Study of Some Nuclear Reactions at Moderate

Study of Some Nuclear Reactions at Moderate Energies

submitted in the partial fullfillment of the award of the degree of

Master of Philosophy in Physics

submitted By

Siddharth Parashari in the supervision of Prof. M. Afzal Ansari Department of Physics Aligarh Muslim University Aligarh, U.P. India-202002 (2016)

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Dr. M. Afzal Ansari Chairperson

DEPARTMENT OF PHYSICS ALIGARH MUSLIM UNIVERSITY ALIGARH – 202 002 (INDIA) Phone : 0571 – 2701001 (O) : 0571 – 2500429 (R) Fax : 0571 – 2701001 E-mail : drmafzalansari@yahoo .com

Residence: 4/1100-D, Sir Syed Nagar, ALIGARH – 202 002, INDIA

Certificate

Certified that the work presented in this M. Phil. dissertation entitled “Study of Some Nuclear Reactions at Intermediate Energies” is the original work of Mr. Siddharth parashari, carried out under my supervision.

(Prof. M. Afzal Ansari)

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Acknowledgement I would like to express my sincere regards to several individuals who in one way or another contributed and provided their valuable assistance in the preparation and completion of this work. First of all, my highest gratitude to my supervisor Prof. M. Afzal Ansari, for his inspiring guidance and generous support for completing this work successfully and for providing the necessary facilities. I highly obliged to him for encouraging me to work hard as well as to refine my path for research. I would like to thank The Chairman, Department of Physics, Aligarh Muslim University, Aligarh and to The Director of Inter University Accelerator Centre (IUAC), New Delhi, India, for providing the all necessary facilities to carried out the present work. I also would like to give my sincere thanks to my colleagues especially to Mr. Harish Kumar for giving his precious time, help and fruitful discussions. Thanks to Mr. Suhail Ahmad Tali and Mr. Asif Ali for being supportive. My sincere thanks also goes to to all my group members especially to Dr. D. Singh and Dr. Rahbar Ali for their inspiration, encouragement and guidance. I am also thankful to all my friends, especially Dr. Kamal Kumar, Mr. Sunil Dutt, Dr.Anand Kumar, Mr. Omveer Singh,

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Mr. Suhel Ahmad, Mr. Mohsin Ilahi, Mr. Gyaprasad, Mr. Anand Somvanshi, Mr. Arphin Islam and Mr. Chetan Verma for their moral support and whole heartedly help. Let me express my sense of gratitude to my parents, to whome, my final gratitude shall always be due and for their prayers and good wishes to my success which helped me always. From the deep of my heart a special thanks to my brother, Mr. Harsh Parashari, for supporting me spiritually throughout writing this dissertation and my life in general. I am so thankful to God for giving me such wonderful family. Last but not the least, I am thankful to all those who wished and boosted me up every time, Without their advice, blessings and encouragement it would have been impossible for me to pursue this work.

Siddharth Parashari

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This work is Dedicated to,

My Mother and Father... for their love and endering support

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Contents 1 Introduction 1.1 Preamble . . . . . . . . . . . . . . . 1.2 Nuclear Reactions . . . . . . . . . . 1.3 Heavy-Ion Induced Rections . . . . . 1.3.1 Complete Fusion Reactions . 1.3.2 In-Complete Fusion Reactions 1.4 Motivation . . . . . . . . . . . . . . . 1.5 Overview: the present work . . . . . .

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1 1 3 5 11 13 15 15

Bibliography

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2 Experimental Details 2.1 15UD Pelletron Accelerator . . . . . . . . . . . . . . . . 2.2 Activation Technique . . . . . . . . . . . . . . . . . . . . 2.3 Target preparation . . . . . . . . . . . . . . . . . . . . . 2.4 Target Irradiation . . . . . . . . . . . . . . . . . . . . . . 2.5 High purity Germanium (HPGe) Detector . . . . . . . . 2.5.1 Resolution and Energy calibration of the Detector 2.5.2 Efficiency of Detector . . . . . . . . . . . . . . . .

21 21 23 24 27 28 30 30

Bibliography

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. . . . . . .

. . . . . . .

. . . . . . .

35

3 Measurements 37 3.1 Identification of Evaporation Residues . . . . . . . . . . . . . . 38 3.2 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2.1 Uncertainities in Measurement . . . . . . . . . . . . . . . 42 ix

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Table of Contents 3.3

Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.3.1 xn and pxn Channels . . . . . . . . . . . . . . . . . . . . 43

Bibliography

53

4 Results and Discussions 55 4.1 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Bibliography

67

List of Figures 1.1 1.2 1.3

1.4 1.5 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.1 3.2

Classical View of HI-induced Reactions . . . . . . . . . . . 7 Effective Potential (Vef f (r)) with respect to the relative separation (r), for 13 C +175 Lu. . . . . . . . . . . . . . . . . 9 Schematic picture of different partial waves contributing to the reaction probability for fusion (CN-formation), deep inelastic collisions, direct reactions of interacting partners. ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 A typical representation of Complete Fusion reaction dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A typical representation of In-complete Fusion reaction dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 15UD Pelletron setup at IUAC, New Delhi . . . . . . . . Annular-Catcher Rings . . . . . . . . . . . . . . . . . . . . . General Purpose Scattering Chamber used for target irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Source detector assembly used for spectrum recording . Schematic diagram of HPGe Detector . . . . . . . . . . . The observed γ-ray spectrum of 152 Eu . . . . . . . . . . . . Efficiency plots for 12 C + 175 Lu system at different distances of source from the axis of detector . . . . . . . . . Efficiency plots for 13 C + 175 Lu system at different distances of source from the axis of detector . . . . . . . . . Half-life plot of Half-life plot of

22 25 27 28 29 32 33 34

Os residue for 12 C +175 Lu . . . . . . . . 38 183m Os residue for 13 C +175 Lu . . . . . . . 39

182

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xii

List of Figures 3.3 3.4

Observed γ-ray spectrum 88 MeV energy. . . . . . Observed γ-ray spectrum 88 MeV energy. . . . . .

of 175 Lu . . . . . of 175 Lu . . . . .

irradiated with 13 C . . . . . . . . . . . irradiated with 12 C . . . . . . . . . . .

beam at . . . . . . 45 beam at . . . . . . 46

4.1

Experimentally measured Angular distribution for 184 Ir Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Experimentally measured Angular distribution for 183 Ir Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Experimentally measured Angular distribution for 182 Ir Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Experimentally measured Angular distribution for 183 Os Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Experimentally measured Angular distribution for 182 Os Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Experimentally measured Angular distribution for 181 Os Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Experimentally measured Angular distribution for 183 Re Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Experimentally measured Angular distribution for 182 Re Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Experimentally measured Angular distribution for 181 Re Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 Experimentally measured Angular distribution for 179 Re Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.11 Experimentally measured Angular distribution for 178 Re Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 57 . 58 . 58 . 59 . 60 . 61 . 62 . 63 . 63 . 64 . 64

List of Tables 1.1

The range of the impact parameter and angular momentum associated, with different type of HI-interactions . .

8

2.1 2.2 2.3

Details of Al annular catcher rings used for 12 C + 175 Lu 26 13 175 Details of Al annular catcher rings used for C + Lu 26 Gamma rays along with their absolute intensities for 152 Eu source . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1

List of identified Reaction Residues (channels) alongwith their spectroscopic properties . . . . . . . . . . . . . Measured differential cross-sections for 184 Ir residue . . Measured differential cross-sections for 183 Ir Residue . . Measured differential cross-sections for 182 Ir Residue . . Measured differential cross-sections for 183 Os Residue . Measured differential cross-sections for 182 Os Residue . Measured differential cross-sections for 181 Os Residue . Measured differential cross-sections for 183 Re Residue . Measured differential cross-sections for 182 Re Residue . Measured differential cross-sections for 181 Re Residue . Measured differential cross-sections for 179 Re Residue . Measured differential cross-sections for 178 Re Residue .

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12

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44 47 48 48 49 49 50 51 51 52 52 52

xiv

List of Tables

Chapter 1 Introduction

The present chapter will enlighten the journey of mankind to understand the basic physics behind the plays in Nuclear physics, or to be very specific; in the low energy Heavy-Ion Induced Reactions, with the help of brief discussions where we have emphasized Complete and In-complete Fusion reactions, which plays an important role at low energy. This chapter also includes the profound ideas and motivations essential for the completeness of this work.

1.1

Preamble

Ever since the discovery of the nucleus and radioactivity, efforts have been made to understand the properties and behaviour of nucleus. Because of very small size, the physics related to nucleus can only be dealt with quantum mechanics, thus can’t be realized directly. Our journey to understand the

Chapter 1. Introduction nature, which has always been a challenge for human beings, started in the very beginning of the 4th century. At that time the idea about atom was revealed, as people believed that each kind of element could be sub-devided into its contituent particles, invisible to naked eye. In 19th cenctury investigators applied the methods of experimental science to understand and to obtain some evidence needed in support of this idea to a full-fledged scientific theory. The journey got accelerated with the discovery of radioactivity in 1896 by Becquerel [1], while investigating phosphorescence in Uranium salts, which led to the realization that the radioactive elements spontaneously got transmuted into other elements. This discovery was further verified with the identification of radio-activity in some materials by the Curies in 1898. J. J. Thomson , a year later, proposed a model of the atom known as plum pudding model [2] in which it is perceived that the atom is like a large positively charged ball with negatively charged electrons embedded inside it. The model successfully explained the stability of the nucleus but it couldn’t account for the discrete wavelengths that can be observed in the spectra of any excited atom. From the results of the famous α-sattering experiment, performed by Hans Gieger and Ernest Marsden [3], Rutherford in 1911 [4] proposed the existance of the nucleus as a tiny central part of an atom. In 1913 Niels Bohr gave his model [5], which was the modification of Rutherford’s model based on quantum mechanics. This model successfully explained the stability of the nucleus along with the observed spectra from excited atom. Niels Bohr in 1922 recieved the Nobel Prize in Physics for his foundational contributions to atomic spectroscopy and quantum mechanics. Later on, from various experiments finally we reached on a stand that matter is made up of atoms with nucleus as the central part and electrons are revolving arround them in almost central orbits. Almost all the mass of an atom is located in the nucleus, with a very small contribution from the orbiting electrons. There are almost 1700 nuclei found on earth naturally. In addition, a large number of others are created in laboratory by transmutation or in the interior of stars. The first outstanding work on ‘artificial transmutation’ of the nucleus was performed by Rutherford in 1919, using energetic alpha-particles as projectile. Later on, with the development of charged particle accelerators by J.D. Cockroft and E.T.S. Walton[6] in 1932, doors have been opened with 2

1.2. Nuclear Reactions full of possibilities in direction of experimental nuclear physics. Now a days the accelerator physics is so enriched that we can probe deep inside the nucleus and thereby today we know that quarks are the constituents of nucleons, from which the nucleus is formed. The nuclear reactions are the fundamental tool to understand the nucleus. Presently a great motivation to the study of nuclear reaction is given by possibilities of formation of Super Heavy Elements (SHE)[7, 8]. In the following sections complete ideas are given about the different types of nuclear reactions and their dependency on various parameters.

