Decrease in the probability of tritium decay in an external electric field
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CLEI Theory
Decrease in the Probability of Tritium Decay in an External Electric Field D. V. Filippov* Institute of General Physics, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991 Russia Received October 11, 2006; in final form, February 27, 2007
Abstract—The probability of tritium beta decay is shown to decrease under the effect of a constant uniform external electric field on the atom. For the tritium atom, the effect is due first to the reduction of the betadecay endpoint energy and second to the reduction of the density of vacant bound electron states at the nucleus. Both of these factors reduce the beta-decay probability: the first reduces the probability of decay to continuum electron states, while the second reduces the probability of decay to a bound state. PACS numbers: 23.40.-s DOI: 10.1134/S1063778807110038
1. INTRODUCTION At the present time, the helium-isotope massspectrometric method [1, 2] makes it possible to determine the beta-decay constant for tritium (atomic or ionized) to a precision of about 0.1%. This precision is sufficient for measuring the difference in the decay constants for the tritium atom and ion and for studying the effect of an external electric field on the beta-decay probability. Changes in the probabilities of allowed and forbidden β − decays of fully ionized atoms in the field of an intense electromagnetic wave were studied theoretically in [3, 4], where a constant electric field was considered as a particular case. The results reported in [3] show that the total probability λ of beta decay increases in a constant electric field owing to an increase in the decay endpoint energy. The effect is proportional to the square of the electric-field strength (hereafter, we use the system of relativistic units in which = c = me = 1, where is the Planck constant, c is the speed of light in a vacuum, and me is the electron mass; the electric-field-strength unit is E0 = 1.13 × 1017 V/m = 3.77 × 1012 CGS); that is, 35 αE 2 ∆λ = ≈ 82.8E 2 , λ 64 Q30
(1)
where Q0 is the beta-decay endpoint energy (for tritium, Q0 = 18.6 keV ≈ 0.0364), E is the electricfield strength, and α is the fine-structure constant. In an electric field of strength E ≈ 1012 V/m ≈ 4 × 107 CGS ≈ 10−5 E0 , the estimate in (1) yields ∆λ/λ ≈ 10−8 . *
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In [3, 4], the electric field of the nucleus being considered was disregarded, which entailed the disregard of both beta decay to a bound electron state and the effect of the atomic shell on the beta-decay probability. It is well known that the beta decay of a nucleus in a neutral atom differs from the beta decay of the respective nucleus in the fully ionized atom [1, 2, 5–12]. Here, we will show that, upon taking into account the changes in the atomic shell and decay to a bound state, the result becomes opposite to that in [3]: an external electric field decreases (rather than increases, as in [3]) the probability of tritium beta decay, the effect being six orders of magnitude greater than the estimate in (1). From [1, 5], it is well known that, in th
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