INVESTIGATION OF 234U(N,F) WITH A FRISCH-GRID IONIZATION CHAMBER

ALI AL-ADILI

LICENTIATE THESIS

(January 2011)

UPPSALA UNIVERSITY DEPARTMENT OF PHYSICS AND ASTRONOMY

UPPSALA, SWEDEN

Investigation of 234U(n,f) with a Frisch-grid

ionization chamber

Ali Al-Adili I, II

January 12, 2011

Licentiate Thesis

Supervisors: Franz-Josef HambschI & Stephan PompII

I. Institute for Reference Materials and MeasurementsJoint Research Centre - European Commission, Geel, Belgium

II. Division of Applied Nuclear PhysicsUppsala University, Sweden

1

INVESTIGATION OF 234U(N,F) WITH A FRISCH-GRID IONIZATION CHAMBER

A. Al-Adili

Abstract

This work treats three topics. The main topic concerns neutron-induced

fission of 234U. The main goal is to investigate the fission-fragments properties

as a function of the incident neutron energy. The study was carried out using a

twin Frisch-grid ionization chamber. The first fluctuations on fragment

properties are presented, in terms of strong angular anisotropy oscillation.

The second part of the work treats the data-acquisition systems in use,

particularly for neutron-induced fission experiments. Modern digital systems

are studied and compared with the conventional analogue systems. It was

shown that the digital systems are superior in drift stability, pile-up correction

and extended the possibilities of offline analysis.

The third part of the work concerns the Frisch-grid inefficiency. The Frisch

grid was introduced in the chamber to remove the angular dependency from the

induced charge. However, the shielding is not perfect and a correction is

needed for the small angular dependency. Two contradicting methods have

been presented in literature, one adding, and the second subtracting the

angular-dependent part from the detected signal. An experiment with Cf(sf)

was designed and performed to solve the pending ambiguity. The results

support the additive model.

UPPSALA UNIVERSITY DEPARTMENT OF PHYSICS AND ASTRONOMY

UPPSALA, SWEDEN

                               

   

Till mina älskade, Sheima & Josef

List of papers

Paper I. Investigation of 234U (n, f) as a function of incident neutron energy

A. Al-Adili, F.-J. Hambsch, S. Oberstedt, S. PompSEMINAR ON FISSION VII conference proceedings, Ghent, Belgium, 17–20 May 2010World Scientific Pub Co Inc, (2010)ISBN=978-981-4322-73-7

Paper II. Comparison of digital and analogue data acquisition systems for nuclear spec-troscopy

A. Al-Adili, F.-J. Hambsch, S. Oberstedt, S. Pomp and Sh. ZeynalovNucl. Instrum. Meth. A624:684 (2010).

Paper III. Ambiguities in the grid-inefficiency correction for Frisch-Grid Ionization Cham-

bers

A. Al-Adili, F.-J. Hambsch, R. Bencardino, S. Oberstedt, S. PompSubmitted for publication in Nucl. Instr. Meth. A (2011).

Comments on my contribution

I have been responsible for the work in all three articles, from planning, preparing and performing theexperiments, developing parts of the analysis routines and analysing the data. Finally, I drafted themanuscripts for all the articles.

2

Contents

1 Introduction 4

2 Theory 52.1 Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 The Frisch Grid Ionization Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Frisch-grid inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Experiments 93.1 The Van de Graaff accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Electrode voltage selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Energy and emission angle determination . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3.1 Summing method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3.2 Drift-time method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.4 Performed experiments on 234U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.5 The grid-inefficiency experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Data acquisition and analysis 144.1 Electronic scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2 Analogue data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.3 Digital-signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.3.1 CR-RC4 shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3.2 Alpha pile up correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.4 Relative calibration and drift monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.5 Energy-loss correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5 Results 205.1 Digital data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.1.1 Drift Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.1.2 Shaping time on CR− RC4 shaping filter . . . . . . . . . . . . . . . . . . . . . . 205.1.3 Alpha pile-up correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.2 Results on emission angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2.1 Drift-time method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2.2 Angular distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2.3 Angular anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.3 Fragment energy- and mass determination . . . . . . . . . . . . . . . . . . . . . . . . . . 255.3.1 Neutron-momentum transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.3.2 Neutron multiplicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.3.3 Pulse-height defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.3.4 Mass calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.3.5 Energy- and mass distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.4 The Frisch-grid inefficiency experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.4.1 Experimental determination of σ . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.4.2 Comparing the two correction methods . . . . . . . . . . . . . . . . . . . . . . . 295.4.3 Impact on energy- and mass distributions . . . . . . . . . . . . . . . . . . . . . . 30

6 Conclusions 316.1 Nuclear electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.2 Fission fragment studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.3 The Frisch-grid inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

7 Acknowledgments 32

A Appendix 33A.1 Calculations on the fission count rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33A.2 Alpha activity of 234U sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33A.3 CR− RC4 filter design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3

1 Introduction

The main task of this project is to investigate the fission-fragment (FF) properties in the neutron-induced fission of 234U, for which the available nuclear data are rather scarce (paper I). This nuclide isthe compound nucleus after the second chance fission of 235U, which makes it interesting for theoreticalmodeling of the reaction 235U (n, f). In addition, 234U is relevant for the Uranium-Thorium fuel cycle.An IAEA Coordinated Research Project requested more high quality data for the nuclei in the U-Thcycle [1]. The cross section of 234U(n,f) contains a strong vibrational resonance in the sub-barrierregion (Fig. 1) around 800 keV in neutron energy. Fluctuations of the FF properties in this energyregion have been observed earlier in literature [2]. One goal is to verify these fluctuations and toparameterize the FF properties using the Multi-Modal Random Neck-Rupture (MM-RNR) model offission [3].

0 1 2 3 4 5 6 7 8 9 1 00 . 0

0 . 5

1 . 0

1 . 5

2 . 0

Cros

s sec

tion [

barns

]

N e u t r o n e n e r g y [ M e V ]

J E F F 3 . 1

0 . 8 1 . 0 1 . 2

1 . 1 2

1 . 2 0

1 . 2 8

N e u t r o n e n e r g y [ M e V ]

Cro

ss se

ction

[barn

s]

J E F F 3 . 1

Figure 1: a: The cross section of 234U (n, f) from JEFF 3.1 [4]. b: Focus on the vibrational resonancearound 800 keV neutron energy, where the fluctuations of the FF properties are studied in finer energysteps.

The second branch (Paper II) of this work concerns the data-acquisition system in used in nuclearspectroscopy. Modern digital-data acquisition systems (DA) are studied and compared with conven-tional analogue data-acquisition systems (AA). The apparent advantage of DA would be the reductionof the amount of electronics in the experiments. Moreover, the digitized signals contain the full infor-mation of the FF properties (mass, kinetic energy, emission angle and charge) for each event. Storingthe entire waveform opens the door for various new possibilities for offline-analysis. The aim for thefuture is to replace the analogue with the digital acquisition systems.

The third part of this work (Paper III) concerns the Frisch-grid ionization chamber. The Frischgrid was originally introduced to remove the angular dependency from the induced charge. In realexperimental conditions, the shielding is not perfect which leaves the induced charge slightly angulardependent. This effect, called the Grid Inefficiency (GI), was introduced and estimated theoreticallyin Ref. [5]. Two contradicting methods of correcting the GI have emerged during the years in litera-ture. The first approach adds the missing part to the detected charge signal [6]. The second approachsubtracts the angular dependent contribution from the detected charge signal [7]. Recently, a theo-retical approach was presented [8], applying the Ramo-Shockley theorem to the problem. The studysupported the additive approach. However, until now, the community has not agreed on the rightcorrection method. Therefore, a dedicated experiment was planned and performed in order to verifythe theoretical results from [8]. The proof of principle was done using two different grids and a 252Cfspontaneous fission source. The effect of using the two grids was studied on the induced charge. Thestudy showed that the additive approach is the only correct approach for GI correction.

4

2 Theory

2.1 Fission

Fission is an interesting interplay between the fundamental forces of nature. The nucleus is governedby the strong force which holds the protons and neutrons together. The strong force which is describedby the Quantum Chromo Dynamics (QCD) is a short-range force, extending only on the fm level (10−15

m). The electromagnetic force which is described by the Coulomb interaction, dominates when thenucleons are farther away. For large nuclei such as the actinides, the nucleus is so large that the outernucleons feel less attraction from others. When the nucleus is perturbed by an incident neutron, itgets excited and starts to deform and vibrate. The two sides of the deformed nucleus extend in theoscillation process. The nuclear force becomes too weak and the proton-proton repulsion separatesthe nucleus apart. The amount of energy released, is shared between the FF have together with theprompt neutrons and the gamma-rays. It is around 200 MeV per fission event and is the result of theelectromagnetic proton repulsion.

The fission process was discovered in 1939 by O. Hahn and F. Strassman. They found Bariumresiduals from neutron-induced fission of Uranium [9]. L. Meitner and O.R. Frisch initiated the term“fission” influenced by the biological cell division [10, 11]. They gave together with N. Bohr and J.A. Wheeler the first qualitative model describing fission using the Liquid Drop Model (LDM). By theassumption of a uniformly charged nuclear droplet, many satisfying explanations can be adapted fromthis successful model. However, the model has clear limitations. It only predicts symmetric fission aswell as only spherical ground state stable nuclei. In fact experiments tell us that the asymmetric fissionis dominating due to the shell effects. When looking at the nuclear potential energy (See Fig. 2) as afunction of deformation, the LDM manifests in a single-humped barrier. Experiments showed evidenceon double- and even triple humped barriers in some actinides [12]. Several attempts were made toimprove fission theory to be more consistent with experiments. For instance the corrections appliedto the LDM from the nuclear shell model [13]. Including the shell effects one can arrive at the doublehumped barrier as seen in Fig. 2. Further development was carried out during the years, enhancingour understanding of the process. The community still regard the proper universal fission theory to beunfound. Despite the phenomenon being discovered more than 70 years ago, it remains puzzling whathappens at the scission point. The main complexity faced is the large amount of degrees of freedomin the process. In order to formulate the universal model, approximations are unavoidable. About 20years ago, Brosa, Grossmann and Muller [3], introduced a new nuclear-scission model based on thehydrodynamical behavior of droplets. The so-called Multi-Modal Random-Neck Rupture (MM-RNR)model gave for the first time a parametrization of the fission fragment shapes, which could be comparedto experimental observables like mean mass and total kinetic energy of the FF. Different fission modesare predicted, having differently elongated nuclear shapes leading to symmetric and asymmetric fission.

