Benutzer:Mschuma3
Martin Schumacher Professor (i.R.) at the University of Göttingen
e-mail: mschuma3@gwdg.de; alias: martin.schumacher@phys.uni-goettingen.de
II. Physikalisches Institut der Universität
Friedrich-Hund-Platz 1
D-37077 Göttingen
1964 - 1984: Experimental research in nuclear physics, atomic physics, and quantum electrodynamics. The experimental work was carried out in Göttingen, Philadelphia (USA), Grenoble (France), Mol (Belgium), Jülich, and Karlsruhe.
Overview: "The present status of Delbrück scattering" A.I. Milstein and M. Schumacher Physics Reports 243 (1994) 183. "Compton scattering by nuclei" M.-Th. Hütt, A.I. L'vov, A.I. Milstein, M. Schumacher, Physics Reports 323 (2000) 457.
1984 - 2002: Experimental research in low-energy particle physics at the high duty-factor electron accelerators in Mainz, Bonn, and Lund (Sweden).
Overview: "Perspectives on Photon Interactions with Hadrons and Nuclei" Proceedings, Göttingen conference 1990, M. Schumacher, G. Tamas (Eds.) Lecture Notes in Physics 365. Springer Verlag. "Polarizability of the Nucleon and Compton Scattering" Martin Schumacher, Prog. Part. Nucl. Phys. 55 (2005) 567.
From 2002: Theoretical studies on Compton scattering by the nucleon and related processes. Structure of the constituent quark and its relevance for the fundamental structure constants of the nucleon and the structure of the nucleon.
Recent publications:
[1] "Structure of the -meson and diamagnetism of the nucleon", M.I. Levchuk, A.I. L'vov, A.I. Milstein, M. Schumacher, Proceedings of the Workshop on the Physics of Excited Nucleons, NSTAR 2005, p. 389; arXiv:hep-ph/0511193.
[2] "Electromagnetic polarizabilities of the nucleon and properties of the -meson pole contribution" Eur. Phys. J. A 30, 413 (2006);ERRATUM: Eur. Phys. J. A 32, 121 (2007); [hep-ph/0609040].
[3] "Electromagnetic polarizabilities and the excited states of the nucleon" Eur. Phys. J. A 31, 327 (2007) [hep-ph/0704.0200].
[4] "Properties of the , , , , and mesons and their relevance for the polarizabilities of the nucleon" M. Schumacher, Eur. Phys. J. A 34, 293 (2007) [ hep-ph/0712.1417].
[5] "Scalar mesons and polarizabilities of the nucleon" M. Schumacher, AIP Conference Proceedings 1030, 129 (2008), arXiv:0803.1074 [hep-ph].
[6] "Note on the magnetic moment of the nucleon" M. Schumacher, arXiv:0805.2823 [hep-ph].
[7] "Polarizabilities of the nucleon and spin dependent photo-absorption" M. Schumacher, Nucl. Phys. A 826 (2009) 131, arXiv:0905.4363 [hep-ph].
[8] "Observation of the Higgs Boson of strong interaction via Compton scattering by the nucleon" M. Schumacher, Eur. Phys. J. C 67, 283 (2010), arXiv:1001.0500 [hep-ph].
[9] "Structure of the nucleon and spin-polarizabilities" Martin Schumacher, M.I. Levchuk, Nucl. Phys. A 858 (2011) 48-66, doi:10.1016/j.nuclphys.2011.04.002; arXiv:1104.3721 [hep-ph].
[10] "Structure of scalar mesons and the Higgs sector of strong interaction" Martin Schumacher, Journal of Physics G: Nucl. Part. Phys. 38 (2011) 083001; arXiv:1106.1015 [hep-ph].
[11] "Conference Report: Structure of scalar mesons and the Higgs sector of strong interaction" Martin Schumacher, XIV International Conference on Hadron Spectroscopy, Munich, Germany 13 - 17 June 2011, arXiv:1107.4226 [hep-ph].