1.2

Nuclear Reactions

A nuclear reaction takes place, when a particularly chosen nuclide (target nucleus) is bombarded by a projectile nucleus of sufficient kinetic energy, to overcome the fusion barrier (Vf us ) between interacting partners. As a result of such an interaction, the projectile and target nuclei come close to each other within the range of nuclear forces, an excited composite system is formed and then it decays to the final stage, consisting of reaction products, like; light ejectile(s) and a residual nucleus followed by the emission of characteristic radiations. A typical nuclear reaction may be represented as; a+X ⇒Y +b+Q

(1.1)

Here, a, X, Y and b are the projectile nucleus, target nucleus, the residual nucleus and the emitted particle, respectively. Where, Q is the energy balance of the reaction. During such a reaction the energy is either evolved or absorbed. The total amount of energy evolved or absorbed is called the “Q-value of the reaction”. The Q-value of the reaction may be written as; Q = (Ma + MX ) − (Mb + MY ) = (Eb + EY ) − (Ea + EX )

(1.2)

Where, Ma , MX , Ea and EX are the masses and energies of particles in the entrance channel; Mb , MY , Eb and EY are the masses and energies of particles in the exit channel. On the basis of Q-value, the nuclear reactions may be categorized as; 3

Chapter 1. Introduction • Exoergic reactions (Q>0), in which energy is evolved, and • Endoergic reactions (Q RN = (R1 + R2 )

Angular momentum (l) l > lN

b ≈ RN b ≤ RN

lN > l > lDIC lDIC > l > lF

b lF

Type of Interaction Rutherford scattering or coulomb excitation Inelastic scattering Trasfer reactions Deep inelastic scattering Fusion (CN formation)

(where RN = R1 + R2 is the sum of radii of interacting partners, and b is the corresponding impact parameter) terms and may be given as, Vef f (r) = Vnucl (r) + Vcoul (r) + Vcent (r)

(1.7)

where; Vnucl (r) is the attractive nuclear potential, however, Vcoul (r) and Vcent (r) are the Coulomb and centrifugal potentials, respectively, which are both repulsive in nature. There are several approaches to represent the complex short range attractive nuclear potential Vnucl (r). The most commonly used form of the nuclear potential is the Woods-Saxon form, which may be given as; vnucl (r) = 1/3

V0 1 + exp( r−R ) a

(1.8)

1/3

Where, R = r0 (AT + AP ), V0 is the depth of the potential, ‘a’ the diffuseness parameter and r0 is generally taken as 1.31f m. The repulsive Coulomb potential VCoul (r) may be expressed as follows; vcoul =

1 Zp ZT e2 4πε0 r

(1.9)

Here, ZP and ZT are the atomic numbers, while RP and RT are the radius of the projectile and the target nuclei, respectively. 8

1.3. Heavy-Ion Induced Rections

3 0 0

f o r

1 3

C +

1 7 5

L u

1 0

l =

3 0

l =

2 5 0

)

l =

e ff

E ffe c tiv e P o te n tia l (V

l =

l =

2 0 0

l = l = l =

1 5 0

l =

1 0 0

2 0 4 0 5 0 6 0 7 0 8 0 9 0

5 0

0 2

4

6

8

1 0

1 2

1 4

1 6

1 8

2 0

R e la tiv e S a p e r a tio n (r )

Figure 1.2: Effective Potential (Vef f (r)) with respect to the relative separation (r), for 13 C +175 Lu.

The repulsive centrifugal potential Vcent (r) is given by; vcent (r) =

}2 l(l + 1) 2µ r2

(1.10)

Here; l is the angular momentum and µ is the reduced mass of the interacting partners. The effective nuclear potential for 13 C +175 Lu reaction is shown in Figure 1.2. The dependence of the reaction probability, for different types of collisions, on the impact parameter ‘b’, can be converted into a dependence on the input angular momenta, using the relation; ~l = p~ × ~b = mp · v~p × ~b

(1.11)

In this expression mp · v~p denotes the asymptotic initial momentum of the projectile nucleus relative to the target nucleus. The different processes dominate in different l-windows and thus the reaction cross-section in different regions 9

Chapter 1. Introduction may be written as; li+1

σli = πλ

2

X

(2l + 1)Tl

(1.12)

li

where, i = 1, 2, ... correspond, respectively, to fusion, deep in-elastic and/or break-up fusion, peripheral collisions, and to Coulomb-excitations. A qualitative picture of the reaction probability (σl ) as a function of entrance channel angular momentum (l) is given in Figure 1.3, for the types of collisions discussed above. As can be observed from Figure 1.3, the area below the dotted segments give the reaction cross-section for CN formation (σCN ), deep inelastic collision (σDIC ), direct reactions (σD ) to the elastic collisions and/or Coulomb excitation (σEL+CE ). As indicated in this figure, different regions are overlapping in

Figure 1.3: Schematic picture of different partial waves contributing to the reaction probability for fusion (CN-formation), deep inelastic collisions, direct reactions of interacting partners. )

different l-values. At present, it is not clear, how large the overlapping regions are for a individual mode of reaction. Further, it is now well established that, 10

1.3. Heavy-Ion Induced Rections in HI-induced reactions at energies near and above the Vf us , some of the most dominant processes are; (i) complete and (ii) in-complete fusion. Brief description of these processes is given in the following sub-sections;

1.3.1

Complete Fusion Reactions

In the complete fusion ( CF ) reaction, a composite system is formed after an initial contact and complete amalgamation of interacting nuclei leading to the formation of an excited composite system. After the equilibration of this system a “compound nucleus” is formed[13, 14, 15], which may decay through the emission of particles and/or γ-radiations depending upon the available excitation energy. For the CN formation to take place, the energy of the projectile must be sufficient enough to overcome the Coulomb barrier and the entrance channel input angular momenta (l) should not exceed the maximum angular momenta 0 ≤ l ≤ lcrit that the composite system can sustain. The lcrit is the upper limit of sustainable input angular momentum by CN[16, 17] . In such a case, the attractive nuclear potential dominates over the sum of repulsive Coulomb and centrifugal potentials. Consequently, the the projectile fuses with target with the involvement of all nucleonic degrees of freedom essentially at the projectile energies comparable to the Vf us or well above it. After the fusion of projectile and the target nucleus, they form a composite nuclear system, which finally leads to the formation of equilibrated compound nucleus. A typical representation of complete fusion reactions is given in Fig.1.4. Some of the signatures of the CF reactions are given below;

Features of CF • Full amalgamation of the projectile and the target nuclei occur for l ≤ lcrit . • Total linear momentum of the projectile is transferred to the composite system and, hence the CF residues recoil at angles very close to the beam direction. 11

Chapter 1. Introduction

P

T

Decay of CN by particle and/or γ-rays

Formation of CN

p n γ

Residual Nucleus

Figure 1.4: A typical representation of Complete Fusion reaction dynamics.

• The mass number and the charge of the composite system is equal to the sum of the mass number and charge of the projectile and the target nuclei. The composite system has pre-determined excitation energy, angular momentum, etc. • The measured excitation functions are satisfactorily reproduced by the statistical model calculations. It has been experimentally observed that the total CF cross-section (σCF ) is smaller than the total reaction cross-section (σR ) at a given projectile energy. Since, l-values are related to the interaction trajectories, therefore, at higher lvalues beyond lcrit or at relatively higher values of impact parameters, minimum mass overlap between projectile and target nuclei takes place, thus entering in 12

1.3. Heavy-Ion Induced Rections the regime of break-up-fusion reactions.

P

pp ps

T

Decay of CN by particle and/or γ-rays

Formation of Composite System

ps

p n γ

Residual Nucleus

Figure 1.5: A typical representation of In-complete Fusion reaction dynamics.

1.3.2

In-Complete Fusion Reactions

In these reactions, a part of the projectile is assumed to fuse with the target nucleus, while remnant flows in the forward direaction without interaction with target nucleus[18, 19, 20]. The concept of such in-complete mass transfer in HI-reactions has originated after the pioneering experimental observation of fast-α-particles by Britt and Quinton[10] at higher energies >10.5 MeV/A. In case of in-complete fusion (ICF) reactions, relatively less nucleonic degrees of freedom are expected to be involved compared to CF . A typical representation of ICF reaction dynamics is given in Fig.1.5. It may be mentioned that, for 13

Chapter 1. Introduction peripheral collisions (at relatively higher l-values) and/or at higher projectile energies, where the centrifugal potential (Vcent ) becomes relatively higher. As such, the nuclear potential is no more strong enough to capture the entire projectile to form the composite system. It may be seen from Figure 1.2, that at l ≤ lcrit , a pocket remains in the potential energy curve, however, the pocket disappears for higher values of l ≥ lcrit . As such, for l ≥ lcrit no fusion can happen unless a part of the projectile is emitted as a spectator (P s ) to provide sustainable input angular momentum[16, 17]. After such an emission, the remnant is supposed to have input angular momenta less than or equal to its own critical limit for fusion. Hence, an excited system is formed with less mass/charge and excitation energy as compared to that formed in CF reactions. This excited composite system then decays via particle (either α-particles or clusters of α-particles, as spectator) and/or γ-emission. Some of the prominent features of ICF reactions, from a qualitative inspection of experimental results are summarized below; Features of ICF • The ICF processes mainly occur for the l-values above the lcrit for CF. • The fused composite system is formed with less mass and charge as compared to the total mass and charge of interacting partners. • The forward recoil velocity of the reaction products formed via ICF has been found to be less than those populated via CF. • The angular distribution of outgoing projectile-like fragments is found to be peaking at forward angles, where the α-particle(s) are emitted with a velocity centered nearly equal to the projectile velocity. The additional break-up degrees of freedom make the fusion process more complicated and the possible reaction processes may participated in the reaction dynamics. Experimentally, it is not possible to distinguish between different processes includes different reaction channels because they might have reached to the same final residues. Hence, the sum of all known reaction channels may be referred to as the total fusion cross-section. 14

