On the photo-absorption sum rules 1 in different environments - - PowerPoint PPT Presentation

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

On the photo-absorption sum rules σ−1 in different environments (atoms,nuclei,nucleons)

S.B. Gerasimov

Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna

EMIN-2015 October 05 – 08, 2015, INR RAS, Moscow

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

Table of contents

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

Preliminaries

Prologue: Non-relativistic dipole sum rules for atomic and nuclear photoeffect. σn(E1) = ∫ ∞

thr

dω ωn σE1(ω) Examples: n = −2 → Kramers-Heisenberg sum rule (SR) for static electric-dipole polarizability of a given quantum system; n = −1 → the bremsstrahlung-weighted SR, dependent of charged-”parton” correlation in a given system; n = 0 → the famous Thomas-Reiche-Kuhn SR, known as a precusor of not less as Quantum Mechanics itself.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

Preliminaries

σ−2(0)(E1) = 4π2Σn(En − E0)∓1| < n|Dz|0 > |2 = 2π2αE1, n = −2; = 2π2 < 0|[Dz[H, Dz]]|0 >, n = 0; σ−1(E1) = 4 3π2 < 0|⃗ D2|0 > . Early estimation of the GDR energy in the photonuclear physics (Migdal(1945)): ¯ Edip = ( σ0(E1) σ−2(E1))1/2 ∼ A−1/3

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

Preliminaries

Another mean value was used for the estimation of the nucleon correlations in atomic nuclei ¯ E

′

dip

= ( σ0(E1) σ−1(E1)) ∼ A A · A2/3 + (corr.terms) The nucleon ↔ the relativistic 3q system → the relativistic generalization of sum rules needed, including the spin degrees of freedom and spin-dependent interactions and correlations of partons.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

Digressing to spin-dependent sum rules

The a.m.m. sum rules express a model-independent correspondence between static properties of a particle (or bound system of particles) and integrals over the photo-absorption

• spectrum. For particles with the spin S = 1/2 the sum rule for the

anomalous magnetic moment κ reads 2π2ακ2 m2 = ∫ ∞

thr

dν ν (σp(ν) − σa(ν))

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

Digressing to spin-dependent sum rules

The validity of the SR was checked in the lowest order of QED (SG, somewhere in the interval 1960-1963,unpubl.),taking the Schwinger’s κ = α

2π successful analytic and partially computer

check of SR was done by Dicus and Vega (2000). Later on, for the physical reasons, we shall replace κ2 entering different sum rules just by its integral expression in the GDH sum rule.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

QED and Atoms

In what follows we will consider relativistic dipole moment fluctuation sum rules in the ”valence-parton” approximation, that is neglecting virtual particle-antiparticle configurations in the ground state of the considered systems or diffractively produced in the final states of photo-absorption reactions.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

QED and Atoms

4π2α[1 3 < D2 > − κ2 4m2 ] = ∫ ∞

thr

dν ν σtot(ν)

• r, using

2π2ακ2 m2 = ∫ ∞

thr

dν ν (σp(ν) − σa(ν)) we get another form to be used later 4π2α[1 3 < D2 >] = ∫ ∞

thr

dν ν (σp(ν)

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

QED and Atoms

We apply derived sum rule to the system of the highly ionized atom Pb81+, thoroughly considered about half-century ago by J.S Levinger and co-workers:Phys.Rev.(1956-1957). Using the form of the sum rule with our included term κatom ≃ µel. , we reduced deviation between left- and right-hand sides of the sum rule to

• ne-half percent. Numerically:

4π2α1 3 < D2 > [937.2b] − 4π2α( κ 2M )2[67.9b] = ∫ ∞

thr

dν ν σtot(ν)[874b]

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

QED and Atoms

The same sum rule for the free electron in the α2-approximation was checked analytically in the work by E.A. Kuraev, L.N.Lipatov and N.P.Merenkov (1973).

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

Current algebra SR and 3N- Nuclei

Yu.K. Khokhlov(1957); L. Foldy(1957) 4π2α NZ A − 1(1 3) · ⟨r2

ch⟩NR =

∫ dν ν σE1(ν) [S.G.] JETP Lett. 5, 337 (1967) G.Barton, Nucl.Phys. A104(1967)289 ”What needs explaining in the photo-disintegration of He-3?” Application of the Cabibbo-Radicati sum rule results in σ−1(I = 1/2) ≃ σ−1(I = 3/2)vsσ−1(pd)exp ≃ σ−1(ppn)exp.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

Current algebra SR and 3N- Nuclei

Theor.-explanation followed by D,Lehman, et al.,PR C19,310,(1979): The average VNN-potential in the spin-singlet and spin-triplet state support the NN-bound state which is lower in the two-particle-pd- than in the 3-nucleon state, thus providing the ”leakage” of the I = 1/2-component from the ppn-nucleon state to the pd-final states.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and Nucleons