[12] "Dispersion theory of nuclear Compton scattering and polarizabilities" Martin Schumacher and Michael D. Scadron, Fortschr. Phys. 61, 703 (2013) arXiv:1301.1567 [hep-ph].
[13] "Dispersion theory of nucleon polarizabilities and outlook on chiral effective field theory"Martin Schumacher, arXiv:1307.2215 [hep-ph].
[14] "Nambu's Nobel Prize, the meson and the mass of visible matter" Martin Schumacher, Ann. Phys. (Berlin) 526, 215 (2014); arXiv:1403.7804 [hep-ph].
[15] "Mass generation via the Higgs boson and the quark condensate of the QCD vacuum" Martin Schumacher, PRAMANA - J. Phys. (2016) 87:44; arXiv:1506:00410 [hep-ph].
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Benutzer:Mschuma3/Wikipedia aktuell Artikel des Tages =Polarizability of the nucleon=
Preface[edit] The polarizabilities belong to the fundamental structure constants of the nucleon, in addition to the mass, the electric charge, the spin and the magnetic moment. The proposal to measure the polarizabilities dates back to the 1950th. Two experimental options were considered (i) Compton scattering by the proton and (ii) the scattering of slow neutrons in the Coulomb field of heavy nuclei. The idea was that the nucleon with its pion cloud obtains an electric dipole moment under the action of an electric field vector which is proportional to the electric polarizability. After the discovery of the photoexcitation of the Δ resonance it became obvious that the nucleon also should have a strong paramagnetic polarizability, because of a virtual spin-flip transition of one of the constituent quarks due to the magnetic field vector provided by a real photon in a Compton scattering experiment. However, experiments showed that this expected strong paramagnetism is not observed. Apparently a strong diamagnetism exists which compensates the expected strong paramagnetism. Though this explanation is straightforward, it remained unknown how it may be understood in terms of the structure of the nucleon. A solution of this problem was found very recently when it was shown that the diamagnetism is a property of the structure of the constituent quarks. In retrospect this is not a surprise, because constituent quarks generate their mass mainly through interactions with the QCD vacuum via the exchange of a σ meson. This mechanims is predicted by the linear σ model on the quark level (QLLσM) which also predicts the mass of the σ meson to be mσ=666 MeV. The σ meson has the capability of interacting with two photons being in parallel planes of linear polarization. We will show in the following that the σ meson as part of the constituent quark structure, therefore, provides the largest part of the electric polarizability and the total diamagnetic polarizability. Definition of electromagnetic polarizabilities[edit] A nucleon in an electric field E and a magnetic field H obtains an electric dipole moment d and magnetic dipole moment m given by.