1.4. Motivation

1.4

Motivation

Recently, much interest has been shown to study the competition between in-complete fusion (ICF) and complete fusion (CF) as well as on the total fusion, in HI -interactions in the energy regime ≈ 4 − 7 MeV/A [18, 21, 22, 3]. Kauffmann and Wolfgang[29] in 1961 observed strongly forward peaked angular distribution of various light nuclear particles. In 1961, Britt and Quinton[10] found two processes competing in the reaction 16 O +209 Bi at energies ≥ 10 MeV/A. Later, Galin et al.[24], termed these reactions as the incomplete fusion reactions. The spin distribution studies by Inamura et. al.[25, 26], using particle−γ−coincidence technique for the identification of CF and ICF channels. In order to explain the ICF reactions several approaches as, SUMRULE model[27], Break-Up Fusion (BUF) model[28], etc., have been proposed. As a matter of fact, the above existing models qualitatively explain the experimental data particularly at E/A ≥ 10.5 MeV, however, none of these models is able to provide satisfactory reproduction of the ICF data at lower incident energies ≈ 4 − 7 MeV/A, which triggered a resurgent interest to study the underlying reaction dynamics. Since, at present there is no theoretical model, which may explain the ICF data at low energies, therefore there is a need of study these ICF reactions to understand the reaction mechanism and also for the theoretical development in the field. After Britt & Quinton[10], an enormous amount of work has been done by several authors to study ICF and CF mechanism but still a lot of work is left to study the associated mechanism with the formation of ICF residues. Angular distributions is the main key to find the actual procedure that took place behind the formation of the ICF residue. In this direction very firstly Kauffmann and Wolfgang[29] in 1961 observed strongly forward peaked angular distribution of various light nuclear particles. But a lot of work is still left to be done to understand the distribution of evaporating residues and the effect of their trajectories on the other mesurements like FRRD’s and EF’s.

1.5

Overview:

the present work

In order to explore some of the important issues related to the HI-reaction dynamics at energies just above the barrier and well beyond it, experiments 15

Chapter 1. Introduction have been performed at the Inter University Accelerator Center ( IUAC ), New Delhi. In the present work Complete and Incomplete Fusion reactions have been studied with the help of Angular Distribution (AD’s) measurements of 12 C +175 Lu and 13 C +175 Lu systems at 88 MeV. The AD’s for several radio-nuclides produced in 12,13 C +175 Lu systems via CF and/or ICF reactions have been measured employing the activation technique followed by off-line γ-spectroscopy. The experimental details regarding the performed experiments are discussed in chapter 2. After the experimental details, all the resulting assets and the comparative studies have been performed in chapter 3. The outcomes regarding the present study are summarized and discussed in chapter 4. For the clarity of reader, references are given at the end of each chapter.

z z z z

16

Bibliography [1] H. Becquerel, Comptes Rendus, 122, 420 (1896). [2] J. J. Thomson, Philosophical Magazine, 44, 293 (1897) [3] E. Rutherford, The Scattering of α and β Particles by Matter and the Structure of the Atom, Philosophical Magazine. Series 6, vol.21. May 1911. [4] E. Rutherford, Philosophical Magazine, 37,537 (1919); ibid 37, 562 (1919); ibid 37, 571 (1919); ibid 37, 581 (1919). [5] N. Bohr, Nature, 137, 344 (1936). [6] J. D. Cockcroft, and E. T. S. Walton, Proc. R. Soc. London A 137, 229 (1932). [7] R. D. Herzberg, et al., Nature, 442, 896 (2006). [8] Yuri Oganessian, Nature, 413, 122 (2001). [9] S. N. Ghoshal, Phy. Rev. 80, 939 (1950). [10] H.C. Britt and A.R. Quinton, Phys. Rev. 124 (1961) 877. [11] P. E. Hodgson, E. Gadioli and E. Gadioli Ebra, Introductory Nuclear Physics, Chap- ter 23, Clarendron Press, Oxford, 1997. [12] P. E. Hodgson, Introductory Nuclear Heavy Ion Reactions, Chapter 1, Clarendron Press, Oxford, 1978. [13] D. Singh, R. Ali, M. Afzal Ansari, M. H. Rashid, R. Guin and S. K. Das, Phys. Rev. C 79 (2009) 054601

Bibliography [14] D. J. Parker, J. Asher, T. W. Conlon and I. Naqib, Phys. Rev. C 30 (1984) 143. [15] B. Bindu Kumar, S. Mukherjee, S. Chakrabarty, B. S. Tomar, A.Goswami and S. B. Manohar, Phys. Rev. C 57 (1998) 743. [16] J. Wilczynski, K. Siwek-wilczynska, J. van Driel, S. Gonggrijp, D. C. J. M. Hageman, and R. V. F. Janssens, Phys. Rev. Lett. 45, 606 (1980). [17] J. Wilczynski, K. Siwek-Wilczynska, J. Van Driel, S. Gonggrijp, D.C.J.M. Hageman, R.V.F. Janssens, J. Lukasiak, R.H. Siemssen, and S.Y. Van Der Werf, Nucl. Phys. A 373, 109 (1982). [18] Rahbar Ali, D. Singh, M. Afzal Ansari, M. H. Rashid, R. Guin and S. K. Das, J. Phys. G: Nucl. Part. Phys. 37 (2010) 115101. [19] B. S. Tomar, A. Goswami, A. V. R. Reddy, S. K. Das, P. P. Burte, S. B. Manohar and Bency John, Phys. Rev. C 49 (1994) 941; Phys. Rev. C 58 (1998) 3478. [20] Pushpendra P. Singh, Manoj Kumar Sharma, Unnati, Devendra P. Singh, Rakesh Kumar, K. S. Golda, B. P. Singh and R. Prasad, Eur. Phys. J. A 34 (2007) 29. [21] D. Singh, R. Ali, M. Afzal Ansari et. al., Phys. Rev. C 81, 027602 (2010). [22] D. Singh, R. Ali, M. Afzal Ansari, B. S. Tomar, et. al., Phys. Rev. C 83, 054604 (2011). [23] Dharmendra Singh,Mohammad Afzal Ansari et. al., Journal of the Phys. Society of Japan 82 (2013). [24] J. Galin, B. Gatty, D. Guerreau, C. Rousset, U. C. Schlotthauer-Voos, and X. Tarrago, Phys. Rev. C 9, 1126 (1974). [25] T. Inamura, T. Kojima, T. Nomura, T. Sugitate, H. Utsunomiya, Phys. Lett. B 84, 71 (1982). [26] T. Inamura, A. C. Kahler, D. R. Zolnowski, U. Garg, T. T. Sugihara, and M. Wakai, Phys. Rev. C 32, 1539 (1985). 18

Bibliography [27] K. Siwek-Wilczynska, E. H. du Marchie van Voorthuysen, J. van Popta, R. H. Siemssen, and J. Wilczynski, Phys. Rev. Lett. 42, 1599 (1979). [28] T. Udagawa and T. Tamura, Phys. Rev. Lett. 45, 1311 (1980). [29] R. Kauffmann and R. Wolfgang, Phys. Rev. 121, 192 (1961); ibid 121, 206 (1961).

19

Bibliography

20

Chapter 2 Experimental Details

This chapter includes the complete description of the procedures that are taken into account at various stages like, activation technique, target preparation, target irradiation and the callibration of HPGe detector. The systems 12 C+175 Lu and 13 C+175 Lu have been studied at 88 MeV using the 15UD Pelletron accelerator at Inter University Accelerator Centre (IUAC), New Delhi.

2.1

15UD Pelletron Accelerator

The 15UD Pelletron accelerator is a tandem Van de graaff type electrostatic accelerator, which is capable to accelerate any ion from proton to Uranium in the energy span from a few tens of MeV to a few hundred MeV[1]. The accelerator is mounted in a vertical geometry in a stainless steel tank which is 26.5 meter high and the diameter of the tank is 5.5 meter. A typical layout of Pelletron setup is shown in Figure 2.1.

2. Experimental Details

Figure 2.1: 15UD Pelletron setup at IUAC, New Delhi

In Pelletron, negative ions are produced and pre-accelerated to 300KeV in the ion source. The negative ions are injected into robust electrical field inside an accelerator tank crammed with SF6 , highly insulating gas, with the assistance of injector magnet. The beam is accelerated towards the high positive potential terminal, increasing its energy to qVt ,where Vt is the high voltage terminal in million volts and situated at the center of tank. At the terminal, these ions made to pass either through a thin foil or any gas used as stripper that strips few electrons from every negative ion, thereby, changing them into positive ions. Since, the terminal is at high positive potential, the positive ions are now repelled and afterward accelerated beneath the terminal to ground potential. During this process if the charge state of the positive ions, after 22

2.2. Activation Technique passing through strippper, at terminal is ’q’, then the energy picked up by these ions in the acceleration underneath the terminal to the base of the tank is qVt . Therefore, after passing through the two stages of acceleration the final energy of the ion beam is given by, E = E0 + (q + 1)Vt

(2.1)

Where, E0 is the energy of ions before acceleration, q is the charge state after stripping. Finally, the accelerated ion beam is switched to the beam line of the perticular interest with the help of switching magnets.