5

0

5

L D M + S H E L L M O D E L

S p o n t a n e o u s f i s s i o n

Poten

tial e

nergy

MeV

)

D e f o r m a t i o n

I s o m e r i c f i s s i o nL D M

Figure 2: The fission barrier. The LDM without shell model correction predicts only a single humpedbarrier. In order for the nucleus to fission it must penetrate the barrier either spontaneously (throughquantum tunneling effect) or by getting excited externally.

2.2 The Frisch Grid Ionization Chamber

The general operation of an ionization chamber (IC) could easiest be explained using arguments basedon the Ramo-Shockley theorem [14, 15]. Before the theorem was introduced, it was necessarily in orderto derive the induced charge on a given electrode, to calculate the instantaneous electric field E in eachpoint along the charge particle’s track. The induced charge Q is then given by integrating the normalcomponent of E over a closed surface S around the electrode according to

Q =˛

S

εE · dS , (1)

where ε is the dielectric constant of the medium surrounding the charge carrier [16]. Due to the largenumber of fields E, the calculation becomes complex. Shockley and Ramo found independently aneasier method of deriving the induced signal on the electrode. The theorem states that a chargedparticle q drifting from its origin in space to electrode 2 through the weighting potential ϕ (z), willinduce a charge equal to:

Q = q∆ϕ . (2)

The weighting potential is obtained by solving the Laplace equation ∇2ϕ = 0. The electrode whichone seeks the induced charge for, is set at unit potential and all other electrodes to 0. The theoremimplies that the actual voltage difference between the electrodes does not affect the charge induction.The theorem also implies that an electron induces at maximum its own charge if the full distance istravelled between the electrodes (especially when considering the method of mirror charges).

2.2.1 Frisch-grid inefficiency

The Twin Frisch Grid Ionization Chamber (TFGIC) shown in Fig. 3, is a well-tested, reliable tool fornuclear spectroscopy, especially FF studies. It suffers no radiation damage, covers almost 4π in solidangle and has a good energy resolution. Typical signals from the FGIC are shown in Fig. 3b. Theenergy of the FF is obtained from the anode signal height. In the ideal case the induced charge onthe anode, QA, is the sum of all electron contributions from the ion pairs n0, created by the ionizationprocess, according to:

QA = −n0e . (3)

6

By inserting a grid, the anode is shielded from the induction of electrons in the cathode-grid region.Hence, the charge induced on the anode plates is proportional to the FF energy independently of theemission angle. The cathode is unshielded and hence the induced signal is angular dependent:

QC = n0e(

1− X

Dcos θ

), (4)

where X/D is the centre-of-gravity of the electron-cloud distribution divided by the cathode-griddistance D. The signal induced on the grid contains also the information on the emission angle:

QG = n0eX

Dcos θ . (5)

The anode signal in Eq. (3) is valid in the ideal case. In reality however, the grid shielding is incompleteand the signals have to be corrected for this so called grid inefficiency (GI) [5]. The GI factor σ forthe parallel-wired gridded IC used in this experiment, is approximately σ = 0.03 as given by:

σ (d, r, a) =(

1 +d

a/2π ((π2r2 · a−2)− ln (2πr · a−1))

)−1

, (6)

where d is the anode-grid distance, r is the grid wire radius and a is the distance between grid wires.Two different methods have bee presented for correcting the GI.

D

_X

p o l y i m i d eA u - c o a t e d

m m

m m

F F 2

F F 1n

n

N E U T R O N B E A M

A N O D E 1+ 1 . 0 k V A N O D E 1+ 1 . 0 k V

G R I D 10 V

A N O D E 1+ 1 . 0 k V G R I D 20 V

A N O D E 2+ 1 . 0 k V A N O D E 2+ 1 . 0 k V

C A T H O D E- 1 . 5 k V

θ

6

3 1

m m

m m6

3 1

1 . 0 5 b a r P - 1 0 g a s( A r 9 0 % + C H 4 1 0 % )

2 3 4 U

b a c k i n g

D

0 1 0 0 2 0 0

0 A n o d e

G r i d

9 0 o

0 o 9 0 o0 o

9 0 o

0 o

Q(t)

T i m e [ a r b . ]

- n 0 e

+ n 0 e

C a t h o d e

Figure 3: a) Schematic drawing of the Twin Frisch-Grid Ionization Chamber (TFGIC) with two anodes,two grids and one common cathode. b) The cathode, grid and anode signals for 0o and 90o.

Additive approach According to Ref. [6], the GI leads to less charge induction on the anodeplate. The explanation is due to the presence of the positive ions in the cathode-grid region. Accordingto this approach, one needs to add the missing part to the detected signal following:

PCorrA = P∗

A + σ · (P∗A − PC) , (7)

where P ∗A and P ∗

C are the detected pulse heights of the charge signals QA and QC. It could bequestioned weather the positive ions really give a significant contribution. Being ˜1000 times slowerthan the electrons, they are nearly stationary in the time-scale of charge integration (2 µs) [17].

Subtractive approach The integration of waveform digitizers into nuclear spectroscopy madeit possible to study the stored charge signals in offline mode. It was observed that a linear rise was

7

seen on the anode before any electrons passed the grid. The conclusion of this was a new approachto correct for the GI [7]. The signal seen on the anode is what is induced on the cathode QC, scaleddown by the factor σ:

QA = −σQC . (8)

The induced signal was regarded as an offset to the total induced charge. Hence it was subtracted,contrary to Eq. (7):

PCorrA = P∗

A − σPC (9)

In Ref. [7] an experimental method was presented to measure σ according to:

σ =∆Q

Quncorr −∆Q, (10)

where ∆Q is the height of the linear fit to the anode signal at time TCOG. Th subtractive approachis embedded in the determination of σ according to Eq. (10), since Quncorr − ∆Q is equivalent tosubtracting the GI from the total induced charge.

Additive approach extended Recently a study was presented, applying the Ramo-Shockleytheorem to the problem [8]. The full theoretical treatment supported the additive approach andpresented a more general formula to correct for the GI:

PCorrA =

P∗A − σ · PC

(1− σ). (11)

According to Ref. [8], the detected charge Q∗A on the anode is:

Q∗A = −n0e

(1− σX

Dcos θ

). (12)

To obtain the correct QA one needs to add the angular-dependent part. The cathode signal holds thesame angular dependency that the anode would feature if the grid was removed. Therefore σ · QC isadded to Eq. (12):

Q∗A + σQC = −n0e (1− σ) (13)

where QC is given by Eq. (4). In order to obtain the correct signal QA, Eq. (13) is divided by (1− σ):

QA = (Q∗A + σQC) (1− σ)−1

. (14)

By using the pulse heights PA = QA and PC = −QC in Eq. (14), one arrives at Eq. (11). Note thatthe charge signals QA and QC have opposite polarities, hence the negative sign.

8

3 Experiments

The experiments for this work were performed at the 7 MV Van De Graaff accelerator at the Insti-tute for Reference Materials and Measurements (IRMM) in Geel, Belgium. Accelerated Protons (ordeuterons) lead to neutron production through four nuclear reactions, TiT (p,n), 7LiF (p,n), D (d,n)and T (d,n). The neutrons induce fission in the target containing 234U

(92 µg/cm2

). The target is

produced through vacuum evaporation on gold-coated polymides. The FF are detected by means of aTFGIC with two anodes, two grids and a common cathode. As counting gas P10 (90% Argon, 10%Methane) was used at a pressure of 1.05 bar and a gas flow of 0.1 `/min. The Uranium sample islocated in the centre of the cathode. Energies and angles of both fragments are measured using thedouble E method (conservation of energy and momentum), to calculate FF masses. The absolute cali-bration for the energy uses the known literature data on thermal induced fission of 235U

(45 µg/cm2

).

The total kinetic energy 〈TKE〉 = 170.5± 0.5 MeV and mean heavy-mass peak at 〈AH〉 = 139.6 amuare used for the energy calibration [18].

3.1 The Van de Graaff accelerator

The 7 MV Van de Graaff accelerator is a belt-driven electrostatic accelerator. It can operate in pulsedas well as DC mode. The protons or deutrons are extracted from an ion source through a high voltagedifference. They are accelerated vertically until reaching the analyzing magnet which deflects the ionsby 90o. This process filters the ions and produces a mono-energetic beam. The ions reach then thetarget after focusing and neutrons are produced by one of the reactions TiT (p,n), 7LiF (p,n), D (d,n)and T (d,n). The energy of the neutrons ranges from 300 keV to 24 MeV. The energy resolution isbest for the 7LiF (p,n) source due to the relative small sample thickness (See Table 2). It is henceused for the study at lower incident neutron energies around the resonance (See Fig. 1). For higherincident neutron energies the other reactions are used due to their higher neutron flux.

3.2 Electrode voltage selection

The high voltage applied on the electrodes in the chamber, was chosen to fulfill the relation:

VA − VG

VG − VC≥

p + pρ+ 0.5 · r(ρ2 − 4 · ln ρ

)a− aρ− 0.5 · r (ρ2 − 4 · ln ρ)

, (15)

where ρ = 2πr · d−1 [5]. The values of the parameters required for the calculation are given in table 1.The anode-grid electric field strength should be preferably ∼ 3 times stronger than the grid-cathode

field strength. This is to minimize electron losses on the grid. The r.h.s. of Eq. (15) gives ∼ 0.54. Thechosen high voltage values are VA = 1 kV, VC = −1.5 kV and VG = 0 V, which fulfills relation (15)since VA/−VC =0.667. In addition the strength of the anode-grid field is VA/0.6cm = 1667 Vcm−1

compared with −VC/3 cm = 500 Vcm−1. Thus, the field strength ratio between anode-grid and grid-cathode is larger than 3.

Table 1: Parameters for the present TFGIC to be used in Eqs. (6) and (15).Parameter Value [cm]

Grid-cathode distance a 3.1Anode-grid distance p 0.6

grid wire spacing d 0.1grid wire radius r 0.005

9

3.3 Energy and emission angle determination

The energy of the fission fragments is given by the total charge collected on the anode electrode. Todeduce the emission angle two possibilities exist, the summing and drift-time methods. In the following,we discuss both methods and compare them both for the digital and analogue case.

