pulse height of the

184

signals were about 950 mV. The output signal of the anode CFD becomes

185

the “Start” pulse for two Time-to-Amplitude Converters (TACs) that are

186

used for X and Y position measurements. It was also used for generating

187

master gate pulse through a Gate & Delay Generator (GDG). The output

188

of the CFDs of the X and Y sense wires are suitably delayed and used as

189

“Stop” pulses for obtaining position information from the corresponding TAC

190

modules. The output pulse heights of both the TAC’s are proportional to the

191

delay between the anode and sense wire signals, which translate the position

192

information of the detector in two dimensions.

193

The linearity of the position signal has been checked by putting a mask

194

on the face of the detector. There were 11 opening holes in X direction of

195

the mask with 1.0 mm diameter and the separation between the center of the

196

two adjacent holes was 10 mm. In the Y-direction 8 opening holes of 1.0 mm

197

diameter, with a separation of 5 mm were used. The peaks corresponding to

198

X and Y directions are shown in Fig. 6. The mean peak position and width

199

have been obtained by fitting the distribution with Gaussian function. The

200

peak channel number corresponding to the center of each opening hole, has

201

been plotted as a function of hole position (in mm), also shown in the same

202

figure (right Y-axis). The error in the Gaussian fitting of the intensity profile

203

and hence in the position measurement is within the size of the circle. It is

10

204

observed that the position peak channels show linear behavior with the peak

205

position. The position resolution (FWHM) both in X and Y directions are

206

obtained from the fitting of the peaks and are found to be about 1.04 ± 0.03

207

mm and 1.06 ± 0.04 mm respectively.

208

The position sensitivity of the detector in two dimensions has also been

209

tested with FFs from a 252 Cf fission source and by putting a mask of “BARC”

210

(acronym of Bhabha Atomic Research Centre) in front of the detector. Each

211

letter of the mask “BARC” was realized in a dot matrix format by drilling

212

small holes of 1.0 mm diameter. The center to center distance of the holes

213

for straight portion of each letter is 5 mm and for the curved portions it is

214

2.5 mm. The 2D position spectrum as shown in Fig. 7, gives a clear image of

215

the acronym “BARC”, demonstrating very good performance of the detector

216

for position measurement in two dimensions.

217

4. Timing characteristics of the BaF2 detector for γ rays

218

The BaF2 detector was of length 2.5 cm, with conical shape having 2.5

219

cm diameter in the front and 3.8 cm in the back face, which was coupled

220

with a photomultiplier tube. The light output pulse from the de-excitation

221

of BaF2 has two components: one with decay time of 630 ns and other

222

with decay time of 0.6 ns. The fast component only accounts for 20% of

223

the total light output of BaF2 , the remaining 80% consists of by the slow

224

component [23]. The time resolution of the BaF2 detector has been obtained

225

by using two identical detectors and measuring the two coincidence γ rays

226

of energies 1.173 and 1.332 MeV, emitted from a

227

voltages (+1700 V) were applied in both the detectors using two independent 11

60

Co source. Positive bias

Figure 5: (Color online) (a) The pulses taken by a digital oscilloscope from the fast pre-amplifier of the anode, X and Y planes after shaping with suitable integration and differentiation using TFA. (b) Pulse shapes of the signals immediately after the fast preamplifier (without using TFA).

228

HV supplies. The γ ray energies were measured after amplifying the signals

229

using a shaping amplifier. The output pulses from the anode of the BaF2

230

detectors were found to be sharp in timing having rise time of ∼ 3.2 ns and

231

in amplitude around 500 mV. The pulses were directly fed to CFD without

232

any shaping or amplification. The output pulse from the CFD of one BaF2

233

was fed to the “Start” of the TAC and the pulse from the CFD of other BaF2

234

was delayed through a delay box and eventually given to the “Stop” of the

235

TAC. The time resolution (FWHM) obtained for the BaF2 -BaF2 detector

236

system from this experiment is about 233 ± 6 ps.