2.2

Activation Technique

The study of the Heavy-Ion (HI) interactions has been a subject of great interest in Experimantal Nuclear Physics from many years. During the interaction of heavy ion with target nucleus, the composite system formed and decay by emitting one or more protons, neutron and alpha particles, leaving behind the excited evaporation residues, then these evaporation residues emit characteristic γ-rays before decay to ground state. In nuclear physics, reaction cross-section is important quantity to explain the complete and incomplete fusion reaction dynamics in heavy ion interaction. Once the reaction cross section is determined, we can utilize these results for the measurement of the yield of the residues produced in a particular reaction. That may be done by using the two famous techniques. 1. In-Beam measurements 2. Off-line measurements In In-Beam measurements the outgoing particles and the residual nuclei are detected and identified by various methods either directly from the chargeto-mass ratio or using coincidence technique, in which particle-γ or γ − γ coincidence methods are employed. To do so, particle detectors are placed at a certain angle from the beam path to collect the particles scattered at that angle covering a small solid angle subtended by the projected area of the detector. However, in off-line measurements, the populated residues are 23

2. Experimental Details collected in catcher foils kept behind the target and are identified by detecting their characteristic γ-rays. This technique is called activation technique[2, 3]. Activation technique is a technique of measuring the concentrations of radioactive nuclei in a given sample by detecting their characteristics γ-rays. The unique decay mode of each radioactive isotope provides a specific way for its measurement and identification. In this technique the sample is irradiated in a fixed geometry by placing the target material normal to the incident beam. The activities in the samples can be induced by their bombardment with light particles, heavy ions or radiations. Off-line method has a relatively low back-ground as compared to that of the In-Beam method thereby the better sensitivity. The biggest advantage of the activation technique is the possibility of measuring cross-sections for the production of a large number of residues in a single irradiation thereby reduces beam-time requirements. In the situation of mixing of γ-rays, which are producing from various radio nuclides, the induced activities from each nuclide can be separated out on the basis of their half-lives and activities for a considerably longer duration[4, 5] . However the off-line measurement is efficient only for the reaction products having the measurable and convenient half-lives. For the reaction products having the similar γ-ray energies and same half life the Beam measurement becomes even more complicated. Also, the precise knowledge of γ-ray energies and complete decay schemes of the residual nuclei is essential for the activation analysis.

2.3

Target preparation

The preparation of target with the required dimensions and thickness is very essential requirement of any experiment related to nuclear physics. Spectroscopically pure self supporting target of stable Lutetium, in the form of thin foil was prepared by rolling method at Target Lab, IUAC, New Delhi. 175 Lu target material was rolled by keeping it inside a folded stainless steel strip. This procedure of rolling was rehashed over and over to accomplish desired thickness ≈ 1.46 mg/cm2 . On other hand, Al-catcher rings of thickness ranging from 0.4 − 0.5mm with different annular ranges were prepared from a sheet of Aluminium. The thickness, inner and outer radius and annular ranges of each ring for both set-up’s used in 12 C+175 Lu and 13 C+175 Lu, is given in Table 24

2.3. Target preparation 2.1 and 2.2 respectively. The schematic diagram of annular rings is shown in Figure 2.2.

Tantalum Collimator

θ2 r1

Al Degrader

θ1

Lu 1.46 mg/cm2 175

Al - Annular Rings 1.6 cm

Figure 2.2: Annular-Catcher Rings

25

4 cm

Ion-Beam

r2

2. Experimental Details Table 2.1: Details of Al annular catcher rings used for

Ring 1 2 3 4 5

Inner Radius r1 (cm) 3.92 6.47 9.017 11.52 15.12

Outer Radius r2 (cm) 6.47 9.017 11.52 15.12 20.0

Thickness (mm) 0.446 0.5 0.456 0.450 0.473

1 2 3 4 5 6

Inner Radius r1 (cm) 0.0 3.92 6.47 9.017 11.52 15.12 ∗

Outer Radius r2 (cm) 3.92 6.47 9.017 11.52 15.12 20.0

Thickness (mm) ∗ 0.446 0.5 0.456 0.450 0.473

+ 175 Lu

Annular Range θ1 − θ2 11.93 - 19.22 19.72 - 26.55 27.13 - 33.20 33.93 - 41.45 42.26 - 50.23

Table 2.2: Details of Al annular catcher rings used for

Ring

12 C

13 C

+ 175 Lu

Annular Range θ1 − θ2 0.0 - 11.64 11.93 - 19.22 19.72 - 26.55 27.13 - 33.20 33.93 - 41.45 42.26 - 50.23

Al-Degrader of thickness ≈ 1.4mg/cm2 was used

An exact learning of the thickness of the objective is vital for the total estimation of cross-section of reaction products. The thickness of the target foil was determined by using microbalance as well as from α-transmission method. The transmission method is based on the measurement of the energy lost by α-particles of energy 5.487M eV obtained from standard 241 Am source while passing through the target material. The rolled target foil was then cut into size of 1.2 x1.2 cm2 and pasted on Al-target holders having concentric hole of 10 mm diameter. Tantalum coating was applied in the form of a foil of same dimensions with the hole at the center, to avoid the interaction of beam with the target holder material. 26

2.4. Target Irradiation

2.4

Target Irradiation

In the present work, our aim is to measure the Angular Distribution of evaporation residues resulting from the bombardment of 12 C and 13 C on 175 Lu target. Therefore to trap evaporation residues, annular Al-catcher rings of thickness ≈0.5 mm to cover the annular range from 0o − 52o are placed after 175 Lu-target. The 175 Lu-target along with the catcher rings were irradiated with 12 C and 13 C beams saperately for about 8 -10 hours in the General Purpose Scattering Chamber (GPSC), IUAC, New Delhi. The typical arrangement of GPSC and the source-detector assembly are shown in Figure 2.3 and Figure 2.4. Behind the target-catcher assembly Faraday cup was placed to collect charge.

Figure 2.3: General Purpose Scattering Chamber used for target irradiation

27


Figure 2.4: Source detector assembly used for spectrum recording

2.5

High purity Germanium (HPGe) Detector

Germanium detectors are mostly used for γ-spectroscopy in nuclear physics, as well as X-ray spectroscopy[6]. Germanium can have a depleted, sensitive thickness of centimeters, and therefore can be used as a total absorption detector for gamma rays up to few MeV. These detectors are also called highpurity germanium detectors (HPGe) or hyperpure germanium detectors. Before the development of purification techniques, germanium crystals could not be produced with purity sufficient to enable their use as spectroscopy detectors. Impurities in the crystals trap electrons and holes, ruining the performance of the detectors. Consequently, germanium crystals were doped with lithium ions (Ge(Li)), in order to produce an intrinsic region in which the electrons and holes would be able to reach the contacts and produce a signal. In solid state radiation detectors, when radiation passes, equal numbers of electron-hole pairs are created along its track. The generated charge is collected by applying an electric field which produces a voltage pulse. When forward biased, even in the absence of ionizing radiation, large current will flow across 28

2.5. High purity Germanium (HPGe) Detector the semiconductor due to thermal excitation.

Figure 2.5: Schematic diagram of HPGe Detector

This current will obscure the small current due to ionizing radiation. Whereas in case of a reverse biased junction, the current flowing through the semiconductor is negligible and the ionization current can be detected. Moreover, the sensitive volume of the detector i.e. the thickness of the depletion region is more, so that the semiconductors are generally reverse biased to be used as radiation detectors. A schematic diagram of HPGe detector is shown in Figure 2.5 [7]. The major drawback of Germanium detectors is that they must be cooled to liquid Nitrogen temperatures to produce spectroscopic data. At higher temperatures, the electrons can easily cross the band gap in the crystal and reach the conduction band, where they are free to respond to the electric field, producing too much electrical noise to be useful as a spectrometer. Cooling to liquid nitrogen temperature, 77K reduces thermal excitations of valence electrons so that only a γ-ray interaction can give an electron the energy necessary to cross the band gap and reach the conduction band. Cooling with 29

2. Experimental Details liquid Nitrogen is inconvenient, as the detector requires hours to cool down to operating temperature before it can be used, and cannot be allowed to warm up during use. Ge(Li) crystals could never be allowed to warm up, as the lithium would drift out of the crystal, ruining the detector. HPGe detectors can be allowed to warm up to room temperature when not in use, hence preferred.

2.5.1

Resolution and Energy calibration of the Detector

Since, the characteristic γ-rays from the recoiled residues have low energies and considerable amount of intermixing is also found in the recording process of spectra, therefore, the detector with high resolution must be used. In present experiment, we made utilization of High purity Germanium HPGe detector of resolution 2.3 keV for 1408 MeV γ-ray of 152 Eu having 100cc active volume coupled to a PC through CAMAC based CANDLE software [8, 9] at IUAC, New Delhi. The HPGe detector has been calibrated using the gamma ray source 152 Eu, of known strength. The 152 Eu source may decay by emission of various intense and well resolved γ–rays having the energy range from 120 keV to about 1410 keV. The prominent γ-rays that are utilized in the calibration of detector along with their intensities are listed in Table 2.3 and characteristic gamma ray energy spectrum of 152 Eu observed is displayed in Figure 2.6.

2.5.2

Efficiency of Detector

The efficiency of the HPGe detector is determined by using the same 152 Eu source. The variation of the efficiency with γ-ray energy for detectors is geometry in dependent, while their absolute values depends on geometry. The geometry dependent efficiency of the detector at a given energy is given by the relation, εG =

N0 Na0 θexp(−λt)

(2.2)

where N0 is the disintegration rate of the γ-ray source at the time of experiment, Na0 is the absolute disintegration rate of 152 Eu γ- ray source at the time of manufacturing, λ is the decay constant, t is the time interval between the date of manufacturing and observation, θ is the absolute intensity of the 30

2.5. High purity Germanium (HPGe) Detector Table 2.3: Gamma rays along with their absolute intensities for source

S. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

152 Eu

γ-Ray Energy (Kev) Absolute Intensity (θ) 121.8 244.7 344.3 411.1 444.0 778.9 867.4 964.1 1085.9 1089.7 1112.1 1213.0 1299.1 1408.0

28.6 7.6 26.5 2.2 2.8 12.9 4.2 14.2 10.2 1.7 13.6 1.4 1.6 21.0

particular γ-ray. The source-detector assembly is shown in Figure 2.3(b). The standard Source and the annular catcher rings after irradiation were counted using the detector setup shown in Figure 2.3. The typical geometry dependent efficiency curves as a function of γ-ray energies at different source-detector angles obtained for 12 C and 13 C beams are shown in Figure 2.7 and 2.8 respectively. A polynomial of degree five having the following form was found to give the best fit for these curves. G = a0 E 0 + a1 E 1 + a2 E 2 + a3 E 3 + a4 E 4 + a5 E 5

(2.3)

Where a0 , a1 , a2 , a3 , a4 and a5 are the constants depending on the sourcedetector distances and can be determined by least square fit and E is the energy of the characteristic γ-ray.