3.3.1 Summing method

The grid signal is bipolar. It has a negative contribution from electrons drifting in the cathode-gridregion and a positive one from electrons in the anode-grid region. To avoid the bipolarity a summationof the grid and anode signals is performed leading to a unipolar sum signal:

QΣ = −n0e(

1− X

Dcos θΣ

), (16)

from which the cosine of the FF emission angle θΣ may be extracted. The FF angle as determinedfrom the summing method is given by:

X

Dcos θΣ =

PA − PΣ

PA, (17)

where PA is the anode pulse height created from QA and PΣ is the summing pulse height from QΣ.The value of X/D depends mainly on the FF energy and is determined as the length of the distributionbetween cos (0o) and cos (90o) as shown in Fig. 4. A linear fit is applied to the data at cos (90o) anda parabola is fitted for cos (0o) at the half maximum of the distribution.

4 0 8 0 1 2 0 1 6 00

6 0

1 2 0

1 8 0

c o s ( 0 o )

(X/D

)cosq

P u l s e h e i g h t l a b o r a t o r y s y s t e m

1 0 . 0 02 5 . 0 05 0 . 0 07 5 . 0 01 0 0 . 01 2 5 . 01 5 0 . 01 7 5 . 02 0 0 . 0

c o s ( 9 0 o )5 0 1 0 0 1 5 0 2 0 0 2 5 0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

C o s q 1

Cosq

2

1 0 . 0 02 0 . 0 04 0 . 0 06 0 . 0 08 0 . 0 01 0 0 . 01 2 0 . 01 6 0 . 0

Figure 4: a: Two-dimensional distribution of(X/D

)cosθΣ versus pulse height. b: The calculated

cosine distributions from both chamber sides versus each other.

3.3.2 Drift-time method

The second method to determine the emission angle is the drift-time (DT) method. The emission angleθT is obtained from the electron DT in the chamber [19]. The time between the start of induction andthe time when the first electrons pass the Frisch-grid is measured. The electrons are assumed to havea constant drift velocity v, thus the drift time T is given by the difference of D and the projection ofthe FF range R on the beam axis R cosθT:

T =D− R cosθT

v, (18)

10

Electrons created from fission events with large angles will have large drift-times, whereas electronscreated in beam-axis direction will reach the grid faster and, hence, have a short drift-time. To deduceT several methods are available (see Fig. 5). The first is to measure the time-difference betweenthe anode’s centre-of-gravity and the start-trigger position of the cathode (CoG method). Otherpossibilities are to use constant fraction discrimination (CFD) or leading-edge (LE) techniques on theanode signal. Once the drift-time T is determined one can obtain cos θT according to:

cos θT =T90o − T

T90o − T0o, (19)

where T0o is determined with a parabola fit to the half height and T90o with a linear or a hyperbolicfit of the edges of the two dimensional drift-time versus pulse-height distribution (see Fig. 13b). Theinvestigation of the drift-time method was done both in AA and DA. In the analogue case, LE principlewas used as stop triggering for the anode pulse. The LE level was adjusted slightly above the noiselevel. An amplitude walk was observed and corrected for in the AA case [19]. In the DA case the anglecould be extracted according to all above mentioned possibilities.

2 0 0 3 0 0 4 0 0 5 0 0

- 4 0 0

- 2 0 0

0

2 0 0

4 0 0

6 0 0

C F D

A n o d e C a t h o d e A n o d e c e n t r e -

o f - g r a v i t y

Volta

ge [m

V]

S a m p l i n g [ c h a n n e l s ]

C o G

L E

D r i f t - t i m e m e t h o d

Figure 5: An example of the drift-time method applied to one event. It measures the start trigger timefrom the cathode signal at a constant fraction discrimination (CFD). The stop trigger comes eitherfrom the time when the electron cloud passes the grid (centre-of-gravity (CoG) method) or from theanode signal as constant fraction or leading edge (LE) (see sec. 4.2).

3.4 Performed experiments on 234U

The count rate was estimated prior to the experiments. The calculation of the fission rate is shown inFig. 6 as function of incident neutron energy (see Appendix A.1 for details). The calculation is basedon the cross-section data from ref. [20], for 10µA beam current, at 75 mm distance between Uraniumsample and neutron-producing target. Due to the higher thickness of the TiT sample, a higher fissionrate is expected but at worse energy resolution. At lower energies around the vibrational resonance,a good energy resolution is important. Therefore the 7LiF (p,n) reaction is used. For higher energiesthe other reactions are used.

11

0 1 2 3 4 50

2

4

6

8

1 0

1 2

Fissio

ns pe

r sec

ond

N e u t r o n e n e r g y ( M e V )

L i F ( p , n ) T i T ( p , n )

Figure 6: Estimated fission count rate according to the calculation for 234U (n, f) for 10µA in beamcurrent and 75 mm distance between Uranium sample and neutron-producing target (see AppendixA.1).

Table 2: The measurements performed for 234U (n, f).En [MeV] Reaction target thickness [µg/cm2] σ [barns] [4] Counts [×103]0.2± 0.07 7LiF (p,n) 830 0.06 120.35± 0.06 7LiF (p,n) 830 0.20 38

0.5± 0.05 (±0.04) 7LiF (p,n) 830, (619) 0.51 1430.64± 0.03 7LiF (p,n) 596 0.84 3660.77± 0.03 7LiF (p,n) 596 1.20 1530.835± 0.03 7LiF (p,n) 619 1.22 800.9± 0.03 7LiF (p,n) 596, (619) 1.14 1721.0± 0.1 TiT (p,n) 1936 1.10 128

1.5± 0.09 (±0.1) TiT (p,n) 1930, 1936, 2130 1.37 3502.0± 0.08 (±0.09) TiT (p,n) 1930, 2130 1.52 967

2.5± 0.07 TiT (p,n) 1930, 1936 1.51 6723.0± 0.06 TiT (p,n) 1936 1.10 2724.0± 0.3 TiD (d,n) 1902 1.38 535.0± 0.18 TiD (d,n) 1902 1.33 130

235U (nth, f) TiT (p,n) 1930, 2130 >500 2914

3.5 The grid-inefficiency experiment

A dedicated experiment was performed on 252Cf (sf) to investigate the GI problem mentioned in sec.2.2.1. The Cf-source (∼ 800 fissions/s) is deposited on a 0.25 µm (200 µg/cm2) Ni-backing and waspositioned in the centre of the cathode (see Fig. 7). The chamber was operating at the same conditions(dimensions, gas type and pressure and electrode voltages) as for the 234U experiment. On the sampleside, two different grids were used with different grid spacing (see table 3). All other settings wereunchanged. A mesh grid was used on the backing side (pitch of 0.48 mm and wire diameter of 0.028mm). The data acquisition for the Cf experiment was performed with DA as seen in Fig. 7. Since theonly changing parameter for the two measurements is the grid-wire spacing, the expected difference in

12

pulse height is due to the GI. A larger GI would imply smaller pulse height according to the additiveapproach (sec. 2.2.1) and higher pulse height according to the subtractive approach (sec. 2.2.1).

Table 3: Two different grid types were used in the GI experiment (sample side).Grid type Wire radius r [m] Wire spacing [mm] σCalc[Eq. (6)]

Wire I 0.005 1.0 0.03Wire II 0.005 2.0 0.09

0 . 0 V1 . 0 k V

0 . 0 V1 . 0 k V

- 1 . 5 k Vd

A N O D E 2M E S H G R I D

C A T H O D E

A N O D E 1

F F 1

N i - F F 2

θ2 5 2 C f

b a c k i n g

X_

W I R E G R I D

Dd

D H V - 1 . 5 k V

H V 1 . 0 k V

A n o d e

G r i d

C a t h o d e

W a v e f o r m d i g i t i z e r 1 2 B I T 1 0 0 M h Z

P C

T i m i n g f i l t e r a m p l i f i e r T R I G G E R

P A

P A

P A C o n s t a n t F r a c t i o n

D i s c r .

Figure 7: TFGIC and electronic scheme for the GI experiment. On the sample side two different wiregrids were used (Table 3). On the backing side a mesh grid was used in both runs (pitch of 0.48 mmand wire diameter of 0.028 mm). The signals from the charge-sensitive preamplifiers are fed into thedigitizer. The trigger comes from the cathode. Five signals are stored, the cathode, the two anodesand the two grids.

13

4 Data acquisition and analysis

4.1 Electronic scheme

Five signals were extracted from the TFGIC (two anodes, two grids and one cathode signal). Inparallel, both acquisition systems were employed to treat the signals independently. The electronicsneeded are presented in Fig. 8 for each chamber side.

T r i g g e rP u l s e g e n e r a t o r

s t a r t t r i g g e r

DIGI

TALT i m i n g f i l t e r

a m p l i f i e r L i n e a r f a n i n

f a n o u t C o n s t a n t

F r a c t i o n d i s c r .D e l a y

g e n e r a t o r

L i n e a r f a n i n f a n o u t

Q u a d F a s t a m p l i f i e r

L i n e a r f a n i n f a n o u t

S p e c t r o s c o p i ca m p l i f i e r S u m m i n gA n a l o g u e t o D i g i t a l

C o n v e r t e r Q u a d F a s t a m p l i f i e r

S p e c t r o s c o p i ca m p l i f i e r P u l s e H e i g h tA n a l o g u e t o D i g i t a l

C o n v e r t e r P u l s e g e n e r a t o r

T i m i n g f i l t e r a m p l i f i e r

T i m i n g f i l t e r a m p l i f i e r

L i n e a r f a n i n f a n o u t

AL e a d i n g

E d g e T i m e t o a m p l i t .

c o n v e r t e rA n a l o g u e t o D i g i t a l

C o n v e r t e r D r i f t t i m e

ANAL

OGUE

G

1 . 0 k V

C- 1 . 5 k V

W a v e f o r m D i g i t i z e r ( 1 2 B i t 1 0 0 M H z )

s t o p t r i g g e r

Figure 8: Scheme of electronics for DA and AA.

The signal are directly fed into a charge-sensitive preamplifier. The preamplifiers are put close tothe chamber (short cables) in order to store the total collected charge with minimal signal-noise contri-bution. Once charges start to drift in the grid-cathode space, the chamber voltage drops correspondingto an equal reduction of charge storage across the capacitance in the pre-amplifier. The output voltageVout is proportional to the induced charge provided that the decay time Γ of the preamplifier is longcompared with the pulse rise-time. Typical FF rise-time in the TFGIC ∼ 0.1− 0.5 µs compared withthe decay time of the preamplifier ∼ 100 µs.