12

(a)

X-position

160

120

120

80

80

40

40

80

Y-position

(b)

80

60

60

40

40

20

20

0

100

200

300

400

X-position (mm)

160

Y-position (mm)

Counts

Counts

200

500

Channel no

Figure 6: (Color online) (a) Position spectrum in X direction as obtained by keeping a mask in front of the detector with 1 mm diameter, having 11 holes and separated by 10 mm. (b) In Y-direction, the position spectrum for 8 holes of 1 mm diameter in the mask

Y-position (mm)

and separated by 5 mm.

40 30 20 25

75

50

100

X-position (mm) Figure 7: (Color online) Two dimensional spectrum of coordinates X and Y obtained by keeping a mask with acronym “BARC” having 1 mm diameter holes placed in front of the detector.

13

237

5. Measurement of the velocity distribution for fission fragments 252

238

from

Cf

239

For the velocity distribution measurement, the fission fragments were

240

detected by using the MWPC, mounted at a distance of 54.5 cm from the

241

source. The prompt γ rays emitted from the fission fragments were measured

242

by using a BaF2 scintillation detector in coincidence with the signals from the

243

MWPC. The TAC spectrum was obtained by using the “Start Signal” from

244

the BaF2 and “Stop Signal” from the anode of the MWPC detector. The

245

measurement was repeated by extending the flight path to 85.5 cm, using a

246

stainless steel tube of known length of 31 cm. From the known path length

247

and measured TOF, the velocity (V) was obtained after processing the event

248

by event list mode data. The partial energy loss (∆E) in the MWPC has been

249

measured from one of the cathodes, by amplifying the signal using a charge

250

sensitive preamplifier (PA) followed by a shaping amplifier. Fig. 8 shows the

251

2D-plot of ∆E vs TOF of the fission fragments (without any degrader foil)

252

for the flight path of 54.5 cm. As the light fragments have larger velocities

253

than the heavy fragments, it is seen from the 2D spectrum that both the

254

fission fragment groups are clearly separated. The TOF distribution spectra

255

obtained by taking the x-projection of the 2-dimensional plot, shown in Fig.

256

8. By using double Gaussian fit to the timing spectrum, we have obtained

257

the width of the TOF distribution. It is observed that the time spread for the

258

heavy fragments is larger than the lighter ones due to the velocity dispersion.

259

The velocity distributions obtained from the present measurement for two

260

distances are consistent. The most probable velocities were obtained by

261

taking the average of the peak velocities measured for both the distances. 14

Figure 8: (Color online) Two dimensional plot of Energy (∆E) vs TOF, showing clear separation for light and heavy fission fragment groups produced from

252

Cf.

262

The most probable velocities for heavy and light fragments are, VH = 1.035

263

± 0.003 and VL = 1.378 ± 0.004 cm/ns respectively. Here, the errors in VL

264

and VH are calculated from the fitted uncertainties in the TOF and assuming

265

the error in flight path measurement to be 0.05 cm.

266

The energy dependence of the TOF distribution for the light and heavy

267

fragment groups have been measured after degrading the fragment energies

268

by keeping a Mylar foil of thickness 2.5 µm very near to the 252 Cf source. Thus

269

the fragments will lose energy in the foil and hence the TOF will increase due

270

to reduction of the fragment velocities. The experiment was repeated for 2, 3

271

and 4 layers of Mylar foils each of 2.5 µm thick. After each degrader foil, the

272

∆E spectra (shown in Fig. 9) were obtained by putting independent banana

273

gates for both heavy and light fragments in ∆E vs TOF two-dimensional

274

plot (e.g., Fig. 8, without any foil) and taking y-projection. Without any

15

Counts

150 120 90 60 30

Mylar thickness = 0 µm (a)

120 90 60 30 120 90 60 30

Light

2.5 µm

Heavy

(b) Light

Heavy

5.0 µm (c)

200 150 100 50

Heavy

7.5 µm

Light

(d) Heavy Fragment

300

Light Fragment

200

10.0 µm

100

(e) 0

100

200

300

400

Energy (∆Ε) ∆Ε) in arb. units Figure 9: The energy (∆E) spectra in MWPC for the FFs from

252

Cf after degradation

with different thicknesses of Mylar foils. Each ∆E spectrum is obtained by taking the “y-projection” of the 2D plot of ∆E vs TOF.

