References - Bogoliubov Laboratory of Theoretical Physics - JINR

A STUDY OF POLARIZED METASTABLE HELIUM-3 ATOMIC BEAM
PRODUCTION
Yu.A. Plis † and Yu.V. Prokofichev
Joint Institute for Nuclear Research, Dubna, Moscow region, Russia
† E-mail: plis@nusun.jinr.ru
Abstract
The problems of metastable 3 He atomic beam formation are considered. The
difference between metastable 3 He and hydrogen or deuterium atoms concerning the
radio-frequency transitions of atomic states is essential. The Schroedinger equation
in the uncoupled basis |ψe,ψh > and also in the basis of stationary states are
received. The results of computer simulations agree with published data. The
possibility to get the positive and negative values of helion polarization by using
two types of the weak field transitions in the metastable helium-3 atom is shown.
1 Introduction
The spin-dependent part of the Hamiltonian for helium-3 atoms in the metastable state
2 3 S1 with electron spin moment one is
ˆH = −μJ � J � B(t) − μh �σh � B(t) − 1
3 ΔW�σh � J, (1)
where �σh are the Pauli spin matrices of the helion, � J are the electron spin matrices
(J =1),B(t) is magnetic field strength, ΔW is hyperfine splitting; ΔW =4.4645 × 10 −24
J= �×4.2335×10 10 rad/s, μJ =2μe = −1.85695275×10 −23 J/T= −�×1.76085977×10 11
rad/s T, μh = −1.07455 × 10 −26 J/T= −� × 1.0189 × 10 8 rad/s T.
We consider that a static magnetic field B directed along a z-axis. The wave functions
of the hyperfine states Ψ(F, MF ) for this magnetic field and in a high field limit are
Ψ1(1/2, +1/2) = − sin βψ +
h ψ0 J +cosβψ− h ψ+
J
Ψ3(1/2, −1/2) = − sin αψ +
h ψ−
J +cosαψ−
h ψ0 J
sin βψ −
h ψ+
J
⇒ ψ+
h ψ0 J ,Ψ5(3/2, −1/2) = cos αψ +
⇒ ψ−
h ψ+
J ,Ψ2(3/2, +3/2) = ψ +
h ψ+
J ,
⇒ ψ−
h ψ0 J ,Ψ4(3/2, +1/2) = cos βψ +
h ψ0 J +
h ψ−
J
+sin αψ−
h ψ0 J
⇒ ψ+
h ψ−
J ,Ψ6(3/2, −3/2)
= ψ −
h ψ−
J ,wheresinβ = √ A+ , cos β = √ 1 − A+ ;sinα = √ A− , cos α = √ 1 − A− ;
A+ = 1
(1 −
2
x +1/3
�
), A− =
x + x2
1 x − 1/3
(1 − �
);
2
x + x2
1+ 2
3
1 − 2
3
x = B
ΔW
, Bc =
Bc −μJ/J + μI/I =
ΔW
=0.2407 T.
−μJ +2μh
The Breit-Rabi diagram of six Zeeman hyperfine components of this metastable state
is shown at Fig. 1, where the numbers correspond to those of the wave functions.
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