4.2 Analogue data acquisition

In the analogue case, the anode signals (fragment energies) are fed into spectroscopic amplifiers with ashaping time τ=2µs, leading to a semi-Gaussian pulse-shape [21]. For the angle determination, bothsumming and drift-time methods were used (see sec. 3.3.1 and 3.3.2).

The anodes are summed with the grids to produce the unipolar angular-dependent sum signal QΣ.The pulse height PΣ is obtained using a spectroscopic amplifier with τ=2µs. For the drift-time method,the LE principle was used for triggering on the anodes and a CFD on the cathode signal. In the LEtriggering one sets a constant trigger level as shown in Fig. 9a. One needs to correct for amplitudewalk as discussed in Ref. [19]. In the CFD triggering, the signal is inverted, delayed and attenuated.Once the output signal crosses the zero-level, the trigger starts (see Fig. 9b). Both start and stoptrigger were inserted into a time-to-amplitude converter (TAC). In case of AA, six values were stored:Two FF pulse heights, two FF angles from summing method and two angles from drift-time method.A MPA Delta box is used as bridge to the computer. Only coincidence triggering from both anodesleads to a stored signal.

14

T 1

- V 1Volta

ge [m

V]

T i m e [ a r b . ]- V 2

T i m e w a l k

T 2 T h r e s h o l d L E

Volta

ge [m

V]

4 . S u m o f s i g n a l s 2 & 3

3 . I n v e r t e d & d e l a y e d

1 . O r i g i n a l w a v e - f o r m

T i m e [ a r b . ]

2 . A t t e n u a t e d w a v e - f o r m

- V

V

x V

V - x VT

Figure 9: a) LE triggering set at a specific threshold. b: The CFD triggers at a constant fraction levelof the pulse height by attenuating, inverting and delaying the signal.

4.3 Digital-signal processing

In the digital case after the preamplifiers, the cathode signal was used for triggering and together withthe grid and anode signals fed into a 12 Bit, 100 MHz FAST waveform digitizer as seen in Fig. 8. TheDA system requires digital-signal processing (DSP) algorithms performing the signal transformationssimilar to the operations performed by the hardware modules in the AA case.

Once a fission event is seen by the cathode, the external CFD triggers the digitizer to sample thefive signals from the chamber (Fig. 10a). The data acquisition is set to start sampling 2.5 µs pre-and 7.5µs post-triggering. In total one wave-form consists of 1024 samples with a resolution of 10 ns.The average value of the first 150 pre-trigger channels is used to correct for base-line displacements.Anode and grid wave-forms are summed to create the sum signal QΣ. The current wave-forms arethen unfolded from the charge signals by differentiating, taking into account the pre-amplifier dischargeeffect “ballistic deficit”:

I (t) =dQdt

=1024∑i=0

[exp

(Γ−1

)Qi (t)−Qi−1 (t)

], (20)

where Γ is the decay time and Q is the time-dependent induced charge signal. The output from thisoperation produces a centre-of-gravity distribution as shown in Fig. 10b by the full line, free fromany ballistic deficit. The unfolded current wave-form’s centre-of-gravity is assigned to the anode pulsecentre-of-gravity. The preamplifier discharge effect is observed in the pulses as an exponential decayafter the total charge has been induced in the preamplifier (see Fig. 10b). To determine Γ (118 µs inour case) one needs to fit the exponential decay to the tail after the full signal development.

15

2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0

- 4 0 0

- 2 0 0

0

2 0 0

4 0 0

6 0 0

A n o d e 1 A n o d e 2 G r i d 1 G r i d 2 S u m 1 S u m 2 C a t h o d e

Volta

ge [m

V]

S a m p l i n g

a

2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0- 3 0 0

- 2 0 0

- 1 0 0

0

1 0 0

Volta

ge [m

V]

b

A n o d e p u l s e B a l l i s t i c - f r e e p u l s e C e n t r e o f g r a v i t y C R - R C 4

S a m p l i n g

Figure 10: a: Wave-forms after baseline correction and sum signal production. b: Wave-form differ-entiation (full line) and ballistic-deficit correction followed by the CR− RC4 filter using τ = 0.5µs inshaping time. One channel corresponds to 10 ns.

4.3.1 CR-RC4 shaping

The stored digitized anode signals contain the total collected charge in their height. It would besufficient to determine the FF energy based on the signal height directly. But in order to enhancethe signal-to-noise ratio the signals are treated with a CR-RC4 shaping filter [22] (see Fig. 12). Itcould be rather puzzling to determine the exact position of the maximum of the pulse due to thenoise. The choice of a shaping filter, producing a noise-free output similar to a Gaussian, simplifiesthe determination process. The principle of a CR-RC filter is shown in figure 11. In the frequencydomain, the differentiating CR process would filter the low frequencies:

f ≤ 12πRC

, (21)

whereas the RC integrator would filter the high frequencies:

f ≥ 12πRC

. (22)

n 0 et i m e

RC R CI N P U T

t i m e

O U T P U T

t i m e

O U T P U Tn 0 e n 0 e

Figure 11: The CR-RC shaping principle. A step-like signal is first differentiated in the CR high passfilter. Later it is integrated with the RC low pass filter.

The parameters R and C determine the shaping time τ = RC. In this work, the CR differentiationalong with the RC4 integration was performed recursively based on the filter design of Ref. [23] (seeappendix A.3). The filter was designed based on the Butter-worth filter [24]:

| Φ (jω) |= 1√1 + (ωτ)2n

, (23)

16

where ω is the angular frequency and τ = RC.The parameters are pre-defined explicitly for the designed filter. The free variable for the user is

the shaping time τ , which is not to be compared to the shaping time of 2µs used in the analoguespectroscopic amplifier. In DSP four different choices of shaping times τ (0.2µs, 0.5µs, 1.0µs and2.0µs) were compared. The output was almost identical for the 0.5µs, 1.0µs and 2.0µs cases (See sec.5.1.2 for details). However the shaping time of 0.2µs gave different result and hence was consideredtoo low. The shaping time of 0.5µs was chosen for all further analysis. The height of the CR− RC4

filter output, shown in Fig. 10b (dashed dotted line), determines the pulse height induced by the FF.The resulting pulse-shape, is different to the semi-Gaussian pulse-shape produced with the analoguespectroscopic amplifier. The same signal processing routines are also applied to the summing signal toproduce the corresponding pulse height PΣ.

6 0 0 0 8 0 0 0

0 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

0 . 0 4

0 . 0 5

Pulse

heigh

t [V]

T i m e [ n s e c ]

I n p u t c h a r g e s i g n a l C R - d i f f e r e n t i a t o r R C - i n t e g r a t i o n R C 2 - i n t e g r a t i o n R C 3 - i n t e g r a t i o n R C 4 - i n t e g r a t i o n

Figure 12: A signal is processed with CR− RCn filter which enhances the signal-to-noise ratio as nincreases. The amplitude of the signal is proportional to the integrated charge.

4.3.2 Alpha pile up correction

The 234U sample is a strong α-particle source (∼230 kBq/mgU) (see appendix A.2). This leads topile-up effects when α-particles are emitted close in time with a FF. One example is shown in Fig. 13a,with three piled-up α-particles. In addition there is hydrogen in the Ar− CH4 counting gas inside thechamber. Neutron-proton elastic scattering will add a small contribution to the pulse height as well,noticeable at higher neutron energies [25]. In the AA case normally the piled up events may be rejectedby sophisticated pulse pile-up rejection systems [6, 26]. Hence, the counting statistics is drasticallyreduced in case of a strong α-emitter. Digital methods add a new dimension of correction possibilitieswhen each signal can be examined for pile-up and corrected for without discarding the whole event.In practical terms, this is done by first differentiating the wave-form as shown earlier in Fig. 10b. Thestrong change of pulse height caused by the FF is observed as the largest peak, whereas α-particlesgenerate small peaks hardly visible among the noise (see Fig. 10b, full line). By restricting the filteringprocess to a small window around the large FF peak and setting all the differentiation outside thisrange to zero, one can eliminate the major part of the pile-ups. A clean wave-form is reproduced byintegration, free from α-particle and proton recoil contributions as seen in Fig. 13a by the full line.

The α-particle pile-up influences also the drift-time angle determination. If an early pile-up occursin coincidence with a FF then the determination of the drift time is biased by the portion of thepresent pile-up. This leads to a false triggering and a displacement of the drift-time distribution. Thiswas observed both in the AA and DA case (see arrows in Fig. 13b). In DA the α-particle pile-upcorrection was reducing the problem, however not entirely in case the α-particle pile-up contributionwas too close in time to the FF and, hence, within the integration window around the centre-of-gravity

17

position. One possible correction is to introduce a narrower integration window around these piled-upevents. In the summing method this contribution is canceled out in first order when applying Eq. (17).

The ballistic-free current signal I(t) from Eq. (20) is integrated to produce the ballistic-free chargesignal. The integration window is restricted around the centre-of-gravity pulse. This is to eliminate pile-up contribution mainly but also to reduce the contribution from the electronic noise. The integrationwindow is dependent on the pulse shape of the signal. The integration window is determined througha CFD on the anode signal rise-time, at 10 % for start trigger Tr10 and at 90 % for stop trigger Tr90.The integration window start 120 channels (1.20 µs) before Tr10 and ends 60 channels (0.6 µs) afterTr90 as expressed in:

Qi (t) = [Qi (t) = 0]Tr10−1200 +

Tr90+60∑i=Tr10−120

Ii (t) + [Qi (t) = n0e]1024Tr90+60 , (24)

where n0e is the average pulse height from the maximum over 20 channels from Tr90 +40 to Tr90 +60.The integration window should preferably be chosen short enough to reduce the major part of thepile-ups and long enough to ensure the total integration of all signals.

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0

- 5 0 0

- 4 0 0

- 3 0 0

- 2 0 0

- 1 0 0

0 O r i g i n a l F F C o r r e c t e d F F

Volta

ge (m

V)

S a m p l i n g ( 1 0 n s / c h a n n e l )

a

3 5 7 0 1 0 5 1 4 0 1 7 5 2 1 00

4 0

8 0

1 2 0

1 6 0

2 0 0

2 4 0b

P u l s e h e i g h t ( c h a n n e l s )

Drift

time (

chan

nels)

1234681 01 22 0

T 0 o

T 9 0 o

Figure 13: a: One event from 234U (n, f), with three α-particle pile-up events before correction (dashedline) and after the correction (full line). b: Drift-time versus pulse-height distribution. False triggeringfrom early α-particle pile-up is observed as time-uncorrelated events (indicated by the arrows).

