Acknowledgement iii

Contents

Acknowledgement iii

Abstract v

Abbreviations vii

Contents ix

List of Figures xiii

List of Tables xix

1 Physics Motivation 1

1.1 Halo nuclei . . . . 1

1.1.1 Why is it interesting? . . . . 7

1.1.2 How to study halo nuclei? . . . . 9

1.2 Transfer reaction . . . . 12

1.2.1 Theoretical reaction model . . . . 15

1.2.2 Experimental techniques . . . . 16

2 Few-body Description of Transfer Reactions 19 2.1 Scattering theory . . . . 20

ix

x CONTENTS

2.1.1 Scattering wave function and notion of cross section . . 20

2.1.2 Case with a spherically symmetric nuclear potential . . 22

2.1.3 Case with a Coulomb interaction . . . . 23

2.1.4 Case of particles with spins . . . . 25

2.1.5 Born approximation . . . . 26

2.2 Optical model . . . . 27

2.3 Single-particle properties . . . . 29

2.3.1 Single-nucleon states . . . . 29

2.3.2 Halo EFT . . . . 30

2.3.3 Supersymmetry (SuSy) method . . . . 31

2.3.4 Resonances . . . . 33

2.4 Modeling ( d, p ) transfer reaction . . . . 34

2.4.1 Theoretical formalism . . . . 34

2.4.2 Distorted wave Born approximation (DWBA) . . . . 37

2.4.3 Adiabatic distorted wave approximation (ADWA) . . . 38

2.4.4 Other options . . . . 41

3 Halo Study with Transfer Calculations 45 3.1

Be( d , p )

Be transfer reaction . . . . 46

3.1.1 ANC extraction . . . . 47

3.1.2 SuSy test . . . . 56

3.1.3 Dependencies . . . . 57

3.1.4 Resonance state . . . . 61

3.2

C( d , p )

C transfer reaction . . . . 65

3.2.1 ANC extraction . . . . 66

3.3 Searching for halos in nuclear excited states . . . . 70

3.3.1 Sub-Coulomb transfer . . . . 71

CONTENTS xi

3.3.2 Searching for a candidate nucleus . . . . 72

3.3.3 Dependencies . . . . 73

4 Investigation of

Li(d,p) transfer 81 4.1 Motivation . . . . 82

4.2 Experimental setup . . . . 82

4.3 Data analysis . . . . 86

4.4 Results and discussion . . . . 96

4.5 Theoretical approach . . . . 99

5 Conclusion and outlook 103

A FRESCO Input 107

B Paper I 109

C Paper II 120

Bibliography 135