[1] {\displaystyle {\mathbf {d} }\,\,=4\pi \,\alpha \,{\mathbf {E} }} Vorlage:\mathbf d\,\,=4\pi \,\alpha \,Vorlage:\mathbf E {\displaystyle {\mathbf {m} }=4\pi \,\beta \,{\mathbf {H} }} Vorlage:\mathbf m=4\pi \,\beta \,Vorlage:\mathbf H in a unit system where the electric charge {\displaystyle e} e is given by {\displaystyle e^{2}/4\pi =\alpha _{e}=1/137.04} e^{2}/4\pi =\alpha _{e}=1/137.04. The proportionality constants {\displaystyle \alpha } \alpha and {\displaystyle \beta } \beta are denoted as the electric and magnetic polarizabilities, respectively. These polarizabilities may be understood as a measure of the response of the nucleon structure to the fields provided by a real or virtual photon and it is evident that we need a second photon to measure the polarizabilities. This may be expressed through the relations {\displaystyle \delta W=-{\frac {1}{2}}\,4\pi \,\alpha \,{\mathbf {E} }^{2}-{\frac {1}{2}}\,4\pi \,\beta \,{\mathbf {H} }^{2}} \delta W=-{\frac 12}\,4\pi \,\alpha \,Vorlage:\mathbf E^{2}-{\frac 12}\,4\pi \,\beta \,Vorlage:\mathbf H^{2} where {\displaystyle \delta W} \delta W is the energy change in the electromagnetic field due to the presence of the nucleon in the field. The definition implies that the polarizabilities are measured in units of a volume, i.e. in units of fm {\displaystyle ^{3}} ^{3} (1 fm= {\displaystyle 10^{-15}} 10^{-15} m). Modes of two-photon reactions and experimental methods[edit] Static electric fields of sufficient strength are provided by the Coulomb field of heavy nuclei. Therefore, the electric polarizability of the neutron can be measured by scattering slow neutrons in the electric field E of a Pb nucleus. The neutron has no electric charge. Therefore, two simultaneously interacting electric field vectors (two virtual photons) are required to produce a deflection of the neutron. Then the electric polarizability can be obtained from the differential cross section measured at a small deflection angle. A further possibility is provided by Compton scattering of real photons by the nucleon, where during the scattering process two electric and two magnetic field vectors simultaneously interact with the nucleon. In the following we discuss the experimental options we have to measure the polarizabilities of the nucleon. As outlined above two photons are needed which simultaneously interact with the electrically charged parts of the nucleon. These photons may be in parallel or perpendicular planes of linear polarization and in these two modes measure the polarizabilities {\displaystyle \alpha } \alpha , {\displaystyle \beta } \beta or spinpolarizabilities {\displaystyle \gamma } \gamma , respectively. The spinpolarizability is nonzero only for particles having a spin. In total the experimental options discussed above provide us with 6 combinations of two electric and magnetic field vectors. These are described in the following two equations: Photons in parallel planes of linear polarization {\displaystyle ({\text{case}}\,1)\,\,\alpha :\,\,\,\,{\mathbf {E} }\uparrow \uparrow {\mathbf {E} }'\quad \quad ({\text{case}}\,2)\,\,\beta :\,{\mathbf {H} }\rightarrow \rightarrow {\mathbf {H} }'\quad \,({\text{case}}\,\,3)\,\,-\beta :\,{\mathbf {H} }\rightarrow \leftarrow {\mathbf {H} }'} ({\text{case}}\,1)\,\,\alpha :\,\,\,\,Vorlage:\mathbf E\uparrow \uparrow Vorlage:\mathbf E'\quad \quad ({\text{case}}\,2)\,\,\beta :\,Vorlage:\mathbf H\rightarrow \rightarrow Vorlage:\mathbf H'\quad \,({\text{case}}\,\,3)\,\,-\beta :\,Vorlage:\mathbf H\rightarrow \leftarrow Vorlage:\mathbf