4.4 Relative calibration and drift monitoring

Prior to the experiment an electronic calibration needs to be done in order to calibrate the differentoutput channels. A precision pulse generator was used for this purpose. The same pulse generatoris used in the experiment to monitor drifts in the electronic circuit. Unfortunately, electronic driftshappen randomly in time and the pulse generator is used to correct for the corresponding pulse heights.

4.5 Energy-loss correction

Once the pulse heights are produced, the FF analysis can start separately in the analogue and digitalcase. Along their linear motion from the place of origin, the FF lose some of their energy in the targetmaterial. The amount of this energy loss is assumed to be proportionally dependent on the emissionangle. The energy losses differ for the two chamber sides due to the backing material on the secondside. Fragments in the sample side go through the material thickness, whereas the other FF travelthrough the sample+backing side. As a result, the sample side is less affected by energy losses thanthe backing side. The energy-loss correction for each chamber side is performed as a mean correction

18

for each segment of solid angle. For each angular segment of ∆cos = 0.005 the average position ofthe pulse-height distribution is plotted as a function of cos−1 (θ) as shown in Fig. 14. To correctfor the energy straggling, linear fits are applied to both chamber sides and extrapolated to the y-axiscorresponding to an ideal energy-loss free channel E0. This imaginary point correspond to an infinitelythin sample without energy losses. The energy difference E0 − 〈E〉 is used to correct each channel toE0.

0 1 2 3 4 5

9 0

1 0 5

1 2 0

1 3 5

Mea

n ene

rgy <

E q> (c

hann

els)

S a m p l e s i d e B a c k i n g s i d e

C o s - 1 ( q )

E 0

Figure 14: The energy-loss correction uses the pulse height as a function of cos−1 θ to extrapolate tothe y-axis. The crossing point between the two chamber sides gives the energy channel correspondingto an infinitely thin sample (no energy losses).

The corrected pulse-height distribution as a function of emission angle is shown in Fig. 15.

2 5

5 0

7 5

1 0 0

1 2 5

1 5 0

1 7 5

Pulse

heigh

t CM

syste

m (ch

anne

ls) 1 01 52 03 55 06 37 51 0 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2

C o s ( q )5 0

7 5

1 0 0

1 2 5

1 5 0

1 7 5

2 0 0

Pulse

heigh

t CM

syste

m (ch

anne

ls) 1 01 52 03 55 06 37 51 0 0

C o s ( q )

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2

Figure 15: Energy-loss correction for the backing side. Before correction in (a) and after correction in(b).

19

5 Results

The results presented in this work are based on papers I, II and III. The measurements performed (Table2) were used to compare the AA and DA systems. The comparison is presented in this work along withthe first results concerning the fluctuation of FF properties in 234U(n, f). The angular anisotropy ismeasured as a function of incident neutron energy. Finally the results from the grid-inefficiency studyis presented.

5.1 Digital data acquisition

5.1.1 Drift Stability

During the experiment it was observed that the DA data showed higher drift stability than the AAdata. These drifts were found in the mean FF pulse height of AA (Fig. 16a). A precision pulsegenerator, continuously running during the experiment confirmed these drifts (Fig. 16b). Only theanode channel from one chamber side was affected. However, this was only seen in the analogue caseand hence, was due to electronic drifts in the NIM modules used in the anode chain (Fig. 8).

1 2 3 4

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

D r i f t

E n = 8 3 5 k e V

D i g i t a l s i d e 1 D i g i t a l s i d e 2 A n a l o g u e s i d e 1 A n a l o g u e s i d e 2

Raw

pulse

heigh

t [arb

.]

M e a s u r e m e n t n u m b e r [ t i m e ]

a

5 0 1 0 0 1 5 0 2 0 02 2 0

2 3 0

2 4 0

2 5 0

T i m e [ a r b . ]

Raw

pulse

heigh

t [arb

.]6 0 0

1 2 0 0

1 8 0 0

2 4 0 0

4 0 0 0

1 0 0 0 0

P u l s e g e n e r a t o r A n a l o g u e2 3 4 U ( n , f ) s i d e 1E n = 8 3 5 k e V

D r i f t

a p i l e - u p

P u l s e r

b

Figure 16: a) During the measurement a drift occurred on the analogue data on side 1. The drift isnot seen in the the AA data from the second side. Both sides from DA data are free from the drifts.b) The drift seen in the third run (a) is visible on the pulse generator signal. The pulse is used tocorrect for the drift.

5.1.2 Shaping time on CR− RC4 shaping filter

In order to choose the shaping time τ for the CR− RC4 filter the following study was performed.Several shaping times (0.2, 0.5, 1.0 and 2.0 µs) were tested during the DSP routines as mentioned insec. 4.3.1. The difference between 0.5, 1.0 and 2.0 µs was negligible. However 0.2 µs was too low andresulted in a modification to the pulse-height distribution (see Fig. 17a). A comparison between theangular distributions of 0.5 and 2.0 µs is shown in Fig. 17b showing no significant difference. Thefurther analysis performed was based on 0.5 µs.

20

5 0 1 0 0 1 5 0 2 0 00

1 0 0 02 0 0 03 0 0 04 0 0 05 0 0 06 0 0 07 0 0 08 0 0 0

Co

unts

P u l s e h e i g h t [ a r b . ]

0 . 2 m s 0 . 5 m s 1 . 0 m s 2 . 0 m s

2 3 5 U ( n , f ) D I G I T A La

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 40

1 0 0 0

2 0 0 0

3 0 0 02 3 5 U ( n , f ) D I G I T A L

Coun

ts

C o s q S

0 . 5 m s 2 . 0 m s

b

Figure 17: Different shaping times tested for the CR− RC4 filter. a) The shaping time of 0.2 µs wastoo low and resulted in a modified pulse-height distribution. Note that as eye guide, the pulse heightsin (a) were shifted so the light mass peaks overlap. b) A comparison of the cosine distributions for 0.5and 2.0 µs. The results are independent from the shaping time used.

5.1.3 Alpha pile-up correction

The energy-loss correction discussed in sec. 4.5 for 234U (n, f) was affected by the high α pile up.The pulse height in the AA case was found to be too high compared to the reference calibration with235U (nth, f) (see Fig. 18a). The pulse height as a function of cos−1 θ was extrapolated to intersectthe y-axis. The ideal energy-loss free channel E0 was about 1.5 MeV higher in case of AA. However,due to the α pile up correction discussed in sec. 4.3.2, the DA data gave consistent results. The highα activity of the 234U sample was successfully corrected for in the digital analysis and the pile-upcontribution was rejected. The events were not discarded but corrected and used for further analysis.In order to correct the AA data on an average base, the DA results were used to scale down E0 to beconsistent with the energy calibration from 235U (n, f).

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 01 3 01 3 51 4 01 4 51 5 01 5 51 6 01 6 51 7 0

a

A N A L O G U E

2 3 4 U ( n , f ) 2 M e V A 1 2 3 4 U ( n , f ) 2 M e V A 2 2 3 5 U ( n , f ) A 1 2 3 5 U ( n , f ) A 2

Pulse

heigh

t (cha

nnels

)

1 / c o s q S 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0

1 3 01 3 51 4 01 4 51 5 01 5 51 6 01 6 51 7 0

2 3 4 U ( n , f ) 2 M e V A 1 2 3 4 U ( n , f ) 2 M e V A 2 2 3 5 U ( n , f ) A 1 2 3 5 U ( n , f ) A 2

Pulse

heigh

t (cha

nnels

)

1 / c o s q S

D I G I T A L

b

Figure 18: a: Energy loss correction in AA for both chamber sides. The crossing point for 234U (n, f)is too high compared to 235U (n, f), due to the α-particle pile-up effect. b: Energy-loss correction indigital case. The successful pile-up correction decreases the PH in case of 234U (n, f). A1 and A2correspond to anode 1 and 2, respectively.

21

5.2 Results on emission angle

5.2.1 Drift-time method

The drift-time technique was investigated in the DA case, using CFD and LE set at different levels oncathode and anode signals in order to simulate the corresponding modules used in AA. The referencefor the comparison was the isotropic cosine distribution of the 235U (nth, f) reaction obtained from thesumming method. In the drift-time method an overshoot at lower cosine values was observed (see Fig.19a). Varying the CFD trigger levels (10%, 5%, 4%, 3%) on the anode signal, we obtained an optimumvalue around 3% of the anode signal as seen in Fig. 19a to determine the correct cosine distribution.The result from the LE technique on the same data set is shown in Fig. 19b. The LE was set justabove the noise level after correcting for grid inefficiency. A third possibility exists in DA, using thecentre-of-gravity from the anode as stop signal. This method was not considered in this work, becauseit cannot be tested in the AA case.

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 20

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

2 5 0 0

3 0 0 0

3 5 0 0

Coun

ts

C o s q T

C F D 1 0 % C F D 5 % C F D 4 % C F D 3 %

a

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 20

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

2 5 0 0

3 0 0 0

3 5 0 0

Co

unts

C o s q T

L e a d i n g E d g eb

Figure 19: a: Angular distribution for CFD set at different levels in the drift-time determination for235U (nth, f). b: The same distribution, when the LE technique was applied to the anode signal.

5.2.2 Angular distribution

The cosine distribution cos θLABΣ calculated from Eq. (17), is transformed from the LAB system to the

CM system according to:

cos θCMΣ =

√1−

ELABpre

ECMpre

(1− cos2 θLAB

Σ

), (25)

where ELABpre and ECM

pre are given by Eqs. (34) and (28). The angular distribution of the FF, for235U(nth, f) is isotropic [27], as seen both in the digital and analogue cases within the experimentaluncertainty (Fig. 20a). In the case of 234U (n, f) at En = 2 MeV and En = 0.5 MeV, the angulardistributions is anisotropic (Fig. 21a and b) [28]. The good agreement between the AA and DA is alsoseen in this case. The angular resolution, which is mainly sample-thickness dependent, is about 0.15at FWHM for the 234U sample. It is determined as the difference between the cosine distributions ofthe two ionization chamber sides (cos θΣ,1 − cos θΣ,2), with no significant difference between AA andDA (Fig. 20b).

