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The electrical polarizability of the meson cloud in the nucleon
7.C
Nuclear Physics9 (1958/59) 426--428 ; ©North-Holland Publishing Co .,Amsterdana Not to be reproduced by photoprint or microfilm without written permission from the publisher
T E ELECT ICAL POLARIZABILITY OF THE MESON CLOUD IN THE NUCLEON V. S. BARASHENKOV and B. M. BARBASHOV joint Institute of Nuclear Research, Laboratory of Theoretical Physics, DuNsa, USSR Received 5 March 1958
An analysis of experiments on the scattering of fast electrons on hydrogen and deuterium, and slow neutrons on atoms leads to a result which is in contradiction to the conclusions of modern meson theory, namely, that the mean root square "electrical radius" of the neutron is practically zero. In this connection it becomes highly important to consider other effects which may reveal the "electromagnetic structure" of the nucleon. One such effect is the scattering of slow nucleons in an inhomogeneous electrical field (in particular, neutrons in the Coulomb field of the nucleus 1-3)), in which the cloud of charges of different signs in the nucleon becomes polarized and the nucleon is transformed into an electric dipole with an induced moment. The electrical polarizability of the charges in the nucleon manifests itself in the Compton effect and in the photoproduction of pions on nucleons 4), as well as in the scattering of slow neutrons on atoms.
nucleon line meson I ine photon line
We estimated the magnitude of the electrical polarizability of the meson cloud in the nucleon by means of the first approximation of Chew's theory s) (see fig. 1). The corresponding matrix element hai the form : 426
THE ELECTRICAL POLARIZABILITI
°I ® --
f u(k) 1s (k')V (n-k)V (k'-n)
f 2 e2,
ks (o
lf
(Wk+W )
with
0)k2
427
= k2+12; u (k)
(u k,+ (on)k'p kP d3(kk' n) (2n)9
( 1)
= f u(x)e_*"d3 x
denotes the form factor of the source, and V(k)
= f V(x)e_¢k - ad3 x
(3)
the scalar electric potential . The remaining designations are the standard ones. Since in the given case the vector part of the electromagnetic field is zero, the interaction with the electromagnetic field can be written down uniquely, and the theory is gauge invariant (cf. ?)) . For the case of a homogeneous field â V (k) = i(2n)3E,. 6(k) âkthe matrix element (1) may be represented in the form M
= - JaE2
where the electrical polarizability x
_
(,u/)2
e2
2
3Z,u
f
CIO
k u2(k) (27k4-34k2 Co o tote
2) -
4k 2cok4 dk dk 12
~~ u(k)
(6
with Wk2 = k 2 + 1 (we utilize the coordinate system for which El = E 2 = E3) . It may be expected, as in the computation of the magnetic moment of the nucleon and the potential of neutron-electron interaction 9), that the higher terms in the series development in the constant //Ft do not essentially affect the result (6). One finds for
it (k) ----
k for u(k) = exp [ 2(5 .6)2
oc = 1.6 X 10 -42 cm3 a = 1 .8x 10-4zcm3 .
(The same form functions have been chosen as in ref. a ) .) These values of a were obtained for /2 /kc = 0.08. The results of the computations are but slightly sensitive to the given choice of u(k) .
428
V. S. BARASHENKOV AND B. M. BARBASHOV
The computed value of a is close to that obtained by Baldin from an analysis of experiments on the photoproduction of pious and the Compton effect on the nucleon 4) 4 X 10-43 cms S oc S 1 .4 X 10-42 cm3 and is considerably less than the value of a obtained by Alexandrov from experiments on the scattering of slow neutrons a-3) (a ;k:% 5 X 10-41 CMS) . A more thorough analysis of these experiments is necessary. We observe that the effects involving the polarizability a rapidly increase with a decrease in the energy of the scattered neutron . We take pleasure in expressing our gratitude to D. 1 . Blokhintsev and A. A. Logunov for numerous discussions. We also thank N. N. Bogolubov for discussing the results with us. eferences l) V . S . Barashenkov, I . P. Stakhanov and Yu . A . Aleksandrov, JETP 32 (1957) 154 2) Yu . A . Aleksandrov, JETP 33 (1957) 294 3) Yu . A . Aleksandrov and V . S. Barashenkov, communication and discussion at the AllUnion Conference on low and average energy nuclear reactions (Moscow, November, (1957 ) 4) A . S. Baldin, Proceedings of the Conference in Padua-Venice (September 1957) 5) Drell and Ruderman, Phy° . Rev. 106 (1957) 561 6) F . Chew, Phys. Rev. 94 (1954) 1748, 1755 7) R . H . Capps, Phys. Rev. 99 (1955) 926 ; R. H . Capps and W . G . Holladay, Phys . Rev . 99 (1955) 931 8) G. Salzman, Phys . Rev . 99 (1955) 973 9) H . Miyazawa, Phys . Rev . 101 (1956) 1564 ; S. Treiman and R . G. Sachs, Phys . Rev . 103 (1956) 435
Nuclear Physics9 (1958/59) 426--428 ; ©North-Holland Publishing Co .,Amsterdana Not to be reproduced by photoprint or microfilm without written permission from the publisher
T E ELECT ICAL POLARIZABILITY OF THE MESON CLOUD IN THE NUCLEON V. S. BARASHENKOV and B. M. BARBASHOV joint Institute of Nuclear Research, Laboratory of Theoretical Physics, DuNsa, USSR Received 5 March 1958
An analysis of experiments on the scattering of fast electrons on hydrogen and deuterium, and slow neutrons on atoms leads to a result which is in contradiction to the conclusions of modern meson theory, namely, that the mean root square "electrical radius" of the neutron is practically zero. In this connection it becomes highly important to consider other effects which may reveal the "electromagnetic structure" of the nucleon. One such effect is the scattering of slow nucleons in an inhomogeneous electrical field (in particular, neutrons in the Coulomb field of the nucleus 1-3)), in which the cloud of charges of different signs in the nucleon becomes polarized and the nucleon is transformed into an electric dipole with an induced moment. The electrical polarizability of the charges in the nucleon manifests itself in the Compton effect and in the photoproduction of pions on nucleons 4), as well as in the scattering of slow neutrons on atoms.