31

C o u n ts

1 2 1 .8 K e V

5

1 0 4

1 0 3

1 0 2

2 0 0 0 4 0 0 0

z z z z

32

C h a n n e l N u m b e r 6 0 0 0

Figure 2.6: The observed γ-ray spectrum of 152 Eu

1 4 0 8 K e V

1 2 1 3 K e V

7 7 8 .9 K e V

3 4 4 .3 K e V

1 1 2 1 .1 K e V

1 0 8 9 .8 K e V

1 0 8 5 .8 K e V

9 6 4 K e V

8 6 7 .4 K e V

4 4 4 K e V

4 1 1 .1 K e V

1 0 2 4 4 .7 K e V


2.5. High purity Germanium (HPGe) Detector

0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

0

0 .0 7

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

0 .0 4

a t 1 0 m m

1 4 0 0

1 6 0 0

a t 3 5 m m

0 .0 6 0 .0 3

0 .0 5 0 .0 4

0 .0 2

0 .0 3 0 .0 2

0 .0 1

E ffic ie n c y

0 .0 1 0 .0 0 0 .0 7

a t 2 0 m m 0 .0 6

0 .0 0

a t 4 0 m m

0 .0 3

E ffic ie n c y

0 .0 5 0 .0 2

0 .0 4 0 .0 3 0 .0 2

0 .0 1

0 .0 1 0 .0 0 0 .0 0 0

a t 3 0 m m

0 .0 4

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

E n e rg y (k e V )

0 .0 3

0 .0 2

0 .0 1

0 .0 0 0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

E n e rg y (k e V )

Figure 2.7: Efficiency plots for HPGe detector(1) at different distances of source from the axis of detector

33


0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

0

2 0 0

1 6 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

0 .0 6

A t 8 m m

0 .0 6

a t 2 3 m m

0 .0 4 0 .0 4

0 .0 2 0 .0 2

0 .0 0

0 .0 0 0 .0 8

0 .0 6

a t 3 0 m m

a t 1 3 m m

E ffic ie n c y

E ffic ie n c y

0 .0 6

0 .0 4

0 .0 4

0 .0 2

0 .0 2

0 .0 0

0 .0 0

0 .0 4

a t 4 0 m m

a t 1 8 m m

0 .0 6

0 .0 3 0 .0 4 0 .0 2

0 .0 2 0 .0 1

0 .0 0 0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

E n e rg y (k e V )

0 .0 0 0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

E n e rg y (k e V )

Figure 2.8: Efficiency plots for HPGe detector(2) at different distances of source from the axis of detector

34

Bibliography [1] D. Kanjilal, S. Chopra, M. M. Narayanan, I. S. Iyer, V. Jha, R. Joshi, and S. K. Datta,Nucl. Instr. and Meth A 328 (1993) 97. [2] E. V. Sayre, Ann. Rev. Nucl. Sci., 13 (1963)145. [3] R.C. Kotch, Activation Analysis Hand Book, Academic Press, New York and London, 1960. [4] E. Gadioli et al, Nuclear Science Research Conference Series, Vol. 12, eds. Z. Wilhelmi and G. Szeflinska, Harwood Academic, London, (1987). [5] D.J. Parker et al., in proceeding of the 5th Intern. Conf. on Nuclear Reaction Mechanism, ed. E. Gadioli, Ricerca Scientifica de Educazione Permanente, Suppl. 66 (Milano, 1988). [6] G.F. Knoll, Radiation Detection and Measurement 3 rd edition (Chapters 12 and 13), John Wiley & Sons, 1999. [7] HPGe Detector Manufacturing, ORTEC, http://www.ortec-online.com. [8] CANDLE: Data Acquisition and Analysis System designed to support the accelerator based experiments at the Inter University Accelerator Centre, New Delhi, India. [9] E. T. Subramaniam, B. P. AjithKumar, and R. K. Bhowmik,http://www. iuac.res.in/NIAS.

Bibliography

36

Chapter 3 Measurements

This chapter includes all the outcomes, that came into picture after all the stages of the experiment and the post irradiation analysis of data. The outcomes from the analysis of Angular Distributions of 12 C +175 Lu and 13 C +175 Lu systems are shown and listed in the respective tables, based on the outgoing reaction channels.

The present experiment to study Angular Distributions of evaporation residues was performed at Inter University Accelerator Centre (IUAC), New Delhi, for the study of dependency of cross-sections of evaporation residues on recoiling angle, formed in incomplete fusion reactions using 12 C and 13 C projectiles with 175 Lu at 88M eV energy.

3. Measurements

3.1

Identification of Evaporation Residues

As a result of irradiation of target foil, evaporated residues thus formed, trapped in the followed annular catcher rings therefore buildup sufficient γ-activity for further recording of spectra. The activities of these rings were recorded spaerately using a pre-calibrated 100cc HPGe detector coupled to PC based data acquisition system. The evaporation residues are identified with the help of observed photo peaks in the recorded spectra of both the systems. To be very specific, since each radioactive isotope has its own decay mode, thus, the observed intensity of the identified γ-ray is a measure of production cross-section. Since, several residues may have nearly the same energy therefore the identification of residues was further confirmed by following their respective half-lives. The half-live curves for few residues produces in 12 C+175 Lu as well as in 13 C+175 Lu are shown in figures 3.1 and 3.2 respectively.

1000 175

12

182

Lu( C, p4n) Os E = 180.2 keV

Counting Rate

100

t 1/2 = 21.6 h = 77760 sec

10

1 0

100000

200000

300000

400000

Lapse Time (sec)

Figure 3.1: Half-life plot of

182 Os

38

residue for

12 C

+175 Lu

3.2. Formulation

1000 175

13

183m

40000

50000

Counting Rate

Lu( C, p4n) Os E = 1108.13 keV

100

t 1/2 = 9.9 h = 35640 sec

10 0

10000

20000

30000

60000

Lapse Time (sec)

Figure 3.2: Half-life plot of

3.2

183m Os

residue for

13 C

+175 Lu

Formulation

Irradiation of target by a particle beam may initiate various prosesses in it. As a result many isotopes are formed by the emission of some particles and the residual nuclei are left in the excited state. The residual nuclei may deacy through their characteristic γ-rays. If φ is the flux of incident beam, N0 is the initial number of nuclei present in the target and σr is the activation crosssection for a particular channel, the rate of decay of the activation product may be given by, N = N0 φσr (3.1) The disintigration rate of the induced activity in the sample after a time t since the irradiation was over may be given by the expression,

dN dt

t

=N

[1 − exp(−λt1 )] exp(λt)

(3.2)

where t1 is the time duration of irradiation of target and λ is the decay constant of induced activity of the residual nuclei which is related with the half-life (T1/2 ) 39

3. Measurements by the expression,

ln2 T1/2

λ=

(3.3)

The factor [1 − exp(−λt1 )] is called the saturation correction. It should also be considered that the radioactive nuclei produced might also decay during the irradiation time. The number of radioactive nuclei decays in a very small time interval dt can be written as, dN = N [1 − exp(−λt1 )exp(−λt)dt

(3.4)

If the induced activity in the irradiated sample is recorded for a time t3 after a lapse time t2 , then the total number of nuclides decayed during the time t2 to t2 + t3 is given by Z C=

t2 +t3

C = N [1 − exp(−λt1 )]

Z t2 +t3

exp(−λt)dt

t2

(3.6)

[1 − exp(−λt3 )]) λexp(λt2 )

(3.7)

[1 − exp(−λt1 )][1 − exp(−λt3 )] λexp(λt2 )

(3.8)

C = N [1 − exp(−λt1 )] C=N

(3.5)

dN

t2

If the induced activity in the sample is recorded by a suitable γ-ray spectrometer having geometry dependent efficiency (εG ), then absolute counting rate ’C’ and the observed counting rate ’A’ may be related as, C=

A (εG )θK

(3.9)

where, θ is the branching ratio of the characteristic γ-ray, K is the self absorption correction factor for the γ-ray in the target and is given as, K=

[1 − exp(−µd)] µd

(3.10)

where, µ is the γ-ray absorption coefficient for the target and d is the 40

3.2. Formulation thickness of the target. Thus, the reaction cross-section σr (E) of the evaporation residue (ERs ), at a given beam energy E can be written as, σr (E) =

Aλexp(λt2 ) N0 φ(εG )θK[1 − exp(−λt1 )][1 − exp(−λt3 )]

(3.11)

where, A is the number of counts under the photo-peak of the characteristic γ-ray. A program based on above formulation, has been used for the calculation of measured reaction cross-section of the populated evaporation residues. The residual nucleus of a particular reaction may in general emit γ-ray of more than one energy. In such cases, the cross-section for the same reaction is determined separately from the observed intensities of γ -rays of different energies originating from the same residue. The weighted average of the crosssection is taken as the final experimental value. The following formulation has been used for determining the weighted average cross-sections. If σ1 , σ2 , σ3 , ......, σn are the measured cross-section and 4σ1 , 4σ2 , 4σ3 ,......, 4σn , are the respective experimental cross-sections for the same reaction due to different γ-rays, then σ1 ± 4σ1 , σ2 ± 4σ2 , σ3 ± 4σ3 ,......, σn ± 4σn are the experimentally measured cross -section for a given reaction due to different γ-rays. Therefore, the weighted average cross-section (σ) is determined as, P

wi σi σ= P wi

(3.12)

1 (4σi )2

(3.13)

where, wi =

The internal error I.E. is given by, I.E. =

X

− 1

wi

2

Thus the I.E. entirely depends on the individual observations. However, the external error E.E. is given by, 41

(3.14)

3. Measurements

wi (σi − σi ) E.E. = P n(n − 1) wi P

1 2

(3.15)

Which depends on difference between observed and the mean value. Therefore, the internal error depends on the internal consistency , whereas the external error is a function of external consistency of the observations. These error calculations have also been incarporated in the computation of desired cross-sections at different γ energies.