16

275

Mylar foil, the energy loss in the gaseous medium due to the heavy and

276

light fragment groups are similar as shown in Fig. 9(a). In case of fission

277

fragments, the specific energy loss is equal for both light and heavy fragment

278

groups in the beginning of the range [21]. However, as the fragments pass

279

through the degrader foil, the fragment energy is reduced and hence the

280

energy loss in the detector is also reduced. Thus, the lighter fragments having

281

higher energies will lose more energy in the gaseous medium as compared to

282

the heavier fragments. It is seen from Fig.9 that for heavy fragment group,

283

the width of the ∆E spectrum reduces significantly after passing through

284

the foil as compared to the light fragments. It is also observed that the

285

energy spectra are better separated for both the fragment groups after energy

286

degradation of the fragments passing through Mylar foils of thickness 5 µm,

287

as shown in Fig.9(c).

288

The TOF spectrum has been obtained by taking x-projection of the ∆E vs

289

TOF plot, as shown in left panel of Fig. 10. It is seen that with the decrease

290

in the energy of the fission fragments, the peaks are broadened due to the

291

energy straggling in the Mylar foil and also become slightly asymmetric. By

292

using double Gaussian fits to the timing spectrum, we have obtained the

293

mean TOF and the width of the peaks in distribution corresponding to light

294

(TL ) and heavy (TH ) fragments. The measured TOF distributions of the

295

fragments were transformed to the velocity distributions by analyzing event

296

by event list mode data. The velocity distribution thus obtained for both

297

the fragment groups are plotted in right panel in Fig. 10. We have obtained

298

the most probable value as well as the width of the distribution (FWHM)

299

from the velocity spectra, by fitting with two Gaussian distributions for the

17

2000 1500

750 600 450 300 150

Mylar degrader = 0.0 µm

1000 500

600

1200 800 400

Counts

Mylar degrader = 0.0 µm

2.5 µm

400

2.5 µm

200

600

450 5 µm

400

300

200

5.0 µm

150

150

600 450 300 150

450

900

450 7.5 µm

300

300

7.5 µm

600

10 µm

10.0 µm

150

300

50 100 150 Time of flight (ns)

0.4 0.8 1.2 1.6 Velocity (cm/ns)

Figure 10: (Color online) The TOF (flight path = 54.5 cm) and velocity distribution spectra for the FFs from

252

Cf after energy degradation with different thickness of Mylar

layer. Solid line in each panel is the double Gaussian fit for heavy and light fragments.

18

300

heavy and light fragment groups as shown by solid lines in Fig.10. The

301

experimental TOF and the mean velocities for most probable heavy and

302

light fragments after passing through each Mylar foil are listed in Table-1.

303

The width (FWHM) of the velocity distributions for both the light and heavy

304

fragment groups have been plotted in Fig. 11 for various fragment energies.

305

From the measured peak values of the velocity distributions (VL and VH )

306

after passing through 0, 1, 2, 3, 4 layers of Mylar foils and known values of

307

the most probable light as well as heavy fragment masses (AL = 108.39, AH

308

= 143.61) [18], the residual energies (EL and EH ) of the most probable FFs

309

were obtained by using the expression, E = 21 AV2 . We have also calculated

310

the residual energies of the fragments after passing through each Mylar foil

311

by using SRIM code [25] for light (Z = 42, A = 108) and heavy (Z = 56, A =

312

144) fragments and compared with the measured values. The experimental

313

values of the residual energies for most probable light and heavy fragments

314

are listed in Table-1 along with SRIM calculations. The experimental data for

315

residual energies agree quite well with the simulated values in the beginning

316

of the range as shown in Table-I. However, the SRIM calculations overpredict

317

the experimental residual energies after passing through large thickness of the

318

foils. As the fission fragments lose large amount of energy in the foils, the

319

straggling effect becomes significantly important and improved theoretical

320

calculations are required to explain the energy loss mechanism.

