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. ∫ ∞ d ω ω n σ E 1 ( ω ) σ n ( E 1) = thr 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 4 π 2 Σ n ( E n − E 0 ) ∓ 1 | < n | D z | 0 > | 2 σ − 2(0) ( E 1) = 2 π 2 α E 1 , n = − 2; = 2 π 2 < 0 | [ D z [ H , D z ]] | 0 >, n = 0; = 4 3 π 2 < 0 | ⃗ D 2 | 0 > . σ − 1 ( E 1) = Early estimation of the GDR energy in the photonuclear physics (Migdal(1945)): E dip = ( σ 0 ( E 1) σ − 2 ( E 1)) 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 ( σ 0 ( E 1) ¯ ′ E = σ − 1 ( E 1)) dip A ∼ A · A 2 / 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 ∫ ∞ 2 π 2 ακ 2 d ν = ν ( σ p ( ν ) − σ a ( ν )) m 2 thr 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 2 π successful analytic and partially computer check of SR was done by Dicus and Vega (2000). Later on, for the physical reasons, we shall replace κ 2 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 ∫ ∞ 3 < D 2 > − κ 2 4 π 2 α [1 d ν 4 m 2 ] = ν σ tot ( ν ) thr or, using ∫ ∞ 2 π 2 ακ 2 d ν = ν ( σ p ( ν ) − σ a ( ν )) m 2 thr we get another form to be used later ∫ ∞ 4 π 2 α [1 d ν 3 < D 2 > ] = ν ( σ p ( ν ) thr 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 Pb 81+ , 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 κ atom ≃ µ el . , we reduced deviation between left- and right-hand sides of the sum rule to one-half percent. Numerically: ∫ ∞ 4 π 2 α 1 3 < D 2 > [937 . 2 b ] − 4 π 2 α ( κ d ν 2 M ) 2 [67 . 9 b ] = ν σ tot ( ν )[874 b ] thr 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 α 2 -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) ∫ d ν 4 π 2 α NZ A − 1(1 3) · ⟨ r 2 ch ⟩ NR = ν σ E 1 ( 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) vs σ − 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 V NN -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 p z → ∞ techniques derivation of the Cabibbo-Radicati or GDH sum rule we can obtain the relation ∫ d ν 4 π 2 α (1 D 2 > − ( κ N 3 < ⃗ ) 2 ) = ν σ res tot ( ν ) , 2 m N We use the definitions 3 ∫ ˆ Q q ( j ) ⃗ x ) d 3 x = ∑ D = ⃗ x ˆ ρ ( ⃗ d j , j =1 3 ∫ 2 ˆ Q q ( j ) ⃗ r 2 x 2 ˆ x ) d 3 x = ∑ 1 = ⃗ ρ ( ⃗ d j j =1 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 Q q ( j ) and ⃗ d j 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
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