А. Я. Силенко Учет вращения Земли в экспериментах по поиску

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¸ ʲÓÉ· Ìμ²μ¤´Ò³¨ ´¥°É·μ´ ³¨ ÔÉ ¶μ¶· ¢± ¶·¥¢ÒÏ ¥É ¸¨¸É¥³ ɨΥ¸±ÊÕ ¶μ£·¥Ï´μ¸ÉÓ ¨§³¥·¥´¨Ö „Œ ´¥°É·μ´ , ¶·¨Î¥³ ¥¥ ÉμδҰ · ¸Î¥É É·¥¡Ê¥É ¤μ¶μ²´¨É¥²Ó´ÒÌ ¨¸¸²¥¤μ¢ ´¨°. ‚ ¸¢Ö§¨ ¸
Ôɨ³ ¤ ²Ó´¥°Ï¥¥ · §¢¨É¨¥ ¤¨Ë· ±Í¨μ´´μ£μ ³¥Éμ¤ ¤μ²¦´μ ¢ §´ Ψɥ²Ó´μ° ¸É¥¶¥´¨ ¸¶μ¸μ¡¸É¢μ¢ ÉÓ
¶·μ£·¥¸¸Ê ¢ ¶μ¨¸±¥ „Œ ´¥°É·μ´ .
Analysis of the problem of taking into account the Earth's rotation in a search for the electric dipole
moment (EDM) of neutron in experiments with ultracold neutrons and in a diffractional experiment
is fulˇlled. Taking into account the Earth's rotation in the diffractional experiment gives an exactly
calculated correction which is negligible as compared with the accuracy reached at present time. In the
experiments with ultracold neutrons, the correction is greater than the systematical error and the exact
calculation of it needs further investigations. In this connection, further developments of diffractional
method would considerably promote progress in the search for the electric dipole moment of neutron.
PACS: 14.20.Dh, 91.10.Nj
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¶μ²¥ ʦ¥ ´¥ Ö¢²Ö¥É¸Ö ¶·¥´¥¡·¥¦¨³μ ³ ²μ°.
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¨ ¤μ¸É ÉμÎ´μ ¸¨²Ó´μ³ Ô²¥±É·¨Î¥¸±μ³ (E ∼ 1 Œ‚/³) ¶μ²ÖÌ (¸³. [1]). ‡ ¢¨¸ÖÐ Ö μÉ ¸¶¨´ Î ¸ÉÓ £ ³¨²ÓÉμ´¨ ´ ³¥¤²¥´´μ ¤¢¨¦ÊÐ¥°¸Ö Î ¸É¨ÍÒ ¢ Ô²¥±É·¨Î¥¸±μ³ ¨ ³ £´¨É´μ³ ¶μ²ÖÌ
· ¢´ d
μ
(1)
H = − s · B − s · E,
s
s
£¤¥ μ Å ³ £´¨É´Ò° ³μ³¥´É; d Å „Œ; s Å μ¶¥· Éμ· ¸¶¨´ Î ¸É¨ÍÒ, ¸¶¨´μ¢μ¥ Ψ¸²μ
s ¢ ¤ ´´μ³ ¸²ÊÎ ¥ · ¢´μ 1/2.
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¤¢ÊÌ ¶·μɨ¢μ¶μ²μ¦´ÒÌ ´ ¶· ¢²¥´¨° ³ £´¨É´μ£μ ¶μ²Ö, ¢ ¦´μ° Ö¢²Ö¥É¸Ö ¶·μ¡²¥³ μ¶·¥¤¥²¥´¨Ö ¢¥²¨Î¨´Ò ³ £´¨É´μ° ¨´¤Ê±Í¨¨. ‚ [1, 2] ÔÉ ¶·μ¡²¥³ ·¥Ï ² ¸Ó ¶ÊÉ¥³ ¨§³¥·¥´¨Ö
μÉ´μÏ¥´¨Ö Î ¸ÉμÉ ¶·¥Í¥¸¸¨¨ ¸¶¨´ ´¥°É·μ´μ¢ ¨ Éμ³μ¢ 199 Hg.