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and Nucleons

Following formally to the pz → ∞ techniques derivation of the Cabibbo-Radicati or GDH sum rule we can obtain the relation 4π2α(1 3 < ⃗ D2 > −( κN 2mN )2) = ∫ dν ν σres

tot(ν),

We use the definitions ˆ D = ∫ ⃗ x ˆ ρ(⃗ x)d3x =

3

∑

j=1

Qq(j)⃗ dj, ˆ r2

1 =

∫ ⃗ x2ˆ ρ(⃗ x)d3x =

3

∑

j=1

Qq(j)⃗ dj

2

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and Nucleons

The defined operators Qq(j) and ⃗ dj are the electric charges and configuration variables of point-like interacting quarks in the infinite-momentum frame of the bound system. Finally, we relate the electric dipole moment operator correlators, sucessively for the proton, the neutron and the pure ”isovector-nucleon” part equal for both nucleons and the isovector part of the mean-squared radii operators, which all are sandwiched by the nucleon state vectors in the ”infinite - momentum frame”, with experimentally measurable data on the resonance parts of the photoabsorption cross sections on the proton and neutron presently known below ∼ 2 GeV.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and Nucleons

The listed operator mean values are parametrized as follows RV = 1 2(< r2

1 >P − < r2 1 >N) = α − 1

2β JP = 1 3 < ˆ D2 >P= 8 27α + 1 27β + 8 27γ − 8 27δ JN = 1 3 < ˆ D2 >N= 2 27α + 4 27β + 2 27γ − 8 27δ JV = 1 3 < ˆ D2 >V = 2 3α + 1 3β + 2 3γ − 4 3δ where < ⃗ d1

2 >=< ⃗

d2

2 >= α,< ⃗

d3

2 >= β, < ⃗

d1 · ⃗ d2 >= γ, < ⃗ d1 · ⃗ d3 >=< ⃗ d2 · ⃗ d3 >= δ indices ”1” and ”2” refer to the like quarks and ”3” to the odd quark.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and Nucleons

Evaluation of the relativistic electric dipole moment fluctuation and the isovector charge radius sum rules for the nucleon was carried out with the available compilation of the resonance pion-photoproduction data on the proton and neutron AP(N)

1/2

and AP(N)

3/2

and all integrals over photoexcited nucleon resonances were taken in the narrow resonance approximation, when Jres

p(a) ≃

4πmn|Ares

3/2(1/2)|2

m2

res − m2 n

, where mn(res) is the nucleon (or resonance)mass.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and Nucleons

Solving the system of the linear equations and evaluating the RV , JP,N,V with the help of experimentally known partial amplitudes of main photo-excited resonances, we find our final results for the numerical values α, β and the opening angle θ12 and θ13 between vectors ⃗ d1 and ⃗ d2 and vectors ⃗ d1 and ⃗ d3: α1/2 = 0.75 ± 0.06fm β1/2 = 0.77 ± 0.12fm θ12 ≃ 1200 θ13 ≃ θ23 ∼ 1200 < r12 >V = 0.25 ± 0.02fm2(exp : .29fm2)

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and Nucleons

The isovector Dirac rms of the valence quark distribution could be at stronger deviation from data because of expected importance of the (omitted in our approach) isovector two-pion exchanges entering in full expressions for the nucleon radii.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and the ”Shape” of Nucleons

The review paper ”The Shape of Hadrons” by C.Alexandrou, C.N. Papanicolas and M. Vanderhaeghen, Rev.Mod.Phys. 84(2012) 1231,refers to 132 original papers devoted to this problem. Large part is devoted aspects of theoretical evaluation and experimental measurement of the small amplitude of non-diagonal electromagnetic transition N∆33 of the E2-type. Despite of the E2(N → ∆) amplitudes are of the order a few percents of the dominant M1-transition the present experiments allowed to establish a deformation in the N/∆ system. A quantitative understanding of these results requires improvement

• f the LQCD simulation at mπ approaching the physical value of

pion mass.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and the ”Shape” of Nucleons

Having got the values of the ”global” parameters α, β, etc. defined in the infinite momentum frame, we put all three vectors with the pertinent numerical parameters into plane transverse to pz → ∞ and define parameters of the closed contour circuscribing their

• ends. Within the indicated uncertainties the resulting curve is

either the circle or the ellipse with rather small excentricitet. The utility of introduced parameters should be useful in dynamical calculations of the characteristics of the photo-produced nucleon resonances within relativistic CQMs.

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments

1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.Current algebra SR and 3N-Nuclei 5.CQM and Nucleons 6.CQM and the ”Shape” of Nucleons

CQM and the ”Shape” of Nucleons

S.B. Gerasimov On the photo-absorption sum rules σ−1 in different environments