H' Photons in perpendicular planes of linear polarization {\displaystyle ({\text{case}}\,\,4)\,\,\gamma _{E}:{\mathbf {E} }\uparrow \rightarrow {\mathbf {E} }'\quad \,\,({\text{case}}\,\,5)\,\,\gamma _{H}:{\mathbf {H} }\rightarrow \downarrow {\mathbf {H} }'\quad \,\,({\text{case}}\,\,6)\,\,-\gamma _{H}:{\mathbf {H} }\rightarrow \uparrow {\mathbf {H} }'} ({\text{case}}\,\,4)\,\,\gamma _{E}:Vorlage:\mathbf E\uparrow \rightarrow Vorlage:\mathbf E'\quad \,\,({\text{case}}\,\,5)\,\,\gamma _{H}:Vorlage:\mathbf H\rightarrow \downarrow Vorlage:\mathbf H'\quad \,\,({\text{case}}\,\,6)\,\,-\gamma _{H}:Vorlage:\mathbf H\rightarrow \uparrow Vorlage:\mathbf H' Case (1) corresponds to the measurement of the electric polarizability {\displaystyle \alpha } \alpha via two parallel electric field vectors E. These parallel electric field vectors may either be provided as longitudinal photons by the Coulomb field of a heavy nucleus, or by Compton scattering in the forward direction or by reflecting the photon by 180°. Real photons simultaneously provide transvers electric E and magnetic H field vectors. This means that in a Compton scattering experiment linear combinations of electric and magnetic polarizabilities and linear combinations of electric and magnetic spinpolarizabilities are measured. The combination of case (1) and case (2) measures {\displaystyle \alpha +\beta } \alpha +\beta and is observed in forward-direction Compton scattering. The combination of case (1) and case (3) measures {\displaystyle \alpha -\beta } \alpha -\beta and is observed in backward-direction Compton scattering.The combination of case (4) and case (5) measures {\displaystyle \gamma _{0}\equiv \gamma _{E}+\gamma _{H}} \gamma _{0}\equiv \gamma _{E}+\gamma _{H} and is observed in forward-direction Compton scattering. The combination of case (4) and case (6) measures {\displaystyle \gamma _{\pi }\equiv \gamma _{E}-\gamma _{H}} \gamma _{\pi }\equiv \gamma _{E}-\gamma _{H} and is observed in backward-direction Compton scattering. Compton scattering experiments exactly in the forward direction and exactly in the backward direction are not possible from a technical point of view. Therefore, the respective quantities have to be extracted from Compton scattering experiments carried out at intermediate angles. Experimental results[edit] The experimental polarizabilities of the proton (p) and the neutron (n) may be summarized as follows[1] [2][3] {\displaystyle \alpha _{p}=12.0\pm 0.6,\quad \beta _{p}=1.9\mp 0.6,\quad \alpha _{n}=12.5\pm 1.7,\quad \beta _{n}=2.7\mp 1.8\,{\text{ in units of}}\,\,10^{-4}\,{\rm {fm}}^{3}} \alpha _{p}=12.0\pm 0.6,\quad \beta _{p}=1.9\mp 0.6,\quad \alpha _{n}=12.5\pm 1.7,\quad \beta _{n}=2.7\mp 1.8\,{\text{ in units of}}\,\,10^Vorlage:-4\,{{\rm {fm}}}^{3}. The experimental spinpolarizabilities of the proton (p) and neutron (n) are {\displaystyle \gamma _{\pi }^{(p)}=-36.4\pm 1.5,\quad \gamma _{\pi }^{(n)}=58.6\pm 4.0\,{\text{ in units of}}\,\,10^{-4}\,{\rm {fm}}^{4}} \gamma _{\pi }^Vorlage:(p)=-36.4\pm 1.5,\quad \gamma _{\pi }^Vorlage:(n)=58.6\pm 4.0\,{\text{ in units of}}\,\,10^Vorlage:-4\,{{\rm {fm}}}^{4}. The experimental polarizabilities of the proton have been obtained as an average from a larger number of Compton