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2ωz = 4πf sin Φ,
f = 1,16 · 10−5 ƒÍ,
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deff =
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· ¢´ (2)
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¶·μ¢μ¤¨³ÒÌ ¶·¨ ¶μ¸ÉμÖ´´μ° μ·¨¥´É ͨ¨ ³ £´¨É´μ£μ ¶μ²Ö [9, 10], μ¸´μ¢´ Ö ¸¨¸É¥³ ɨΥ¸± Ö μϨ¡± ¡Ò² μ¡Ê¸²μ¢²¥´ ¥£μ ˲ʱÉÊ Í¨Ö³¨, ±μÉμ·Ò¥ ¡Ò²μ ´¥¢μ§³μ¦´μ ¤¥±¢ É´μ
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¢ ± Î¥¸É¢¥ ±μÉμ·μ£μ ¨¸¶μ²Ó§ÊÕÉ¸Ö ¶μ²Ö·¨§μ¢ ´´Ò¥ Éμ³Ò 199 Hg.
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¢· Ð¥´¨¥³ ‡¥³²¨, ´¥ ʳ ²Ö¥É ¢ ¦´μ¸É¨ ¶·μ¢¥¤¥´¨Ö Ô±¸¶¥·¨³¥´Éμ¢ É¨¶ [1, 2]. ¤´ ±μ
ÔÉμ ¤¥² ¥É ´¥μ¡Ì줨³Ò³ · §¢¨É¨¥ ¨ Ê¸μ¢¥·Ï¥´¸É¢μ¢ ´¨¥ ²ÓÉ¥·´ ɨ¢´ÒÌ ³¥Éμ¤μ¢ ¶μ¨¸± „Œ ´¥°É·μ´ .
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´ ¶μ¨¸±¥ ¢· Ð¥´¨Ö ¸¶¨´ , μ¡Ê¸²μ¢²¥´´μ£μ ¢§ ¨³μ¤¥°¸É¢¨¥³ „Œ ´¥°É·μ´ ¸ Ô²¥±É·¨Î¥¸±¨³ ¶μ²¥³ ´¥Í¥´É·μ¸¨³³¥É·¨Î´μ£μ ±·¨¸É ²² [11]. ‚¥²¨Î¨´ ÔÉμ£μ ¶μ²Ö ´ 4Ä5
¶μ·Ö¤±μ¢ ¶·¥¢ÒÏ ¥É ¶μ²Ö, ¤μ¸É¨¦¨³Ò¥ ¢ ² ¡μ· Éμ·´ÒÌ Ê¸²μ¢¨ÖÌ, ¨ ¤μ¸É¨£ ¥É 1010 Ä
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¸¶¨´ [13]. ‡´ ± ¨ ¢¥²¨Î¨´ Ô²¥±É·¨Î¥¸±μ£μ ¶μ²Ö, ¤¥°¸É¢ÊÕÐ¥£μ ¢ ±·¨¸É ²²¥ ´ ´¥°É·μ´ ¸ Ô´¥·£¨¥°, ¡²¨§±μ°, ´μ ´¥ · ¢´μ° Ô´¥·£¨¨ ¡·Ô££μ¢¸±μ£μ μÉ· ¦¥´¨Ö, ³μ£ÊÉ ¡ÒÉÓ
¨§³¥´¥´Ò ¡¥§ ¶¥·¥¢μ·μÉ · ¡μÎ¥£μ ±·¨¸É ²² [14], ÎÉμ μ¡²¥£Î ¥É ʸɷ ´¥´¨¥ ¸¨¸É¥³ ɨΥ¸±¨Ì μϨ¡μ± ¨ ¸´¨¦ ¥É É·¥¡μ¢ ´¨Ö ´ μ¸É Éμδҥ ³ £´¨É´Ò¥ ¶μ²Ö ¢ Ê¸É ´μ¢±¥ [15].