321

It is observed that for the heavy fission fragments, the width of the ve-

322

locity peak decreases with the reduction in the fragment energies, but for

323

light fragments the width does not show significant energy dependence. This

324

behavior of energy dependence might be explained from Fig.9, where, it is

19

Velocity width (cm/ns)

0.30 252Cf spontaneous fission

0.25 0.20 0.15 0.10

Heavy fragments Light fragments

0.05 20

40

60

80

100 120 140

Fragment Energy (MeV)

Figure 11: The velocity width (FWHM) plotted with fission fragment energies after degradation with Mylar foils of different thicknesses. Dotted and dashed lines are shown to guide the eye.

325

seen that for heavy fragments, there is a significant reduction in the width

326

of the energy spectra as the fragments traverse through the foils. However it

327

is observed that the change in the energy width is relatively small for lighter

328

fragments. These differences in energy spectral shapes of light and heavy

329

fragments reflect in velocity distribution width. Present results will provide

330

very useful information in understanding the fragment velocity dependence

331

of energy loss mechanism in nuclear fission.

332

6. Measurement of the velocity distribution for fission fragments 28

Si+197 Au reaction

333

in

334

For the measurement of fission fragment mass distribution employing the

335

double velocity (2v ) method, two identical MWPC detectors as described

336

above were used in an in-beam experiment at BARC-TIFR Pelletron-LINAC

337

accelerator facility, Mumbai. Pulsed beam of

338

with 1.5 ns width and a period of 107.3 ns was used in this measurement. 20

28

Si having 154.6 MeV energy

Gas in Gas out Fragment-1

Target Ladder

MWPC1

MWPC2 Fragment-2

Beam

Figure 12: (Color online) Photograph of the experimental setup showing two MWPC detectors mounted inside a general purpose scattering chamber at Pelletron-LINAC facility, for measuring fission fragment mass distribution from the fragment velocity measurement. 28

Si+197 Au reaction, were detected in co-

339

The fission fragments produced in

340

incidence by using two position-sensitive MWPC detectors mounted inside a

341

general purpose scattering chamber of diameter 1.5 meter, on two movable

342

arms as shown in Fig. 12. The anode plane was normal to the particle tra-

343

jectories passing though the center of the detectors. The target was ∼ 250

344

µg/cm2 self supporting gold foil. One of the detectors was placed at a dis-

345

tance of 55.0 cm (MWPC1) from the target ladder, while the other was kept

346

at a distance of 27.5 cm (MWPC2). The angular coverage of the MWPC1

347

and MWPC2 were around 18.0◦ and 35.3◦ , respectively. The folding angle for

348

349

28

Si+197 Au reaction at a beam energy of 154.6 MeV is 144◦ and the detectors

were mounted at θ1 = 72◦ and θ2 = -72◦ .

350

For the detection of fission fragments, isobutene gas at a pressure of 3.0

351

Torr was filled inside the MWPCs. The X,Y positions, the energy loss in each 21

352

of the detectors, the time difference between the arrivals of the coincident

353

fragments at the detectors and individual TOF of the fragments with respect

354

to RF beam bunching signal were recorded event by event. The position

355

calibration of the detectors were carried out using the known positions of the

356

edges of the detectors, when the events were collected in singles mode using

357

252

Cf source. The velocities were reconstructed from the timing and position

358

information obtained in X and Y directions. In Fig. 13 we have plotted

359

V1cm and V2cm , along with velocities measured by MWPC1 and MWPC2

360

in lab frame as V1lab and V2lab respectively. It is observed that the velocity

361

distribution as well as the mean velocities are similar for the fission fragments

362

measured by both the MWPCs. In case of

363

MeV, the velocity distributions show single broad peak in both the MWPCs

364

because of the symmetric fission in heavy-ion induced fission reactions at

365

higher excitation energies. Whereas, for spontaneous fission of

366

have observed two distinct peaks in the velocity distribution as seen Fig.10,

367

corresponding to light and heavy fragment groups due to asymmetric fission.

368

The mass distribution for 28 Si+197 Au reaction was obtained from the mea-

369

sured velocity distribution of both the fission fragments by using the kine-

370

matic coincidence method [16]. Symmetric mass distribution was observed

371

having peak position at around A/2 and details will be presented in Ref. [26].

372

We have estimated the fission fragment mass resolution for the present TOF

373

setup and the detailes are discussed in the APPENDIX. The mass resolution

374

obtained by this method was found to be 4.26% for

22

28

Si+197 Au reaction at 154.6

28

252

Cf, we

Si+197 Au reaction.

