PHYS490: Nuclear Physics. 6/20/2019 PHYS490 : Advanced Nuclear Physics : E.S. Paul 1

Advanced Nuclear Physics

The Nucleon – a Spin ½ Fermion

The Ford Nucleon (1957) nuclear powered car

The Nucleon – a spin ½ Fermion

mediators) must also be considered

 Only 2% of the mass (Higgs mechanism) comes from

quark masses. The other 98% arises from the kinetic energy of the constituents

 Only 30% of the intrinsic spin can be accounted for from the constituent quarks

Building Blocks and

Energy Scales

 Depending on energy and length scales, different constituents may be

considered as the building blocks of the atomic nucleus

Fundamental Forces

 Quantum behaviour of atomic nuclei results from the

underlying properties of many-body nuclear interactions, which are among the most complex in nature

Fundamental Particles & Forces

 Force Mediators (bosons):

Photon (γ)

Gluon (g)

Z particle

The Strong Force

 The strong force is fundamentally an interaction between quarks

 It is really a residual colour force mediated by the exchange of gluons

Properties of the N-N Force

 The force is (nearly) charge independent  The force is spin dependent

 The force has a non-central component

 The force depends on the relative velocity or

momentum of the nucleons

 The force has a repulsive core

One Pion Exchange

 The origin of the nuclear force arises at the fundamental level from the exchange of gluons between the

constituent quarks of the nucleons

 At low energies (<1 GeV/nucleon; >1 fm) the interaction can be regarded as being mediated by the exchange of

Spin σ and Isospin τ

 Matrix mechanics was formulated by Born, Heisenberg and Jordan (1925)

 Nucleon intrinsic spin takes only two values: up and down Introduction of Pauli 2x2 spin matrices

 Same formalism used to describe nucleon: isospin up (neutron), isospin down (proton)

Introduction of Pauli 2x2 isospin matrices

One-Pion Exchange Potential

 At large distances the potential is constructed as arising from the exchange of one pion: OPEP

 The form of the potential is:

V_OPEP = g_s2 _{(1/3 σ} A.σB + SAB [1/3 + 1/μr + 1/(μr)2]) x τ_A.τ_B 1/r μ2_e-μr where: μ = m_πc/ħ and: S_AB = 3(σ_A.r)( σ_B.r)/r2 _{- σ} A.σB

Addition of (Iso)Spins

 Spin σ and isospin τ are vectors  Cosine rule gives:

(σ_A + σ_B )2 _{= σ}

A2 + σB2 + 2 σA.σB

 Parallel spins (triplet state): σ_A.σ_B = 1  Antiparallel spins (singlet state): σ_A.σ_B = -3

Quark Meson Coupling Model

 The Quark Meson Coupling (QMC) Model of the nucleus takes into account both the fundamental interactions among quarks within the neutrons and protons, and also the interactions between the

neutrons and protons (meson

Calculations for Light Nuclei

 In addition to two-body N-N interactions, three-body

Repulsive Core (Pauli Principle)

 Radius of nucleon:

~ 1 fm

 Radius of hard core:

~ 0.2 fm

 Nucleon mean free path:

~ 7 fm

 Volume of hard cores is only ~ 2%

Hydrogen Isotopes

 Hydrogen 1H has 1 proton (p) and 0 neutrons (n) (and 1 electron)

 Deuterium 2H (or D) has 1 proton and 1 neutron  Heavy water D₂O exists in the oceans

 The deuterium nucleus is known as the deuteron (d)  Tritium 3H has 1 proton and 2 neutrons

 The tritium nucleus is known as the triton (t)

The Deuteron

 The deuteron consists of a bound proton-neutron system

 Its ground-state is the only state which is bound; the first excited state is unbound

 The ground state has spin and parity Iπ _{= 1}+

 The deuteron is not a spherical nucleus

Deuteron Quadrupole Moment

the deuteron shows that it is not a spherical system  More…

Deuteron Magnetic Moment

 A discrepancy between theoretical and experimental values of the magnetic dipole moment of the deuteron also indicates a non-spherical geometry

 There is a non-central interaction between the

proton and neutron which violates the conservation of orbital angular momentum

Deuteron Ground State

Range of the Nuclear Force

 The range of an interaction is related to the mass of the exchanged particle

 The Heisenberg Uncertainty Principle gives: ΔE Δt ≈ ħ  A particle can only create another particle of mass m for

a time t ≈ ħ/mc2 _{during which interval the particle can}

travel at most ct

 Taking ct as an estimate of the range R gives: R ≈ ħ / mc  This yields R ≈ 1.4 fm for pion exchange

Deuteron Wavefunction

 The maximum of the

wavefunction is only just

inside the potential well with a considerable

exponential tail outside

 The RMS separation

between the neutron and

proton is 4.2 fm, larger than the range of the nuclear force (~ 1.4 fm)  The deuteron is loosely

Hypernuclei

Nuclei including excited nucleons including heavy quarks:

Summary



Protons and Neutrons are “Nucleons”



Properties of N-N force



Spin and Isospin