Š·μ³¥ Éμ£μ, ¶·¨ ¶·μ¢¥¤¥´¨¨ Ô±¸¶¥·¨³¥´É ¶·¨ Ê£²¥ ¤¨Ë· ±Í¨¨, · ¢´μ³ 90◦ , Ô²¥±É·¨Î¥¸±μ¥ ¶μ²¥ ±·¨¸É ²² ¶ · ²²¥²Ó´μ ¸±μ·μ¸É¨ ´¥°É·μ´ ¨ Ï¢¨´£¥·μ¢¸±μ¥ ¢§ ¨³μ¤¥°¸É¢¨¥,
Ö¢²ÖÕÐ¥¥¸Ö μ¸´μ¢´Ò³ ¨¸Éμδ¨±μ³ ¸¨¸É¥³ ɨΥ¸±¨Ì μϨ¡μ±, · ¢´μ ´Ê²Õ. ‘ÊÐ¥¸É¢¥´´μ,
ÎÉμ É·¥¡μ¢ ´¨Ö ± ¸μ¢¥·Ï¥´¸É¢Ê ¨¸¶μ²Ó§Ê¥³ÒÌ ±·¨¸É ²²μ¢ ´¥ μÎ¥´Ó ¢Ò¸μ±¨ [14].
˜¢¨´£¥·μ¢¸±μ¥ ¢§ ¨³μ¤¥°¸É¢¨¥ μ¡Ê¸²μ¢²¥´μ ¢§ ¨³μ¤¥°¸É¢¨¥³ ³ £´¨É´μ£μ ³μ³¥´É ´¥°É·μ´ ¸ ³ £´¨É´Ò³ ¶μ²¥³, ¢μ§´¨± ÕШ³ ¢ ¥£μ ¸¨¸É¥³¥ ¶μ±μÖ, ¨ ¨³¥¥É ¢¨¤
H=−
2μ
s · [E × v].
c
(3)
‘ÊÐ¥¸É¢μ¢ ´¨¥ Ï¢¨´£¥·μ¢¸±μ£μ ¢§ ¨³μ¤¥°¸É¢¨Ö ¶μ§¢μ²Ö¥É μ¶·¥¤¥²¨ÉÓ ¢¥²¨Î¨´Ê ´ ¶·Ö¦¥´´μ¸É¨ Ô²¥±É·¨Î¥¸±μ£μ ¶μ²Ö (´ ¶·¨³¥·, ¶ÊÉ¥³ ¨§³¥·¥´¨Ö ¤¥¶μ²Ö·¨§ ͨ¨ ´¥°É·μ´´μ£μ
¶Êα [16]). ˆ´É¥·¥¸´μ° μ¸μ¡¥´´μ¸ÉÓÕ Ö¢²Ö¥É¸Ö Éμ, ÎÉμ ¶·¨ ¤¨Ë· ±Í¨¨ ¶μ ‹ ÊÔ ¸ÊÐ¥¸É¢¥´´μ ¢μ§· ¸É ¥É ¢·¥³Ö ¶·¥¡Ò¢ ´¨Ö ´¥°É·μ´ ¢ ±·¨¸É ²²¥, ÎÉμ ¶·¨ Ê£² Ì ¤¨Ë· ±Í¨¨,
¡²¨§±¨Ì ± 90◦ , Ê¢¥²¨Î¨¢ ¥É ¢·¥³Ö ¤¥°¸É¢¨Ö Ô²¥±É·¨Î¥¸±μ£μ ¶μ²Ö. ‚ ¶·μ¢¥¤¥´´ÒÌ ¢ [17]
¨§³¥·¥´¨ÖÌ ¸±μ·μ¸ÉÓ ¶·μÌ즤¥´¨Ö ´¥°É·μ´ Î¥·¥§ ±·¨¸É ²² · ¢´Ö² ¸Ó 40 ³/¸ ¶·¨
¸±μ·μ¸É¨ ´ ²¥É ÕÐ¥£μ ´¥°É·μ´ 800 ³/¸.
