12 th CNS International Summer School CNSSS 13

12 th CNS International Summer School (CNSSS 13) 28 August to 03 September 2013 -- CNS Wako Campus Nuclear Forces - Lecture 1 History, Facts and Phenomenology R. Machleidt University of Idaho Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 1

Nuclear Forces - Overview of all lectures • Lecture 1: History, facts, and phenomenology • Lecture 2: The meson theory of nuclear forces • Lecture 3: QCD and nuclear forces; effective field theory (EFT) for low-energy QCD • Lecture 4: Nuclear forces from chiral EFT R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 2

Lecture 1: History, Facts, and Phenomenology ¤Historical review ¤Properties of the nuclear force ¤Phenomenological descriptions R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 3

History of Nuclear Forces: Phase I 1930’s R. Machleidt Chadwick (1932): Neutron Heisenberg (1932): First Phenomenology (Isospin) Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 4

Heisenberg and his contribution of 1932 Heisenberg Niels Bohr Pauli R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 5

Zeitschrift fuer Physik 77, 1 (1932) On the Structure of Atomic Nuclei. I. …. … Chadwick … … suggests the assumption that atomic nuclei are built from protons and neutrons without electrons … R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 6

Zeitschrift fuer Physik 77, 1 (1932), cont’d … the force … between proton and neutron … …. . in analogy to the H 2+-ion --- an exchange of negative charge will take place, … This exchange can be visualized by electrons which do not have spin and follow the rules of bose statistics … Precursor of the idea of Boson Exchange! R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 7

History, Phase I cont’d 1930’s Chadwick (1932): Neutron Heisenberg (1932): First Phenomenology (Isospin) Yukawa (1935): Meson Hypothesis R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 8

Yukawa and his idea Tomonaga Yukawa Sakata S. Tomonaga, H. Yukawa, and S. Sakata in the 1950 s. R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 9

From: H. Yukawa, Proc. Phys. Math. Soc. Japan 17, 48 (1935). R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 10

R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 11

R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 12

History, Phase I cont’d 1930’s Chadwick (1932): Neutron Heisenberg (1932): First Phenomenology (Isospin) Yukawa (1935): Meson Hypothesis 1940’s Discovery of the pion in cosmic ray (1947) and in the Berkeley Cyclotron Lab (1948). Nobelprize awarded to Yukawa (1949). Taketani, Nakamura, Sasaki (1951): 3 ranges. 1950’s “Pion Theories” R. Machleidt One-Pion-Exchange (OPE): o. k. Multi-pion exchanges: Problems! Taketani, Machida, Onuma (1952); Brueckner, Watson (1953). Nuclear Forces(1953) - Lectureand 1 Goldberger (1960) Quotes by Bethe History, Facts, Phen. (CNSSS 13) 13

Scientific American, September 1953 What Holds the Nucleus Together? by Hans A. Bethe In the past quarter century physicists have devoted a huge amount of experimentation and mental labor to this problem – probably more man-hours than have been given to any other scientific question in the history of mankind. R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 14

“There are few problems in nuclear theoretical physics which have attracted more attention that of trying to determine the fundamental interaction between two nucleons. It is also true that scarcely ever has the world of physics owed so little to so many … … It is hard to believe that many of the authors are talking about the same problem or, in fact, that they know what the problem is. ” M. L. Goldberger Midwestern Conference on Theoretical Physics, Purdue University, 1960 R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 15

History, Phase I (The first pion period) 1930’s Chadwick (1932): Neutron Heisenberg (1932): First Phenomenology (Isospin) Yukawa (1935): Meson Hypothesis 1940’s : d o i Discovery of the pion in cosmic ray (1947) and in the Berkeley Cyclotron Lab (1948). Nobelprize awarded to Yukawa (1949). r e p on er i p t s r Taketani, Nakamura, Sasaki (1951): 3 ranges. 1950’s T i f he “Pion Theories” R. Machleidt t s a s i d One-Pion-Exchange (OPE): o. k. Multi-pion exchanges: Problems! a n i s lt Taketani, Machida, Onuma (1952); u s re Brueckner, Watson (1953). Nuclear Forces(1953) - Lectureand 1 Goldberger (1960) Quotes by Bethe History, Facts, Phen. (CNSSS 13) 16

Phase II: The meson period 1960’s Many pions = multi-pion resonances: One-Boson-Exchange Model R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 17

Phase II: The meson period 1960’s Many pions = multi-pion resonances: One-Boson-Exchange Model R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 18

Phase II: The meson period 1960’s Many pions = multi-pion resonances: One-Boson-Exchange Model Refined Meson Theories 1970’s Sophisticated models for two-pion exchange: Paris Potential (Lacombe et al. , PRC 21, 861 (1980)) Bonn potential (Machleidt et al. , Phys. Rep. 149, 1 (1987)) R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 19