(a)

(b)

Figure 13: (Color online) Velocity distribution of the fission fragments in lab frame and c.m. frame shown in panel (a) and (b) respectively for

28

Si+197 Au at a beam energy of

154.6 MeV. Black and red color represents fragments detected by MWPC1 and MWPC2 respectively.

375

7. Summary and Conclusions In summary, the velocity distribution of fission fragments from sponta-

376

252

377

neous fission of

378

method using a BaF2 detector as “Start” and MWPC as “Stop” detector.

379

Two position sensitive MWPC detectors have been developed for the de-

380

tection of FFs and the timing characteristics have been investigated using a

381

252

Cf source has been measured by employing a new TOF

Cf source. The position information has been obtained by using the delay-

382

line method and the position resolution is about 1.0 mm in both X and Y

383

directions. The velocity distribution for FFs from

384

measured TOF using two detectors (BaF2 and MWPC) having fast timing

385

signals and known travel path by the fission fragments is found to be very ac-

386

curate. The width of the velocity distribution has been measured for various

387

fragment energies by degrading them using Mylar foils of four different thick-

388

ness (2.5-10 µm). It is observed that the width of the distribution decreases 23

252

Cf obtained from the

389

with the reduction in the fragment energies for the heavy fission fragments,

390

but the light fragments show a weak dependence on energy. Since the anode

391

pulses from the MWPC are very fast (rise time ∼ 6 ns), two similar MWPCs

392

have been found to be suitable for studying the fragment mass distribution

393

in heavy-ion induced fission reactions providing a mass resolution of about

394

4.26%.

395

8. Acknowledgments

396

We acknowledge Dr. T.K. Ghosh and Dr. B.V. John for many fruitful

397

discussions. We are grateful to the staff of MDPDS, BARC workshop for

398

fabricating the mechanical structure of the MWPCs. We are also thankful

399

to the Pelletron-LINAC accelerator operating staff for smooth running of the

400

machine during the experiment. S.D. acknowledges financial support from

401

the UGC-DAE-CSR, Kolkata.

402

9. APPENDIX: Kinematic details to obtain mass resolution in

403

TOF measurement

404

The kinematic diagram for binary fission process is shown in Fig.14. From

405

the conservation of linear momentum it follows that: MP V~P MP + MT M1 V~1cm = M2 V~2cm V~cm =

406

(1) (2)

407

where, V~cm is the c.m. velocity, which is equal to the recoil velocity of the

408

compound nucleus. MP and V~P are the mass and velocity vector of the 24

FF1

V1cm

V1lab

θ1lab Vcm θ1cm θ2cm

θ2lab V2lab FF2

V2cm

Figure 14: Kinematics of symmetric binary fission from compound nucleus.

409

projectile. MT is the target mass and M1,2 are the masses of the FFs and

410

V~1,2cm are the fragment velocities in the center-of-mass frame. From the

411

velocity vectors shown in Fig.14, we can write

412

V~1cm = V~1lab − V~cm

(3)

V~2cm = V~2lab − V~cm

(4)

413

Here, V~1,2lab are the velocity vectors of the fission fragments in the laboratory

414

frame.

415

416

From the above equation, the magnitude of the fragment velocities in the c.m. frame are deduced as: V1cm =

417

V2cm =

q

q

2 2 − 2cosθ + Vcm (V1lab 1lab V1lab Vcm )

(5)

2 2 − 2cosθ + Vcm (V2lab 2lab V2lab Vcm )

(6)

25

418

Here θ1,2lab are the exit angles of the fission fragments with respect to the

419

beam direction. Using these c.m. velocities of both the fragments and emply-

420

oing the two-body kinematics for binary fission, the masses of the fragments

421

are determined as follows; M1 =

V2cm MCN V1cm + V2cm

(7)

M2 =

V1cm MCN V1cm + V2cm

(8)

422

where, MCN is the mass of the compound nucleus. The deviations in the

423

calculation will be due to the emission of light charged particles or neutrons.

424

Using the above equations, the velocities of the fission fragments were cal-

425

culated in the c.m. frame (V1cm and V2cm ) and for

426

beam energy of 154.6 MeV.