3.2.1

Uncertainities in Measurement

The errors in the measured production cross-sections may arise mainly due to following reasons; • Fluctuations in the beam current may result in the variation of incident flux. Proper care has been taken to minimize the beam current fluctuations as far as possible and, corrections in flux determination have been applied. • The non-uniform thickness of samples may lead to the uncertainty in the determination of the number of target nuclei. To check the uniformity of the sample, thickness of the each sample was measured at different positions by the α-transmission method. It is estimated that the error in the thickness of the sample material is ≤ 1%. • Uncertainty in the determination of geometry dependent efficiency of γ-spectrometer. The error in the efficiency determination due to the statistical fluctuations in counts is estimated to be ≤ 2% for the present measurements. • The loss of the product nuclei recoiling out of the sample may introduce large errors in the measured cross-sections. In order to reduce it, the thickness of the catcher foils was kept sufficient to stop even the most energetic residues populated in complete momentum transfer events. Moreover, in the present measurements both the sample and the catcher foils were counted together and hence, the loss due to the recoiling of nuclei is further avoided. 42

3.3. Measurements • The dead time of the spectrometer may also introduce errors in the measured cross-sections. The dead time of the spectrometer in the present measurements has been kept ≤ 10% by suitably adjusting sample-detector distance and corrections for it were applied. The overall errors from all the aforementioned factors are estimated to be ≤ 15%, including statistical errors. These errors exclude the uncertainty of the nuclear data like branching ratio, decay constant etc., which have been taken from the Table of Isotopes [1, 2]. The detailed information regarding the errors in the measurements are also given in our group reference [3].

3.3

Measurements

The cross-section of various ER’s populated in both systems have been calculated using the following expression[4], given in section 3.2, σr (E) = A

λexp(λt2 ) N0 φ(εG )θK[1 − exp(−λt1 )][1 − exp(−λt3 )]

(3.16)

The calculated production cross-sections for each ER in given in saperate tables in the following sections 3.1.1. The Q-Value for various reactions have been calculated using Atomic Mass table of Wapstra and Grove[5]. The various spectroscopic inputs such as half-life, absolute γ-ray intensity, γ-ray energies and J π of the residues are taken from Table of Isotopes[6, 7] and Nuclear Wallet Card[8]. The evaporation residues found to be produced in the interaction of 12 C and 13 C with 175 Lu are tabulated in table 3.1 and the recorded spectra for 13 C +175 Lu and 12 C +175 Lu systems are also shown in Figure 3.3 and Figure 3.4.

3.3.1

xn and pxn Channels

The excited CN may decay through various decay modes, which can be, through emitting neutrons, protons, neutrons and protons both or a cluster of these particles along with the α-particles. Therefore, on the basis of these outgoing channels the evaporation residues may be classified as xn, pxn and α-emitting 43

3. Measurements Table 3.1: List of identified Reaction Residues (channels) alongwith their spectroscopic properties

Reaction Residue

Channel 13 C C

12

Half-life T1/2

SpinP arity Jπ

Eγ (KeV)

Intensity ‡ (I γ )

119.7 390.3 228.5 282.4 392.4 126.9 273.1 114.4 167.9 381.78 1102.8 1108.1 180.2 263.3 238.6 242.7 162.3 1121.3 1189.1 1221.4 229.3 351.0 360.7 365.5 289.9 430.2 106.06

30.3 25.7 6.9 4.9 10.4 34.4 43.0 20.7 7.7 77.0 52.0 23.8 34.7 6.6 44.0 6.1 24.0 31.8 14.8 25.0 29.0 11.1 20.0 57.0 26.9 28.0 23.1

184

Ir

*

(4n)

3.0 h

5−

183

Ir

(4n)

(5n)

57 m

5− 2

182

Ir

(5n)

(6n)

15 m

5+

183g

Os

(p3n)

(p4n)

13.0 h

9+ 2

(p3n)

(p4n)

9.9 h

1+ 2

183m

Os

182

Os

(p4n)

(p5n)

21.6 h

0+

181

Os

(p5n)

*

1.8 h

1− 2

Re 182m Re

(α) (αn)

* (α2n)

70 d 64.0 h

5+ 2 +

7

182g

Re

(αn)

(α2n)

12.7 h

2+

181

Re

(α2n)

(α3n)

19.9 h

5+ 2

179

Re

(α4n)

(α5n)

19.7 m

5+ 2

178

Re

(α5n)

*

13.2 m

3+

183

h = hours, m = minutes, d = days, ‡ intensities are absolute, Residues marked by (*) could not observed 44

3.3. Measurements

Figure 3.3: Observed γ-ray spectrum of 175 Lu irradiated with 13 C beam at 88 MeV energy.

45

3. Measurements

Figure 3.4: Observed γ-ray spectrum of 175 Lu irradiated with 12 C beam at 88 MeV energy.

46

3.3. Measurements channels. when the excited CN decay via a number of neutrons or with both neutron and proton the mode of production is said to xn and pxn channel and the residue thus formed must have, the maximum linear momentum transferred from the CN and since the emission of a number of neutrons takes place therefore, the emission of neutrons from CN may be symmetric in 4π geometry. In the present experiment following reactions are found to be present as case of study;

xn Channels Following reactions are found to go through the decay of CN via emitting neutrons... Lu[13 C, 4n]184 Ir, 175 Lu[13 C, 5n]183 Ir and 175 Lu[13 C, 6n]182 Ir 175 Lu[12 C, 4n]183 Ir and 175 Lu[12 C, 5n]182 Ir.

175

Out of these, the variation of production cross-sections with recoiling angles for the reactions residues 184 Ir, 183 Ir and 182 Ir are given in Tables 3.2, 3.3 and 3.4 respectively. Table 3.2: Measured differential cross-sections for

Annular Range (deg)

184 Ir

Diff. cross-sections (mb/deg) 175

0.0 - 11.6 11.9 - 19.2 19.7 - 26.5 27.1 - 33.2 33.9 - 41.4 42.2 - 50.2

Lu[13 C, 4n]184 Ir 1.76 ±0.28 0.93 ±0.21 0.601 ±0.13 0.47 ±0.07 0.35 ±0.025 0.26 ±0.03

47

residue

3. Measurements Table 3.3: Measured differential cross-sections for

Annular Range (deg)

Residue


Lu[12 C, 4n]183 Ir

0.0 - 11.6 11.9 - 19.2 19.7 - 26.5 27.1 - 33.2 33.9 - 41.4 42.2 - 50.2

175

2.01 ±0.22 1.04 ±0.26 0.94 ±0.13 0.82 ±0.13 0.49±0.05

Lu[13 C, 5n]183 Ir 22.82 ±0.59 12.48 ±0.13 9.23 ±0.40 8.06 ±0.23 4.74 ±0.21 2.09 ±0.15

Table 3.4: Measured differential cross-sections for

Annular Range (deg)

183 Ir

182 Ir

Residue

Diff. cross-sections (mb) 175

Lu[12 C, 5n]182 Ir

0.0 - 11.6 11.9 - 19.2 19.7 - 26.5 27.1 - 33.2 33.9 - 41.4 42.2 - 50.2

175

23.62±1.28 15.20±0.45 11.64±0.52 8.64±0.54 4.33±0.18

Lu[13 C, 6n]182 Ir 41.06 ±2.71 19.20 ±3.14 10.34 ±4.61 6.05 ±0.90 3.79 ±0.51 1.94 ±0.27

pxn Channels Following reactions are found to go through the decay of CN via emitting neutrons alongwith the protons ...

175

Lu[13 C, p4n]183(m+g) Os,

175

175

Lu[12 C, p3n]183(m+g) Os,

Lu[13 C, p5n]182 Os,

175

Lu[12 C, p4n]182 Os and 48

175

Lu[12 C, p5n]181 Os.

3.3. Measurements Out of these, the variation of production cross-sections with recoiling angles for the reaction residues 183 Os, 182 Os and 181 Os are shown in Tables 3.5, 3.6 and 3.7 respectively.


Annular Range (deg)

175

Lu[12 C, p3n]183 Os

175

2.899 ±0.19 2.014 ±0.26 2.223 ±0.07 2.003 ±0.03 0.86±0.86

Lu[13 C, p4n]183 Os 33.6±1.13 20.72 ±0.73 13.89 ±0.52 12.05 ±0.47 7.1 ±0.65 3.92 ±0.63


Annular Range

0.0-11.6 11.9-19.2 19.7-26.5 27.1-33.2 33.9-41.4 42.2-50.2

Residue

Diff. cross-sections (mb/deg)

0.0-11.6 11.9-19.2 19.7-26.5 27.1-33.2 33.9-41.4 42.2-50.2

(deg)

183 Os

182 Os

Residue


Lu[12 C, p4n]182 Os 14.69±0.45 11.52±0.30 12.01±0.52 11.94±0.75 4.62±0.17

49

175

Lu[13 C, p5n]182 Os 29.26 ±2.12 18.08 ±0.66 12.54 ±0.46 11.78 ±0.42 7.046 ±0.25 3.54 ±0.13


Annular Range (deg)

181 Os

Residue


0.0-11.6 11.9-19.2 19.7-26.5 27.1-33.2 33.9-41.4 42.2-50.2

Lu[12 C, p5n]181 Os 2.366 ±0.178 1.708 ±0.09 2.00 ±0.19 2.12 ±0.09 0.70 ±0.05

α-Emitting Channels The decay of CN with emitting α, 2α and α along with neutrons and protons as partners is the main course of present study. At low projectile energies the incomplete fusion process comes in play very strongly and starts competing with the complete fusion. As discussed earlier, projectile break-up takes place for the lagrer values of impact perameter, consequently one of the fragment fuses with the target and form CN with less excitation energy and the remainant takes away a significant amount of projectile energy. Therefore, the residues thus formed as a result of ICF reactions have much less linear momentum and hence less forward velocity, as compared to those formed with CF reactions. Since, the forward velocity is less, the distribution of ICF residues may not be symmetric in 4π geometry. Therefore, it is interesting to have some clearer picture that, “do these residues have any angular dependency ?” Following residues are found to produced via α channels in different reactions. The production cross-sections of residues having similar channel are listed and compared below. 175

Lu[13 C, α2n]182(m+g) Re,

175

Lu[13 C, α3n]181 Re and 50

175

Lu[13 C, α5n]179 Re.

3.3. Measurements 175

Lu[12 C, α]183 Re, 175 Lu[12 C, αn]182(m+g) Re, 175 Lu[12 C, α2n]181 Re, Lu[12 C, α4n]179 Re and 175 Lu[12 C, α5n]178 Re.

175

The variation of production cross-sections with recoiling angles for the reaction residues 183 Re, 182 Re, 181 Re, 179 Re and 178 Re are listed in Tables 3.8-3.12.