22

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 20 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

1 . 4 D I G I T A L A N A L O G U E

2 3 5 U ( n t h , f )

C o s q S ( C M )

Cou

nts (n

orm)

a

- 0 . 3 - 0 . 2 - 0 . 1 0 . 0 0 . 1 0 . 2 0 . 30

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

2 5 0 0

3 0 0 0

3 5 0 0

F W H MD I G I T A L = 0 . 1 4 9A N A L O G U E = 0 . 1 5 0

2 3 4 U ( n , f ) 2 M e VD i g i t a lA n a l o g u e

Coun

ts

C o s q S 1 - C o s q S 2 ( L A B )

b

Figure 20: a) Cosine distributions in the CM system for the isotropic reaction 235U (nth, f). b) Thedifference between the cos θ distribution, from the two TFGIC sides. The angular resolution is about0.15 at FWHM for both DA and AA.

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 20 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

1 . 4

E n = 2 . 0 M e V

2 3 4 U ( n , f )

Coun

ts (no

rm)

C o s q S ( C M )

D I G I T A L A N A L O G U E

a

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 20 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

1 . 4

E n = 0 . 5 M e V

2 3 4 U ( n , f )

D I G I T A L A N A L O G U E

Coun

ts (no

rm)

C o s q ( C M )

b

Figure 21: Cosine distribution for the anisotropic 234U(n, f) at 2 MeV (a) and 0.5 MeV (b).

5.2.3 Angular anisotropy

In order to calculate the angular anisotropy for the measured energies of 234U (n, f) (Tab. 2), the angu-lar distributions are divided by the angular distribution from 235U (nth, f). The isotropic distributionshown in Fig. 21 is taken as a reference. The ratio of the distributions is then fitted with the two firsteven Legendre polynomials P0 and P2 for 0.3 ≤ cos θCM

Σ ≤ 0.9. The parametrization (Fig. 22) of thesetwo polynomials is given by

W (θΣ) = A0

(1 +A2

(1.5 cos2 θCM

Σ − 0.5))

, (26)

where the parameters A2 is used to determine the anisotropy W (0o) /W (90o) according to

W (0o)W (90o)

=3A2

2−A2+ 1 . (27)

23

0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 00 . 60 . 70 . 80 . 91 . 01 . 11 . 21 . 31 . 41 . 51 . 6

2 3 4 U ( 2 M e V )2 3 5 U ( t h )

L e g e n d r e f i t ( P 0 & P 2 )

W(q)

c o s ( q C M S )

Figure 22: Legendre fit to the ratio of angular distributions from 234U and 235U.

The anisotropy as a function of neutron energy, is shown and compared to literature data in Fig.23.

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 00 . 4

0 . 6

0 . 8

1 . 0

1 . 2

1 . 4

1 . 6

1 . 8

ANISO

TROP

Y

E n e r g y ( M e V )

I R M M 2 0 1 0 B e h k a m i 1 9 6 8 L a m p h e r e 1 9 6 2 S i m m o n s 1 9 6 0 J E F F s

Figure 23: The angular anisotropy for 234U (n, f) relative to the isotropic 235U (nth, f). Stronganisotropic behavior is observed around the vibrational resonance in agreement with literature data[28, 29, 30].

The Legendre fit was performed also for other ranges. In Fig. 24 the difference in anisotropy isseen for different fit ranges.

24

0 1 2 3 4 50 . 6

0 . 8

1 . 0

1 . 2

1 . 4

1 . 6

1 . 8

R a n g e : 0 . 2 5 - 0 . 9 R a n g e : 0 . 3 - 0 . 9 R a n g e : 0 . 3 5 - 0 . 8 5

A N A L O G U E S u m m i n g m e t h o d 2 3 4 U ( n , f )

ANISO

TROP

Y

E n e r g y ( M e V )

Figure 24: Angular anisotropy for different Legendre-fit ranges.

5.3 Fragment energy- and mass determination

In order to calculate the pre-neutron emission fragment masses and their energies, the following cor-rections have to be introduced.

5.3.1 Neutron-momentum transfer

The impinging neutron (mass mn) with the laboratory energy ELABn , transfers a linear momentum to

the compound nucleus (mass mcn). The FF in the backing side (i=2) gets a boost in the direction ofmotion whereas the energy of the fragment in the sample side is reduced (i=1). The FF energies inthe LAB system ELAB

i are corrected and transferred to the CM system ECMi according to:

ECMi = ELAB

i ± 2m−1cn

√m∗

i mnELABi ELAB

n cos θLABi + m−2

cn mnm∗i ELAB

n , (28)

where the negative sign applies for the chamber side closest to the neutron beam (i=1). The provisionalfragment masses m∗

i are determined using the conservation of linear momentum:

m∗1ELAB

1 = m∗2ELAB

2 . (29)

Using conservation of mass m∗1 + m∗

2 = mcn in Eq. (29) gives the so-called provisional masses:

m∗1 =

mcnELAB2

ELAB1 + ELAB

2

and m∗2 =

mcnELAB1

ELAB1 + ELAB

2

. (30)

5.3.2 Neutron multiplicity

The highly excited FF evaporate on average two to three neutrons per fission, to get rid of the majorpart of the excitation energy. The neutron multiplicity ν (A,TKE, En) is a critical parameter in thecalculation of mass distributions. Since we do not measure the neutrons directly, an indirect way needsto be applied in order to deduce ν (A,TKE, En). For 234U (n, f) the neutron multiplicity as a functionof mass, ν (A) , is not known. Hence, it is calculated based on experimental data of 233U (n, f) and235U (n, f) [31] as seen in Fig. 25a. The calculation deduces the mean neutron multiplicity as functionof fragment mass ν (A)

ν234 (A) = ν233 (A)(

1 +12

(ν235 (A)ν233 (A)

− 1))

(31)

25

The prompt neutron multiplicity also depends on the TKE as well as the incident neutron energy. TheTKE-dependency in ν(A,TKE) was parameterized based on Eq. (32) according to Ref. [32]

ν234 (A,TKE) = ν234 (A) +ν234 (A)

ν234 (A) + ν234 (ACN −A)〈TKE (A)〉 − TKE

Esep, (32)

where Esep = 8.6 MeV is the neutron separation energy. A correction for the neutron-energy depen-dency of total ν was introduced based on experimental values from Ref. [33].

8 0 1 2 0 1 6 0

0 . 8

1 . 6

2 . 4

n( Apr

e )

P r e - n e u t r o n e m i s s i o n m a s s ( A p r e )

2 3 4 U ( n , f ) 2 3 5 U ( n , f ) 2 3 3 U ( n , f ) 2 3 8 U ( n , f )

a

0 1 2 3 4 5

2 . 4

2 . 6

2 . 8

3 . 0

3 . 2 2 3 3 U M a n e r o 1 9 7 2 2 3 5 U M a n e r o 1 9 7 2

n(E)

N e u t r o n e n e r g y ( M e V )

2 3 4 U I n t e r p o l a t i o n 2 3 4 U M a t h e r 1 9 6 5

b

Figure 25: a) The sawtooth shape of the neutron multiplicity with experimental data from [31] forν233 (A) and ν235 (A) . b) The neutron multiplicity dependency on the neutron energy interpolated toexperimental data [33, 34].

5.3.3 Pulse-height defect

The amount of ionized atoms n0 for each fission event should stay constant until the full charge signaln0e has been developed on the anode. In reality n0 decreases due to some inherent properties withinthe counting gas. The electrons could shortly after they are liberated, recombine with their atoms orwith other positive ions in the gas. Changes in electric field locally due to the concentration of electriccharges can also decrease the charge. In addition, not all interactions between the FF and the gasresult in an ionization. All these effects normally attributed to the pulse-height defect (PHD) needto be corrected in the analysis. The PHD is mainly dependent on the fragment mass and energy. Aparametrization of the PHD is done using

PHD(Apost, Epost

LAB

)= αEpost

LAB +ApostEpost

LAB

β+Apost

γ. (33)

The parameters α, β and γ are determined once for the calibration run of 235U (nthermal, f) and thenused for 234U (n, f). The parameters are together with the channel-to-energy calibration factor (k)tuned in order to achieve the mean heavy mass peak 〈AH〉 = 139.6 amu and the total kinetic energy〈TKE〉 = 170.5± 0.5 MeV.

5.3.4 Mass calculation

To calculate the pre-neutron emission masses and energies, an iterative process is followed. The post-neutron emission energies in the LAB system ELAB

post are used to calculate the pre-neutron emissionenergies ELAB

pre as:

ELABpre =

Apre

Apre − ν (A,TKE)ELAB

post . (34)

26

To transform ELABpre to ECM

pre , the calculated value from Eq. (34) is inserted in Eq. (28). ECMpre is then

used to calculated the pre-neutron masses according to:

m1,pre =mcnECM

2,pre

ECM1,pre + ECM

2,pre

and m2,pre =mcnECM

1,pre

ECM1,pre + ECM

2,pre

. (35)

The calculated mpre values from Eq. (35) are used to re-calculate ν234 (A,TKE) from Eq. (32). Thenew neutron multiplicities lead to new post-neutron emission masses since

mpost = mpre − ν234 (A,TKE) . (36)

The new masses mpost lead to new PHD values through Eq. (33), and hence to new energies ELABpost

and ELABpre . The process is looped until the difference between the latest and former masses mpre is less

than 1/16. Only masses from events with cos θCMΣ ≥ 0.5 are used in the further calculation, in order

to minimize effects from high angles with bad angular resolution.Finally when the masses are calculated, the energy calibration described in sec. 5.3.3 is used to

obtain the mean heavy mass peak 〈AH〉 = 139.6 amu and the total kinetic energy 〈TKE〉 = 170.5±0.5MeV for 235U (nthermal, f) (see Fig. 26).

6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0

1 4 0

1 6 0

1 8 0

2 0 0

P r e - n e u t r o n e m i s s i o n m a s s ( A p r e )

TKE (

MeV)

24 01 0 02 0 04 0 06 0 08 0 01 , 0 0 01 , 5 0 0

1 7 0 . 5 M e V

1 0 5 . 6

6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 02

3

4

5

PHD

(MeV

)

E n e r g y ( M e V )

2 3 8 U ( n , f ) V i v e s 1 9 9 8

11 02 55 01 0 02 0 05 0 07 0 01 , 0 0 0

ba

Figure 26: a) Pulse-height defect compared to data from [35]. b) Total kinetic energy (TKE) as functionof pre-neutron emission fragment mass. The channel-to-energy factor and the PHD parameters arefine-tuned to obtain the literature data of 235U (nthermal, f).

