Quantum states of neutrons in the earth's gravitational field
Quantum states of neutrons in the earth's gravitational field
Quantum states of neutrons in the earth's gravitational field
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3. Theoretical description<br />
The model <strong>of</strong> tunnel<strong>in</strong>g through <strong>gravitational</strong> barrier<br />
ξ >> 1<br />
3<br />
4<br />
2<br />
D ( ξ)<br />
≈ Exp[<br />
− ⋅ξ ], Γn<br />
( ξ ) = ωn<br />
⋅ D(<br />
ξ)<br />
3<br />
ω<br />
n<br />
≈<br />
n+<br />
( E<br />
1<br />
− En) / h<br />
⎧1,<br />
ξ < 0<br />
⎪<br />
D(<br />
ξ ) = ⎨<br />
⎪An<br />
⋅ Exp[<br />
−<br />
⎩<br />
4<br />
3<br />
⋅ξ<br />
3<br />
2<br />
], ξ<br />
> 0<br />
P n<br />
( ξ ) Exp(<br />
−Γ ( ξ ) ⋅τ<br />
)<br />
=<br />
n<br />
P ( ξ )<br />
n<br />
= Exp(<br />
−Γ ( ξ ) ⋅<br />
n<br />
L<br />
V<br />
hor<br />
)<br />
⎛ ⎛<br />
⎜ ⎜ L<br />
F( ∆z,<br />
V ∑⎜<br />
hor ) = βn<br />
⋅ Exp⎜−α<br />
⋅<br />
⎜<br />
n<br />
⎜ V<br />
⎝ ⎝<br />
hor<br />
⋅C<br />
2<br />
n<br />
⎛<br />
⎜<br />
⋅ Exp⎜−<br />
⎜<br />
⎝<br />
4 ⎛ ∆z<br />
− z<br />
⋅⎜<br />
3<br />
⎝ z0<br />
09.06.05 INSTITUT MAX VON LAUE - PAUL LANGEVIN<br />
V.V.Nesvizhevsky<br />
n<br />
⎞<br />
⎟<br />
⎠<br />
3<br />
2<br />
⎞⎞⎞<br />
⎟⎟⎟<br />
⎟⎟⎟<br />
⎟ ⎟<br />
⎟<br />
⎠<br />
⎠⎠
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