Annular Range (deg)

Lu[12 C, α]183 Re

0.0-11.6 11.9-19.2 19.7-26.5 27.1-33.2 33.9-41.4 42.2-50.2

2.16 2.27 2.54 3.36 0.83

±0.24 ±0.22 ±0.22 ±0.16 ±0.15


(deg) 0.0-11.6 11.9-19.2 19.7-26.5 27.1-33.2 33.9-41.4 42.2-50.2

Residue


Annular Range

183 Re

182 Re

Residue

Diff. cross-sections (mb) 175

Lu[12 C, αn]182 Re 2.78 ±0.47 2.18 ±0.36 1.46 ±0.38 2.015 ±0.37 0.76 ±0.11

51

175

Lu[13 C, α2n]182 Re 6.95 5.22 4.52 6.60 1.78 1.05

±0.83 ±0.83 ±0.56 ±0.74 ±0.30 ±0.18


Annular Range (deg)

181 Re

Residue


Lu[12 C, (α2n)]181 Re

0.0-11.6 11.9-19.2 19.7-26.5 27.1-33.2 33.9-41.4 42.2-50.2

175

Lu[13 C, (α3n)]181 Re

4.30 ±0.99 3.046 ±0.11 2.68 ±0.67 4.69 ±0.38 1.18 ±0.22

1.40 ±0.29 0.86 ±0.06 0.49 ±0.06 0.911 ±0.09 0.33 ±0.02 0.21 ±0.03


Annular Range (deg)

179 Re

Residue


Lu[12 C, α4n]179 Re

0.0-11.6 11.9-19.2 19.7-26.5 27.1-33.2 33.9-41.4 42.2-50.2

3.22 1.22 0.98 1.36 0.34

175

Lu[13 C, α5n]179 Re

±0.37 ±0.10 ±0.10 ±0.04 ±0.03

3.53±0.06 2.089±0.10 1.77±0.11 2.50±0.10 0.68±0.03 0.16±0.006


Annular Range (deg)

178 Re


0.0-11.6 11.9-19.2 19.7-26.5 27.1-33.2 33.9-41.4 42.2-50.2

Lu[12 C, α5n]178 Re 3.66 ±0.30 1.77 ±0.33 0.65 ±0.11 0.914 ±0.09 0.53 ±0.02

52

Residue

Bibliography [1] Website : http://www.nndc.bnl.gov [2] E. Brown and R. B. Firestone, Table of Isotopes, Wiley, New York, 1986. [3] Dharmendra Singh,Mohammad Afzal Ansari et. al., Journal of the Phys. Society of Japan 82 (2013). [4] M. Afzal Ansari, R. K. Y. Singh, M. L. Sehgel, V. K. Mittal, D. K. Avasthi, Ann. Nucl. Energy 11 (1984) 173. [5] H. Wapstra and N. B. Grove, Nucl. Data Tables A9 (1971) 303. [6] Website : http://www.nndc.bnl.gov [7] E. Brown and R. B. Firestone, Table of Isotopes, Wiley, New York, 1986. [8] J. K. Tuli, Nuclear Wallet Card, National Nuclear Data Center, Brookhaven National Laboratory, Upton, New York, USA (2000).

Bibliography

54

Chapter 4 Results and Discussions

This chapter deals with the angular distributions of evaporation residues, recoiled in annular Al rings at different angles. It included the final outcomes of the present work, which is followed by the discussions based on the results obtained. Furthermore, the residues are interpreted in the framework of Complete fusion (CF) and/or In-Complete Fusion (ICF) process.

As already mentioned, the angular distributions of heavy-ion reaction products may provide useful insight into the involved reaction dynamics[1]. The Angular Distributions of heavy-ion reaction products produced in the 12 C +175 Lu and 13 C +175 Lu systems have been measured at projectile energy ≈88 MeV. Angular distributions of several residues populated via xn, p-xn and α-xn emission channels have been measured for both systems. In case of 12 C +175 Lu system, the populated residues are as follows;

4. Results and Discussions Lu[12 C, 4n]183 Ir, 175 Lu[12 C, 5n]182 Ir, 175 Lu[12 C, p3n]183(m+g) Os, 175 Lu[12 C, p4n]182 Os, 175 Lu[12 C, p5n]181 Os, 175 Lu[12 C, α]183 Re, 175 Lu[12 C, αn]182(m+g) Re, 175 Lu[12 C, α2n]181 Re, 175 Lu[12 C, α4n]179 Re and 175 Lu[12 C, α5n]178 Re.

175

On the other hand, in case of are as follows;

13

C +175 Lu system, the populated residues

Lu[13 C, 4n]184 Ir, 175 Lu[13 C, 5n]183 Ir, 175 Lu[13 C, 6n]182 Ir, 175 Lu[13 C, p4n]183(m+g) Os, 175 Lu[13 C, p5n]182 Os, 175 Lu[13 C, α2n]182(m+g) Re, 175 Lu[13 C, α3n]181 Re and 175 Lu[13 C, α5n]179 Re.

175

The details regarding the residues identification from the decay curve analysis have been provided in chapter 3. The cross-sections for each residue have been measured at different recoiling angles and also given in respected tables of chapter 3. In order to neutralize the effect arised due the annular ring’s geometry, the measured corss-sections are then normalized with respect to the recoiling angles sustained by a respective annular catcher ring.

4.1

Discussions

From the angular distribution measurements, one may differentiate the CF and ICF processes on the basis of specific angular distribution, which is associated with the various recoiling angles. Fused fragment mass plays an important role in the recoiling of evaporation residues at different angles. Entire mass transfer may give rise to maximum excitation energy to the compound nucleus (CN). On the other hand, partial mass transfer results in the lesser excitation energy as that in previous case. For a different excitation energy, the residues may have different recoiling angles in annular rings. Owing to the different excitation energies, the evaporation residues populated via ICF channels may recoil at larger angles as compared to those populated by CF channels. The experimentally measured angular distributions of the recoiling residues populated in 12,13 C +175 Lu at ≈88 MeV energies are shown in Figures 4.1-4.11. 56

4.1. Discussions

xn Channels The angular distribution of residue 184 Ir produced in 13 C +175 Lu system is shown in Figure 4.1. It is clear from this figure that angular distribution of residue 184 Ir is peaked only in forward cone at an angle less than 10o , leading to the fact that this residue is formed via CF process, which is in good agreement with the compound nucleus mechanism. 13

C+

175

Lu ⇒

∗

188

Ir

⇒184 Ir + 4n

(4.1)

In this process, the emission of neutrons from the CN is symmetric in all the directions and no charge paticle is emitted along with the neutrons. Thereby, the residues thus formed have no such angular dpendency and observed in the forward cone within angles less than 10o , which is inferred to be formed via CF process. In Figure 4.2, the angular distribution for 183 Ir produced in 12,13 C +175 Lu systems is shown. This figure clearly shows that angular distributions of residue 183 Ir is also peaked only in forwad cone, which reveals that the residues 183 Ir is also populated via the CF process.

L u [

1 3

C ,4 n ]

1 8 4

Ir

D iff. C r o s s -s e c tio n (m b -d e g

-1

)

1 7 5

1

0 .1 0

1 0

2 0

3 0

4 0

5 0

A n g le ( d e g )

Figure 4.1: Residue

Experimentally measured Angular distribution for

57

184 Ir

4. Results and Discussions


-1

)

1 7 5 1 7 5

1 0 0

L u [ L u [

1 3 1 2

C ,5 n ] C ,4 n ]

1 8 3

Ir

1 8 3

Ir

1 0

1

0 .1 0

1 0

2 0

3 0

4 0

5 0

A n g le ( d e g )

Figure 4.2: Residue


1 0 0

1 7 5


-1

)

1 7 5

L u [ L u [

1 3 1 2

C ,6 n ] C ,5 n ]

1 8 2

Ir

1 8 2

Ir

183 Ir

1 0

1

0

1 0

2 0

3 0

4 0

5 0

A n g le ( d e g )

Figure 4.3: Residue


58

182 Ir

4.1. Discussions Similar trend is observed for the residue 182 Ir produced in 12,13 C +175 Lu systems and shown in Figure 4.3 respecively. This figure clearly show that angular distributions of residues 182 Ir are also peaked only in forwad cone. Hence, the residues 182 Ir are also populated via the CF process.

pxn Channels The residues 183 Os, formed in 12,13 C +175 Lu reactions via p-xn channels are shown in Figure 4.4. It can be seen clearly from this figure that the angular distribution is forward peaked at an angle less than 10o . It is also observed that the distribution pattern is slightly different at higher angles as that observed in xn channels. This difference may be arised due to the emission of one charged particle (protron) along with the neutrons [3], which in terms of excitation energy is incorported.

1 7 5

1 0 0


-1

)

1 7 5

L u [ L u [

1 3 1 2

C ,p 4 n ] C ,p 3 n ]

1 8 3 1 8 3

O s o s

1 0

1

0

1 0

2 0

3 0

4 0

5 0

A n g le ( d e g )

Figure 4.4: Residue


59

183 Os


13

C+

12

C+

175

175

Lu ⇒

Lu ⇒

∗

188

Ir

∗

187

Ir

⇒183 Os + p4n

(4.2)

⇒183 Os + p3n

(4.3)

A similar trend is also observed for 182 Os and in Figure 4.5 and Figure 4.6 respectively.

181

Os residues and displayed

1 0 0 1 7 5


-1

)

1 7 5

L u [ L u [

1 3 1 2

C ,p 5 n ] C ,p 4 n ]

1 8 2 1 8 2

O s o s

1 0

1 1 0

Figure 4.5: Residue

2 0

3 0

A n g le ( d e g )

4 0

5 0


60

182 Os

4.1. Discussions

L u [

1 2

C ,p 5 n ]

1 8 1

o s


-1

)

1 7 5

1 0

1

0 .1 0

1 0

2 0

3 0

4 0

5 0

A n g le ( d e g )

Figure 4.6: Residue


181 Os

α Emitting Channels The residues 183 Re, 182 Re, 181 Re, 179 Re and 178 Re are expected to be populated via CF/ICF processes. It is well understood that in case of CF process the entire projectile amulgamation with target takes place and the formed CN may decay by emitting an light particle like protons, neutrons and characteristic γ-rays. On the other hand, in case of ICF process, projectile may breakup in two parts near the target nuclear field. One of the parts fuses with the target and other moves in the forward direction as the spectator with almost the beam energy. This spectator carries the excess energy and leaves the composite system with much less excitation energy as compared to that formed via CF[5, 6]. Hence, the excitation energy of composite system formed by CF is higher as compared to the excitation energy of composite system formed in ICF. The angular distribution of 183 Re is shown in Figure 4.7. A maxima is 61

4. Results and Discussions observed in the distribution pattern of 183 Re at an angle around 38o . It may be pointed out that known compound nucleus formation process which termed as ICF reaction mechanism contributes in the formation of 183 Re, produced via α-emission channel. The absence of forward peak around 10o infers that this residue entirely populated via In-complete Fusion, in which one of the components 8 Be in the break-up of 12 C fuses with the target to form the composite system 183 Re. 12

C+

175

Lu ⇒

∗

187

Ir

⇒183 Re + α

(4.4)

In Figure 4.8, the angular distribution for 182 Re is shown. The distribution pattern indicates that 182 Re is likely to be peaked forward around 10o and have a maxima around 38o (for 12 C) and 30o (in case of 13 C). It is observed that both CF and ICF contributes in the formation of 182 Re. A similar trend is observed in residues 181 Re and 179 Re as shown in Figures 4.9 and Figure 4.10 respectively. It may be pointed out from these figures, that these residues are also populated via both CF and ICF processes.