28

Si+197 Au reaction at a

427

By employing TOF method with two MWPCs, the fission fragment mass

428

distribution is measured. We have obtained the total uncertainty in mass

429

resolution by adding the velocity dispersion in quadrature.

430

From Eq. (7) we can write, δM1 =

431

2 2 δV1cm δV2cm + 2 2 V1cm V2cm

(9)

We have MCN = M1 + M2 and replacing V2cm in the above equation;

δM1 = 432

V1cm V2cm MCN (V1cm + V2cm )2

s

2 V1cm M1 (M1

+ M2 )/M2 2  1 V1cm + V1cm M M2

s

2 2 δV1cm δV2cm + 2 2 V1cm V2cm

(10)

After solving we get,

δM1 M2 = M1 M1 + M2

s

26

2 2 δV1cm δV2cm + 2 2 V1cm V2cm

(11)

433

Assuming symmetric fission; δM1 1 = M1 2

434

435

s

2 2 δV1cm δV2cm + 2 2 V1cm V2cm

In the Eq. 3, Vcm is constant for a given target projectile combination and a fixed beam energy. Therefore, by differentiating the Eq. 3; |δ V~1cm | = |δ V~1lab |

436

437

(13)

Let’s consider only magnitude and divide above equation with V1cm ;   V1lab δV1lab δV1cm = (14) V1cm V1cm V1lab Uncertainty in the distance can be neglected, hence; δt δVlab = Vlab t

438

(12)

(15)

Using Eq. 15 into Eq. 14 δV1cm δt = V1cm t1



V1lab V1cm



(16)

439

where, δt is the total uncertainty of either of the detector, which has two

440

contributions: (i) from width of the RF which provides the start trigger and

441

(ii) time resolution of the MWPC which gives stop trigger. Therefore, q δt = δt2RF + δt2M W P C

(17)

442

The width of RF used in the present heavy-ion experiment is around 1.5 ns.

443

Time resolution for the MWPCs used in the present work is around 180 ps as

444

measured in Ref. [24] for a MWPC having similar configuration. Therefore,

445

time uncertainty for the RF and one MWPC would be, 1.51 ns. For the 27

446

mass resolution estimation purpose we can consider only peak values of the

447

lab and center-of-mass velocities of the fission fragments. In the present

448

work, we can see from Fig.14 that the peak values of the velocities in the

449

lab and center-of-mass frame are 1.32 cm/ns and 1.25 cm/ns respectively. In

450

this measurement the MWPC1 and MWPC2 were kept at distances of 55 cm

451

452

and 27.5 cm, respectively. Therefore,   δV1cm δt V1lab = 0.0377 = V1cm t1 V1cm Similarly, δV2cm = 0.0765 V2cm

453

(18)

(19)

Using Eq. 18 and 19 into Eq. 12 we get, δM1 = 4.26% M1

28

(20)

Table 1: Measured TOF (TL ,TH ), mean velocities (VL ,VH ) and energies (EL ,EH ) for most probable light and heavy fragments are listed. The SRIM calculated values of residual energy are also presented for a light (ZL = 42, AL = 108) and a heavy (ZH = 56, AH = 144) fragment after passing through different foil thickness.

Mylar

TL

TH

(µm)

(ns)

(ns)

0.0

39.45(6)

52.49(12)

1.378(1)

1.035(1)

2.5

44.61(6)

61.67(13)

1.223(1)

0.883(1)

5.0

7.5

10.0

1a

50.87(8)

63.46(12)

73.02(17)

94.06(21)

83.46(20) 124.09(35)

VL

VH

(cm/ns ) (cm/ns )

1.071(1)

0.855(2)

0.643(2)

0.744(1)

0.575(1)

0.432(1)

EL

EH

(MeV)

(MeV)

106.65 (15) 79.73(15) 84.04(14)

58.06(13)

85.941a

60.941a

64.39(12)

41.21(11)

66.491a

44.471a

41.03(19)

24.63(09)

48.801a

30.681a

23.20(14)

13.88(06)

33.391a

19.891a

SRIM calculation

454

455

456

457

458

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