scattering experiments. The experimental electric polarizability of the neutron is the average of an experiment on electromagnetic scattering of a neutron in the Coulomb field of a Pb nucleus and a Compton scattering experiment on a quasifree neutron, i.e. a neutron separated from a deuteron during the scattering process. The two results are (see [1]) {\displaystyle \alpha _{n}=12.6\pm 2.5} \alpha _{n}=12.6\pm 2.5 from electromagnetic scattering of a slow neutron in the electric field of a Pb nucleus, and {\displaystyle \alpha _{n}=12.5\pm 2.3} \alpha _{n}=12.5\pm 2.3 from quasifree Compton scattering by a neutron initially bound in the deuteron. The average given above is obtained from these two numbers. Furthermore, there are ongoing experiments at the University of Lund (Sweden) where the electric polarizability of the neutron is determined through Compton scattering by the deuteron. Calculation of polarizabilities[edit] Recently great progress has been made in disentangling the total photoabsorption cross section into parts separated by the spin, the isospin and the parity of the intermediate state, using the meson photoproduction amplitudes of Drechsel et al.[4] The spin of the intermediate state may be {\displaystyle s=1/2} s=1/2 or {\displaystyle s=3/2} s=3/2 depending on the spin directions of the photon and the nucleon in the initial state. The parity change during the transion from the ground state to the intermediate state is {\displaystyle \Delta P={\text{yes}}} \Delta P={\text{yes}} for the multipoles {\displaystyle E1,\,M2,\cdots } E1,\,M2,\cdots and {\displaystyle \Delta P={\text{no}}} \Delta P={\text{no}} for the multipoles {\displaystyle M1,\,E2,\cdots } M1,\,E2,\cdots . Calculating the respective partial cross sections from photo-meson data, the following sum rules can be evaluated: {\displaystyle \alpha +\beta ={\frac {1}{2\pi ^{2}}}\int _{\omega _{0}}^{\infty }{\frac {\sigma _{\rm {tot}}(\omega )}{\omega ^{2}}}d\omega } \alpha +\beta ={\frac {1}{2\pi ^{2}}}\int _{{\omega _{0}}}^{\infty }{\frac {\sigma _{{{\rm {tot}}}}(\omega )}{\omega ^{2}}}d\omega , {\displaystyle \alpha -\beta ={\frac {1}{2\pi ^{2}}}\int _{\omega _{0}}^{\infty }{\sqrt {1+{\frac {2\omega }{m}}}}\left[\sigma (\omega ,E1,M2,\cdots )-\sigma (\omega ,M1,E2,\cdots )\right]{\frac {d\omega }{\omega ^{2}}}+(\alpha -\beta )^{t}} \alpha -\beta ={\frac {1}{2\pi ^{2}}}\int _{{\omega _{0}}}^{\infty }{\sqrt {1+{\frac {2\omega }{m}}}}\left[\sigma (\omega ,E1,M2,\cdots )-\sigma (\omega ,M1,E2,\cdots )\right]{\frac {d\omega }{\omega ^{2}}}+(\alpha -\beta )^{t}, {\displaystyle \gamma _{0}=-{\frac {1}{4\pi ^{2}}}\int _{\omega _{0}}^{\infty }{\frac {\sigma _{3/2}(\omega )-\sigma _{1/2}(\omega )}{\omega ^{3}}}d\omega } \gamma _{0}=-{\frac {1}{4\pi ^{2}}}\int _{{\omega _{0}}}^{\infty }{\frac {\sigma _Vorlage:3/2(\omega )-\sigma _Vorlage:1/2(\omega )}{\omega ^{3}}}d\omega , {\displaystyle \gamma _{\pi }={\frac {1}{4\pi ^{2}}}\int _{\omega _{0}}^{\infty }{\sqrt {1+{\frac {2\omega }{m}}}}\left(1+{\frac {\omega }{m}}\right)\sum _{n}P_{n}[\sigma _{3/2}^{n}(\omega )-\sigma _{1/2}^{n}(\omega )]{\frac {d\omega }{\omega ^{3}}}+\gamma _{\pi }^{t}} \gamma _{\pi }={\frac {1}{4\pi ^{2}}}\int _{{\omega _{0}}}^{\infty }{\sqrt {1+{\frac {2\omega }{m}}}}\left(1+{\frac {\omega }{m}}\right)\sum _{n}P_{n}[\sigma _Vorlage:3/2^{n}(\omega )-\sigma _Vorlage:1/2^{n}(\omega )]{\frac {d\omega }{\omega ^{3}}}+\gamma _{\pi }^{t}, {\displaystyle P_{n}=-1\,{\text{for}}\,E1,M2,\cdots \,{\text{multipoles and}}\,P_{n}=+1\,{\text{for}}\,M1,E2,\cdots \,{\text{multipoles}}} P_{n}=-1\,{\text{for}}\,E1,M2,\cdots \,{\text{multipoles and}}\,P_{n}=+1\,{\text{for}}\,M1,E2,\cdots \,{\text{multipoles}}. {\displaystyle (\alpha -\beta )^{t}={\frac {1}{2\pi }}\left[{\frac {g_{\sigma NN}{M}(\sigma \to \gamma \gamma )}{m_{\sigma }^{2}}}+{\frac {g_{f_{0}NN}{M}(f_{0}\to \gamma \gamma )}{m_{f_{0}}^{2}}}+{\frac {g_{a_{0}NN}{M}(a_{0}\to \gamma \gamma )}{m_{a_{0}}^{2}}}\tau _{3}\right]} (\alpha -\beta )^{t}={\frac {1}{2\pi }}\left[{\frac {g_Vorlage:\sigma NN{M}(\sigma \to \gamma \gamma )}{m_{\sigma }^{2}}}+{\frac {g_{{f_{0}NN}}{M}(f_{0}\to \gamma \gamma )}{m_{{f_{0}}}^{2}}}+{\frac {g_{{a_{0}NN}}{M}(a_{0}\to \gamma \gamma )}{m_{{a_{0}}}^{2}}}\tau _{3}\right], {\displaystyle \gamma _{\pi }^{t}={\frac {1}{2\pi m}}\left[{\frac {g_{\pi NN}{M}(\pi ^{0}\to \gamma \gamma )}{m_{\pi ^{0}}^{2}}}\tau _{3}+{\frac {g_{\eta NN}{M}(f_{0}\to \gamma \gamma )}{m_{\eta }^{2}}}+{\frac {g_{\eta 'NN}{M}(a_{0}\to \gamma \gamma )}{m_{\eta '}^{2}}}\right]} \gamma _{\pi }^{t}={\frac {1}{2\pi m}}\left[{\frac {g_Vorlage:\pi NN{M}(\pi ^{0}\to \gamma \gamma )}{m_{{\pi ^{0}}}^{2}}}\tau _{3}+{\frac {g_Vorlage:\eta NN{M}(f_{0}\to \gamma \gamma )}{m_{\eta }^{2}}}+{\frac {g_Vorlage:\eta 'NN{M}(a_{0}\to \gamma \gamma )}{m_Vorlage:\eta '^{2}}}\right]. where {\displaystyle \omega } \omega is the photon energy in the lab frame. The sum rules for {\displaystyle \alpha +\beta } \alpha +\beta and {\displaystyle \gamma _{0}} \gamma _{0} depend on nucleon-structure degrees of freedom only, whereas the sum rules for {\displaystyle \alpha -\beta } \alpha -\beta and {\displaystyle \gamma _{\pi }} \gamma _{\pi } have to be supplemented by the quantities {\displaystyle (\alpha -\beta )^{t}} (\alpha -\beta )^{t} and {\displaystyle \gamma _{\pi }^{t}} \gamma _{\pi }^{t}, respectively. These are {\displaystyle t} t-channel contributions which may be interpreted as contributions of scalar and pseudoscalar mesons being parts of the constituent-quark structure. The sum rule for {\displaystyle \alpha +\beta } \alpha +\beta depends on the total photoabsorption cross section and, therefore, does not require a disentangling with respect to quantum numbers. The sum rule for {\displaystyle \alpha -\beta } \alpha -\beta requires a disentangling with respect to the parity change of the transition. The sum rule for {\displaystyle \gamma _{0}} \gamma _{0} requires a disentangling with respect to the spin of the intermediate state. The sum rule for {\displaystyle \gamma _{\pi }} \gamma _{\pi } requires a disentangling with respect to spin and parity change. The {\displaystyle t} t-channel contributions depend on those scalar and pseudoscalar mesons which (i) are part of the structure of the constituent quarks and (ii) are capable of coupling to two photons. These are the mesons {\displaystyle \sigma (600)} \sigma (600), {\displaystyle f_{0}(980)} f_{0}(980) and {\displaystyle a_{0}(980)} a_{0}(980) in case of {\displaystyle (\alpha -\beta )^{t}} (\alpha -\beta )^{t}, and the mesons {\displaystyle \pi ^{0}} \pi ^{0}, {\displaystyle \eta } \eta and {\displaystyle \eta '} \eta ' in case of {\displaystyle \gamma _{\pi }^{t}} \gamma _{\pi }^{t}. The contributions are dominated by the {\displaystyle \sigma } \sigma and the {\displaystyle \pi ^{0}} \pi ^{0} whereas the other mesons only lead to small corrections. Results of calculation[edit] The results of the calculation are summarized in the following eight equations [2][3]: {\displaystyle \alpha _{p}=\,\,\,+4.5\,{\text{(nucleon)}}+7.5\,{\text{(const. quark)}}=+12.0} \alpha _{p}=\,\,\,+4.5\,{\text{(nucleon)}}+7.5\,{\text{(const. quark)}}=+12.0 {\displaystyle \beta _{p}=\,\,\,+9.4\,{\text{(nucleon)}}-7.5\,{\text{(const. quark)}}=\,\,\,+1.9} \beta _{p}=\,\,\,+9.4\,{\text{(nucleon)}}-7.5\,{\text{(const. quark)}}=\,\,\,+1.9 {\displaystyle \alpha _{n}=\,\,\,+5.1\,{\text{(nucleon)}}+8.3\,{\text{(const. quark)}}=+13.4} \alpha _{n}=\,\,\,+5.1\,{\text{(nucleon)}}+8.3\,{\text{(const. quark)}}=+13.4 {\displaystyle \beta _{n}=+10.1\,{\text{(nucleon)}}-8.3\,{\text{(const. quark)}}=\,\,\,+1.8\,\,{\text{in units of}}\,\,10^{-4}{\rm {fm}}^{3}} \beta _{n}=+10.1\,{\text{(nucleon)}}-8.3\,{\text{(const. quark)}}=\,\,\,+1.8\,\,{\text{in units of}}\,\,10^Vorlage:-4{{\rm {fm}}}^{3} {\displaystyle \gamma _{0}^{(p)}=\,\,\,-0.58\pm 0.20\,{\text{(nucleon)}}} \gamma _{0}^Vorlage:(p)=\,\,\,-0.58\pm 0.20\,{\text{(nucleon)}} {\displaystyle \gamma _{0}^{(n)}=\,\,\,+0.38\pm 0.22\,{\text{(nucleon)}}} \gamma _{0}^Vorlage:(n)=\,\,\,+0.38\pm 0.22\,{\text{(nucleon)}} {\displaystyle \gamma _{\pi }^{(p)}=\,\,\,+8.5\,{\text{(nucleon)}}-45.1\,\,{\text{(const. quark)}}=-36.6} \gamma _{\pi }^Vorlage:(p)=\,\,\,+8.5\,{\text{(nucleon)}}-45.1\,\,{\text{(const. quark)}}=-36.6 {\displaystyle \gamma _{\pi }^{(n)}=+10.0\,{\text{(nucleon)}}+48.3\,\,{\text{(const. quark)}}=+58.3\,\,{\text{in units of}}\,\,10^{-4}{\rm {fm}}^{4}} \gamma _{\pi }^Vorlage:(n)=+10.0\,{\text{(nucleon)}}+48.3\,\,{\text{(const. quark)}}=+58.3\,\,{\text{in units of}}\,\,10^Vorlage:-4{{\rm {fm}}}^{4} The electric polarizabilities {\displaystyle \alpha _{p}} \alpha _{p} and {\displaystyle \alpha _{n}} \alpha_n are dominated by a smaller component due to the pion cloud (nucleon) and a larger component due to the {\displaystyle \sigma } \sigma meson as part of the constituent-quark structure (const. quark). The magnetic polarizabilities {\displaystyle \beta _{p}} \beta _{p} and {\displaystyle \beta _{n}} \beta _{n} have a large paramagnetic part due to the spin structure of the nucleon (nucleon) and an only slightly smaller diamagnetic part due to the {\displaystyle \sigma } \sigma meson as part of the constituent-quark structure (const. quark). The contributions of the {\displaystyle \sigma } \sigma meson are supplemented by small corrections due to {\displaystyle f_{0}(980)} f_{0}(980) and {\displaystyle a_{0}(980)} a_{0}(980) mesons [2] .