L u [

1 2

C ,a ]

1 8 3

R e


-1

)

1 7 5

1 0

1

0 .1 0

1 0

2 0

3 0

4 0

5 0

A n g le ( d e g )

Figure 4.7: Residue


62

183 Re

4.1. Discussions

1 7 5


-1

)

1 7 5

1 0

L u [ L u [

1 3 1 2

C ,a 2 n ] R e 1 8 2 C ,a n ] R e 1 8 2

1

0 .1 0

1 0

2 0

3 0

4 0

5 0

A n g le ( d e g )

Figure 4.8: Residue


1 7 5


-1

)

1 7 5

L u [ L u [

1 3 1 2

C ,a 3 n ] C ,a 2 n ]

1 8 1

R e

1 8 1

R e

182 Re

1 0

1

0 .1 0

1 0

2 0

3 0

4 0

5 0

A n g le ( d e g )

Figure 4.9: Residue


63

181 Re


1 7 5

1 0


-1

)

1 7 5

L u [ L u [

1 3 1 2

C ,a 5 n ] C ,a 4 n ]

1 7 9

R e

1 7 9

R e

1

0 .1 0

1 0

2 0

3 0

4 0

A n g le ( d e g )

5 0

Figure 4.10: Experimentally measured Angular distribution for Residue

L u [

1 2

C ,a 5 n ]

1 7 8

R e


-1

)

1 7 5

1 0

179 Re

1

0 .1 0

1 0

2 0

3 0

A n g le ( d e g )

4 0

5 0

Figure 4.11: Experimentally measured Angular distribution for Residue

64

178 Re

4.2. Summary In Figure 4.11 the angular distribution for the residue 178 Re is displayed. This residue is also peaked forward at an angle around 10o and have a maxima around 38o , which suggests that the residue 178 Re is formed by CF as well as ICF process. With the two processes described above we can understand the observed enhancement at two angular regions. The residues formed by xn or pxn channels are observed at only smaller angles i.e. almost in the beam direction and formed via onle CF process and the residues formed by α-xn are likely to observed at both smaller and larger angles, because of CF and ICF both the processes are participating in their formation.

4.2

Summary

• Angular Distributions of 183 Ir, 182 Ir, 183 Os, 182 Os, 181 Os , 183 Re, 182 Re, 181 Re, 179 Re and 178 Re for the 12 C +175 Lu and 184 Ir, 183 Ir, 182 Os, 183 Os, 182 Os , 182 Re, 181 Re, and 179 Re for the 13 C +175 Lu systems at ≈88 MeV have been measured. • The evaporation residues produced via xn and p-xn channels for 175 Lu systems are observed likely to be peaked forward.

12,13

C+

• The evaporation residues formed via α-emission are found to be trapped at larger angles in annular rings, which is a signature that two processes are involved in the production of the evaporation residues. • Along with the excitation energy, charge transfer also plays a crucial role in the angular distribution of evaporation residues. • Because of the heavy ejectile masses, residues produced via α-emission in 13 C +175 Lu system are observed at around 30o [7] and for 12 C +175 Lu system the recoiling angle is around 38o [8]. Moreover, along with the Complete Fusion, In-Complete Fusion is also plays an important role in the formation of evaporation residues. The excitation energy, linear momentum and the charge transferred to the composite system 65

4. Results and Discussions is responsible for the observed behavior of recoiling residues and the measured cross-sections has a strong dependency over the recoiling angles. Thus, there is a need for the precise measurement of the Angular Distributions of the HI-induces reaction products in order to have a better understanding and to have perfect modeling of ICF dynamics. z z z z

66

Bibliography [1] M. Cavinato, E. Fabrici, E. Gandolini, E. Gadioli Erba, P. Vergani, M. Crippa, G. Colombo, I. Redaeli, and M. Ripamonti, Phys. Rev. C 52, 2577 (1995). [2] A. Gavron, Phys. Rev. C 21 (1980) 230. [3] R. Bimbot, D. Gardes and M.F. Rivet, Nucl. Phys. A189 (1972) 193-219. [4] Unnati Gupta, Pushpendra P. Singh, Devendra P. Singh, Manoj Kumar Sharma, Abhishek Yadav, R. Kumar, S. Gupta, H. D. Bhardwaj, B. P. Singh, and R. Prasad, Phys. Rev. C 80, 024613 (2009) [5] R. Ali, D. Singh, M. Afzal Ansari, M. H. Rashid, R. Guin and S. K. Das, J. Phys. G: Nucl. Part. Phys. 37 (2010) 115101. [6] D. Singh, Ph.D Thesis, Aligarh Muslim University, Aligarh, (2008). [7] Siddharth Parashari, Harish Kumar, M. Afzal Ansari, Suhail A. Tali, Asif Ali, D. Singh, Rahbar Ali, Kamal Kumar, N. P. M. Sathik, R. Dubey, Indu Bala, Rakesh Kumar, R. P. Singh, S. Muralithar Presented in National Conference on Recent Trends in Nuclear Physics, held at Department of Physics, AMU, Aligarh during Feb. 15-16, 2016. [8] Siddharth Parashari, Harish Kumar, M. Afzal Ansari, D. Singh, Rahbar Ali, Suhail A. Tali, Asif Ali, Kamal Kumar, N. P. M. Sathik , R. Dubey, Indu Bala, R. P. Singh, S.Muralithar, Rakesh Kumar, DAE Symp. On Nuclear Phys, 60 (2015) 476 .

Bibliography

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List of Publications Paper Published in Conferences: 1. Angular Distribution : A probe for incomplete fusion investigation Siddharth Parashari, Harish Kumar, M. Afzal Ansari, Suhail A. Tali, Asif Ali, D. Singh, Rahbar Ali, Kamal Kumar, N. P. M. Sathik, R. Dubey, Indu Bala, Rakesh Kumar, R. P. Singh, S. Muralithar Presented in National Conference on Recent Trends in Nuclear Physics, held at Department of Physics, AMU, Aligarh during Feb. 15-16, 2016. 2. Study of projectile break-up process at intermediate energies Harish Kumar, Siddharth Parashari, M. Afzal Ansari, Suhail A. Tali, Asif Ali, D. Singh, Rahbar Ali, Kamal Kumar, N. P. M. Sathik, R. Dubey, Indu Bala, Rakesh Kumar, R. P. Singh, S. Muralithar Presented in National Conference on Recent Trends in Nuclear Physics, held at Department of Physics, AMU, Aligarh during Feb. 15-16, 2016. 3. An approach to understand incomplete fusion dynamics from recoil range distribution measurements Suhail A. Tali, Harish Kumar, M. Afzal Ansari, Asif Ali, Siddharth Parashari, D. Singh, Rahbar Ali, Kamal Kumar, N. P. M. Sathik, R. Dubey, Indu Bala, Rakesh Kumar, R. P. Singh, S. Muralithar Presented in National Conference on Recent Trends in Nuclear Physics, held at Department of Physics, AMU, Aligarh during Feb. 15-16, 2016. 4. Investigation of incomplete fusion dynamics below 8 MeV/nucleon energies

Bibliography Asif Ali, Harish Kumar, M. Afzal Ansari, Suhail A. Tali, Siddharth Parashari, D. Singh, Rahbar Ali, Kamal Kumar, N. P. M. Sathik, R. Dubey, Indu Bala, Rakesh Kumar, R. P. Singh, S. Muralithar Presented in National Conference on Recent Trends in Nuclear Physics, held at Department of Physics, AMU, Aligarh during Feb. 15-16, 2016. 5. Investigation of Incomplete Fusion Dynamics from the Measurement of Angular Distributions at E≈88 MeV Siddharth Parashari, Harish Kumar, M. Afzal Ansari, D. Singh, Rahbar Ali, Suhail A. Tali, Asif Ali, Kamal Kumar, N. P. M. Sathik , R. Dubey, Indu Bala, R. P. Singh, S.Muralithar, Rakesh Kumar, DAE Symp. On Nuclear Phys, 60 (2015) 476. 6. Linear Momentum Transfer Effect on Incomplete Fusion Process at Energy ≈88 MeV Harish Kumar, Siddharth Parashari, M. Afzal Ansari, D. Singh, Rahbar Ali, Suhail A. Tali, Asif Ali, Kamal Kumar, N. P. M. Sathik, R. Dubey, Indu Bala, R. P. Singh, S.Muralithar, Rakesh Kumar, DAE Symp. On Nuclear Phys, 60 (2015) 474. 7. Probing of Incomplete Fusion from the Measurement of Recoil Range Distributions Suhail A. Tali, Harish Kumar, M. Afzal Ansari, D. Singh, Rahbar Ali, Asif Ali, Siddharth Parashari, Kamal Kumar, N. P. M. Sathik, R. Dubey, Indu Bala, Rakesh Kumar, R. P. Singh, S. Muralithar, DAE Symp. On Nuclear Phys, 60 (2015) 520. 8. Competition between Complete and Incomplete Fusion Reaction Mechanism below 8 MeV/nucleon energies Asif Ali, Harish Kumar, M. Afzal Ansari, D. Singh, Rahbar Ali, Suhail A. Tali, Siddhart Parashari, Kamal Kumar, N. P. M. Sathik, R. Dubey, Indu Bala, Rakesh Kumar, R. P. Singh , S. Muralithar, DAE Symp. On Nuclear Phys, 60 (2015) 554.

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