5.3.5 Energy- and mass distributions

The FF energy distribution for 235U (nth, f) in the CM system is shown in Fig. 27a. The results fromAA and DA are in perfect agreement. The mean value of both energy distributions, differ no more than20 keV. The resolution in terms of peak-to-valley ratio is nearly identical. However, for 234U (n, f),the α-particle pile-up causes a difference in resolution. The DA result implied better resolution (Fig.27b), since the α-particle pile-up correction was carried out on event-by-event basis. The correction inthe AA case is only an average correction to the pulse-height distribution, leading to a deteriorationof the resolution due to the added pulse height. This affects the distribution populating more in thevalley region and broadening both distribution peaks. The peak-to-valley ratio is 14.3 for DA and 8.5for AA.

27

6 0 9 0 1 2 00 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

0 . 0 4

2 3 5 U ( n t h , f )Co

unts

(norm

)

E n e r g y ( M e V )

D I G I T A L A N A L O G U E

a

6 0 9 0 1 2 00 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

0 . 0 4b

2 3 4 U ( n , f ) 2 M e V D I G I T A L A N A L O G U E

Coun

ts (no

rm)

E n e r g y ( M e V )

Figure 27: a) Energy distributions in CM system for 235U (n, f) with a perfect agreement betweenAA and DA. b) The DA results gives better energy resolution as seen in the energy distributions of234U (n, f) at 2 MeV. The improvement is attributed to the successful α pile up correction.

The final pre-neutron emission mass distribution, obtained using Eq. (35) is shown in Fig. 28 for235U (nth, f). The results from DA and AA are both consistent with experimental data from Ref. [36].For 234U (n, f) the mass distributions are still under investigation. However the first results confirms theexpected increment of symmetric fission around mass numbers A=117 and A=118, with the increasedneutron energy.

8 0 1 0 0 1 2 0 1 4 0 1 6 00

1

2

3

4

5

6

7

8A N A L O G U E D I G I T A L

S I M O N 1 9 9 02 3 5 U ( n t h , f )

Yield

(%)

M a s s ( A )

a

1 0 0 1 0 5 1 1 0 1 1 5 1 2 0 1 2 5 1 3 00 . 0 0

0 . 0 5

0 . 1 0

0 . 1 5

0 . 2 0

0 . 2 5

0 . 3 0

Yield

(%)

M a s s ( A )

3 5 0 k e V 5 0 0 k e V 2 M e V 2 . 5 M e V 4 M e V 5 M e V

2 3 4 U ( n , f )b

Figure 28: a) Mass distribution of 235U (nth, f) for DA and AA systems compared with literature data[36]. b) Mass distributions for a subset of the measurements of 234U (n, f) shows that the symmetricfission increases with neutron energy.

5.4 The Frisch-grid inefficiency experiment

The study on the GI correction (see sec. 3.5) resulted in a support for the additive approach confirmingthe results reported in Ref. [8]. The use of different grids implied different inefficiency values. As aresult, the detected pulse height was lower for the grid with higher GI (See the sample side in Fig.29a). For the backing side, the same mesh grid was used, hence the identical distribution was faced.This fact ensures that no drifts occurred which could have shifted the pulse heights on both chambersides.

28

4 0 0 0 6 0 0 0 8 0 0 00 . 0 0 0

0 . 0 0 2

0 . 0 0 42 5 2 C f ( s f )

No

rmali

sed c

ounts

A n o d e p u l s e h e i g h t [ a r b . ]

G I 1 m m s I = 0 . 0 3 1 G I I 2 m m s I I = 0 . 0 8 3

as a m p l e s i d e

2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 00 . 0 0 0

0 . 0 0 2

0 . 0 0 4

b a c k i n g s i d e

b

Norm

alise

d cou

nts

A n o d e p u l s e h e i g h t [ a r b . ]

G I 1 m m s M = 0 . 0 1 1 G I I 2 m m s M = 0 . 0 1 1

2 5 2 C f ( s f )

Figure 29: a) A lower pulse-height distribution is observed in the sample side due to the double grid-wire spacing, i.e. a higher σ. b) Perfect overlap of pulse-height distributions from the raw data of GridI and II measurements, backing side. The same mesh was used in both runs.

5.4.1 Experimental determination of σ

In order to estimate the values of σ the following procedure was followed. A linear fit was applied toboth QA and QC in the region between TC and TG (See Fig. 30a). In this region Eq. (8) is validwhich implies that the ratio of the angular coefficients gives σ. For all three grids, σ is measured andpresented in Fig. 30b. Since QC contains the induction from both fragments in each hemisphere, QΣ

was used instead, since QC = QΣ is valid individually for each chamber side.

2 4 0 3 2 0 4 0 0

0

4 0 0

8 0 0 Q A - s I I Q C - Q C

a

Volta

ge [m

V]

S a m p l i n g [ c h a n n e l s ]

T AT GT C

( s I I = 0 . 0 8 3 )T C O G

0 . 0 0 0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

1 . 4 s M s I s I I

m e s h g r i d I 1 m m g r i d I I 2 m m

Norm

alise

d cou

nts

s ( E x p e r i m e n t a l )

= 0 . 0 8 3 � 0 . 0 0 3

= 0 . 0 1 1 � 0 . 0 0 6= 0 . 0 3 1 � 0 . 0 0 3

s I [ B u n ] = 0 . 0 3 0 s I I [ B u n ] = 0 . 0 9 0

b

Figure 30: a) The voltage output from the preamplifier as a function of time (10 ns/channel) for gridII (σII = 0.083). After the time TC the electrons start to drift away from the cathode, at TG theyreach the grid and at time TCOG, the centre-of-gravity of the electron cloud passes the grid. Finally,at TA the last electrons reach the anode. b) The GI distributions for the three grids as determinedexperimentally from Eq. (8). The given σ are the mean values of the distributions. The calculatedvalues σcalc according to Eq. (6) are also given.

5.4.2 Comparing the two correction methods

Both corrections were applied to the data from Fig. 29, using the GI values shown in Fig. 30b. Theadditive correction following Eq. (11),corrected properly for the difference in the sample side. Thepulse-height distributions from the two measurements were perfectly overlapping as seen in Fig. 31a.

29

Applying the subtractive approach presented in Eq. (9) to the same data, increased the difference asseen in Fig. 31b. The subtractive approach fails of give grid-independent results.

4 0 0 0 6 0 0 0 8 0 0 00 . 0 0 0

0 . 0 0 2

0 . 0 0 4

a d d i t i v e c o r r e c t i o n

a 2 5 2 C f ( s f )

Norm

alise

d cou

nts

P u l s e h e i g h t [ a r b . ]

G I 1 m m s I = 0 . 0 3 1 G I I 2 m m s I I = 0 . 0 8 3

s a m p l e s i d e

4 0 0 0 6 0 0 0 8 0 0 00 . 0 0 0

0 . 0 0 2

0 . 0 0 4

G I 1 m m s I = 0 . 0 3 1 G I I 2 m m s I I = 0 . 0 8 3

s u b t r a c t i v e c o r r e c t i o n

b 2 5 2 C f ( s f )

Norm

alise

d cou

nts

A n o d e p u l s e h e i g h t [ a r b . ]

s a m p l e s i d e

Figure 31: Pulse-height distribution from the two identical measurements with 1 mm and 2 mm grids,after GI correction. The additive correction (Eq. (11)) leads to identical distributions (a). Thesubtractive method (Eq. (10)) fails to result in the same distributions (b).

5.4.3 Impact on energy- and mass distributions

In the previous section, it was shown that the additive approach is the proper way of treating the GI.Due to the incomplete shielding, less signal is induced which implies that Eq. (11) is right rather thanEq. (9). In order to understand the impact of choosing the wrong treatment, both equations wereused on the data from 235U(nth, f). The use of either correction method was giving consistent resultsin terms of energy- and mass distribution as seen in Fig. 32.

3 0 6 0 9 0 1 2 00 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

0 . 0 4

0 . 0 5

Norm

alise

d cou

nts

E n e r g y C M [ M e V ]

A d d i t i v e c o r r . S u b t r a c t i v e c o r r .

2 3 5 U ( n t h , f )P r e - n e u t r o n e m i s s i o n E C M

a

6 0 9 0 1 2 0 1 5 0012345678b 2 3 5 U ( n t h , f )

Yield

[%]

P r e - n e u t r o n e m i s s i o n m a s s [ A ]

A d d i t i v e c o r r . S u b t r a c t i v e c o r r . S i m o n

( 1 9 9 0 )

Figure 32: Energy- (a) and mass (b) distributions for the 235U (nth, f) reaction. Both correctionmethods are shown to be consistent with literature [36].

30

6 Conclusions

6.1 Nuclear electronics

The first study concerned the nuclear electronics in use particularly in neutron-induced fission exper-iments. An investigation was carried out to compare modern digital data acquisition systems withthe well-tested conventional analogue systems. The DA gave consistent angle-, energy- and mass dis-tributions for the 235U (n, f). The agreement with the AA data was nearly perfect. However, whenintroducing the high α active 234U sample, the DA was Superior. The energy resolution was betterdue to the successful pile-up correction. The events were not discarded but simply corrected and usedthereafter. The DA allowed for extended possibilities for off-line analysis, since the whole digitizedwaveform was stored. The optimum settings for the drift-time method could be done offline. Con-cerning drift stability, the DA was found far more stable than AA. The conclusion from this study isthat digital acquisition systems is superior to the conventional analogue systems. With this respect,the replacement of AA with DA is natural.

6.2 Fission fragment studies

The second part of the work concerns the physics of the fission process. The angular anisotropy showsstrong variations around the vibrational resonance at 800 keV incident neutron energy. The resultswere in good agreement with literature data. The preliminary results on the mass distributions for234U (n, f) shows the expected increased symmetric fission with the incident neutron energy. Concerningthe absolute calibration reference, 235U (nth, f), the calculated mass distribution was in good agreementwith literature data.