The exponential tail of phase II (or the epigone period of meson theory) 1980’s Nijmegen: We need more precision!!! “A χ²/dat of ≈ 2 is not good enough, it has to be 1. 0” 1993: The high-precision Nijmegen phase shift analysis 1990’s 1994 -2001: High-precision NN potentials: Nijmegen I, II, ’ 93, Reid 93 (Stoks et al. 1994) Argonne V 18 (Wiringa et al, 1995) CD-Bonn (Machleidt et al. 1996, 2001) R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 20

1960’s Many pions = multi-pion resonances: Gell-Mann and Zweig (1963): 3 quarks! One-Boson-Exchange Model Gell-Mann R. Machleidt Zweig Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 21

Phase III: The QCD/EFT period 1980’s 1990 – today R. Machleidt Nuclear physicists discover QCD: Quark cluster models. Nuclear physicists discover Effective Field Theory (EFT): Weinberg (1990); Ordonez, Ray, van Kolck (1994/96). Another “pion theory”; but now right: constrained by chiral symmetry Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 22

Phase III: The QCD/EFT period 1980’s he : d rio e p on Nuclear physicists discover Effective Field Theory 1993: The high-precision Nijmegen phase shift analysis (EFT): i p d ! r n e o t s c a e s s di 1990’s 1990 today R. Machleidt Nuclear physicists QCD: Nijmegen: We needdiscover more precision!!! Quark cluster models. 1994 -2001: High-precision NN potentials: Weinberg (1990); Ordonez, Ray, van Kolck Nijmegen I, II, ’ 93, Reid 93; (1994/96). Argonne V 18; Another “pion theory”; but now right: CD-Bonn. constrained by chiral symmetry No Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 23

Properties of the nuclear force • • Finite range Intermediate-range attraction Short-range repulsion (“hard core”) Spin-dependent non-central forces: - Tensor force - Spin-orbit force • Charge independence R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 24

Finite range • Comparison of the binding energies of show that the nuclear force is of finite range (1 -2 fm) and very strong within that range (Wigner, 1933). • “Saturation”. Nuclei with A>4 show saturation: Volume and binding energies of nuclei are proportional to the mass number A. R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 25

Intermediate-range attraction Nuclei are bound. The average distance between nucleons in nuclei is about 2 fm which must roughly correspond to the range of the attractive force. R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 26

Short-range repulsion (“hard core”) Analyze 1 S 0 phase shifts and compare to 1 D 2 phase shifts. R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 27

Non-central forces Tensor Force: First evidence from the deuteron Deuteron R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 28

Tensor force, cont’d R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 29

Tensor force, cont’d R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 30

Non-central forces Spin-Orbit Force left right Nucleus or proton Proton 2 Proton 1 R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 31

Summary: Most important parts of the nuclear force Short Intermediate Long range Central force Taketani, Nakamura, Sasaki (1951): 3 ranges Tensor force Spin-orbit force R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 32

Charge-independence • After correcting for the electromagnetic interaction, the forces between nucleons (pp, nn, or np) in the same state are almost the same. • “Almost the same”: Charge-independence is slightly broken. • Notation: Equality between the pp and nn forces: Charge symmetry. Equality between pp/nn force and np force: Charge independence. • Better notation: Isospin symmetry; invariance under rotations in isospin space. R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 33

Charge-independence breaking: Evidence Since the scattering length is a magnifying glass on the interaction, charge-independence breaking (CIB) is seen most clearly in the different scattering lengths of pp, nn, and np low-energy scattering. Charge-symmetry breaking (CSB) - after electromagnetic effects have been removed: Charge-independence breaking (CIB): R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 34

Phenomenological descriptions • Symmetries and the general expression for the NN potential • Historically important examples of phenomenological NN potentials R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 35

The symmetries • • Translation invariance Galilean invariance Rotation invariance Space reflection invariance Time reversal invariance Invariance under the interchange of particle 1 and 2 Isospin symmetry Hermiticity R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 36

Most general two-body potential under those symmetries (Okubo and Marshak, Ann. Phys. 4, 166 (1958)) central spin-orbit tensor quadratic spin-orbit another tensor with R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 37

Potentials which are based upon the operator structure shown on the previous slide (but may not include all operators shown or may include additional operators) are called “Phenomenological Potentials”. Some historically important examples are given below. • Gammel-Thaler potential ( Phys. Rev. 107, 291, 1339 (1957)), hard-core. • Hamada-Johnston potential (Nucl. Phys. 34, 382 (1962)), hard core. • Reid potential (Ann. Phys. (N. Y. ) 50, 411 (1968)), soft core. • Argonne V 14 potential (Wiringa et al. , Phys. Rev. C 29, 1207 (1984)), uses 14 operators. • Argonne V 18 potential (Wiringa et al. , Phys. Rev. C 51, 38 (1995)), uses 18 operators. R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 38

End Lecture 1 R. Machleidt Nuclear Forces - Lecture 1 History, Facts, Phen. (CNSSS 13) 39