De studie van de sterke wisselwerking tussen kerndeeltjes (nucleonen, dat wil zeggen protonen en neutronen) is binnen de kernfysica een actief onderzoeksveld geweest vanaf de vroege jaren dertig van de vorige eeuw. Sinds ongeveer 30 jaar weten we dat de fundamentele theorie van de sterke wisselwerking de quantumkleurdynamica, 'quantum chromodynamics' of QCD, is.  ...

Zie: Samenvatting

Cozma, Mircea Dan,

De studie van de sterke wisselwerking tussen kerndeeltjes (nucleonen, dat wil zeggen protonen en neutronen) is binnen de kernfysica een actief onderzoeksveld geweest vanaf de vroege jaren dertig van de vorige eeuw. Sinds ongeveer 30 jaar weten we dat de fundamentele theorie van de sterke wisselwerking de quantumkleurdynamica, 'quantum chromodynamics' of QCD, is. ... Zie: Samenvattin

Cozma, Mircea Dan

NARCIS 

Proton-proton bremsstrahlung and elastic nucleon-nucleon scattering: relativistic formulations

University of Groningen

Proton-proton bremsstrahlung and elastic nucleon-nucleon scattering:relativistic formulations

ARTS repository - University of Groningen

English

University of Groningen Research Database

  
 University of Groningen
Proton-proton bremsstrahlung and elastic nucleon-nucleon scattering
Cozma, Mircea Dan
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from
it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date:
2004
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Cozma, M. D. (2004). Proton-proton bremsstrahlung and elastic nucleon-nucleon scattering: relativistic
formulations Groningen: s.n.
Copyright
Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).
Take-down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the
number of authors shown on this cover page is limited to 10 maximum.
Download date: 10-02-2018
Proton-proton bremsstrahlung and
elastic nucleon-nucleon scattering:
relativistic formulations
Druk: Stichting drukkerij C. Regenboog, Groningen, Augustus 2004.
Rijksuniversiteit Groningen
Proton-proton bremsstrahlung and
elastic nucleon-nucleon scattering:
relativistic formulations
Proefschrift
ter verkrijging van het doctoraat in de
Wiskunde en Natuurwetenschappen
aan de Rijksuniversiteit Groningen
op gezag van de
Rector Magnificus, dr. F. Zwarts,
in het openbaar te verdedigen op
maandag 20 september 2004
om 16.15 uur
door
Mircea Dan Cozma
geboren op 29 april 1976
te Sibiu, Roemenie¨
Promotores: Prof. dr. J.A. Tjon
Prof. dr. R.G.E. Timmermans
Copromotor: Dr. O. Scholten
Beoordelingscommissie: Prof. dr. J.H. Koch
Prof. dr. M. de Roo
Prof. dr. S.J. Wallace
Contents
1 Introduction 1
2 Relativistic model for bremsstrahlung 5
2.1 A relativistic covariant model for bremsstrahlung . . . . . . . . . . . . . . 5
2.1.1 The Martinus et al . ppγ model . . . . . . . . . . . . . . . . . . . . 6
2.2 Other models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Nakayama et al . model . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Soft-photon models . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Comparison with the experimental KVI data . . . . . . . . . . . . . . . . 13
3 Non-relativistic toy-model for pp bremsstrahlung 17
3.1 The two-potential formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.2 The bremsstrahlung amplitude . . . . . . . . . . . . . . . . . . . . 18
3.2 Proton-proton scattering in effective field theory . . . . . . . . . . . . . . 20
3.2.1 Effective field theories for nucleon-nucleon scattering . . . . . . . . 20
3.2.2 Leading order amplitude in presence of the Coulomb interaction . 21
3.2.3 Next-to-leading order contributions . . . . . . . . . . . . . . . . . . 26
3.3 A separable potential model . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Results for elastic scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5 Toy model for ppγ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.1 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 Bremsstrahlung and the low energy NN interaction 43
4.1 Analysis of the discrepancy . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Coulomb correction to ppγ at 190 MeV . . . . . . . . . . . . . . . . . . . 47
4.3 On-shell sensitivity of ppγ . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5 Two-pion-exchange contributions: the formalism 57
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 The quasipotential approach to NN scattering . . . . . . . . . . . . . . . 57
5.3 Chiral symmetry and the NN interaction . . . . . . . . . . . . . . . . . . 59
v
vi CONTENTS
5.4 Effective theory of strong interactions . . . . . . . . . . . . . . . . . . . . 61
5.5 Construction of the effective Lagrangian . . . . . . . . . . . . . . . . . . . 64
5.6 Explicit expressions for the two-pion diagrams . . . . . . . . . . . . . . . . 67
5.7 The quasipotential direct box . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.8 Method of evaluation of one-loop integrals . . . . . . . . . . . . . . . . . . 71
5.9 An example: the c0 triangle diagram . . . . . . . . . . . . . . . . . . . . . 73
5.10 Partial-wave decomposition of the amplitude . . . . . . . . . . . . . . . . 75
Appendix A: Tree-level potentials in the OBE model . . . . . . . . . . . . 78
Appendix B: Scalar moments . . . . . . . . . . . . . . . . . . . . . . . . . 78
Appendix C: Spinors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6 Two-pion exchange contributions: results 81
6.1 Phenomenological interpretation of the LECs . . . . . . . . . . . . . . . . 81
6.2 Potential in coordinate space . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.3 Peripheral waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.4 Effect of the iteration of the potential on the phase shifts . . . . . . . . . 97
6.5 Numerical accuracy of the results . . . . . . . . . . . . . . . . . . . . . . . 98
6.6 The lower partial waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7 Concluding remarks 109
Samenvatting 111
Acknoledgements 113
Bibliography 114


University of Groningen Digital Archive

Proton-proton bremsstrahlung and elastic nucleon-nucleon scattering : relativistic formulations

https://pure.rug.nl/ws/files/2957067/c6.pdf

Proton-proton bremsstrahlung and elastic nucleon-nucleon scattering : relativistic formulations

Abstract

Similar works

Full text

Available Versions

NARCIS

University of Groningen

ARTS repository - University of Groningen

ARTS repository - University of Groningen

University of Groningen Research Database

University of Groningen Digital Archive