nucleon line meson I ine photon line
We estimated the magnitude of the electrical polarizability of the meson cloud in the nucleon by means of the first approximation of Chew's theory s) (see fig. 1). The corresponding matrix element hai the form : 426
THE ELECTRICAL POLARIZABILITI
°I ® --
f u(k) 1s (k')V (n-k)V (k'-n)
f 2 e2,
ks (o
lf
(Wk+W )
with
0)k2
427
= k2+12; u (k)
(u k,+ (on)k'p kP d3(kk' n) (2n)9
( 1)
= f u(x)e_*"d3 x
denotes the form factor of the source, and V(k)
= f V(x)e_¢k - ad3 x
(3)
the scalar electric potential . The remaining designations are the standard ones. Since in the given case the vector part of the electromagnetic field is zero, the interaction with the electromagnetic field can be written down uniquely, and the theory is gauge invariant (cf. ?)) . For the case of a homogeneous field â V (k) = i(2n)3E,. 6(k) âkthe matrix element (1) may be represented in the form M
= - JaE2
where the electrical polarizability x
_
(,u/)2
e2
2
3Z,u
f
CIO
k u2(k) (27k4-34k2 Co o tote
2) -
4k 2cok4 dk dk 12
~~ u(k)
(6
with Wk2 = k 2 + 1 (we utilize the coordinate system for which El = E 2 = E3) . It may be expected, as in the computation of the magnetic moment of the nucleon and the potential of neutron-electron interaction 9), that the higher terms in the series development in the constant //Ft do not essentially affect the result (6). One finds for
it (k) ----
k for u(k) = exp [ 2(5 .6)2
oc = 1.6 X 10 -42 cm3 a = 1 .8x 10-4zcm3 .
(The same form functions have been chosen as in ref. a ) .) These values of a were obtained for /2 /kc = 0.08. The results of the computations are but slightly sensitive to the given choice of u(k) .
428
V. S. BARASHENKOV AND B. M. BARBASHOV
The computed value of a is close to that obtained by Baldin from an analysis of experiments on the photoproduction of pious and the Compton effect on the nucleon 4) 4 X 10-43 cms S oc S 1 .4 X 10-42 cm3 and is considerably less than the value of a obtained by Alexandrov from experiments on the scattering of slow neutrons a-3) (a ;k:% 5 X 10-41 CMS) . A more thorough analysis of these experiments is necessary. We observe that the effects involving the polarizability a rapidly increase with a decrease in the energy of the scattered neutron . We take pleasure in expressing our gratitude to D. 1 . Blokhintsev and A. A. Logunov for numerous discussions. We also thank N. N. Bogolubov for discussing the results with us. eferences l) V . S . Barashenkov, I . P. Stakhanov and Yu . A . Aleksandrov, JETP 32 (1957) 154 2) Yu . A . Aleksandrov, JETP 33 (1957) 294 3) Yu . A . Aleksandrov and V . S. Barashenkov, communication and discussion at the AllUnion Conference on low and average energy nuclear reactions (Moscow, November, (1957 ) 4) A . S. Baldin, Proceedings of the Conference in Padua-Venice (September 1957) 5) Drell and Ruderman, Phy° . Rev. 106 (1957) 561 6) F . Chew, Phys. Rev. 94 (1954) 1748, 1755 7) R . H . Capps, Phys. Rev. 99 (1955) 926 ; R. H . Capps and W . G . Holladay, Phys . Rev . 99 (1955) 931 8) G. Salzman, Phys . Rev . 99 (1955) 973 9) H . Miyazawa, Phys . Rev . 101 (1956) 1564 ; S. Treiman and R . G. Sachs, Phys . Rev . 103 (1956) 435