·μ¢¥¤¥´´Ò° ¢ [18] ´ ²¨§ ¶μ± § ², ÎÉμ ¤²Ö ʦ¥ ¨³¥ÕÐ¨Ì¸Ö ¸¥°Î ¸ ¢ ´ ²¨Î¨¨ ´¥Í¥´É·μ¸¨³³¥É·¨Î´ÒÌ ±·¨¸É ²²μ¢ ±¢ ·Í ¨ ¶ÊÎ±μ¢ Ìμ²μ¤´ÒÌ ´¥°É·μ´μ¢ ³μ¦´μ ¤μ¸É¨ÎÓ
Éμδμ¸É¨ ¨§³¥·¥´¨Ö „Œ ´¥°É·μ´ ∼ 10−26 e · ¸³, ÎÉμ ¸ÊÐ¥¸É¢¥´´μ ²ÊÎÏ¥, Î¥³ ¸μ¢·¥³¥´´μ¥ μ£· ´¨Î¥´¨¥ ´ „Œ, ¶μ²ÊÎ¥´´μ¥ ¸ ¨¸¶μ²Ó§μ¢ ´¨¥³ ʲÓÉ· Ìμ²μ¤´ÒÌ ´¥°É·μ´μ¢. ˆ¸¶μ²Ó§μ¢ ´¨¥ ´μ¢μ£μ ±² ¸¸ ´¥Í¥´É·μ¸¨³³¥É·¨Î´ÒÌ ±·¨¸É ²²μ¢ ³μ¦¥É ¶·¨¢¥¸É¨
± ¤ ²Ó´¥°Ï¥³Ê ʲÊÎÏ¥´¨Õ Éμδμ¸É¨ ¥Ð¥ ± ± ³¨´¨³Ê³ ´ ¶μ·Ö¤μ± [18]. ’ ±¨³ μ¡· §μ³, ¤¨Ë· ±Í¨μ´´Ò° ³¥Éμ¤ ¶μ Éμδμ¸É¨ ³μ¦¥É ±μ´±Ê·¨·μ¢ ÉÓ ¸ É· ¤¨Í¨μ´´Ò³ ³¥Éμ¤μ³,
¡ §¨·ÊÕШ³¸Ö ´ ¨§³¥·¥´¨¨ Î ¸ÉμÉÒ ² ·³μ·μ¢¸±μ° ¶·¥Í¥¸¸¨¨ ¸¶¨´ ʲÓÉ· Ìμ²μ¤´ÒÌ
´¥°É·μ´μ¢.
…¸É¥¸É¢¥´´μ, ¡μ²ÓÏ Ö ¢¥²¨Î¨´ ´ ¶·Ö¦¥´´μ¸É¨ Ô²¥±É·¨Î¥¸±μ£μ ¶μ²Ö ¢ ¤¨Ë· ±Í¨μ´´μ³ Ô±¸¶¥·¨³¥´É¥ [18] ¶·¨¢μ¤¨É ± · ¤¨± ²Ó´μ³Ê ʳ¥´ÓÏ¥´¨Õ ·μ²¨ ¢· Ð¥´¨Ö ‡¥³²¨
¶μ ¸· ¢´¥´¨Õ ¸ Ô±¸¶¥·¨³¥´É ³¨ ¸ ʲÓÉ· Ìμ²μ¤´Ò³¨ ´¥°É·μ´ ³¨. Ϩ·μÉ¥ ‘ ´±É¥É¥·¡Ê·£ , £¤¥ ¶·μ¨§¢μ¤¨É¸Ö ¤¨Ë· ±Í¨μ´´Ò° Ô±¸¶¥·¨³¥´É (Φ ≈ 60◦ ), ¨ ¤²Ö ¨§³¥·¥´´μ£μ ¢ [16] ¶μ²Ö ¶²μ¸±μ¸É¨ (110) ±·¨¸É ²² ±¢ ·Í (E = (2,24 ± 0,05(0,20)) · 1010 ‚/³)
“봃 ¢· Ð¥´¨Ö ‡¥³²¨ ¢ Ô±¸¶¥·¨³¥´É Ì ¶μ ¶μ¨¸±Ê „Œ ´¥°É·μ´ 787
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μ²ÊÎ¥´μ 20 ´μÖ¡·Ö 2006 £.