6.3 The Frisch-grid inefficiency

The third part of this work was treating the GI. As discussed earlier, the pending ambiguity regardingthe proper correction approach was investigated. A TFGIC equipped with a 252Cf (sf) source, wasused with two Frisch grids with different wire spacing. Different GI values were encountered due tothe difference in wire spacing. The higher GI value implied a lower pulse height. Hence it was shownthat the additive approach is the correct approach in agreement with the most recent study on the GI[8]. The effect of choosing either correction approach was studied as well, and it was found that theinfluence of whatever approach chosen on energy- and mass distributions is indeed negligible.

6.4 Outlook

The next step is to complete the main task, namely to accurately determine the TKE- and massdistributions for the different measurements as a function of the incident neutron energies. The twodimensional mass distributions will be parametrized with the fission modes predicted by theory tocalculate the contributions for the different modes. The vibrational resonance region mentioned inthe introduction will be examined in finer steps to search for the predicted fluctuations of the FFproperties.

31

7 Acknowledgments

To IRMMI owe my deepest gratitude to my supervisor Josch Hambsch, for his wise leadership, broad knowledgeand never-closing door. In addition he is a source of inspiration! Another excellent mentor is StephanOberstedt who generously shares his expertise in the group. I have been privileged with two years ofworking with these two front figures in the field.

The Van De Graaff staff, Carlos Chaves, Thierry Gamboni and Wouter Geerts should be creditedfor their dedicated work to provide a decent beam. Also Marzio Vidali for his technical supports. Iam particularly indebted to Shakir Zeynalov for his patient guidance and master skills in the fieldof digital-signal processing. Regards to Catalin Matei, Imrich Fabry and Raffaele Bencardino forinteresting discussions and warm friendship. Greetings to all the colleagues whom it is a delight to workamong: Antonin Krasa, Andreas Oberstedt, Arjan Plompen, Giorginis Georgios, Goran Lovestam,Johan Karlsson, Klaas Okkinga, Letizia Sergi, Livio Lamia, Mikael Hult, Robert Billnert, RuxandraBorcea and Tomasz Brys.

To UppsalaTo my great home university I owe my education. Regards to all professors and teachers I had especiallyLeif Karlsson and Bo Hoistad. I would like to thank Stephan Pomp for his administrative work andsupervision at Uppsala University. Greetings to all the people of the Applied nuclear physics division:Ane Hakansson, Cecilia Gustavsson, Mattias Lantz, Matthias Weiszflog, Michael Osterlund, PeterAndersson, Peter Wolniewicz, Riccardo Bevilacqua, Sophie Grape, Stefan Jakobsson Svard and VasilySimutkin.

I send my deep regards to Par-Anders Soderstrom and Johan Nyberg. Also Carl-Oscar Gullstromfor all the years we studied physcis together.

Last but not least, there is one man who is really the reason why I am writing this work today. Aman who guided me to the PhD position at IRMM. I cannot thank you enough for believing in me,Jan Blomgren.

To family and friendsMy dear family, thanks for being such a good foundation. From my parents I am granted with loveand support. I hope you are proud. To my beloved brother and sister, I wish you good luck in yourstudies. Regards to all the friends I have and had during the years. Finally, to my wife Sheima andmy son Josef, I live for you. My dear wife thank you! This work is done thanks to you.

32

A Appendix

A.1 Calculations on the fission count rate

In order to estimate the fission count rate, one needs the cross section σ, neutron flux φ and the numberof target nuclei Nk. The yield Y is given by

Y = σφNk . (37)

The number of nuclei Nk is dependent on the sample volume V, material density ρ and the atomicmass A. It is given by

Nk =VρNA

A, (38)

where NA is Avogadro’s constant. The sample surface- thickness ∆ and surface area S are used in Eq.(38) since S∆ = V ρ resulting the expression

Y =σφS∆NA

A. (39)

The count rate is calculated for the values A=234, NA = 6.022 · 1023, S = 7.067 cm2 and ∆ =92.133 cm2. The cross section σ is taken from Ref. [20] and the neutron flux is calculated dependingon the neutron energy according to the program EnergySet [37]. The calculation is valid for the beamcurrent of 10µA and at 75 mm distance between the neutron-producing target and Uranium sample.The calculation is shown as function of the incident neutron energy in Fig. 6.

A.2 Alpha activity of 234U sample

The high α-activity for our sample was estimated prior to the experiment. The half-life of 234U is

T 12

= 245500 years = 7.74209 · 1012 s. (40)

In terms of life time this gives

λ =ln 2T 1

2

= 8.95297 · 1014 s−1. (41)

The radioactive decay law (equation 42), differentiated gives the activity equation 43:

N = N0e−λt , (42)

−dNdt

= λN0e−λt = λN . (43)

The number of uranium nuclei, N, in the sample is

N =∆SNA

A, (44)

where ∆ = 91.667 · 10−6gcm−2 is the target thickness, S = πr2 = 7cm2 is the sample surface area,NA = 6.022 · 1023 and A is the atomic mass 234. Hence in the sample there are Nk = 1.6677 · 1018

Uranium-nuclei. Finally the α-activity is

−dNdt

= 149300 α/s . (45)

This was confirmed from the tabulated specific activity data of 234U which is 231.3MBq/g. The massof the sample is

m = ∆ · S = 0.000648 g . (46)

33

The α-activity according to this estimation is

dNdt

= 231.3 MBqg−1 × 0.000648 g = 149900 α/s , (47)

which is close to the earlier obtained value in 45.

A.3 CR− RC4 filter design

For an input waveform W[i] the CR− RC4 filter operation produces the output function Ψ[i]:

Ψ[i] = Ψ[1] + Ψ[2] + Ψ[3] + Ψ[4] + Ψ[i] . (48)

The first four samples Ψ[1− 4] are given by:Ψ[1] = ζ0 ·W [1] + ζ1 ·W [0]Ψ[2] = ζ0 ·W [2] + ζ1 ·W [1] + ζ3 ·Ψ[1]Ψ[3] = ζ0 ·W [3] + ζ1 ·W [2] + ζ3 ·Ψ[2] + ζ4 ·Ψ[1]Ψ[4] = ζ0 ·W [4] + ζ1 ·W [3] + ζ3 ·Ψ[3] + ζ4 ·Ψ[2] + ζ5 ·Ψ[1]

(49)

where the coefficients ζi are given by:

x = e−τ

ζ0 = 0.5 · (1− x)4 (1 + x)ζ1 = −0.5 · (1− x)4 (1 + x)ζ2 = 5 · xζ3 = −10 · x2

ζ4 = 10 · x3

ζ5 = −5 · x4

ζ6 = x5

. (50)

For the channels 5 ≤ i ≤ 1024, the output Ψ[i] is:

Ψ[i] = ζ0 ·W [i]+ζ1 ·W [i−1]+ζ2 ·Ψ[i−1]+ζ3 ·Ψ[i−2]+ζ4 ·Ψ[i−3]+ζ5 ·Ψ[i−4]+ζ6 ·Ψ[i−5] . (51)

34

List of abbreviations

• A= Anode

• AA = Analogue data Acquisition

• C = Cathode

• Cf= Californium

• CFD= Constant Fraction Discrimination

• CM = Center of Mass system

• CoG= Centre of Gravity

• DA = Digital data Acquisition

• DSP = Digital Signal Processing

• DT= Drift time

• G = Grid

• GI = Grid Inefficiency

• FGIC = Frisch Grid Ionization chamber

• FF = Fission Fragment

• JEFF= Joint Evaluated Fission and Fusion File

• LAB = Laboratory system

• LDM = Liquid Drop Model

• LE = Leading Edge

• MeV = Mega Electron Volt ( 1 eV = 1.6021765 · 10−19 J)

• MM-RNR = Multi-Modal Random Neck-Rupture

• PHD = Pulse Height Defect

• SA = Spectroscopic Amplifier

• TAC= Time to Digital Converter

• TFA = Timing Filter Amplifier

• TFGIC = Twin Frisch Grid Ionization Chamber

• TKE = Total Kinetic Energy

• U = Uranium

35

List of Tables

1 Dimensions of the chamber and electrodes. . . . . . . . . . . . . . . . . . . . . . . . . . 92 The measurements performed for 234U (n, f). . . . . . . . . . . . . . . . . . . . . . . . . . 123 Two different grid types were used in the GI experiment (sample side). . . . . . . . . . 13

List of Figures

1 Cross-section of 234U (n, f). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 The fission barrier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Schematic view of the ionization chamber and typical signals. . . . . . . . . . . . . . . . 74 Cosine determination using the summing method. . . . . . . . . . . . . . . . . . . . . . 105 Explanation of the drift-time method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Calculated fission count rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Ionization chamber and electronic scheme used for the GI experiment. . . . . . . . . . . 138 Electronic scheme for the experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Leading-edge and Constant-Fraction discrimination principles . . . . . . . . . . . . . . 1510 The digital signal processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1611 CR− RC4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1612 CR− RCn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1713 Alpha pile-up correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1814 Energy-loss correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1915 Before and after energy-loss correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1916 Experimental drifts during experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2017 Impact of different shaping time in the CR-RC4 filter. . . . . . . . . . . . . . . . . . . . 2118 Energy loss correction for analogue and digital systems. . . . . . . . . . . . . . . . . . . 2119 Constant Fraction Discrimination and Leading-edge for the Drift-time method . . . . . 2220 Angular distribution for 235U (nth, f) and angular resolution. . . . . . . . . . . . . . . . . 2321 Angular distributions for 234U(n, f) at incident energies 2 MeV (a) and 0.5 MeV. . . . . 2322 Legendre fit for the angular anisotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2423 Angular anisotropy for 234U (n, f) as function of incident neutron energy. . . . . . . . . 2424 Angular anisotropy for different Legendre-fit ranges. . . . . . . . . . . . . . . . . . . . . 2525 Neutron multiplicity as function of fragment mass and incident neutron energy. . . . . 2626 Plots of pulse-height defect and total kinetic energy. . . . . . . . . . . . . . . . . . . . . 2727 Energy distributions of 234U (n, f). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2828 Mass distributions of 235U (nth, f) and 234U (n, f) . . . . . . . . . . . . . . . . . . . . . . 2829 Uncorrected distributions from the GI experiment. . . . . . . . . . . . . . . . . . . . . . 2930 Experimental determination of GI values. . . . . . . . . . . . . . . . . . . . . . . . . . . 2931 Both GI corrections applied to data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3032 Impact of GI correction approach on mass and energy distributions. . . . . . . . . . . . 30

36

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