[3][5][6][7][8][9] The spinpolarizabilities {\displaystyle \gamma _{0}^{(p)}} \gamma _{0}^Vorlage:(p) and {\displaystyle \gamma _{0}^{(n)}} \gamma _{0}^Vorlage:(n) are dominated by destructively interfering components from the pion cloud and the spin structure of the nucleon. The different signs obtained for the proton and the neutron are due to this destructive interference. The spinpolarizabilities {\displaystyle \gamma _{\pi }^{(p)}} \gamma _{\pi }^Vorlage:(p) and {\displaystyle \gamma _{\pi }^{(n)}} \gamma _{\pi }^Vorlage:(n) have a minor component due to the structure of the nucleon (nucleon) and a major component due to the pseudoscalar mesons {\displaystyle \pi ^{0}} \pi ^{0}, {\displaystyle \eta } \eta and {\displaystyle \eta '} \eta ' as structure components of the constituent quarks (const. quark). The agreement with the experimental data is excellent in all eight cases. Summary[edit] In the foregoing we have shown that the polarizabilities of the nucleon are well understood. Differing from previous belief the mesonic structure of the constituent quark is essential for the sizes and the general properties of the polarizabilities. Linear polarizability[edit] In the definition of the polarizability the Induced dipole is proportional to the electric field. Shouldn't it be mentioned in the article that this assumes low enough electric fields such that only the linear term that contribute to the induced dipole. I believe the article should also mention higher order processes or refer to them, which each have their own non-linear susceptibility. Eranus (talk) 09:15, 25 February 2014 (UTC) Answer: The polarizabilities are dependent on the photon energy {\displaystyle \omega } \omega . The numbers given above refer to the case {\displaystyle \omega \rightarrow 0} \omega \rightarrow 0. Details may be found in references [7] and [8] given below. ^ Jump up to: a b c M. Schumacher, Prog. Part. Nucl. Phys. 55 (2005) 567, arXiv:hep-ph/0501167. ^ Jump up to: a b c M. Schumacher, Nucl. Phys. A 826 (2009) 131, arXiv:0905.4363 [hep-ph]. ^ Jump up to: a b c M. Schumacher, M.I. Levchuk. Nucl. Phys. A 858 (2011) 48, arXiv:1104.3721 [hep-ph]. Jump up ^ D. Drechsel, S.S. Kamalov, L. Tiator, Eur. Phys. J. A 34 (2007) 69, arXiv:0710.0306 [nucl.-th]. Jump up ^ M. Schumacher, Eur. Phys. J. C 67 (2010) 283, arXiv:1001.0500 [hep-ph]. Jump up ^ M. Schumacher, Journal of Physics G: Nucl. Part. Phys. 38 (2011) 083001, arXiv:1106.1015 [hep-ph]. Jump up ^ M. Schumacher, M.D. Scadron, Fortschr. Phys. 61, 703 (2013); arXiv:1301.1567 [hep-ph] Jump up ^ M. Schumacher, arXiv:1307.2215 [hep-ph] Jump up ^ M. Schumacher, Ann. Phys. (Berlin) 526, 215 (2014); arXiv:1403.7804 [hep-ph] Categories: Start-Class physics articlesStart-Class physics articles of Mid-importanceMid-importance physics articlesStart-Class physics articles of High-importanceHigh-importance physics articles Navigation menu Mschuma3 Alert (1) Notice (1) TalkSandboxPreferencesBetaWatchlistContributionsLog outArticleTalkReadEditNew sectionView historyWatch More Search Search Wikipedia Go Main page Contents Featured content Current events Random article Donate to Wikipedia Wikipedia store Interaction Help About Wikipedia Community portal Recent changes Contact page Tools What links here Related changes Upload file Special pages Permanent link Page information Print/export Create a book Download as PDF Printable version Languages This page was last edited on 28 April 2016, at 18:00. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. 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